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Metallacycles Capabilities in Host–Guest Chemistry Miguel Ponce-Vargas*[a] Awarding Institute: Universidad Andrs Bello (Chile) Date Awarded: January 20th, 2015 Supervisor: Dr. Alvaro MuÇoz Castro, Universidad Autnoma de Chile, Carlos Antfflnez 1920, Santiago (Chile)

open_201500125_sm_miscellaneous_information.pdf

Ph.D. in Molecular Physical Chemistry

Metallacycles Capabilities in Host-Guest Chemistry

Presented by Miguel Armando Ponce Vargas Advisor Dr. Alvaro Rafael Muñoz Castro Thesis Committee Dr. Irma Crivelli Dr. Diego Venegas Yazigi Dr. Desmond MacLeod-Carey Dr. Pablo Jaque Olmedo

Santiago, Chile 2015

Acknowledgments

I am using this opportunity to express my gratitude to everyone who supported me throughout the course of this Ph.D., particularly to Dr. Ramiro Arratia-Pérez who gave me the opportunity to be part of this prestigious program. I express my warm thanks to my advisor Dr. Alvaro Muñoz Castro for his support and guidance. He is the friendlier supervisor that one could have. Thanks also to Claudia Valdivia, Desmond McLeod-Carey, William Tiznado and Plinio Cantero for their cooperation and friendship. And finally I want to give special thanks to my beloved María de los Ángeles Cortés for her support and for gave me a family here in Chile.

Summary

Metallacycles offer structural diversity and interesting properties based on their highly symmetric frameworks and host-guest chemistry. They can be used as molecular recognition agents, photochromic devices, catalysts, and surface patterning structures, just to mention a few applications. The aim of this work is to gain a deeper understanding into the coupling forces within metallacycle complexes possessing metal centers acting as binding sites, by using density functional calculations. We focus on the electrostatic contribution to total interaction energy, which can be divided in ion-dipole, ion-quadrupole, dipole-dipole, dipolequadrupole, etc., according to the multipole expansion of the electrostatic potential. We choice two representative case studies: halide-centered hexanuclear copper(II) pyrazolate- and di-halide cyclic pentameric perfluoroisopropylidenemercury complexes, due to the presence of metal centers capable of interacting directly with the guest entities. The current approach, allows us to determine the role of certain Coulombic terms in the electrostatic nature of the coupling forces, leading to a clear rationalization of the soft-soft or hard-soft preferences into the formation of the host-guest entities. The non-covalent forces involving the hexanuclear copper(II) pyrazolate complexes and a halide guest [trans-Cu6{µ-3,5-(CF3)2pz}6(µ-OH)6X]- (X = F, Cl, Br, I), describe an electrostatic character (about 70% of the stabilizing terms) where the ion-dipole and ionquadrupole contributions to the electrostatic term range from 95.0% to 77.0%, going from F- to I-, describing the increasing role of higher order interactions, such as quadrupoledipole and quadrupole-quadrupole into the coupling as the guest becomes softer. In

di-halide

cyclic

pentameric

perfluoroisopropylidenemercury

complexes,

[(HgC(CF3)2)52X]2- (X = Cl, Br, I), our results reveal an interesting case where the

expected soft acid–soft base pair is not the more stable situation. Instead, a surprising hardsoft pair arises as the preferred species, with stronger forces towards Cl - than those corresponding to I- by about 24 kcal/mol. The almost linear mercury local geometry and the D5h molecular symmetry determine the shape of the local quadrupole moments at the binding sites leading to an in-plane distribution, preventing the arise of a significant quadrupole component perpendicular to the Hg5 plane, that could contribute to higher order electrostatic terms such as quadrupole-quadrupole, which is related to the soft-soft preference. In summary, the results here presented suggest that metallacycles hosts with metal centers acting as binding sites, can offer great advantages in comparison to their organic counterparts, prompted by the versatility of such centers, which can modulate their electron density according to the incoming guest. This work was made possible by the CONICYT 63130036 Doctoral fellowship, and the financial support of UNAB-DI-403-13/I Internal Project, 1140358 FONDECYT Grant and RC120001 MILLENNIUM Project.

Table of Contents

Chapter 1 Introduction..........................................................................................................................10 1.1. Host-Guest Chemistry..............................................................................................10 1.2. Metallacycles............................................................................................................13 1.3. Metallacycles acting as hosts species.......................................................................15 1.4. Hard and Soft Acids and Bases Principle.................................................................17 Hypothesis............................................................................................................................20 General and Specific Objectives..........................................................................................21 Chapter 2 Methodologies......................................................................................................................22 2.1. Density Functional Theory.......................................................................................22 2.2. Relativistic Corrections............................................................................................25 2.3. Energy Decomposition Analysis..............................................................................28 2.4. Atomic Multipole Expansion....................................................................................29 2.5. Natural Population Analysis.....................................................................................32 2.6. Non-covalent Interactions Analysis..........................................................................34

3

Chapter 3 A Study on the Versatility of Metallacycles in Host-Guest Chemistry. Interactions in Halide-centered hexanuclear copper(II) pyrazolate complexes...........................................37 3.1. Introduction..............................................................................................................37 3.2. Computational Details..............................................................................................39 3.3. Results and Discussion.............................................................................................41 3.4. Conclusions..............................................................................................................52 Chapter 4 Heavy Element Metallacycles: Insights into the Nature of Host-Guest Interactions involving Di-Halide Mercuramacrocycle Complexes..........................................................54 4.1. Introduction..............................................................................................................54 4.2. Computational Details..............................................................................................56 4.3. Results and Discussion.............................................................................................57 4.4. Conclusions..............................................................................................................67 Overall Conclusions.............................................................................................................68 Scientific Contributions........................................................................................................69 Supplementary Information..................................................................................................71 Bibliographic References.....................................................................................................79

4

List of Figures

Figure 1. K+ ⊂ dibenzo-18-crown-6 (where ⊂ denotes encapsulation).............................10 Figure 2. Schematic diagram of an azobenzene nanotube assembly based on host-guest molecular recognition...........................................................................................................11 Figure 3. Illustration of the tunable catalytic activity of the nanoscale cage [Cu 4L4]4+ (L = 1,3,5-tris(1-benzylbenzimidazol-2-yl)benzene)...........................................................13 Figure 4. I. [{Pd(en)(µ-4,4'-bipy)4}]8+ (en = ethylendiamine, bipy = bipyridine) II. [Cu(3,5(C6H5)2pz)]4 ((3,5-(C6H5)2pz)- = 3,5-diphenylpyrazolate)....................................................14 Figure 5. I. C6H6 ⊂ [{(CO)3Re(µ-L)Re-(CO)3}2(µ-4,4'-bipy)2] (L=5,8-dyhidroxy-1,4naphtoquinone). II. LiCl2[12-MCMn(III)N(shi)-4]- (shi3- = salicylhydroxamate trianion)...........15 Figure 6. The metallacycle complexes subject of this study I. [trans-Cu6(3,5(CF3)2pz)6(OH)6Cl]-, II. [(HgC(CF3)2)52Cl]2-........................................................................17 Figure 7. NCI Analysis of a diphenol dimer where hydrogen bond is denoted as a blue region and weak London interactions as a green region......................................................36 Figure 8. Optimized structure for trans-Cu6{µ-3,5-(CF3)2pz}6(µ-OH)6 (1), viewed from the z-axis....................................................................................................................................42 Figure 9. Graphical representation of the copper dipole moments in 1-Cl.........................45 5

Figure 10. Graphical representation of the Electric Quadrupole tensors of the studied systems.................................................................................................................................48 Figure 11. NCI Analysis for the halide complexes 1-X (X = F, Cl, Br, I)...........................51 Figure 12. Calculated structures for the mercuramacrocycle (HgC(CF 3)2)5 (1) and the [(HgC(CF3)2)52X]2- (1-2X) series.........................................................................................58 Figure 13. Quadrupole moment tensor (Θ) representation for a Hg(II) center, in the studied systems.................................................................................................................................64 Figure 14. NCI Analysis of the 1-2X mercuramacrocycle complexes................................67 Figure S1. Representation of the quadrupole moment tensor (Θ) for a representative Cu(II) center, in the hypothetical noble gas-centered pyrazolate complexes 1-Ne, 1-Ar, 1-Kr and 1-Xe......................................................................................................................................73 Figure S2. Electrostatic potential map for (HgC(CF3)2)5 (1), (HgC(CH3)2)5 (2), and (HgCH2)5 (3) hosts................................................................................................................78

6

List of Tables

Table 1. Classification of some relevant species according to the Hard and Soft Acids and Bases (HSAB) Principle proposed by Pearson....................................................................18 Table 2. Geometry optimizations of the 1-Cl, 1-Br and 1-I complexes using TPSS, PBE and B3LYP functionals, and their comparison with experimental data (Å and degrees).....40 Table 3. Selected distances (Å) and angles (degrees) of the host and halide complexes....42 Table 4. Energy Decomposition (EDA) (kcal/mol) and Natural Population Analysis (NPA) (a.u.) of the studied systems.................................................................................................44 Table 5. Principal components of the electronic quadrupole tensor of the studied systems, for a representative cooper and guests (Buckinghams)........................................................50 Table 6. Selected distances (Å) and angles (degrees) of the host and di-halide mercuramacrocycle complexes............................................................................................58 Table 7. Energy Decomposition Analysis (EDA) (kcal/mol) for a series of hypothetical mono-halide mercuramacrocycle complexes.......................................................................60 Table 8. Energy Decomposition Analysis (EDA) (kcal/mol) and Natural Population Analysis (NPA) (a.u.) for host and di-halide mercuramacrocycle complexes.....................62

7

Table 9. Principal components of the electronic quadrupole tensor of the studied systems for a representative mercury and guests (Buckinghams).....................................................65 Table S1. Selected calculated distances (Å) and angles (degrees) of the 1-Ne, 1-Ar, 1-Kr and 1-Xe complexes.............................................................................................................71 Table S2. Energy Decomposition Analysis for the 1-Ne, 1-Ar, 1-Kr and 1-Xe complexes (kcal/mol).............................................................................................................................71 Table S3. Selected calculated distances (Å) and angles (degrees) of the hypothetical transCu6{µ-3,5-(CH3)2pz}6(µ-OH)6 host (2) and [trans-Cu6{µ-3,5-(CH3)2pz}6(µ-OH)6X]- (X = F, Cl, Br, I) (2-X) complexes....................................................................................................72 Table S4. Natural population analysis (NPA, a.u.) of the hypothetical trans-Cu6{µ-3,5(CH3)2pz}6(µ-OH)6 host (2) and [trans-Cu6{µ-3,5-(CH3)2pz}6(µ-OH)6X]- (X = F, Cl, Br, I) complexes (2-X)...................................................................................................................72 Table S5. Comparison of the performance of several hybrid, GGA, and meta-GGA functionals in the calculation of the Electronic Quadrupole Tensors of the different noblegas guests, denoting on the principal axis system (Buckinghams)......................................74 Table S6. Selected calculated distances (Å) and angles (degrees) for the hypothetical 1-X guest-centered mercuramacrocycle complexes....................................................................74 Table S7. Selected calculated distances (Å) and angles (degrees) for the hypothetical 1-X guest-apical located mercuramacrocycle complexes...........................................................75 Table S8. Selected calculated distances (Å) and angles (degrees) for the hypothetical 1-2Ng mercuramacrocycle complexes.................................................................................75

8

Table S9. Energy Decomposition Analysis for the hypothetical 1-2Ng mercuramacrocycle complexes (kcal/mol)...........................................................................................................76 Table S10. Selected calculated distances (Å) and angles (degrees) for the hypothetical 2-2X mercuramacrocycle complexes...................................................................................76 Table S11. Energy Decomposition Analysis for the hypothetical 2-2X mercuramacrocycle complexes (kcal/mol)...........................................................................................................77 Table S12. Selected calculated distances (Å) and angles (degrees) for the hypothetical 3-2X mercuramacrocycle complexes...................................................................................77 Table S13. Energy Decomposition Analysis for the hypothetical 3-2X mercuramacrocycle complexes (kcal/mol)...........................................................................................................78

9

Chapter 1

Introduction

1.1. Host-Guest Chemistry The Host-guest chemistry encompasses the study of highly structured molecular complexes composed of at least two entities associated by non-covalent interactions, one possessing convergent binding sites, the host; and another possessing divergent binding sites, the guest[1],

[2].

Among other species, the host could be a crown ether, a calixarene, or a

metallacycle, whereas the guest could be virtually any small to medium size species. In 1967, Charles Pedersen synthesized the first series of macrocyclic crown ethers capable to selectively bind alkali and alkaline earth ions generating host-guest complexes. One of these, dibenzo-18-crown-6 is shown in Figure 1, with a potassium cation in the role of guest[3].

