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Atom- and Ion-Centered Icosahedral Shaped Subnanometer-Sized Clusters of Molecular Hydrogen Meenakshi Joshi,†,§ Ayan Ghosh,‡,§ and Tapan K. Ghanty*,†,§ †

Theoretical Chemistry Section, Chemistry Group, Bhabha Atomic Research Centre, Mumbai 400085, India Laser and Plasma Technology Division, Beam Technology Development Group, Bhabha Atomic Research Centre, Mumbai 400085, India § Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India ‡

S Supporting Information *

ABSTRACT: The recently observed “new form of condensed hydrogen” has motivated us to investigate the structures of H@H24−, H@H64−, and H@H88− clusters and to explore their stability by using dispersion-corrected density functional theory. Stability of these clusters has been explained with the help of high values of the highest occupied molecular orbital−lowest unoccupied molecular orbital (HOMO−LUMO) gap and geometrically closed shell of 12, 32, and 44 hydrogen molecules around the central hydride ion, which in turn form electronically closed shell systems. The H@H24− cluster has been observed as the most stable cluster followed by H@H64− and H@H88−. Apart from the hydride-centered clusters, we have also predicted various other metal and nonmetal atom- and ion-centered new clusters with large HOMO−LUMO gap and high binding energy. The structures and stability of some of the smaller clusters have been investigated by using MP2 and CCSD(T) methods as well, and the MP2-calculated binding energies are found to be very close to the corresponding CCSD(T) computed values. Calculated results indicate that both electronic shell closing and geometric shell closing are equally important in explaining the structure and stability of these systems. It has been shown that the binding energy of icosahedral H24 to an ionic core is heavily dependent on the encapsulated central ion. given to the negatively charged hydrogen clusters.32−37 In the last many years, only H 3 − ion has been observed unambiguously in experiment,37 though small-sized odd number Hn− clusters (n = 3−13) have been investigated computationally,33,38,39 and H@H24− in solid hydrogen has been studied through infrared (IR) spectroscopy.20 To the best of our knowledge, large size anionic hydrogen clusters, Hn− with n ∼ 100 have not been reported in the literature, except the very recent experimental work where Hn− clusters (with size up to 130 atoms) have been proposed as a “new form of condensed hydrogen”.40 It has been suggested that the hydride anion can act as a nucleating agent in the formation of Hn− clusters. It is interesting to note that the mass spectra for the Hn− clusters show high intense peaks corresponding to the H@ H24−, H@H64−, and H@H88− clusters, termed as the magic clusters, the structures of which are intuitively suggested to be icosahedral based on the structure of charged noble gas atom doped helium nanodroplets.41 It may be noted that this is the first direct experimental evidence of a negatively charged hydrogen cluster, Hn−, with n > 3.40 In the present article, for the first time we have determined the structures and the properties of all the hydride ion-centered magic clusters, viz., H@H24−, H@H64−, and H@H88−, by using

1. INTRODUCTION After the discovery of Buckminsterfullerene,1 research activity on nanoclusters and nanoparticles has gained tremendous momentum because of their important role in the design of novel materials with fascinating properties for potential applications in various fields including catalysis, biology, medicine, etc.2−5 Almost all the elements of the periodic table belonging to s-, p-, and d-blocks are shown to form various clusters, and the shape, structure, and properties of them are strongly dependent on their size.6−10 Comparatively, little attention has been paid to the clusters formed by the simplest element of the periodic table, viz., hydrogen. Nevertheless, in the past few decades, this element has received considerable attention from researchers because of its direct relevance in the chemistry of interstellar medium11,12 and its important role in an alternative source of energy, viz., hydrogen energy.13−15 Of late, hydrogen has attracted significant attention from scientists because of its metallic form under specific conditions and its potential use as room-temperature superconductors.16−18 Moreover, synthesis of alkali metal polyhydrides at high pressures has attracted scientists for their possible role in the design of high-temperature superconductors.19 In the past few years, various hydrides have been explored extensively because of their application in hydrogen storage systems.20−24 As far as clusters of hydrogen molecules are concerned, positively charged small-size clusters have been studied extensively;25−31 however, very little attention has been © 2017 American Chemical Society

Received: March 27, 2017 Revised: June 7, 2017 Published: June 16, 2017 15036

DOI: 10.1021/acs.jpcc.7b02877 J. Phys. Chem. C 2017, 121, 15036−15048

Article

The Journal of Physical Chemistry C first-principles-based dispersion-corrected density functional theory (DFT-D3), which has been highly successful in predicting the structure and properties of noncovalently bonded systems.42 Subsequently, the concept of the gold− hydrogen analogy43−48 has been used to investigate auride ioncentered Hn clusters, viz., Au@Hn−, with n as 24, 64, and 88. For the purpose of comparison, Cu and Ag analogues of these clusters have also been investigated. In addition, we have explored the possibility of using various other metal and nonmetal atoms or ions (F−, Cl−, Br−, Cu−, Ag−, Au−, Be, Mg, Zn, Cd, B2−, C−, N3−, P3−, O2−, S2−, Se2−) as the nucleating agent in place of the H− ion to predict new clusters of hydrogen.

atoms-in-molecule (AIM) analysis has been carried out by using dispersion-corrected PBE method with def2-TZVPP basis set utilizing the Multiwfn program.75

3. RESULTS AND DISCUSSION To begin, we studied various properties like ionization energy, bond length, binding energy, highest occupied molecular orbital−lowest unoccupied molecular orbital (HOMO− LUMO) gap of molecular hydrogen, and HOMO−LUMO gap for atomic hydrogen using various methods like PBE-D3, TPSS-D3, B3LYP-D3, MP2, CCSD, and CCSD(T) along with def2-TZVPP, def2-QZVPP, and AVTZ basis sets. Experimental values of H−H bond length, ionization potential, and binding energy of H2 molecule are found to be 0.741 Å, 15.426 eV, and −4.48 kcal mol−1, respectively.76,77 It is important to note that with almost all the methods, the calculated values of various properties of H2 molecule are found to be very close to the corresponding experimentally reported results, as compared in Table 1.

2. COMPUTATIONAL METHODOLOGY In the present work, all the calculations have been carried out using Turbomole 7.0.49 We have used density functional theory with generalized gradient approximation (GGA) using Perdew−Burke−Ernzerhof (PBE),50 nonempirical meta-generalized gradient approximation (meta-GGA) using Tao− Perdew−Staroverov−Scuseria (TPSS)51 functional, and Becke 3-parameter exchange and Lee−Yang−Parr correlation (B3LYP) hybrid functional52,53 with def2-TZVPP and def2QZVPP basis sets54 for optimization of all the atom- or ioncentered H24, H64, and H88 clusters. Furthermore, frequency calculation for all the clusters has been performed using def2TZVPP basis set to obtain the true minima structures of the concerned systems studied here. We have used dispersioncorrected density functional theory for all our calculations.55−57 It is worthwhile to mention that the dispersion corrections can lead to significant improvements in accuracy of the results while the cost associated with the dispersion correction calculations is negligible. Effective core potential (ECP)58 has also been employed for heavier elements, viz., 60 core electrons for Au and 28 core electrons for Ag and Cd. In addition, the Møller− Plesset second-order perturbation theory (MP2)59 has also been employed to optimize the clusters in order to cross check the results with the data obtained by density functional theorybased methods. Moreover, to check the accuracy of Møller− Plesset second-order perturbation theory, we have used CCSD and CCSD(T) methods60−62 for the single-point calculation of a few smaller systems using MOLPRO 2012.63 We have also used Dunning’s aug-cc-pVTZ (AVTZ), aug-cc-pVQZ (AVQZ), and aug-cc-pV5Z (AV5Z) basis sets64−68 for all the atoms except Au, Ag, and Cd to check the effect of basis sets on the interaction energy. In the case of Au, Ag, and Cd atoms, the aug-cc-pVTZ-PP69 basis set along with 60, 28, and 28 core ECP, respectively, has been employed.70 The interaction energy, IE, has been calculated as IE = E(X@H 2n−) − E(X−) − nE(H 2)

Table 1. Calculated Values of Ionization Energy (IP in eV), H−H Bond Length (RH−H in Å), Interaction Energy (BE in kcal mol−1), HOMO−LUMO Energy Gap (ΔEGap in eV) for H2 Molecule and HOMO−LUMO Energy Gap (ΔEGap in eV) for H Atom As Obtained by Using PBE-D3, TPSS-D3, B3LYP-D3, MP2, CCSD, and CCSD(T) Methods with def2TZVPP, def2-QZVPP, and AVTZ Basis Sets H atom

H2 molecule methods PBE-D3

TPSS-D3

B3LYP-D3

MP2

CCSD CCSD(T) exptl.