Figure 1. K+ ⊂ dibenzo-18-crown-6 (where ⊂ denotes encapsulation)[3]. The host molecule 'recognizes' by complexing best, those guest entities that contain the array of binding sites and steric features that complements it. Once the complex is formed, the interactions vary in strength from strong ionic forces (20-80 kcal/mol), through hydrogen bonding, cation-π, and π-π stacking, to weak forces (< 1 kcal/mol)[4]. 10

One of the most important applications of host-guest chemistry is the separation of similar compounds by enclathration, involving the choice of a suitable host which exposed to a mixture of guests binds selectively one of them, generating a crystalline inclusion compound[5]. In this context, crown ether-based calixarenes have been used in ion-selective electrodes, as ionophores for alkali metals, transition metals, and lanthanides[6]. The design and fabrication of highly ordered surface patterning structures of functional molecules is another important perspective of host-guest chemistry. In this regard, fullerenes can be placed within a calixarene to form an ordered array making possible to operate them and fabricate nanoscale circuits[7]. For instance, it has been synthesized a tetraacidic azobenzene molecule that forms a two-dimensional molecular template which offers two different types of binding sites capable to accommodate fullerenes as guest species[8]. Furthermore, nanotubes functionalized with azobenzenes could recognize and attach onto well-defined regions of thiolated α-CD SAMs (α-Ciclodextrins Self-Assembled Monolayers) via host-guest molecular recognition. The binding between the azobenzene nanotubes and the α-CD SAMs is controlled by UV radiation as is represented in Figure 2[9].

trans

cis

Figure 2. Schematic diagram of an azobenzene nanotube assembly based on host-guest molecular recognition[9]. Polymers can also be functionalized with host-guest complementary groups leading to an effective polymer blending. This is well illustrated by polystyrene functionalized with tetraphosphonate cavitand hosts, and polybuthyl methacrylate modified with N11

methylpyridinium guests, resulting in a copolymer fully miscible in the solid state over a wide molar ratio[10]. Hybrid materials and functional devices utilizing switchable host-guest systems have provided compelling demonstrations of the structural control and selectivity afforded by non-covalent interactions. The conjunction of gold nanoparticles and host-guest systems based on supramolecular macrocycles has led to the development of novel hybrid materials, combining the electronic, thermal and catalytic properties of nanoparticles, with the switchable molecular recognition and selectivity of macrocyclic compounds. In this line, Yang and co-workers have demonstrated that supramolecular hosts, such as monoCD, bridged CD dimer, and carboxylatopyllarene could be used as stabilizing ligands for the morphology control of gold nanoparticles (AuNPs), enhancing their recognition and sensing abilities on gold surfaces, which is promising for miniaturization of electronic devices[11]. Furthermore, the formation of a three-dimensional assembly driven by hostguest interactions between CD-modified AuNPs and the redox active metal complex [Os(CAIPA)3](ClO4)2 (CAIPA = 2-(4-carboxyphenyl)imidazo-[4,5-f][1,10]-phenantroline1-adamantylamine) has been reported by Zeng and co-workers, where the higher homogeneous charge transport diffusion coefficient in comparison to a solid deposit of the complex alone, suggests that the incorporated AuNPs promote the electron transfer between the osmium centers[12]. Finally, the intermolecular catalysis toward the oxidation of hydrocarbons has been studied with a nanoscale coordination cage [Cu4L4]4+ (L = 1,3,5-tris(1-benzylbenzimidazol-2yl)benzene) with multiple Cu(I) redox active ions located at the vertices, where the catalytic reactions take place outside the cage and the catalytic activity can be modulated inside by multiple guest anions (NO3-, ClO4-, CH3C6H4SO3-, and CF3SO3-). The nitrate ion, for instance, leaves one Cu(I) active site free, whereas perchlorate interacts with all of them precluding the catalytic action outside the cavity. This host-guest tunable catalyst is represented in Figure 3[13].

12

Figure 3. Illustration of the tunable catalytic activity of the nanoscale cage [Cu4L4]4+ (L = 1,3,5-tris(1-benzylbenzimidazol-2-yl)benzene)[13].

1.2. Metallacycles Traditionally, the term 'metallacycle' refers only to compounds containing two metalcarbon bonds as part of a cyclic framework, but now is commonly used to denote any ring system incorporating a metal[14]. They are usually constructed via the self-assembly of well-designed organic ligands in combination to transition metal ions through the formation of coordination bonds[15]. In 1990, the first metallacycle, the molecular square [{Pd(en)(µ-4,4'-bipy)4}](NO3)8 (en = ethylendiamine, bipy = bipyridine), was synthesized by Fujita and coworkers via the self-assembly of a cis-protected square-planar Pd(II) precursor with two adjacent labile ligands [Pd(en)(ONO 2)2], and the linear linker 4,4'bipyridine (Figure 4. I)[16], [17]. The chemistry of metallacycles has been a major area of organometallic chemistry because of their role as key intermediates in the metathesis and oligomerization of alkenes catalyzed by transition metal complexes. In this regard, metallacyclobutanes of molybdenum, tungsten, and ruthenium with a four member-ring structure are known as intermediates in olefin metathesis catalyzed by the corresponding transition-metal complexes[18].

13

Figure 4. I. [{Pd(en)(µ-4,4'-bipy)4}]8+ (en = ethylendiamine, bipy = bipyridine)[16], [17] II. [Cu(3,5-(C6H5)2pz)]4 ((3,5-(C6H5)2pz)- = 3,5-diphenylpyrazolate)[23]. In the field of biochemistry, the anticancer activity of a series of cationic metallacycles based on arene ruthenium units has been evaluated. This confirms the potential use of metallacycles as anticancer drugs[19]. The biological study of tetranuclear vacant metallacycles with mixed ligand composition reveals another potential application. The systems [12-MC Ni(II)N(Hshi)2(pko)2-4](L)2, where pko- is the anion of di-2-pyridyl-ketonoxime and L - = SCN-, NNN-, and OCN-, have shown the ability of modify DNA structure, suggesting that these compounds could act as antibacterial agents[20]. Some metallacycles provide a suitable geometry that allows multiple metal atoms to be placed in a small volume, promoting the alignment of single-ion-anisotropy axes, leading to large axial molecular anisotropies, which result in single-molecular magnetism [21]. In this concern, Dy(III)(CH3COO)(NO3)2[14-MCMn(III)Dy(III)(μ-O)(μ-OH)N(shi)-5], a compound with the above mentioned features, exhibits slow magnetic relaxation, a hallmark of single molecular magnets[22]. The capabilities of metallacycles as catalysts in organic reactions also have been studied. For instance [Cu(3,5-(C6H5)2pz)]4, where (3,5-(C6H5)2pz)- is 3,5-diphenylpyrazolate, has been demonstrated its catalytic action in the oxidation of primary aromatic amines leading to the corresponding azobenzenes (Figure 4. II)[23].

14

1.3. Metallacycles acting as hosts species The hollow structure of metallacycles allows them to act as host species for charged and neutral species. Examples include a trinuclear carboxylato-bridged iron(II) complex, [Fe3(O2CCH3)3(BPG)3] (BPG- = bis(2-pyridylmethyl)glycinate), capable of bind a fourth metal ion to generate the tetranuclear complex [Fe4(O2CCH3)3(BPG)3]2+[24], Ln[15-MCCu(II), pheHA

-5] (pheHA = phenylalanine hydroxamic acid) which selectively binds carboxylate

guests[25], [TiO(O2CC6F5)2] with the capability to interact simultaneously with two toluene molecules[26], [15-MCCu(II), picha-5] (picha = picoline hydroxamic acid) that can accommodate a wide variety of lanthanide ions in the center of its cavity [27], and the rhenium-based rectangular metallacycles [{(CO)3Re(µ-L)Re-(CO)3}2(µ-4,4'-bipy)2] (L=5,8-dyhidroxy1,4-naphtoquinone), containing a large and tunable hydrophobic cavity which selectively recognizes benzene molecules (Figure 5. I)[28].

Figure 5. I. C6H6 ⊂ [{(CO)3Re(µ-L)Re-(CO)3}2(µ-4,4'-bipy)2] (L=5,8-dyhidroxy-1,4naphtoquinone)[28]. II. LiCl2[12-MCMn(III)N(shi)-4]- (shi3- = salicylhydroxamate trianion)[29]. An unusual case in ion recognition is offered by [12-MC Mn(III)N(shi)-4] (where shi3- is the trivalent anion of salicylhydroxamic acid), a simultaneous cation and anion selective system. On the basis of its synthetic preference, the trend for the cation affinity is Li+ > Na+ > K+ and that for anion affinity is Cl - > Br- > TFA- (trifluoroacetate) > F- ≈I3(Figure 5. II)[29]. Usually, the metallacycle host interacts with the guest species through the oxygen or nitrogen atoms located within the supporting ligands, while only to a lesser extent, the 15

metal centers within the host structure play this role, offering a more interesting scenario driven by the versatility of a discrete number of redox centers into a single molecular entity[30],

[31].

In this regard, interesting systems, due to their high symmetry and easy

preparation, are the halide-centered hexanuclear, anionic copper(II) pyrazolate complexes [trans-Cu6(3,5-(CF3)2pz)6(OH)6X]-, X = F, Cl, Br, I, where the Cu(II) centers are linked by hydroxo and dimethilpyrazolate groups. They have been isolated in a good yield from the redox reaction of the trinuclear copper(I) pyrazolate complex [μ-Cu3(3,5-(CF3)2pz)3] with PPh3AuX and [Bu4N]X, X = F, Cl, Br, I. In these compounds each unit has a core containing a hexanuclear Cu(II) ring which interacts directly with several halide guest species[32]. Interestingly, 3,5-Dimetihylpyrazole and Cu(II) ions are also able to produce an octameric copper(II)-hydroxo complex [Cu8(3,5-(CF3)2pz)8(OH)8]. However, guest molecules cannot be located within its central cavity until now[33]. Recently, Cañon-Mancisidor and coworkers have obtained an isostructural metallacycle [trans-Cu6{µ-3,5-(CH3)2pz}6(µ-OH)6·CH3CN·CHCl3] which packs in the solid state as a tubular framework and is capable of trapping carbon dioxide molecules[34]. This research focus on two representative metallacycle systems: the above mentioned halide-centered hexanuclear copper(II) pyrazolate complexes[32] and the di-halide cyclic pentameric perfluoroisopropylidenemercury complexes synthesized by Antipin and coworkers, in which one metallacycle interacts simultaneously with two anionic guest species (Figure 6)[35],

[36].

This choice is based on the presence of metal centers inside them,

capable of interacting directly with the guest species.

16

Figure 6. The metallacycle complexes subject of this study I. [trans-Cu6(3,5(CF3)2pz)6(OH)6Cl]- [32], II. [(HgC(CF3)2)52Cl]2- [35], [36].

1.4. Hard and Soft Acids and Bases Principle Hard species are those of small size and high charge, while soft species conversely, are large in size with low charge[37]. The hard and soft acids and bases (HSAB) principle proposed by Ralph Pearson states that maintaining all other factors equal (binding sites array, steric and medium effects, kinetic control, etc.), hard acids prefer to coordinate with hard bases and soft acids prefer to coordinate with soft bases [38], [39]. It implies an extra stabilization energy when the soft acid-soft base and hard acid-hard base pairs occur, a fact that has been verified in most of the chemical reactions [40]. In this concern, Mg2+ and Al3+ which form stable complexes with F - but not I-, in water, can be considered hard acids whereas Hg2+ and Pt2+, which form very stable complexes in aqueous solution with iodide ions, and weak or no complexes with fluoride ions can be labeled as soft acids [41]. Part of the original Pearson's classification is presented in Table 1[42]. In the field of host-guest chemistry, in order to achieve strong selective binding, the host binding sites should not only be complementary to the guest in terms of size and shape, additionally there must exist a chemical complementarity, as occurs, for instance, with the hard alkali metal cations, which can be very strongly attracted by the hard oxygen atoms of crown ethers[43]. In this regard, an efficient way to change the metal ion affinity of crown 17

ethers is to insert nitrogen atoms instead of oxygen ones, making the structures more sensitive to Ag+, Hg2+ and Cd2+ ions. One example is N,N'-dibenzyl-4,13-diaza-18crown-6, where two oxygens of an 18-crown-6 have been replaced by nitrogen atoms in order to enhance the affinity of the system for Hg2+[44]. Table 1. Classification of some relevant species according to the Hard and Soft Acids and Bases (HSAB) Principle proposed by Pearson[41]. Acids Hard

Soft

H+, Li+, Na+, K+

Cu+, Ag+, Au+, Tl+, Hg22+

Be2+, Mg2+, Ca2+, Sr2+, Mn2+

Pd2+, Cd2+, Pt2+, Hg2+

Al3+, Sc3+, Ga3+, In3+, La3+

CH3Hg+, Co(CN)52-

N3+, Cl3+, Gd3+, Lu3+

Pt4+, Te4+

Cr3+, Co3+, Fe3+, As3+, CH3Sn3+

Tl3+, Tl(CH3)3, BH3, Ga(CH3)3

Si4+, Ti4+, Zr4+, Th4+, U4+, Pu4+, Ce3+

GaCl3, GaI3, InCl3

Borderline Fe2+, Co2+, Ni2+, Cu2+, Zn2+, Pb2+, Sn2+, Sb3+, Rh3+, Ir3+, SO2, NO+, Ru2+ Bases Hard

Soft

H2O, OH-, F-

R2S, RSH, RS-

CH3COO-, PO43-, SO42-

I-, SCN-, S2O32-

Cl-, CO32-, ClO4-, NO3-

R3P, R3As, (RO)3P

NH3, RNH2, N2H4

C2H6, C6H6 Borderline

C6H5NH2, C5H5N, N3-, Br-, NO2-, SO32-, N2 Ion selectivity features of thiacrown compounds toward metal cations are primarily based on HSAB concepts. For this reason, several sulfur atom-containing molecules cannot be used as ion-sensing materials in ion-selective electrodes as they preclude the reversible potentiometric response to transition metal ions, due to the very stable complexes they form. Thus, when a thiacrown compound is used in the manufacturing of such electrodes, 18

the number and the position of the sulfur atoms is carefully considered in the design of the ionophore chemical structure[45]. By adopting the HSAB principle it would be possible to generate the organoaluminium fluoride cluster [Ag(Toluene)3]+ [{((SiMe3)3C)2Al2F5}2Li]- with two cations of different hardness in its structure. There, hard Li+ is incorporated into the cluster core by coordination to the hard fluorine atoms, while Ag +, being soft, is placed outside the core surrounded by toluene molecules[46]. The affinity of the Calix[4]-bis-monothiacrown-5 toward K+ and Ag+ has been monitored by H1NMR, revealing a higher affinity of the thiacrown for the potassium cation both in the solid and solution states, which can be explained in terms of the hard-hard interaction between the O4S ring and the alkali cation[47]. Finally, Claramunt and co-workers conducted a research involved two hosts that replicate the behavior of streptavidin protein, and five urea derivative guests. Their results reveal that the most rigid host binds better the more flexible guest and vice versa, suggesting that applicability of the HSAB principle should be tested against new hosts and guests[48].

19

Hypothesis

The presence of metal centers in a host structure plays a key role in its recognition capability. Therefore, a study of the electronic structures of metallacycle hosts, focused mainly in those atoms which experience the more pronounced multipole changes with the guest arrival i.e. the metal centers, will give us a deeper knowledge of the host-guest interactions involving inorganic systems. The host-guest binding can be explored by: Energy Decomposition Analysis according to the Morokuma-Ziegler scheme, a method which provides a bridge between physical laws of quantum mechanics and heuristic models of chemistry; multipole moment tensors, that allow us to measure the departure from spherical symmetry experienced by the metal centers with the guests arrival; and a Non Covalent Index (NCI) analysis which enables us a real-space visualization of the interactions, based on electron density properties.