(1)

E(X@H2n−), E(X−), and E(H2) the X@H2n− cluster, X− ion,

where the terms represent the total energy of and the H2 molecule, respectively, and n = 12, 32, and 44. Here, a negative sign of interaction energy indicates the stable nature of a system. Throughout this paper we have considered interaction energy per H2 molecule, which is obtained as IE/n and is denoted as BE. Basis set superposition error (BSSE) has been calculated by using the counterpoise method71−73 with the GAMESS program.74 Charge calculation has been done using the natural population analysis (NPA) scheme. Furthermore, to obtain a clear insight into the nature of chemical bonding existing between the constituent atoms quantitatively, the

basis sets def2TZVPP def2QZVPP AVTZ def2TZVPP def2QZVPP AVTZ def2TZVPP def2QZVPP AVTZ def2TZVPP def2QZVPP AVTZ AVTZ AVTZ

IP

RH−H

BE

ΔEGap

ΔEGap

15.143

0.751

−4.54

11.45

13.45

15.148

0.750

−4.54

11.10

10.86

15.142 15.493

0.751 0.744

−4.53 −4.90

10.58 12.38

8.03 8.82

15.497

0.743

−4.90

11.89

8.52

15.493 15.414

0.744 0.744

−4.89 −4.78

11.20 13.38

7.98 7.89

15.422

0.743

−4.78

12.95

7.72

15.413 16.226

0.743 0.737

−4.78 −4.49

12.22 −

7.53 −

16.274

0.736

−4.54





16.231 15.519 16.366 15.426

0.737 0.743 0.743 0.741

−4.50 −4.71 −4.71 −4.48

− − − −

− − − −

Because the H@H24− cluster has been experimentally observed as the most abundant cluster followed by H@H64− and H@H88− in the mass spectra of Hn− clusters (n = 5− 130),40 we first attempted to find the most stable geometry for the H@H24− cluster. For this, we performed calculations with different initial geometries, namely, Oh, D3h, and Ih (Figure 1). We found that only the Ih structure is associated with all real vibrational frequencies at PBE-D3/def2-TZVPP and PBE-D3/ def2-QZVPP levels, and for the D3h and Oh geometries, imaginary frequencies are found either with def2-TZVPP or 15037

DOI: 10.1021/acs.jpcc.7b02877 J. Phys. Chem. C 2017, 121, 15036−15048

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Figure 1. Optimized geometries of H@H24− cluster as obtained by using the PBE-D3/def2-TZVPP and PBE-D3/AVTZ level of theory.

Table 2. Comparison of H−H Bond Length (RX−H and RH−H in Å) and Interaction Energy (BE in kcal mol−1) per H2 Molecule for H@H24− Cluster As Obtained by Using PBED3 and MP2 Methods with def2-TZVPP, def2-QZVPP, AVTZ, AVQZ, and AV5Z Basis Sets

with def2-QZVPP basis sets (Table S1), contrary to earlier proposed structure.20 Because electron correlations are explicitly included in the MP2 method, we have also used the MP2 method for the optimization of H@H24− system using def2-TZVPP and def2-QZVPP basis sets. The reported results in Table S1 reveal that the MP2-calculated relative energy values for the D3h and Oh structures agree quite well with the corresponding PBE-D3 calculated values. Consequently, the icosahedral geometry represents the most stable structure for the H@H24− cluster. Though the effect of basis set on the calculated properties of the H2 molecule is minimal (reported in Table 1), the same has been found to be important while calculating the interaction energy for the H@H24− cluster with def2-TZVPP54 and def2QZVPP54 basis sets in both the PBE-D3 and MP2 methods, as reported in Table S2. This can be attributed to the fact that for the H2 molecule only covalent bonding is involved; however, clusters investigated in the present work involve weak interactions. Therefore, it is important to establish the basis set limit for the smallest H@H24− system using larger basis sets such as aug-cc-pVTZ, aug-cc-pVQZ, and aug-cc-pV5Z (denoted as AVTZ, AVQZ, and AV5Z, respectively)64−68 in addition to the def2-TZVPP and def2-QZVPP basis sets, as augmented basis sets are expected to provide better results for the weakly bonded systems. The interaction energy of the H@ H24− system calculated using the def2-TZVPP basis set is found to be −4.49 kcal mol−1, which is somewhat different from the def2-QZVPP basis set value (−3.89 kcal mol−1) using the PBED3 method. Similarly, the MP2 computed interaction energy values (−2.94 and −2.50 kcal mol−1) are also found to be different using def2-TZVPP and def2-QZVPP basis sets, respectively. Likewise, using large size AVTZ basis set again we have found some change in the interaction energy values relative to that of the def2-TZVPP and def2-QZVPP basis sets values as reported in Table 2. Thus, the interaction energy is found to decrease with increase in the size of basis set up to AVTZ. Later, we have used much larger AVQZ and AV5Z basis sets for the optimization of the H@H24− cluster. However, interaction energy values of H@H24− system calculated using AVQZ and AV5Z basis sets are found to be almost the same as those obtained by using the AVTZ basis set in both PBE-D3 and MP2 methods. Also, the calculated results of H@H24−, obtained by using PBE-D3 and the MP2 methods reported in Table 2, reveal that the structural parameters are generally close to each other. However, the calculated interaction energy values of the H@H24− system using MP2 method are found to be somewhat lower than the corresponding PBE-D3 calculated value. Here, the calculated value of interaction energy for the H@H24− system at the PBE-D3 level is found to be −4.49, −3.89, −3.16, −3.15, and −3.14 kcal mol−1 as compared to the corresponding MP2 calculated values of −2.94, −2.50, −1.99,

method

basis set

RX−Ha

RH−Hb

BE

PBE-D3

def2-TZVPP def2-QZVPP AVTZ AVQZ AV5Z def2-TZVPP def2-QZVPP AVTZ AVQZ AV5Z

2.387 2.378 2.387 2.387 2.382 2.473 2.456 2.473 2.460 2.460

0.762 0.761 0.762 0.761 0.761 0.745 0.744 0.746 0.745 0.745

−4.49 −3.89 −3.16 −3.15 −3.14 −2.94 −2.50 −1.99 −1.96 −1.95

MP2

a

RX−H value corresponds to the distance between the central hydride ion with the hydrogen molecules of the first shell. bRH−H values indicate the shortest H−H bond distances in the H2 molecules present at the vertices of the first shell.

−1.96, and −1.95 kcal mol−1 using def2-TZVPP, def2-QZVPP, AVTZ, AVQZ, and AV5Z basis sets, respectively, as reported in Table 2. Consequently, the AVTZ basis set has been found to be the most appropriate for providing good results similar to AVQZ and AV5Z calculated results at a lower computational cost in both PBE-D3 and MP2 methods. Therefore, we have used the AVTZ basis set for the calculations of all the H@H24−, H@H64−, and H@H88− clusters and other atom- or ioncentered hydrogen clusters considered in the present paper. It is important to note that the calculated geometrical parameters of H@H24− cluster (RX−H and RH−H) are found to be almost the same using def2-TZVPP and AVTZ basis sets in both PBE-D3 and MP2 methods; however, only the interaction energy value and HOMO−LUMO gap are found to decrease with increase in the size of the basis set up to the AVTZ basis set (Table 2). Therefore, we have used the smaller def2-TZVPP basis set for the geometry optimization and frequency calculation for all the clusters to get their most stable ground-state geometry followed by reoptimization of all the structures with the AVTZ basis set. Here, all the studied clusters, viz., X@H24 (X = H−, Be, Mg, B2−, C−, N3−, P3−, O2−, S2−, Se2−, F−, Cl−, Br−, Cu−, Ag−, Au−, Zn, and Cd), X@H64 (X = H−, F−, Cl−, Br−, C−, Ag−, and Au−), and X@H88 (X = H−, B2− and S2−) are found to be optimized in icosahedral geometry with real frequency values. Similarly, all the bare clusters are also found to possess icosahedral geometry with real frequency value except the neutral H24 system, which has been found to exist in Ci geometry with real frequency values. The H24 structure with Ci symmetry is found to be a distorted icosahedron where the alignments of the H2 molecules are 15038