20

General and Specific Objectives

The principal objective of this research is: Obtain a deeper understanding of the host-guest interactions involving metallacycle hostguest systems with the metal centers acting as binding sites. It will be done via the following specific objectives: I. Search the best exchange correlation functional to calculate metallacycles properties. II. Optimize the structure of metallacycle host-guest systems with the metal centers acting as binding sites, by using DFT techniques, starting from their X-ray crystallographic data. III. Deconvolute the host-guest interactions by using the Morokuma-Ziegler partitioning analysis, thus providing a bridge between DFT results and classic models of traditional chemistry. IV. Establish a relation between the multipole moments located at the binding sites and the coupling forces by an atomic multipole moments analysis. V. Carry out a Non-covalent Interactions (NCI) analysis in order to describe the host-guest forces, including their position and nature, in the studied systems.

21

Chapter 2

Methodologies

2.1. Density Functional Theory Density Functional Theory (DFT) is now one of the most widely used computational procedures for molecular electronic calculations. It has become a extensively used tool in most branches of chemistry. The development of DFT begins at 1964, when Pierre Hohenberg and Walter Kohn proved that the ground-state energy E of a molecular system, is a functional of the electron density ρ , given by[1]

E=E [ρ ] (1) This energy functional may be divided into three parts: E [ρ ]=T [ ρ]+ E ne [ ρ ]+ E ee [ρ ] (2) where each term in the formula has the following meaning T [ ρ ]: Kinetic Energy E ne [ ρ ]: Nucleus−electron attraction E ee [ ρ ]: Electron−electron repulsion In turn, the E ee [ ρ ] term can be partitioned into a Coulomb J [ ρ ] , and an exchange K [ ρ ] part, both implicitly including correlation. Now, we have E [ρ ]=T [ ρ]+ E ne [ ρ ]+ J [ ρ ]+ K [ρ ]

(3)

Kohn and Sham considered a fictitious reference system of non-interacting electrons, where each electron experiences the same external potential-energy υeff (r ) . This potential is such as to make the density of the reference system equal to the exact density of the molecule in which we are interested on. Since the reference system consists of noninteracting particles, we can use a Slater determinant as the ground-state wave function. The comprising orbitals of this determinant are called Kohn-Sham orbitals øi

[2].

Based on 22

the Kohn and Sham method, the kinetic energy functional can be divided into two terms, one corresponding to the reference system of non-interacting electrons and a small correction term. The first term is given as N

1 T S =∑ ⟨øi|− ∇ 2|øi ⟩ 2 i =1

(4)

where the subscript S denotes the use of a Slater determinant. The remaining kinetic energy and the exchange part K [ρ ] , are absorbed into an exchange-correlation term E xc [ ρ ] . A general DFT energy expression can be written as E DFT [ ρ]=T S [ ρ ]+ E ne [ρ ]+ J [ ρ ]+ E XC [ ρ ] (5) Equaling the exact energy E [ρ ] , with the DFT energy E DFT [ ρ] , we obtain the following expression for E xc [ ρ ] E xc [ ρ ]=(T [ ρ]−T S [ ρ ])+( E ee [ ρ ]−J [ρ ]) (6) The first parenthesis in this equation may be considered the kinetic correlation energy, while the second contains both exchange and correlation energy. The major problem in DFT is deriving suitable formulas for E xc [ ρ ] . Even if this functional is available, the problem is similar to that found in Hartree-Fock theory: determine the set of orthogonal orbitals which minimize the energy. The orbital orthogonality constraint may be solved by the Lagrange method. Then, we define a functional L[ ρ ] L[ ρ ]=E DFT [ρ ]−∑ λij [⟨øi|ø j ⟩−δ ij ]

(7)

where λ ij is a set of Lagrange multipliers, and ⟨øi|ø j ⟩=δij is the constraint referred to the orthogonality. Requiring the variation of L to vanish, provides a set of equations involving an effective one-electron operator. We may again select an unitary transformation which makes the matrix of the Lagrange multipliers diagonal, producing a set of canonical KohnSham orbitals. The resulting equations are known as Kohn-Sham equations 1 2 (− ∇ + υeff )øi=εi øi 2

(8)

where υeff (r ) , the effective potential is expressed as follows υeff (r )=υ ne (r)+∫

ρ (r ' ) dr ' + υ XC ( r ) (9) |r−r '| 23

The Kohn-Sham orbitals may be determined by numerical methods, or expanded in a set of basis functions. The corresponding exchange-correlation potential υ XC (r ) , required in υeff (r ) is given by the derivative of the energy with respect to the density[3].

υ XC (r )=

∂ E XC [ ρ (r )] ∂ ρ (r )

(10)

The usual scheme in a DFT calculation is as follows: we guess the electron density, ρ (r ) , typically by using a superposition of atomic densities. With this density and some approximate form of the functional E xc [ ρ ] , we compute υ XC (r ) . Then, the Kohn-Sham equations are solved to obtain an initial set of Kohn-Sham orbitals, which in turn are used to compute an improved density. The process is repeated until the density and exchangecorrelation energy have converged within some tolerance. Finally the electronic energy is computed from E [ρ ] . Density functionals fail to provide a consistent description of weak intra- (i.e. short range) and inter- (i.e. long range) molecular interactions arising from nonoverlapping electron densities. A pragmatic way to remedy this problem is to add an empirical potential to the usual DFT energy, according to the widely employed pairwise Grimme dispersion correction[4], in which an attractive energy term summed over all atomic pairs is subsequently included[5]. Thus, the dispersion corrected total energy E MF −D is given by E MF −D =E MF + E disp

(11)

where E MF is the usual mean-field energy and E disp is the empirical dispersion correction term given by N at −1 N next

E disp =−s 6

∑ ∑ i=1

j=i +1

C ij6 R6ij

f dmp (Rij )

(12)

Here, N at is the number of atoms in the system, C ij6 denotes the dispersion coefficient for the atomic pair ij, s6 is a global scaling factor, Rij is the interatomic distance, and f dmp is a damping function. Recently, Corminboeuf and Steinmann introduced computationally efficient dispersion coefficients and advanced damping functions which improve the performance of standard density functionals for various reaction energies and weakly interacting systems[6]. 24

2.2. Relativistic Corrections[7],[8],[9],[10] Relativistic effects have been shown to be largely responsible for the chemical differences between the fifth and sixth row elements. They account for the so called “inner pair” effect, contribute to the lanthanide contraction and are probably responsible of the unusual stability of Hg22+. The Dirac equation for a single particle satisfies all the requirements of special relativity and quantum mechanics, and is able to predict several properties with remarkably accuracy. The time-independent Dirac equation with potential V =− Zr can be written as h^ D Ψ D=ε Ψ

D

(13)

D where the Dirac Hamiltonian h^ can be expressed as

( c σV⋅p

h^ D =

c σ⋅p V −2 m0 c 2

)

(14)

where V represents the potential energy; σ , the three component Pauli spin matrix; and p , the three-component momentum operator. The corresponding wave function is

Ψ Here Ψ

L

and Ψ

S

D

L

( )

= Ψ Ψ

S

(15)

represent the large and small two-component wave functions that

include the α and β spin functions. Thus, the matrix form of the Dirac equation is

(

V c σ⋅p Ψ 2 c σ⋅p V −2 m0 c Ψ

L

L

S

S

)( )=ε( ΨΨ )

(16)

from which two equations can be obtained VΨ

c σ⋅p Ψ

L

L

+ c σ⋅p Ψ

S

=

L

= εΨ

+ (V − 2 m0 c 2 ) Ψ

We can solve the second equation for Ψ

Ψ

S

S

(17)

= εΨ

S

(18)

S

cσ ⋅ p Ψ ( ε−V +2 m0 c 2 )

L

(19)

The Pauli expansion results from taking 2 m0 c 2 out of the denominator of Eq. (19)

25

Ψ

S

=

1

ε − V ( 2 m0 c ) 1 + 2 m0 c2

(

2

)

c σ⋅p Ψ

L

(20)

Then, replacing Eq. (20) into Eq. (17) ( V −ε ) Ψ

L

+ ( σ⋅p )

1 L ( σ⋅p ) Ψ =0 ε − V 2 m0 1+ 2 m0 c 2

(

)

(21)

Now we expand the denominator of the second term in a Taylor series

(

1 ε − V 1 + 2 m0 c 2

)

= 1 −

ε − V + ⋯ (22) 2 m0 c 2

obtaining ( V −ε ) Ψ

L

+

1 ε − V L ( σ⋅p ) 1 − + ⋯ ( σ⋅p ) Ψ =0 2 m0 2 m0 c 2

(

)

(23)

Taking into account that the expansion is only valid when ε−V ≪ 2 m0 c2 . Assuming

the

Coulomb

potential

as

−Z /r ,

using

the

vector

identity

( σ⋅u )( σ⋅v ) =( u⋅v ) +i σ ( u×v ) , and renormalizing, we arrive to the Pauli equation

[

p2 Z p4 Zπ ( ) Z s⋅l − − + δr+ 3 2 2 2 2 m0 r 8 m0 c 2 m0 c 2 m20 c 2 r 3

]

Ψ

L

= εΨ

L

(24)

The first two terms are the non-relativistic kinetic and potential energy operators, the p4 term is called the mass-velocity correction due to the dependence of the electron mass on the velocity. The next is the Darwin correction, which corresponds to the oscillation of the electron around its mean position. The last term is the spin-orbit term ( s is the electron spin and l is the angular momentum operator r × p ), which corresponds to an interaction of the electron spin with the magnetic field generated by the orbital movement of the electron. The mass-velocity and Darwin corrections are often called the scalar (spin-free) relativistic corrections. In the Pauli equation resulting from extract 2 m0 c 2 of the denominator in Eq. (19), E and V can be potentially larger in magnitude than 2 m0 c 2 , and so the expansion will be not valid. To overcome this problem a family of methods were developed based on regular approximations to the ( ε − V + 2 m0 c 2 )−1 term. Thus, instead of factoring 2 m0 c 2 in 26

Eq. (19) we take out the term 2 m0 c 2−V , which is always positive for the nuclear potential and always greater than 2 m0 c 2 .

Ψ

S

=

c σ⋅ p Ψ ε ( 2 m0 c −V )(1+ ) 2 m 0 c 2−V

(25)

L

2

With this choice we may eliminate the small component by writing the Eq. (17) as ( V −ε ) Ψ

L

+

2

2 m0 c 1 ( σ⋅p ) 2 2 m0 2 m0 c −V

(

)(

1

L ( σ⋅p ) Ψ =0 (26) ε 1 + 2 m0 c 2−V

)

In the development of the Pauli Hamiltonian, truncation of the power series expansion of the inverse operator after the first term, gives the non-relativistic Hamiltonian. The zero-order term is obtained by setting the expression

1

(

1 +

ε 2 m0 c 2−V

)

to 1 in

Eq. (26) resulting in ( V −ε ) Ψ

(

V+

L

2 m0 c 2 1 L + ( σ⋅p ) ( σ⋅p ) Ψ =0 2 2 m0 2 m0 c −V

(

) ) )

2 m0 c 2 1 L ( σ⋅p ) ( σ⋅p ) Ψ =ε Ψ 2 2 m0 2 m0 c −V

(

L

(27) (28)

from which we arrive to the zeroth-order regular approximation (ZORA) Hamiltonian 2 ^h ZORA=V + 1 ( σ⋅ p)( 2 m0 c )( σ⋅p ) 2 m0 2 m0 c 2−V

(29)

The scalar relativistic ZORA Hamiltonian is just the previous expression without the Pauli matrices 2

2 m0 c 1 h^ ZORA p p SR =V + 2 m0 2 m0 c2 −V

(30)

The great advantage of h^ ZORA lies in its variational stability. At zeroth-order the regular approximation is energy independent and relatively easy to apply. Higher orders terms depends on energy, which complicate their computational implementation. As we deal with heavy elements belonging to the studied metallacycles, the ZORA Hamiltonian is employed in this work. 27

2.3. Energy Decomposition Analysis[11], [12]

The Energy Decomposition Analysis (EDA) proposed by Morokuma provides insights into intermolecular interactions by separating the total interaction energy into various terms such as electrostatic, exchange repulsion, and orbital overlapping. In this analysis, we consider any host-guest system subject of this research as a the entity AB with the corresponding wavefunction Ψ AB , and total energy E AB . AB is the result of interactions between fragments A0 and B0 in their electronic and geometric ground states Ψ0A and Ψ0B , with energies E 0A and E 0B respectively. Fragments A0 and B0 are distorted from their equilibrium geometries and wavefunctions to those encountered in AB, and present the wavefunctions Ψ A and Ψ B , and the energies E A and E B . The total energy necessary to distort the fragments is called the preparation energy Δ E prep Δ E prep= E A−E 0A+ E B −E 0B

(31)

The difference between the energy of AB E AB , and the energies of the prepared fragments E A and E B is termed Δ E i nt Δ E i nt =E AB −E A−E B (32) Now, we will focus on the bond formation according to the EDA. In the first step, the distorted fragments with frozen charge densities A and B are brought from infinite separation to their position in the final system AB. This state is referred as the promolecule with the product wavefunction Ψ A Ψ B and the energy E 0AB . The interaction between the frozen charge densities of A and B at the equilibrium geometry of AB is called the Coulomb or electrostatic interaction Δ E elec , and is calculated subtracting the Coulomb integral of the fragments from that corresponding to the overall system Δ E elec =

1 2

α, β

α ,β

∑∑

i ∈ AB j ∈ AB

⟨ ii| jj ⟩+ E nuc AB −

1 2

α ,β α ,β

∑ ∑ ⟨ii| jj ⟩+ E nuc A − i∈A j∈A

α ,β α ,β

1 ∑ ∑ ⟨ii| jj⟩+ E nuc B 2 i ∈B j ∈B

(33)

In the second step, the product wavefunction Ψ A Ψ B , which is normalized but violates the Pauli principle, is antisymmetrized and renormalized to give an intermediate state Ψ0 28

with the corresponding energy E 0 . The energy difference between E 0AB and E 0 is termed Pauli repulsion Δ E Pauli : 0

Δ E Pauli= E AB −E

0

(34)

In the third step, Ψ0 is relaxed to yield the final state Ψ AB corresponding to AB, with energy E AB . The associated energy lowering comes from the orbital mixing, and thus, it can be identified as the covalent contribution. It is termed orbital interaction Δ E orb : Δ E orb =E AB −E 0 (35) Adding Δ E elec , Δ E Pauli , and Δ E orb we obtain the total interaction energy Δ E i nt : Δ E i nt =Δ E elec + Δ E Pauli + Δ E orb

(36)

The numerical results of the EDA calculations are carried out by using DFT methodologies depending on the exchange-correlation functional employed.

2.4. Atomic Multipole Expansion[13]

Close to any atom the electrostatic potential is mainly determined by the charge distribution around this atom; or within the atomic multipole expansion, by the atomic multipoles near to that point. The charge analysis derived from an atomic multipole expansion gives an accurate description of the electrostatic potential from the charge distribution in molecules. This is achieved in three steps: 2.4.1. The total density is written as a sum of atomic densities expressed in terms of atomic functions A molecular charge density ρ is usually obtained in a basis set expansion (with atom indices A, B, basis functions χ j , basis functions indices i, j and the P ijAB element of the density matrix) (37) ρ =∑ ρ AB =∑ P ijAB χiAB χ AB j AB

ABij

29

which defines the density as a sum of atom pair densities ρ AB . These atom pair densities are expressed in terms of atomic functions f i ~ ρ AB =∑ d iA f iA+ ∑ d Bj f Bj i

(38)

j

where the coefficients are obtained minimizing the density differences

ρ AB|d τ ∫|ρ AB−~

(39)

The total density now can be written in terms of the atomic functions ~ ρ =∑ ~ ρ =∑ (∑ d A f A + ∑ d B f B ) (40) AB

AB

i

AB

i

j

i

j

j

A

A

=∑ c i f i

(41)

Ai

2.4.2. A set of atomic multipoles is defined from the atomic functions f i The electrostatic potential in a point s is given by V (r s)=∑ V A ( r s )=∑ ∑ ciA∫ A

A iϵ A

f iA(r ) dr |r s−r|

(42)

Next, an atomic multipole expansion of the r-1 term can be used: m=l

V (r s )=∑ A

l



m=−l

^ sA) 4 π M lm Z lm ( R l+ 1 2 l +1 RsA

(43)

with the real spherical harmonics Z lm and the multipole moments M lm , where R sA is the distance vector from nucleus A to a point r s . These moments can be obtained from the coefficients as: A M lm =∑ c iA∫ f iA (r 2 )r l2 Z lm ( r 2 ) d τ 2 (44) iϵ A

2.4.3. The atomic multipoles are reconstructed exactly by distributing charges over all atoms For each atom, we reconstruct the set of multipoles located on that atom by adding charges q s , A to all atoms that preserve that particular set of multipoles. The represented multipole moments of the charges q s , A are obtained with the position vectors relative to atom A, r is , A as: 3 1 repr 2 Θ jk , A=∑ q s , A ( r js , A r ks , A− δ jk r s , A) 2 2 s

(45)

30

When the number of atoms is larger than the total number of multipole moments (per atom) to be reconstructed, there are multiple forms to distribute the charges. We use a weight function that falls off rapidly to keep the atomic multipoles as local as possible, i.e., as close as possible to the atom where the multipoles are located:

ω s=exp (

−ζ |r s−r A| ) dA

(46)

where dA is the distance from atom A to its nearest neighbor, ζ is an exponential prefactor, and ω s the weight for atom s when distributing the multipole moments of atom A. Now, we want the redistributed charges to be as small as possible, and at the same time constrain the represented multipoles Θrepr jk , A to be equal to the atomic multipoles from the multipole expansion Θ MPE jk , A . We achieve this by minimizing the following function where the constrains are met by using Lagrange multipliers α A , βi , A , γ jk , A , Δ lmn , A : q2s , A repr MPE repr MPE repr g A =∑ + α A (Q MPE A −Q A )+ ∑ β i , A ( μi , A − μ i , A )+ ∑ γ jk , A (Θ jk , A−Θ jk , A ) (47) s 2 ωs, A i jk MPE repr + ∑ Δlmn , A (Ω lmn, A−Ω lmn, A ) lmn

With this choice of function, we ensure that the distribution mainly takes place close to the atom A where the multipoles are located. For the redistributed charges q s , A we obtain the following equation: 3 1 2 q s , A =ω s , A ( α A + ∑ βi , A r is , A + ∑ γ jk , A ( r js , A r ks , A − δ jk r s , A )+ ∑ Δlmn (...)) (48) 2 2 i jk lmn that clearly shows that points far away from atom A (and thus, a small weight ω s ) get a small redistributed charge. Using the constraints, we obtain for the Lagrange multipliers: Q A−∑ q s , A =0 s

3 1 Q A =α A ∑ ωs , A + ∑ βi , A ∑ ω s , A r is, A + ∑ γ jk , A ∑ ω s , A ( r js, A r ks, A − δ jk r 2s , A )+⋯ 2 2 s i s jk s

(49)

μt , A −∑ q s , A r ts , A =0 s

μ t , A =α A ∑ ω s , A r ts, A + ∑ βi , A ∑ ω s , A r ts , A r is , A s

i

s

(50)

3 1 + ∑ γ jk , A ∑ ω s , A r ts, A ( r js , A r ks, A− δ jk r 2s , A )+⋯ 2 2 jk s 31

3 1 2 Θtu, A−∑ q s , A ( r ts , A r us , A − δtu r s , A )=0 2 2 s 3 1 (51) Θtu , A =α A ∑ ω s , A ( r ts , A r us , A − δtu r 2s , A ) 2 2 s 3 1 + ∑ βi , A ∑ ω s , A ( r ts , A r us , A − δtu r 2s , A ) r is, A 2 2 i s and a similar equation for the octupole moments. This results for each atom in a set of linear equations for the Lagrangian multipliers, which are solved by a standard routine. Finally, the values obtained for the Lagrange multipliers are used to get the redistributed atomic charges, which sum, result in the Multipole Derived Charges (up to some order X): q MDC =∑ q s , A S

(52)

A

2.5. Natural Population Analysis[14]

Natural Population Analysis (NPA) involves partitioning the molecular charge into the so called “natural atomic orbitals” (NAOs), orthonormal atomic (one-center) orbitals of maximal occupancy for a given wave function, constructed by dividing the electron density matrix into sub-blocks with the appropriate symmetry. This analysis represents the occupancies (diagonal one-particle density matrix elements) of these natural atomic orbitals, which form an orthonormal set, exhibiting natural populations inherently positive, and summing correctly the total number of electrons. Moreover, the NAOs are intrinsic to the wave function, rather than to a particular choice of basis orbitals, and are found to converge smoothly toward well-defined limits as the wave function is improved, with stable populations. The NAOs are derived from atomic angular symmetry sub-blocks

Γ

(Alm)

of the density matrix Γ , localized on a particular atom, and remain localized in a

great extent on individual atoms as a molecule forms. The construction of NAOs involves two essential steps: 32

2.5.1. Diagonalization of one-center angular symmetry blocks Γ

(Alm)

of the density matrix

This leads to a set of pre-NAOs, an orthonormal set of orbitals for each atom. The preNAOs can be divided into two sets based on their occupancy: a) The minimal set, corresponding to all atomic subshells of non-zero occupancy in the atomic ground state electron configuration. b) The Rydberg set, consisting of the remaining (formally unoccupied) orbitals. In the molecular environment, their occupancies are not necessarily zero, but they play only a secondary role in describing the electron density associated with the atom. The Rydberg set includes all the pre-NAOs whose overlap with adjacent centers increases without limit as the basis set is enlarged, and is therefore treated separately in the orthogonalization procedure. The pre-NAOs of one center overlap those of other centers, so that the occupancies of these orbitals can not be used directly to assess the atomic charge. 2.5.2. Removal of interatomic overlap The general objective in this step is to orthogonalize the complete set of orbitals, while preserving the atom-like character of pre-NAOs as nearly as possible. The orthogonalization sequence starting with the pre-NAOs is indicated as follows a) The pre-NAOs { φ i } on each center are first separated into the minimal { φ i m } and Rydberg { φ i R } sets, where the minimal set represents the small number of functions that exactly describe the atomic electron density in the self consistent field approximation, and the Rydberg set corresponds to a large number of functions from the basis set having little or no role in describing the atomic electron density. ^ is performed on all the b) An occupancy-weighted symmetric orthogonalization W

minimal functions { φ i m } ; ^ { φ i m }={ φ i( Wm ) } (53) W 33

The reason to adopt this particular form of orthogonalization is that such a transformation will have a minimum deviation with respect to the untransformed one, namely 2

∑ ω i‖φ imW − φ im‖ = minimum (

)

(54)

i

with a weighting factor ωi⩾0 representing the occupancy of orbital φ im in the given system. Then, orbitals of low occupancy are free to distort significantly in the orthogonalization transformation, whereas orbitals of high ωi will be strongly preserved. c) The Rydberg sets { φ i R } are Schmidt orthogonalized (with Schmidt transformation S^ ) ( ) S^ { φi R }={ φi SR }

(55)

d) The occupancy-weighted symmetric orthogonalization is performed on the Rydberg set

{φ i(RS) } ; ^ {φ i( RS) }= { φ i( WR ) } (56) W The effect of these transformations is to describe each atomic species as nearly as possible in terms of its natural minimal basis orbitals. Only the remaining electron density which can not be described by them will end up as occupancy in the natural Rydberg basis orbitals, which have zero occupancy for the ground state wave function of the isolated atoms. Summing all contributions from orbitals belonging to a specific center we obtain the atomic charge. It is usually found that the natural minimal basis orbitals contribute more than 99% of the electron density, thus representing a very compact representation of the wave function in terms of atomic orbitals.

2.6. Non-covalent Interactions Analysis[15], [16]

The Non-covalent Interactions (NCI) analysis provides an index, based on the electron density and its derivatives, that enables the identification of non-covalent interactions. The NCI index is based on a 2D plot of the reduced density gradient, s , and the electron density ρ , where 34

s=

1 ∇ρ 2 1 /3 4/ 3 2(3 π ) ρ

When a weak inter- or intramolecular interaction is present, there is a crucial change in the reduced gradient between the interacting atoms, producing density critical points, with troughs in s ( ρ) associated with each one. Since the behavior of s at low densities is dominated by ρ , s tends to diverge except in the regions around a density critical point, where ∇ ρ dominates, and s approaches zero. The main difference in the s ( ρ) plots between a monomer and a dimer is the steep trough at low density. When we search for the points in real space giving rise to this feature, the noncovalent region clearly appears in the supramolecular complex. Further analysis of the electron density in the troughs is required to assign their origin (steric interactions, hydrogen bonds, etc.) The electron density values within the troughs are an indicator of the interaction strength. However, both attractive and repulsive interactions (i.e., hydrogen-bonding and steric repulsion) appear in the same region of density/reduced gradient space. To distinguish between them, we examine the second derivatives of the density along the main axis of variation. On the basis of the divergence theorem, the sign of the Laplacian ( ∇ 2 ρ ) of the density indicates whether the net gradient flux of density is entering ( ∇ 2 ρ 0 ) an infinitesimal volume around a reference point. Hence, the sign of ∇ 2 ρ determines if the density is concentrated or depleted at that point, relative to the surroundings. To distinguish between different types of weak interactions, contributions to the Laplacian along the axes of its maximal variation must be analyzed. These contributions are the eigenvalues λ i of the electron density Hessian (second derivative) matrix, such that ∇ 2 ρ= λ1 + λ 2 + λ 3, ( λ 1 < λ2 < λ2 ) . At the nuclei, all of the eigenvalues are negative, while away from them, λ 3 > 0 . In molecules, the λ 3 values vary along the internuclear direction, while λ 1 and λ 2 report the variation of density in the plane normal to the λ 3 eigenvector. Interestingly, the second eigenvalue ( λ 2 ) can be either positive or negative, depending on the interaction type. Then, bonding interactions, such as hydrogen bonds, are characterized by an accumulation of density perpendicular to the bond with 35

λ 2 < 0 , non-bonded interactions, such as steric repulsion, produce density depletion with λ 2 > 0 , and finally, weak interactions are characterized by a negligible density overlap that gives λ 2 ≾ 0 . Thus, analysis of the sign of λ 2 enables us to distinguish different types of non-covalent interactions, while the density itself enables us to assess the interaction strength. The NCI analysis of a phenol dimer is presented in Figure 7.

Figure 7. NCI Analysis of a diphenol dimer where hydrogen bond is denoted as a blue region and weak London interactions as a green region[15].

36

Chapter 3

A Study on the Versatility of Metallacycles in Host-Guest Chemistry. Interactions in Halide-centered hexanuclear copper(II) pyrazolate complexes.

3.1. Introduction* The term 'metallacycle' is generally used to refer to any cyclic framework with at least one metal center[1]. These systems offer interesting properties based on their unique structures, and ability to incorporate several guest species, representing a step forward in fields such as molecular recognition[2], catalysis[3],[4], molecular magnetism[5], and biomedicine[6], among others. Metallacycles acting as host species, allow organic compounds [7],[8] and multiple ions[9],[10] to be incorporated into their structures mainly via long-range noncovalent interactions (van der Waals forces). Usually, the host moiety interacts with the guest through the oxygen or nitrogen atoms located within the supporting ligands [11], [12], [13], [14];

whereas, to a lesser extent, the metal centers within the host structure play this role

* This chapter is based on the following article: Ponce-Vargas, M.; Muñoz-Castro, A. Phys. Chem. Chem. Phys. 2014, 16, 13103-13111.

37

offering a more interesting scenario driven by the versatility of a discrete number of redox centers into a single molecular entity[15], [16]. In this concern, we focus on the series of halide-centered hexanuclear anionic copper (II) pyrazolate complexes [trans-Cu6{µ-3,5-(CF3)2pz}6(µ-OH)6X]- (X = F, Cl, Br, I), synthesized by Mohamed and co-workers[17], since they represent an interesting case study to evaluate the host-guest capabilities involving a multimetal array. Such systems are based on a ring consisting of six Cu(II) centers interacting with different halide ions of increasing softness, depicting a highly symmetric structure (D3d). The metal centers are bridged by six hydroxo and six pyrazolate ligands, arranged alternately, denoting a local square planar coordination geometry at each copper site. The resulting cavity size allows the inclusion of a halide ion, as has been described by the authors. The Cu 6 ring is formed by Cu(II) ions, considering as borderline Lewis acids under the Pearson Hard and Soft Acid-Base (HSAB) principle, which interact with F-, Cl-, Br- and I-, a series of Lewis bases going from hard to soft[18]. The affinity of a host for a given guest depends on shape, size, conformation, and surface charge distribution of the moieties[19], where non-covalent interactions forces, play a crucial role in organizing the supramolecular structure [20]. As these forces are related to the electronic density distribution surrounding the host-guest pair nuclei, the theoretical description of the local electronic quadrupole moments is of great interest in order to obtain a deeper rationalization of the host-guest phenomenon [21],

[22].