DOI: 10.1021/acs.jpcc.7b02877 J. Phys. Chem. C 2017, 121, 15036−15048

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The Journal of Physical Chemistry C different as compared to that in the icosahedral H24 cluster. The geometrical as well as energetic parameters of all the bare hydrogen clusters (H24, H24−, and H242−) are reported in Table S3 calculated at the DFT-D3/def2-TZVPP and MP2/def2TZVPP level of theory. Later we have optimized all the abovementioned clusters using AVTZ basis set for calculating their basis set independent ground-state energy. In the following, we have discussed the results using the AVTZ basis set throughout the paper unless or otherwise stated. Apart from the hydride-centered H24 cluster, we have optimized the bare H24, H24−, and H242− clusters with Ci and Ih symmetries using PBE-D3 and MP2 methods by using the AVTZ basis set. For the neutral H24 cluster, the Ci geometry is found to be energetically more stable by 2.08 kcal mol−1 as compared to the Ih geometry using the PBE-D3 method. In contrast, for H24− and H242− clusters, icosahedral geometry is found to be more stable by 0.01 and 2.93 kcal mol−1, respectively, as compared to Ci geometry obtained by using the PBE-D3 method. The geometrical parameters and HOMO− LUMO gap for the bare H24, H24−, and H242− clusters calculated using PBE-D3 and MP2 methods are reported in Table 3. The shortest distance from the cage center to the

Thus, after establishing the basis set limit, we have optimized the H@H24− cluster with Ih, D3h, and Oh symmetries (Table 4), Table 4. Calculated Relative Energy Values (Erel in kcal mol−1) of Oh and D3h Symmetric Structures with Respect to the Ih Symmetric Geometry of X@H24 (X = H−, F−, Cl−, Br−,Cu−, Ag−, and Au−) Clusters As Obtained by Using PBED3 and MP2 Methods with AVTZ Basis Set

symmetry

method

RH−Ha

RH−Hb

RH−Hc

ΔEGap

H24

Ci

H24−

Ih

H242−

Ih

PBE-D3 MP2 PBE-D3 MP2 PBE-D3 MP2

2.858 2.998 2.457 2.678 2.553 2.662

2.800 2.984 2.5982 2.816 2.684 2.799

0.752 0.738 0.760 0.740 0.760 0.740

9.626 − 0.296 − 0.367 −

method

Erel(Oh)

Erel(D3h)

PBE-D3 MP2 PBE-D3 MP2 PBE-D3 MP2 PBE-D3 MP2 PBE-D3 MP2 PBE-D3 MP2 PBE-D3 MP2

2.50 1.82 2.70 2.65 0.55 0.57 0.18 0.24 1.04 −0.09 0.22 −0.25 0.41 0.66

1.80 2.33 −0.15 0.10 0.97 0.92 0.45 0.29 1.56 −0.44 0.50 −0.31 0.84 0.95

F@H24− Cl@H24− Br@H24− Cu@H24− Ag@H24− Au@H24−

Table 3. Calculated Values of H−H Bond Length (RH−H in Å), Interaction Energy (BE in kcal mol−1) per H2 Molecule, and HOMO−LUMO Energy Gap (ΔEGap in eV) for H24, H24−, and H242− Clusters as Obtained by Using PBE-D3 and MP2 Methods with AVTZ Basis Set cluster