Dispersion

contribution to total interaction can be evaluated according to the widely employed pairwise Grimme correction[23], which is subsequently included by adding an attractive energy term summed over all atomic pairs in the system. The parameterization of this method is still an active field of research[24]. Under this framework, we suggest that a reasonable manner to understand the different interactions governing the host-guest formation is given by the study of multipole moment tensors located at the binding sites, that will allow us to acquire a deeper knowledge about the electronic-density departure experienced at the relevant sites of the metallacycle complexes. The atomic multipole moments (Θ) can be obtained from the method developed by Swart and co-workers, where a charge analysis derived from an atomic 38

multipole expansion enables the access not only to molecular multipole moments, also to local atomic multipoles[25]. The anisotropies of such quantities are associated with electron density fluctuations, responsible for non-covalent interactions. Taking advantage of this, it is possible to gain insights into the interaction pattern via the graphical projection of the multipole moments, providing a more complete description of the host-guest coupling[26]. The aim of this work is to gain a deeper understanding of non-covalent forces inside hexanuclear copper(II) pyrazolate complexes by using DFT methodologies, where the nature of the guest, according to the HSAB principle, goes from a hard to a soft Lewis base. The host-guest interactions strength is evaluated according to the Ziegler-Morokuma energy partitioning scheme including the dispersion term in line with the pairwise Grimme approach[23], whereas the multipole analysis at the binding sites is carry out according to the Swart methodology[25]. Finally, the graphical representation of the host-guest interactions is obtained according to the Non-covalent interactions (NCI) analysis[27].

3.2. Computational Details Relativistic density functional theory[28] calculations are carried out by using the ADF 2010.02 code[29], via the scalar ZORA Hamiltonian. An all electron triple-ξ Slater basis set plus a polarization function (STO-TZP) is employed within the meta-generalized gradient approximation (meta-GGA) of Tao, Perdew, Staroverov, and Scuseria (TPSS) [30]. Geometry optimizations are conducted via the analytical energy gradient method implemented by Verluis and Ziegler [31]. In addition to the TPSS functional, the Perdew, Burke, and Ernzerhof exchange correlation functional (PBE) [32], representative of the Generalized Gradient Approximation (GGA); and the hybrid Becke, three parameter LeeYang-Parr functional (B3LYP)[33] are used in the geometry optimization of the studied systems (Table 2), obtaining good results with both of them, but slightly far from experimental data in comparison to TPSS. The performance of the TPSS functional has also exhibited good performance in the calculation of dissociation energies and geometries of hydrogen-bonded complexes[34], binding energies of transition metal dimers[35], and 39

excitation energies of small molecules and atoms [36]. For the aforementioned reasons we selected the TPSS functional to carry out this work. The dispersion Grimme correction is added in order to account for long-range interactions[23]. The strong antiferromagnetic coupling observed for the copper centers inside the [trans-Cu6{µ-3,5-(CF3)2pz}6(µ-OH)6Cl]-[37] and [trans-Cu6{µ-3,5-(CH3)2pz}6(µOH)6·CH3CN·CHCl3] structure[8], enables us to consider only the singlet state form of the studied systems. Table 2. Geometry optimizations of the 1-Cl, 1-Br and 1-I complexes using TPSS, PBE and B3LYP functionals, and their comparison with experimental data (Å and degrees). 1-Cl

1-I

TPSS

PBE

B3LYP

Exp.

TPSS

PBE

B3LYP

Exp.

TPSS

PBE

B3LYP

Diam Cu6

6.057

6.145

6.245

6.181

6.088

6.153

6.266

6.210

6.195

6.247

6.366

6.325

Cu-Cu

3.071

3.073

3.122

3.091

3.075

3.076

3.135

3.105

3.088

3.123

3.174

3.163

Cu···center

3.068

3.073

3.122

3.091

3.043

3.076

3.135

3.105

3.098

3.123

3.174

3.163

117°

118°

119°

118°

116°

118°

119°

117°

116°

118°

118°

117°

123°

123°

122°

122°

124°

122°

123°

123°

124°

123°

124°

123°

Exp.

< (Cu6)(Cu-N-N-Cu) < (Cu6)-(CuO-Cu) a

1-Br

a

Structural data for 1-F have not been reported.

The atomic quadrupole moments ( Θ ) calculation is conducted in three stages: first, the molecular charge density is expressed as a sum of atomic densities, then from these atomic densities a set of atomic multipoles is defined and then used to obtain the electrostatic potential outside the charge distribution, finally these atomic multipoles are reconstructed by using a scheme that distributes charges over all atoms to reproduce the multipoles exactly[25]. The Θ values are calculated from a single-point calculation at the optimized geometries, neglecting any symmetry operation leading to the C1 point group, whereas the graphical representation of the atomic quadrupole tensors is obtained based on the method employed by Autschbach and coworkers[38], considering a function written in spherical coordinates representing the f ( r ) =∑ r i r j Θij expression, centered at the respective nuclei, ij

whereby a surface representation of the Θ jk angular dependence can be obtained[39]. All 40

tensors are plotted by using the Chemcraft software[40]. The non-covalent interactions (NCI) analysis is carried out by using the NCIPLOT-3.0 program developed by Weitao Yang and coworkers [27] based on the analysis of electron density descriptors. NCI isosurfaces are plotted by using the Visual Molecular Dynamics (VMD) software[41].

3.3. Results and Discussion 3.3.1. Structural Parameters The calculated structure for the trans-Cu6{µ-(3,5-(CF3)2pz)}6(µ-OH)6 (1) is shown in Figure 8. To the best of our knowledge, this cyclic structure without a guest has not been isolated until now. Recently, Cañon-Mancisidor and coworkers have obtained an isostructural metallacycle [trans-Cu6{µ-3,5-(CH3)2pz}6(µ-OH)6·CH3CN·CHCl3] which packs in the solid state as a tubular framework [8]. In 1, each Cu(II) has a local square planar geometry, and the pyrazolate anions alternate positions with the µ-OH moieties above and below the plane generated by the six Cu(II) ions resulting in a structure that belongs to the D3d symmetry group. The expected high spin of the metallacycle due to the presence of six paramagnetic centers is quenched by a strong antiferromagnetic coupling within the host structure[37]. The host-guest systems, involve the formation of four halide-centered metallacyles derived from 1, namely 1-F, 1-Cl, 1-Br and 1-I[17]. Selected distances and angles for the host and the halide-centered copper(II) pyrazolate complexes are given in Table 3. The calculated bond distances are in good agreement with experimental data, suggesting that methods here used are reliable to optimize this kind of structures. All the optimized structures belong to the D3d symmetry point group, denoting Cu-Cu bond distances of about ~ 3.1 Å, which are out of the van der Waals radii sum range (2.8 Å) [42]. This point suggests a negligible direct Cu-Cu interaction, thus the stabilization of the Cu 6based structure is given mainly by the pyrazolate and hydroxo bridging ligands.

41

Figure 8. Optimized structure for trans-Cu6{µ-3,5-(CF3)2pz}6(µ-OH)6 (1), viewed from the z-axis (copper (■), nitrogen (■), carbon (■), fluorine (■)). Table 3. Selected distances (Å) and angles (degrees) of the host and halide complexes. 1

1-F

Calc.

Calc.

Exp.b

Calc.

Exp.b

Calc.

Exp.b

Calc.

Diam. Cu6

6.373

6.149

6.057

6.145

6.088

6.153

6.195

6.247

Cu−Cu

3.187

3.074

3.071

3.073

3.075

3.076

3.088

3.123

Cu···center

3.187

3.074

3.068

3.073

3.043

3.076

3.098

3.123

< (Cu6)−(Cu-O-Cu)

115°

115°

123°

121°

124°

122°

124°

123°

117°

117°

117°

118°

116°

118°

116°

118°

171°

171°

172°

171°

172°

170°

172°

171°

< (Cu6)− (Cu-N-N-Cu) < (Cu-N-N-Cu)((CF3)2pz) b

1-Cl

1-Br

1-I

Structural data from reference [17].

The diameter depicted by the Cu6 ring including the halide guest, ranges from 6.145 Å to 6.247 Å, which is contracted with respect to 1 (6.373 Å) due to the host-guest interactions. Going from 1-Cl to 1-I it is observed an increase of the cavity diameter with the guest size: 6.145 Å (1-Cl), 6.153 Å (1-Br) and 6.247 Å (1-I), in line with the increase of the Cu-Cu distance: 3.073 Å (1-Cl), 3.076 Å (1-Br) and 3.123 Å (1-I), reflecting the Cu6 ring capacity to adapt its size according to the incoming guest. Additionally, with the larger guests 42

incorporation (Cl-, Br- and I-), the dihedral angle between the Cu 6 and Cu-O-Cu planes increases from 115° to about 122°, probably due to steric repulsion forces between the oxygen atoms and these halide ions. By the other hand, the dihedral angles Θ33 , in order to describe the more negative component by Θ33 . The graphical representation of such quantities is given in Figure 10, where positive values of Θ jk describe positive electron-deficient regions, and negative values, electron-rich regions around the respective nuclei. In our particular case (D3d point group), the central guest describes a relationship given by Θ11 = Θ22 ≠ Θ33 , where the axial component ( Θ33 ) presents negative values and the perpendicular components ( Θ11 and Θ22 ) positive ones. This implies that the central guest quadrupole moment is distorted axially (Figure 10), being the electronic charge removed from the plane containing the Θ11 and Θ22 components and concentrated along the main axis[46]. This distortion of the electronic density could be attributed to the dipolequadrupole host-guest interaction occurring in the Cu6 plane, in addition to the ion-dipole interaction. The same electronic departure for the guest species is observed in the 1-Ng series (Table S5). 47

Figure 10. Graphical representation of the Electric Quadrupole tensors of the studied systems. With the aim to quantifying the quadrupole moment distortion from spherical symmetry, we introduce the quadrupole anisotropic component ( Θaniso ) in analogy to the Haeberlen convention employed in solid-state NMR experiments[47],[48], where Θaniso is defined by Θaniso =Θ33−

(Θ11+Θ22 ) 2

The more polarizable iodide guest exhibits the largest Θaniso , which accounts for the higher ∆Eelec term in the stabilization of the host-guest couple inside the series. By the other hand, the six Cu(II) centers, considered as borderline Lewis acids according to the Pearson Hard 48

and Soft Acids and Bases (HSAB) principle, experience different distributions of the surrounding electron density in each complex, varying its quadrupole moment according to the softness of the involved guest, reaching its maximum value in 1-I (Table 5). In Figure 10, it can be observed the variation of the local quadrupole of a representative Cu(II) center, given by the graphical representation of such second-rank tensor. For 1, the local quadrupole moment components are mainly distributed over two principal axes, the Cu first one pointing toward the metallacycle center ( Θ11 ), and the second one defined by

the Cu-O bond ( CuΘ33 ). In the host-guest complexes, the local quadrupole exhibits a different shape driven by the electron-rich region now located between the Cu-O and Cu···X regions. Going from 1-F to 1-I, the

Cu

Θ33 component is located in a large extent toward the axis determined by the

Cu···X interaction, resulting in a negatively-charged region at the Cu 6 plane, whereas the electro-positive component ( CuΘ11 ) is oriented along the Cu-N bond, generating positively charged regions above and below the Cu6 ring. We suggest that these electron-deficient regions are those that mainly interact with the negative axial distribution of the guest, leading to the quadrupole-quadrupole forces. Interestingly, the

X

Θ33

guest axial

component reaches its more negative value in the 1-I case, where a more effective match occurs with the metallacycle electron deficient regions defined by the copper quadrupole positive lobes. Thus, this methodology gives a clear description of quadrupole-quadrupole host-guest forces which are mainly located above and below the Cu 6 plane, in contrast to the ion-dipole and quadrupole-dipole interactions, located in the Cu6 plane. The copper sites at the metallacycle framework, exhibits different amounts of distortion of its quadrupole moment ( Θaniso ), that could be related to the increase of the stabilizing terms which overcome the Pauli repulsion (∆EPauli), resulting in a favorable host-guest coupling. The study of the hypothetical uncharged counterparts reveals a different tensor shape which is retained for 1-Ne, 1-Ar, 1-Kr and 1-Xe, where the located along the Cu-N bond and

Cu

Θ11 component is

Cu

Θ33 along the Cu-O bond, which could be attributed to

the absence of ion-dipole interactions (Figure S1). 49

Table 5. Principal components of the electronic quadrupole tensor of the studied systems, for a representative cooper and guests (Buckinghams). Cu

X

Θ11

Θ22

Θ33

Θaniso

Θ11

Θ22

Θ33

Θaniso

1

0.280

0.008

-0.288

-0.43

-

-

-

-

1-F

-0.237

-0.022

0.259

0.39

0.022

0.022

-0.044

-0.06

1-Cl

-0.211

-0.161

0.372

0.56

0.176

0.176

-0.352

-0.53

1-Br

-0.233

-0.167

0.401

0.60

0.118

0.118

-0.236

-0.35

1-I

-0.393

-0.160

0.553

0.83

1.297

1.297

-2.594

-3.89

1-Ne

0.233

0.027

-0.260

-0.39

0.008

0.008

-0.016

-0.02

1-Ar

0.227

0.079

-0.306

-0.46

0.024

0.024

-0.049

-0.07

1-Kr

0.265

0.034

-0.299

-0.45

0.041

0.041

-0.082

-0.12

1-Xe

-0.343

-0.092

0.435

0.65

0.565

0.565

-1.130

-1.70

The observed variation of the quadrupole moment of the host Cu(II) centers reveals that metallacycles acting as hosts present great advantages in comparison to their organic counterparts, prompted by the large versatility of the metal centers (Cu(II), in our case), that can vary their electron densities according to the involved guest, leading to different ranges of electron-density anisotropies ( Θaniso ), associated to electron density fluctuations, and hence, to non-covalent interactions. In this respect, Severin and coworkers based on a Mulliken

population

analysis

found

that

in

the

ruthenium

metallacycle

[(C6H6)Ru(C5H3NO2)]3, oxygen atoms adjacent to metal centers present more negative charges in comparison to those belonging to similar crown ethers, as a result of the high polarization of the metal-oxygen bonds, favoring the binding of cationic guests via electrostatic forces[49]. A comparison of the performance of several hybrid, GGA, and meta-GGA functionals in the calculation of the Electronic Quadrupole Tensors of the 1-Ng series is presented in Table S5 (See Supplementary Information) where is observed the same trend in the electron density departure regardless the functional employed. 50

3.3.3. Non-covalent Interactions Index In 2010 Johnson[50] and coworkers proposed a descriptor for non-covalent interactions (NCI), based on the reduced density gradient ( s ) at low density regions ( ρ (r ) ). This analysis provides a graphical index, which allows the characterization of the binding forces within the host-guest pair. The reduced density gradient is given by s=

1 ∇ρ 2 1 /3 2(3 π ) ρ4 /3

The reduced density gradient at low density regions verifies the presence of non-covalent interactions. Each point in this region is correlated with the second eigenvalue of the electron density Hessian ( λ 2 ) times the electron density.

Figure 11. NCI Analysis for the halide complexes 1-X (X = F, Cl, Br, I). 51

The values of λ 2 give information about the type of binding force: attractive forces, such as hydrogen bonds ( λ 2 < 0 ), weak interactions λ 2 ≈ 0 or repulsive forces ( λ 2 > 0 ). The non-covalent interactions analysis for the 1-X series is presented in Figure 11, where for all systems the region involving non-covalent interactions is located between the Cu 6 ring and the central guest. This region denoting stabilizing forces ( λ 2 < 0 ) could be associated with the quadrupole-dipole and quadrupole-quadrupole forces established between the guest and host moieties, in line with the multipole analysis aforementioned.

3.4. Conclusions The non-covalent forces into the host-guest systems involving the hexanuclear copper (II) pyrazolate complexes and a halide guest (F-, Cl-, Br-, I-), describe an electrostatic character (~70% of the stabilizing terms) whereas the dispersion term contributes to a rather small extent representing about 5%. The evaluation of the hypothetical noble-gas counterparts allows us to obtain a case for comparison, where the electrostatic term of the stabilizing energy is highly quenched, allowing to evaluate by difference the contribution of the ion-dipole/quadrupole interactions to the overall host-guest formation. According to our results, the iondipole/quadrupole contribution to the stabilizing electrostatic term ranges from 95.0% to 77.0% going from 1-F to 1-I, describing the increasing role of higher order interactions such as quadrupole-dipole and quadrupole-quadrupole into the host-guest pair formation. The natural population analysis of the hypothetical trans-Cu6{µ-3,5-(CH3)2pz}6(µ-OH)6 host (2) and the corresponding [trans-Cu6{µ-3,5-(CH3)2pz}6(µ-OH)6X]- (X = F, Cl, Br, I) complexes (2-X) reveals by comparison with the original series the importance of the -CF 3 groups in promoting the charge transfer process occurring during the host-guest coupling. According to the inclusion of a given halide ion, the local dipole moment and local electric quadrupole moment of the host binding sites, namely Cu(II), vary in different amounts. Thus, this observed variation reveals that the inclusion of metallacycles as host species into the formation of host-guest pairs represents great advantages in comparison to their organic 52

counterparts, as the metal centers can modulate their electron densities in a considerable extent in order to maximize the host-guest interactions. The graphical representation of the local quadrupole moments ( Θ ) describes that the electron-deficient regions above and below the Cu 6 plane are those that mainly interact with the negative axial distribution of the guest, leading to quadrupole-quadrupole hostguest forces, which increase as Θaniso of the guest goes towards more negative values, as occurs in the 1-I case. Our methodology involving the graphic representation of Θ , offers a clear representation of the high-order interactions. Hence, ion-dipole and quadrupole-dipole forces are located at the Cu6 ring plane, whereas quadrupole-quadrupole interaction, mainly above and below such plane.

53

Chapter 4

Heavy

Element

Metallacycles:

Insights

into

the

Nature of Host-Guest Interactions involving Di-Halide Mercuramacrocycle Complexes.

4.1. Introduction* Since they discover on 1967 by Pedersen [1], [2], great interest has been devoted to study and synthesize host-guest systems given their increasing relevance in materials science [3], [4], [5], [6], [7], [8].

Such systems can be defined as highly structured molecular frameworks

composed of at least two complementary entities associated through non-covalent interactions, where the host possess convergent binding sites and steric features that complements the guest entity[9],

[10], [11].

In this context, metallacycles offer significant

advantages over organic systems in terms of ion recognition, as their preference for a specific guest can be adjusted in several ways, such as: by modifying the cavity size, through the variation of the metal centers and the nature of the organic ligands [12], [13], and by the functionalization of such ligands with electron withdrawing groups becoming more * This chapter is based on the following article: Ponce-Vargas, M.; Muñoz-Castro, A. J. Phys. Chem. C. 2014, 118, 28244-28251.

54

acidic the metal centers and hence, the entire host cavity[14]. Furthermore, the large range of different coordination numbers displayed by the metal centers, in contrast to the limitations concerning the coordination of organic hosts[15], and the multidentate nature and pre-organization exhibited by the cavity also represent distinctive features [16]. All these factors lead to the development of inorganic cages [17] and metallacycles[18], toward the design of multimetallic catalysts[19] and enzyme mimics[20], and also applications in materials science[21]. Among the wide range of metallacycles, mercuramacrocycles constitute an interesting case study as they present mercury(II) centers in a cyclic array, which can be considered as soft acids under the Pearson HSAB theory [22]. For instance, several mercuramacrocycles, such as mercuracarborands[23],

[24], [25],

have been reported as host species with the mercury

centers acting as electrophilic binding sites, forming two almost colinear primary σ bonds, and

showing

appreciable

Lewis

acidity.

In

the

same

way,

mercuraazametallamacrocycles[26], [27] have shown the ability to trap Cu(I) and Ag(I) ions suggesting Hg(II)···Cu(I)···Hg(II) and Hg(II)···Ag(I)···Hg(II) metallophilic interactions in a linear conformation. Similar host capabilities have been exhibited by perfluorated mercuramacrocycles, presenting a large number of electron-withdrawing fluorine atoms that increase the Lewis acidity of the metal ring structure, thereby enhancing the anion receptor character of such systems. Among them, trimeric perfluoro-ortho-phenylene mercury(II), (o-C6F4Hg)3, can interact with arenes[28], crown ethers[29], thiacrown ethers[30], and many other species[31] via non-covalent forces, whereas cyclic pentameric perfluoroisopropylidenemercury, (Hg(C(CF3)2)5, characterized by Antipin and co-workers is able to couple simultaneously two halide ions, generating a bipyramidal central core [32], [33],

which represents an interesting model for understanding non-covalent interactions and

the nature of the host-guest interactions involving heavy elements. The understanding of intermolecular forces can be extended by studying the molecular charge distribution via multipole moments [34], [35]. In this context, the work about binding forces between trinuclear silver pyrazolate metallacycles and acetonitrile molecules[36] where an electron-deficient region at the center of the metallacycles is available to significant quadrupole-dipole interaction with Lewis-basic acetonitrile molecules, and the 55

fluorinated benzenes solubility study, rationalized in terms of molecular dipole and quadrupole moments[37] represent interesting contributions. Hence, we suggest that a reasonable

manner

to

study

the

electronic

cloud

departure

experienced

by

mercuramacrocycles with the guest entry, which accounts for higher order interactions such as dipole-quadrupole, quadrupole-quadrupole, etc., is via dipole moment vectors and quadrupole moment tensors located at the binding sites. As part of our current interest in acquiring a deeper knowledge into host-guest coupling concerning metallacycles[38], here we evaluate the interactions involving a series of dihalide pentameric perfluoroisopropylidenemercury complexes, [(HgC(CF3)2)52X]2- (X = Cl, Br, I), where the Hg(II) centers constitute soft acids according to the Hard and Soft Acid and Bases (HSAB) principle[22], and with halide species going from hard (Cl-) to soft (I-) bases. This study is conducted by using relativistic density functional methods in conjunction with the energy decomposition analysis according to the Morokuma scheme. In addition, a multipole moments study[39] and a Non Covalent Index (NCI) analysis [40], [41] is carried out to unravel the nature of the host-guest coupling.

4.2. Computational Details Relativistic density functional theory[42] calculations are conducted using the ADF 2012.02 code[43], via the scalar ZORA Hamiltonian. All electrons are treated employing triple-ξ Slater basis set plus a polarization function (STO-TZP) within the meta-generalized gradient approximation of Tao, Perdew, Staroverov, and Scuseria (TPSS)[44]. The TPSS functional depends on density, ρ ( r ) , density gradient, ∇ ρ ( r ) , and the kinetic energy density,

2 1 KS | ∇ φ ( r )| , where φ KS represents the Kohn-Sham orbitals. The performance ∑ 2

of TPSS functional has been evaluated in the calculation of dissociation energies and geometries of hydrogen-bonded complexes[45], binding energies of transition metal dimers[46], and excitation energies of small molecules and atoms[47]. Geometry optimizations are carrried out via the analytical energy gradient method implemented by 56

Verluis and Ziegler[48]. In order to consider long-range interactions, the dispersion Grimme correction[49] is added both for geometry optimizations and energy decomposition analysis. The local multipole moments calculation is conducted in three stages according to the method developed by Swart and co-workers[39], where at the first step, the molecular charge density is expressed as a sum of atomic densities. Then, a set of atomic multipoles is defined from such atomic densities and used to obtain the electrostatic potential outside the charge distribution. Finally, by using a scheme that distributes charges over all atoms, the atomic multipoles are reproduced exactly. To keep the atomic multipoles as local as possible, a weight function that falls off rapidly is used. The graphical representation of the quadrupole tensor ( Θ ) is obtained based on the method employed by Autschbach and coworkers[50], considering a function written in spherical coordinates representing the f ( r ) =∑ r i r j Θij expression centered at the ij

respective nucleus, depicting its angular dependence and sign. The non-covalent interactions (NCI) analysis is carried out by using the NCIPLOT-3.0 program developed by Weitao Yang and coworkers[40], [41], based on the analysis of electron density descriptors. All isosurfaces and figures are carried out with the software packages Chemcraft [51] and Visual Molecular Dynamics (VMD)[52].

4.3. Results and Discussion The calculated structures for (HgC(CF3)2)5 (1) and [(HgC(CF3)2)52X]2- (1-2X) (X=Cl, Br, I) are shown in Figure 12. Geometry optimizations are carried out without any symmetry constraint, resulting in a D5h structure with the mercury centers lying in the same plane, depicting almost linear C-Hg-C inner angles (178.3°) within the ring, and Hg-C-Hg angles (109.7°) very close to those typical of tetrahedral carbon atoms. The obtained structures lie in a stationary point on the potential energy surface (PES) as given from the vibrational analyses, which describes negative frequencies (~ 20 cm -1) corresponding to the rotation of the fluoromethyl groups. Relevant structural parameters are summarized in Table 6. The good agreement between the available experimental data [53], [54] and calculated structures 57

suggests methods here used are reliable in the optimization of this type of metallacycles. The inclusion of the halogen ions by reacting 1 and the respective [PPh4]+X- salt, results in a structure where two anions are located above and below the Hg5 plane (Figure 12), as has been reported by Antipin and co-workers[32],[33].

Figure 12. Calculated structures for the mercuramacrocycle (HgC(CF3)2)5 (1) and the [(HgC(CF3)2)52X]2- (1-2X) series (mercury (■), carbon (■), fluorine (■)). Table 6. Selected distances (Å) and angles (degrees) of the host and di-halide mercuramacrocycle complexes. [(HgC(CF3)2)5X2]2-, X = Cl, Br, I

(HgC(CF3)2)5 1

d

1-2Cl

1-2Br

1-2I

Exp.d

Cal.

Exp.d

Cal.

Exp.d

Cal.

Exp.d

Cal.

Hg-Hg

3.33

3.331

3.310

3.348

3.300

3.372

3.337

3.425

Hg-C

2.11

2.163

2.103

2.163

2.123

2.170

2.120

2.182

< Hg-C-Hg

105°

110°

104°

101°

102°

102°

104°

103°

< C-Hg-C

184°

182°

186°

187°

187°

186°

185°

184°

Hg···X

-

-

3.221

3.327

3.327

3.412

3.48

3.571

X···center

-

-

1.568

1.719

1.789

1.848

1.986

2.066

X···X

-

-

3.253

3.437

3.616

3.696

4.04

4.132

Experimental data from References [32], [33].

All the calculated complexes derived from 1 belong to the D5h symmetry point group, and exhibit a slight increase in the Hg-Hg distances from 3.331 Å to 3.425 Å in line with the size of the guest species. The X···Hg distances are shorter than the sum of the van der 58

Waals radii of the isolated atoms (Hg-Cl = 3.9 Å, Hg-Br = 4.0 Å, Hg-I = 4.2 Å) [55] suggesting an interaction involving more than weak forces between the mercury centers and the halide guests. An orbital analysis reveals that the highest occupied molecular orbital (HOMO), is mainly formed by the halide npz atomic orbitals, whereas the lowest unoccupied molecular orbital (LUMO), by the metallacycle orbitals. Furthermore, the HOMO-LUMO energy gap becomes narrower according to the variation of the guests, being 3.67 eV in 1-2Cl, 3.56 eV in 1-2Br, and 3.36 eV in 1-2I. In order to gain more insights into the different terms contributing to ∆E int, an energy decomposition analysis (EDA) according to the Morokuma−Ziegler scheme is conducted[56],[57]. In this framework, ∆Eint can be decomposed into several terms according to: ∆Eint = ∆Eorb + ∆Eelec + ∆Edisp + ∆EPauli Here, the ∆Eelec stabilizing term refers to the electrostatic character of the interaction, which is obtained by considering each defined fragment (namely, A and B) in its unperturbed (frozen) electron density as isolated species ( Ψ A Ψ B ). Next, the repulsive ∆EPauli term accounts for the four-electron two-orbital interaction between occupied orbitals, which is calculated from the energy change in the process of antisymmetrization and renormalization of the overlapped fragment densities, which is related to steric repulsion effects. Lastly, the stabilizing ∆Eorb term obtained when the densities of the constituent fragments relax into the final molecular orbitals ( Ψ AB ), accounts for the covalent character of the interaction. In addition, the pairwise correction of Grimme (DFT-D3)[49] allows to evaluating the dispersion interaction (∆E disp) related to London forces. To overcome basis set superposition error (BSSE), the counterpoise method is employed[58]. First, with the aim to evaluate the most favorable array within the studied moieties, we describe two hypothetical series involving the inclusion of one guest into the mercuramacrocycle structure (1). The first series corresponds to the halide guest in an apical position, whereas the latter, deals with the halide-centered situation. The structural parameters of the one-guest complexes are presented in Tables S6 and S7, while EDA 59

results are presented in Table 7. The results show that the centered-halide structure is less stabilizing than the apical conformation according to the following order 0.81 < 4.49 < 10.55 kcal/mol going from the Cl- to the I- complex. From the EDA analysis of the ∆Eint, it can be observed that the destabilizing ∆E Pauli term is the most influenced quantity with the inclusion of the centered halide guest. The obtained ∆E Pauli rises from 105.45 kcal/mol to 224.53 kcal/mol going from 1-2Cl to 1-2I, favoring the apical conformation in order to overcome the steric repulsion given by the size of the incoming anion. Interestingly, in the halide centered case the stabilizing ∆E elec term increases as a consequence of the guest size, denoting a more efficient electrostatic interaction between the halide and the Hg 5 ring. This effect is related to an increase of the electrostatic character of ∆E int, due to the role of Coulombic attractive forces, such as ion-dipole interaction. However, the more favorable ∆Eelec term in the centered case does not provide enough stabilization to overcome the steric repulsion given by the anion size. Table 7. Energy Decomposition Analysis (EDA) (kcal/mol) for a series of hypothetical mono-halide mercuramacrocycle complexes. [(HgC(CF3)2)5X]1- (X = Cl, Br, I) 1-Cl Apical

1-Br Center

Apical

1-I Center

Apical

Center

∆Eorb

-41.37

24.27%

-43.32

22.51%

-41.57

23.77%

-46.68

19.85%

-42.83

24.41%

-54.67

18.68%

∆Eelec

-124.61

73.11%

-145.24

75,30%

-127.66

73.01%

-183.34

77.97%

-124.08

70.73%

-230.96

78.93%

∆Edisp

-4.46

2.62%

-4.23

2.19%

-5.63

3.22%

-5.12

2.18%

-8.52

4.86%

-6.99

2.39%

∆EPauli

82.19

105.45

90.81

155.58

96.79

224.53

∆Eint

-88.25

-87.44

-84.05

-79.56

-78.64

-68.09

Making a comparison between the series it can be observed that in the apical configuration the electrostatic term overcomes the Pauli repulsion more efficiently (ΔE elec − ΔEPauli = −42.42; −36.85; −27.29 kcal/mol) than in the centered configuration (−39.79; −27.76; −6.43 kcal/mol). However, we can also notice how the gap between the Pauli repulsion and the electrostatic attraction becomes narrower as the size of the guest species increases. Then, the preference for the apical configuration is more pronounced as the guest becomes larger. Thus, the preferred apical mono-halide structures exhibit values of ∆E int ranging 60

from -88.25 kcal/mol to -78.64 kcal/mol going from Cl - to I-, denoting a more favorable interaction with the hardest anion (Cl-) in the series, according to the Hard and Soft Acid and Base Principle (HSAB)[22]. The inclusion of two halide anions (X = Cl, Br, I) above and below the Hg 5 ring leads to energetically favorable [(HgC(CF3)2)52X]2- complexes, as denoted by the interaction energy (∆Eint) between (HgC(CF3)2)5 and 2X2-, which varies from -186.16 to -161.83 kcal/mol going from 1-2Cl to 1-2I, similarly to their hypothetical monohalide counterparts, where the harder anion in the series leads to the more stable host-guest entity. Through the EDA, the nature of coupling forces within the di-halide mercuramacrocycle complexes is evaluated. These analyses are carried out considering as the first fragment the metallacycle host (HgC(CF3)2)5, and as the second one, the halide ions pair (2X2-, X = Cl, Br, I) (Table 8). The EDA reveals ∆E elec as the major stabilizing term, representing about 64% of total coupling forces, and denoting the main electrostatic character of the interaction, suggesting that stabilization of 1-2X is given mainly from Coulombic-type interactions such as ion-dipole, ion-quadrupole, dipole-dipole, ion-quadrupole, among others, occurring between the halide guests and the soft mercury(II) centers. By the other hand, the orbital term (∆E orb) experiences a slight variation, ranging from -84.93 kcal/ mol to -82.45 kcal/mol denoting that the overall charge transfer is similar along the series. The last stabilizing term, ∆Edisp, according to the pair-wise correction goes from -10.78 kcal/mol to -19.03 kcal/mol suggesting that weak forces contribute of about 5% to the overall interaction energy reaching its larger value in the iodide complex. The destabilizing quantity related to the Pauli repulsion term, ∆E Pauli, exhibits a similar trend to the hypothetical mono-halide case, where the bulkier anion results in a less favorable structure. This fact is reflected by the values of ∆E Pauli, which increases with the guest size going from 71.57 kcal/mol to 125.64 kcal/mol becoming the main factor in the preference of the mercuramacrocycle host for harder halide guests. Interestingly, this observation denotes that the expected soft-acid soft-base pair preference is not obtained in the present case involving the (HgC(CF 3)2)5 metallacycle presenting soft-acid Hg(II) centers, which in principle should exhibit a more stable situation in the iodide case.

61

Table 8. Energy Decomposition Analysis (EDA) (kcal/mol) and Natural Population Analysis (NPA) (a.u.) for host and di-halide mercuramacrocycle complexes. EDA ∆Eorb ∆Eelec ∆Edisp ∆EPauli ∆Eint NPA X [Hg5] [(C(CF3)2)5]

1

[(HgC(CF3)2)52X]2-, X = Cl, Br, I 1-2Cl 1-2Br -84.93 32.95% -85.00 30.94% -162.02 62.86% -176.74 64.34% -10.78 4.18% -12.95 4.71% 71.57 100.30 -186.16 -174.39 1 +5.60 -5.60 0.00

1-2Cl -0.89 +5.95 -6.17 -0.21

1-2Br -0.88 +5.95 -6.14 -0.25

1-2I -82.45 -185.99 -19.03 125.64 -161.83

28.68% 64.70% 6.62%

1-2I -0.83 +5.80 -6.14 -0.35

The natural population analysis allows us to evaluate the charge distribution in the resulting host-guest complexes (Table 8) accounting for the ∆E orb term. As result, it can be seen a net charge transfer from the halide ions toward the mercury centers denoted by a charge of about -0.87 |e| over the ions rather than their formal -1 |e| charge, thus donating of about 0.13 |e| towards the host structure. Going from 1-2Cl to 1-2I, the charge transfer slightly increases in the series. The charge distribution is given by the [Hg 5]5.6+ [(C(CF3)2)5]5.6-. As a consequence of the inclusion of the halide centers, the electron withdrawing group receives more electronic charge, denoted by the rise from -5.60 |e| to about -6.15 |e| of the fragment [(C(CF3)2)5] (Table 8), leading to a more positively charged metal core. Thus, the charge donation from the halide centers is distributed mainly over the trifluoromethyl groups. In order to gain a deeper understanding of the main stabilizing interaction energy term and the preference of the heavy elements metallacycle containing soft-acids centers (Hg(II)), for hard bases (Cl-), we evaluate the contribution from different Coulombic type interactions to the electrostatic term (∆E elec). Since the stabilizing nature of ∆E elec is given by ion-dipole, ion-quadrupole and higher order interactions such as dipole-dipole, dipole62

quadrupole, etc., an analysis based on the comparison with hypothetical di-noble gas (Ng) mercuramacrocycle analogues, namely 1-2Ng, neutral species and isoelectronic with the corresponding halide guests is conducted (Table S9). This approach enables an assessment of the interaction energy neglecting the ion-dipole and ion-quadrupole contributions to the electrostatic term allowing us to evaluate the role of higher order interactions of smaller magnitude, which contribute to the preference in the formation of soft acid-soft base pairs[22]. In the 1-2Ng series the electrostatic contribution decreases significantly ranging in the hypothetical noble gases counterparts from -4.29 kcal/mol to -9.35 kcal/mol, in contrast to the halide case which ranges from -162.02 kcal/mol to -185.99 kcal/mol, as a consequence of the absence of ion-dipole/quadrupole interactions. To quantify the relevance of ion-dipole and ion-quadrupole interactions over the higher order electrostatic terms, the ∆Eelec terms corresponding to 1-2Ng and 1-2X are related according to (1-(Ng∆Eelec/X∆Eelec))%, providing a simple parameter for the contribution of the halide ionic character to the electrostatic term. This treatment reveals the chloride complex as the system with the major ion-dipole/quadrupole contribution (97.35%) to ∆Eelec, followed by the bromide (96.11%) and iodide systems (94.97%), denoting the quite small contribution (less than 5%) from other Coulombic terms, suggesting that the formation of

1-2X is ruled mainly by the ion-dipole/quadrupole interactions. As a

consequence, the expected soft-acid capabilities of 1 which should favors the 1-2I formation, are modified by the electron withdrawing trifluoromethyl (-CF 3) groups increasing the size of their local dipole moments, thus preferring hard-bases. The electron withdrawing role of the trifluoromethyl substituents in 1 is clearly advised by evaluating its -CH3 and -H counterparts, namely (HgC(CH3)2)5 (2) and (HgCH2)5 (3), which exhibit a less positive central cavity (Figure S2). Then, the comparison of the interaction energies in [(HgC(CH3)2)52X]2- (2-2X) and [(HgCH2)52X]2- (3-2X) confirms the relevant role of the highly electron-withdrawing -CF3 groups into the Lewis acid capabilities of the Hg5 core, since in the former, ∆Eint ranges from -92.90 kcal/mol to -81.26 kcal/mol (Table S11) whereas in the latter, ranges from -74.12 kcal/mol to -62.91 kcal/mol (Table S13), being both smaller in magnitude than those corresponding to [(HgC(CF 3)2)52X]2-. These results could be attributed to the more pronounced electronic cloud distortion at the 63

mercury centers occurring in 1-2X driven by the -CF3 groups, leading to a more positive cavity, which enhances the ion-atomic multipole interactions. We propose that a reasonable manner to gain a deeper understanding of the small contribution to the host-guest coupling from the quadrupole moment ( Θ ) at the binding sites is the evaluation of the local quadrupole moment tensors in each metal center. With the aim to obtain a clear representation of such quantities, which contribute to the dipolequadrupole, quadrupole-quadrupole, and related interactions. Such tensor is considered under its principal axis system (PAS) where the principal Θ jk components are denoted independently to the molecular axis system, according to Θ11 > Θ22 > Θ33 in order to describe the more negative component by Θ33 . The graphical representation of Θ jk is given in

Figure 13, denoting a non-axial symmetry ( Θ11 ≠ Θ22 ≠ Θ33 ), where the Θ11

and Θ33 components are located within the Hg5 plane.

Figure 13. Quadrupole moment tensor (Θ) representation for a Hg(II) center, in the studied systems. It can be seen through the series that spatial distribution of such tensor does not vary to a large extent, in agreement to the small contribution (< 5%) to the overall interaction 64

energy, suggesting that such effect is given by the almost lineal local geometry at the mercury centers and the D5h molecular symmetry involving a mirror plane in the Hg 5 plane. These structural features cause the positive Θ11 component to be located along the axis formed by the Hg-C bonds, and the negative component Θ33 to be distributed in the Hg5 plane pointing toward the center of the structure, preventing the arise of a significant quadrupole component perpendicular to the Hg5 plane, that could contribute to the higher order electrostatic terms such as quadrupole-quadrupole, related to the soft-soft preference (Table 9). Table 9. Principal components of the electronic quadrupole tensor of the studied systems for a representative mercury and guests (Buckinghams). Hg

X

Θ11

Θ22

Θ33

Θaniso

Θ11

Θ22

Θ33

Θaniso

1

0.130

0.039

-0.169

-0.254

-

-

-

-

1-2Cl

-0.743

-0.056

0.798

1.198

-0.055

-0.055

0.110

0.165

1-2Br

-0.690

-0.087

0.777

1.166

-0.031

-0.031

0.062

0.093

1-2I

-0.707

-0.158

0.864

1.297

0.063

0.063

-0.126

-0.189

The departure from spherical symmetry (i.e. Θ11 = Θ22 = Θ33 ) of the quadrupole moment can be related to the mercury electronic cloud distortion induced by the guest. For a clear quantization of such distortion, it is useful to calculate the quadrupole anisotropic component ( Θaniso ), in analogy to the Haeberlen convention from solid-state NMR [59] resulting in a single an easy to interpret parameter. Our results denotes that the local Θaniso term for a representative Hg(II) center in the host (HgC(CF 3)2)5 is of -0.254, while with the guests arrive increases to about 1.22 for all the studied di-halide complexes ([(HgC(CF3)2)52X]2-, X=Cl, Br, I). The almost constant value of Θaniso along the series, which remains almost independent from the hard to soft halide, denotes the small contribution of higher-order interactions such as dipole-quadrupole, quadrupolequadrupole, etc., expected to be of major importance in the iodide counterpart to the overall interaction energy, as suggested by the EDA analysis along the series. 65

Lastly, in order to gain a deeper knowledge of the spatial distribution of the discussed binding forces, we calculate the non-covalent interactions (NCI) [41] index for [(HgC(CF3)2)52X]2-. The NCI index offers a suitable description of non-covalent interactions based on the reduced density gradient ( s ) at low-density regions ( ρ (r) < 0.06 a.u). The s quantity is employed to denote an inhomogenous electron distribution, and is given by: s=

1 ∇ρ 2 1 /3 4 /3 2(3 π ) ρ

where s exhibits small values in regions where both covalent bonding and noncovalent interactions are located. To distinguish the nature of the interaction, each point in this region is correlated with the second eigenvalue of the electron density Hessian ( λ 2 ) which accounts for the accumulation (attractive) or depletion (repulsive) of density in the plane perpendicular to the interaction. The product between ρ (r) and the sign of λ 2 has been proposed as a useful descriptor to reveal stabilizing or attractive interactions ( λ 2 < 0 ), weak interactions ( λ 2 ≈ 0 ) or repulsive interactions ( λ 2 > 0 ), thus ρ (r) times the sign of

λ 2 ranges from negative to positive values according to the nature of the non-covalent interactions. The NCI analysis for the studied [(HgC(CF 3)2)52X]2- series is presented in Figure 14, with stabilizing forces denoted as blue regions ( λ 2 < 0 ) located between the mercury centers and the halide guests species. These forces could be related with the match between the electron-deficient region of the metal centers and the negative charged halide guests, in agreement to the discussion given above. The same type of stabilizing interactions have been reported in the mercury complexes [Hg(X)3]- (X = F, Cl, Br)[41]. Additionally, in all studied systems, weak forces denoted as green regions can be observed between the carbon atoms belonging to the ring and the guest species. Only, in 1-2I, weak interactions between the fluorine atoms and the iodide guests can be advised from the NCI analysis.

66

Figure 14. NCI Analysis of the 1-2X mercuramacrocycle complexes, where blue regions denote strong stabilizing forces and green regions denote weak interactions.

4.4. Conclusions The study of the formation of host-guest systems involving the heavy element metallacycle, (HgC(CF3)2)5, namely, [(HgC(CF3)2)52X]2- (X=Cl, Br, I) reveals an interesting case where the expected soft acid-soft base pair is not the more stable situation, revealing a surprising hard-soft coupling as the preferred host-guest species. The interaction with Cl- is more favored than the corresponding with I-, by an energy amount of about 24 kcal/mol. To understand such situation, the use of a detailed analysis of the energy decomposition terms suggests the electrostatic character of the host-guest pair, which is ruled by the ion-dipole/quadrupole term by about 97%, favoring the inclusion of the hard base namely, Cl- instead of the softer one, I-. The lineal mercury local geometry given by the Hg-C bonds, and the D5h molecular symmetry determine the shape of the local quadrupole moment at the binding site leading to an in-plane distribution, preventing the arise of a significant quadrupole component perpendicular to the Hg5 plane, that can contribute to the higher order electrostatic terms, related to the soft-soft preference. The current approach, allows determining the role of certain Coulombic terms to the electrostatic interaction nature, leading to a clear rationalization of the soft-soft or hard-soft preferences into the formation of host-guest pairs. 67

Overall Conclusions

The good agreement between the calculated structures and experimental data suggests that density functional calculations at the TPSS/ZORA level including the Dispersion Grimme correction are reliable in the study of the metallacycle host-guest systems subject of this research. The Energy Decomposition Analysis according to the Morokuma-Ziegler scheme reveals the electrostatic term as the major contributor to the stabilizing forces in the studied systems. The arise of higher order electrostatic terms as the guest softness increases, is evidenced by our methodology involving the replacement of the halide guests by noble gases, suggesting that metal centers modulate their electron density according to the incoming guests. Our methodology involving the graphic representation of the quadrupole moment tensors, provides a clear representation of the higher-order electrostatic interactions within the studied systems, such as dipole-quadrupole or quadrupole-quadrupole forces. The Non Covalent Index (NCI) analysis clearly denotes the interactions between the metal centers and the halide guest species, and its stabilizing nature.

68

Scientific Contributions

The following articles were published in international peer-reviewed scientific journals, during the Ph.D. Miguel Ponce Vargas, Alvaro Muñoz Castro. Heavy Element Metallacycles: Insights into the Nature of Host-Guest Interactions Involving Di-Halide Mercuramacrocycle Complexes. The Journal of Physical Chemistry C, 2014, 118, 28244-28251. Miguel Ponce Vargas, Alvaro Muñoz Castro. A study on the versatility of metallacycles in host–guest chemistry: Interactions in halide- centered hexanuclear copper(II) pyrazolate complexes. Physical Chemistry Chemical Physics, 2014, 16, 13103-13111. Carolina Olea, Miguel Ponce Vargas, Rafael Matos Piccoli, Giovanni Finoto Caramori, Gernot Frenking, Alvaro Muñoz Castro. [2.2.2]Paracyclophane, Preference for η6 or η18 Coordination Mode Including Ag(I) and Sn(II): A Survey into the Cation-π Interaction Nature Through Relativistic DFT Calculations. RSC Advances, 2015, 5, 7803-7811. Carolina Olea Ulloa, Miguel Ponce Vargas, Raúl Guajardo Maturana, Alvaro Muñoz Castro. Theoretical study of the binding strength and magnetical response properties involved in the formation of the π-donor/π-acceptor [TTF–CBPQT] 4+ host–guest system. Polyhedron, 2013, 54, 119–122.

69

Raúl Guajardo Maturana, Miguel Ponce Vargas, Alvaro Muñoz Castro. Survey of long d10-d10 metallophilic contacts in four-membered rings of Ag(I) and Au(I) supported by carbene-pyrazole mixed ligands. The Journal of Physical Chemistry A, 2012, 116, 87378743.

70

Supplementary Information

5.1. Chapter 3 Table S1. Selected calculated distances (Å) and angles (degrees) of the 1-Ne, 1-Ar, 1-Kr and 1-Xe complexes. [trans-Cu6{µ-3,5-(CF3)2pz}6(µ-OH)6Ng], Ng = Ne, Ar, Kr, Xe 1-Ne

1-Ar

1-Kr

1-Xe

Diam. Cu6

6.405

6.441

6.447

6.489

Cu−Cu

3.203

3.220

3.224

3.245

Cu···center

3.203

3.220

3.224

3.245

H···center

3.619

3.646

3.666

3.694

< (Cu6)−(Cu-O-Cu)

114°

116°

116°

117°

118°

117°

117°

116°

< (Cu6)− (Cu-N-N-Cu)

Table S2. Energy Decomposition Analysis for the 1-Ne, 1-Ar, 1-Kr and 1-Xe complexes (kcal/mol). [trans-Cu6{µ-3,5-(CF3)2pz}6(µ-OH)6Ng], Ng = Ne, Ar, Kr, Xe 1-Ne

1-Ar

1-Kr

1-Xe

∆Eorb

-0.15

2.19%

-3.54

15.0%

-5.87

16.0%

-11.24

18.4%

∆Eelec

-2.89

42.19%

-11.70

49.7%

-20.82

56.7%

-38.07

62.3%

∆Edisp

-3.81

55.62%

-8.30

35.3%

-10.03

27.3%

-11.80

19.3%

∆EPauli

4.12

22.99

40.10

67.16

∆Eint

-2.73

-0.55

3.38

6.05

71

Table S3. Selected calculated distances (Å) and angles (degrees) of the hypothetical trans-Cu6{µ-3,5-(CH3)2pz}6(µ-OH)6 host (2) and [trans-Cu6{µ-3,5-(CH3)2pz}6(µ-OH)6X]- (X = F, Cl, Br, I) (2-X) complexes. 2

2-F

2-Cl

2-Br

2-I

Diam. Cu6

6.368

6.174

6.268

6.249

6.344

Cu−Cu

3.184

3.089

3.134

3.124

3.172

Cu···center

3.184

3.089

3.134

3.124

3.172

H···center

3.352

3.104

3.121

3.223

3.236

< (Cu6)−(Cu-O-Cu)

115°

116°

116°

119°

118°

114°

117°

117°

116°

116°

< (Cu6)− (Cu-N-N-Cu)

Table S4. Natural population analysis (NPA, a.u.) of the hypothetical trans-Cu6{µ-3,5-(CH3)2pz}6(µ-OH)6 host (2) and [trans-Cu6{µ-3,5-(CH3)2pz}6(µ-OH)6X]- (X = F, Cl, Br, I) complexes (2-X). X [Cu6] Ld (OH)6

2 +7.35 -3.62 -3.73

2-F -0.94 +7.48 -3.87 -3.67

2-Cl -0.92 +7.45 -3.85 -3.68

2-Br -0.90 +7.40 -3.85 -3.66

2-I -0.83 +7.33 -3.81 -3.68

d

L = [3,5-(CH3)2pz]6

72

Figure S1. Representation of the quadrupole moment tensor (Θ) for a representative Cu(II) center, in the hypothetical noble gascentered pyrazolate complexes 1-Ne, 1-Ar, 1-Kr and 1-Xe.

73

Table S5. Comparison of the performance of several hybrid, GGA, and meta-GGA functionals in the calculation of the Electronic Quadrupole Tensors of the different noble-gas guests, denoting on the principal axis system (Buckinghams). [trans-Cu6{µ-3,5-(CF3)2pz}6(µ-OH)6Ng], Ng = Ar, Kr, Xe 1-Ar

1-Kr

1-Xe

Θ11

Θ22

Θ33

Θ11

Θ22

Θ33

Θ11

Θ22

Θ33

B1LYP

0.017

0.017

-0.035

0.034

0.034

-0.067

0.527

0.527

-1.054

B3LYP

0.019

0.019

-0.038

0.036

0.036

-0.072

0.539

0.539

-1.078

O3LYP

0.021

0.021

-0.041

0.038

0.036

-0.074

0.561

0.564

-1.125

BP86

0.027

0.027

-0.053

0.045

0.045

-0.091

0.572

0.572

-1.144

PW91

0.025

0.025

-0.050

0.043

0.043

-0.086

0.570

0.570

-1.139

PBE

0.025

0.025

-0.050

0.044

0.044

-0.089

0.574

0.574

-1.490

PBE0

0.025

0.025

-0.050

0.044

0.044

-0.089

0.575

0.575

-1.149

M06L

0.020

0.020

-0.039

0.042

0.042

-0.085

0.478

0.478

-0.956

TPSS

0.024

0.024

-0.049

0.041

0.041

-0.082

0.565

0.565

-1.130

5.2. Chapter 4 Table S6. Selected calculated distances (Å) and angles (degrees) for the hypothetical 1-X guest-centered mercuramacrocycle complexes. [(HgC(CF3)2)5X]-, X = Cl, Br, I 1-Cl

1-Br

1-I

Hg-Hg

3.531

3.569

3.654

Hg-C

2.189

2.201

2.229

< Hg-C-Hg

108°

108°

110°

< C-Hg-C

181°

180°

180°

Hg···X

3.001

3.038

3.108

74

Table S7. Selected calculated distances (Å) and angles (degrees) for the hypothetical 1-X guest-apical located mercuramacrocycle complexes. [(HgC(CF3)2)5X]-, X = Cl, Br, I 1-Cl

1-Br

1-I

Hg-Hg

3.495

3.490

3.507

Hg-C

2.180

2.177

2.181

< Hg-C-Hg

107°

107°

107°

< C-Hg-C

183°

184°

184°

Hg···X

3.084

3.226

3.435

X···center

0.819

1.126

1.702

Table S8. Selected calculated distances (Å) and angles (degrees) for the hypothetical 1-2Ng mercuramacrocycle complexes. [(HgC(CF3)2)5Ng2], Ng = Ar, Kr, Xe 1-2Ar

1-2Kr

1-2Xe

Hg-Hg

3.546

3.543

3.547

Hg-C

2.168

2.169

2.169

< Hg-C-Hg

110°

110°

110°

< C-Hg-C

182°

182°

182°

Hg···Ng

3.764

3.841

4.031

Ng···center

2.252

2.390

2.674

Ng···Ng

4.504

4.779

5.347

75

Table S9. Energy Decomposition Analysis for the hypothetical 1-2Ng mercuramacrocycle complexes (kcal/mol). [(HgC(CF3)2)5Ng2], Ng = Ar, Kr, Xe 1-2Ar

1-2Kr

1-2Xe

∆Eorb

-4.68

22.55%

-5.28

19.24%

-7.20

20.61%

∆Eelec

-4.29

20.67%

-6.87

25.04%

-9.35

26.76%

∆Edisp

-11.78

56.77%

-15.29

55.72%

-18.39

52.63%

∆EPauli

9.21

15.89

23.37

∆Eint

-11.54

-11.55

-11.57

Table S10. Selected calculated distances (Å) and angles (degrees) for the hypothetical 2-2X mercuramacrocycle complexes. [(HgC(CH3)2)5X2]2-, X = Cl, Br, I 2-2Cl

2-2Br

2-2I

Hg-Hg

3.366

3.385

3.440

Hg-C

2.167

2.172

2.181

< Hg-C-Hg

102°

102°

104°

< C-Hg-C

186°

186°

184°

Hg···X

3.489

3.609

3.750

Hg···center

2.863

2.879

2.926

X···X

3.986

4.351

4.692

76

Table S11. Energy Decomposition Analysis for the hypothetical 2-2X mercuramacrocycle complexes (kcal/mol). [(HgC(CH3)2)5X2]2-, X = Cl, Br, I 2-2Cl

2-2Br

2-2I

∆Eorb

-61.65

45.39%

-53.58

38.65%

-47.80

31.71%

∆Eelec

-63.24

46.57%

-71.71

51.73%

-83.49

55.39%

∆Edisp

-10.92

8.04%

-13.33

9.62%

-19.45

12.90%

∆EPauli

42.91

53.97

69.48

∆Eint

-92.90

-84.65

-81.26

Table S12. Selected calculated distances (Å) and angles (degrees) for the hypothetical 3-2X mercuramacrocycle complexes. [(HgCH2)5X2]2-, X = Cl, Br, I 3-2Cl

3-2Br

3-2I

Hg-Hg

3.402

3.407

3.444

Hg-C

2.140

2.142

2.147

< Hg-C-Hg

105°

105°

107°

< C-Hg-C

183°

183°

181°

Hg···X

3.567

3.661

3.824

Hg···center

2.894

2.899

2.930

X···X

4.171

4.474

4.914

77

Table S13. Energy Decomposition Analysis for the hypothetical 3-2X mercuramacrocycle complexes (kcal/mol). [(HgCH2)5X2]2-, X = Cl, Br, I 3-2Cl

3-2Br

3-2I

∆Eorb

-47.03

42.99%

-40.56

35.47%

-34.11

28.43%

∆Eelec

-52.74

48.20%

-62.39

54.56%

-69.13

57.61%

∆Edisp

-9.64

8.81%

-11.40

9.97%

-16.75

13.96%

∆EPauli

35.29

46.66

57.08

∆Eint

-74.12

-67.69

-62.91

Figure S2. Electrostatic potential map for (HgC(CF3)2)5 (1), (HgC(CH3)2)5 (2), and (HgCH2)5 (3) hosts.

78

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