system H@H24−

and it has been found that D3h and Oh geometries are energetically less stable by 1.80 and 2.50 kcal mol−1, respectively, as compared to the Ih geometry using the PBED3 method. Moreover, optimization of the Ih, D3h, and Oh geometries of H@H24− cluster has also been carried out without any symmetry restriction, and we have found no significant change in the energies of Ih, D3h, and Oh geometries without any symmetry constraint. In the icosahedral geometry of the H@H24− cluster, 12 hydrogen molecules occupy the vertices of an icosahedron while the hydride anion stays at the center of the cage (Figure 1), as intuitively proposed by Renzler et al.40 The bond distance between the H− anion and each hydrogen molecule has been found to be 2.387 Å. This cluster has a large HOMO−LUMO gap of 2.32 eV, and the H−---H24 interaction energy (X− + 12H2 → X@H24−) has been found to be −3.16 kcal mol−1 per H2 molecule using the PBE-D3 method. Subsequently, considering the Au/H chemical analogy,43−48 we have investigated auride-centered H24 cluster, Au@H24−, which has been optimized in D3h, Oh, and Ih symmetry, where Ih and Oh geometries are found to be associated with real frequency values. Furthermore, we have compared the stability of all the three different geometries (D3h, Oh, and Ih) at the most suitable PBE-D3/AVTZ method; however, in both the cases, the Ih geometry has been found as the lowest-energy isomer as reported in Table 4. Thereby, the interaction energy value and geometrical parameters calculated by using PBE-D3 and MP2 methods for icosahedral Au@H24− system have been included in Table 5. Because of the similarity of hydrogen with other coinage metal atoms (Cu and Ag),79 we have also studied the Cu− and Ag− encapsulated H24 cluster and found the icosahedral geometry as the lowest-energy structure as compared to the D3h and Oh geometry. Among all the clusters, H@H24− and Au@H24− clusters possess the higher HOMO− LUMO gap of 2.32 and 2.79 eV, respectively, by using the PBED3 method, as reported in Table 5. Similar to the H@H24− cluster, the MP2 calculated interaction energy values of Cu@ H24−, Ag@H24−, and Au@H24− clusters (−1.15, −1.70, and

a

RH−H value corresponds to the distance from the center to the hydrogen molecules of the first shell. bRH−H value represents the H--H bond distances between the two closest H2 molecules along the edges of the Ih structure of the first shell. cRH−H values indicate the shortest H−H bond distances in the H2 molecules present at the vertices of the first shell.

peripheral hydrogen molecules and the H---H distance between the two closest H2 molecules are found to be the largest in the H24 cluster (with Ci geometry) as compared to that in H24− and H242− clusters (Ih symmetry). Consequently, the bonding strength between two hydrogen molecules in neutral H24 cluster is weaker as compared to the same in H24− and H242− clusters. However, surprisingly the HOMO−LUMO gap of the neutral H24 cluster (9.626 eV) is observed to be very large as compared to that of the H24− and H242− clusters (0.296 and 0.367 eV, respectively). Moreover, we have checked the stability of H24, H24−, and H242− systems with respect to the H@H24− system via H− + H24 → H@H24−, H + H24− → H@ H24−, and H+ + H242− → H@H24− reactions, respectively. All the bare hydrogen clusters (H24, H24−, and H242−) are found to be energetically less stable by 1.33, 2.17, and 18.17 eV, respectively, as compared to the H@H24− cluster obtained by using the PBE-D3 method. Therefore, it is clear that incorporation of H− ion into the less stable H24 cluster stabilizes the H24 cluster, analogous to the stabilization of Au12 icosahedral cage through incorporation of a W atom.78 15039

DOI: 10.1021/acs.jpcc.7b02877 J. Phys. Chem. C 2017, 121, 15036−15048

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Table 5. Calculated Values of X−H Bond Length (RX−H in Å), H−H Bond Length (RH−H in Å) in H2 Molecules, Interaction Energy per H2 Molecule (BE in kcal mol−1), HOMO−LUMO Energy Gap (ΔEGap in eV), Atomic Charge on X, and Dispersion Energy Correction (DE in kcal mol−1) of X@H24 (X = H−, Be, Mg, B2−, C−, N3−, P3−, O2−, S2−, Se2−, F−, Cl−, Br−,Cu−, Ag−, Au−, Zn, and Cd) Clusters at the PBE-D3/AVTZ and MP2/AVTZ Levels of Theory RX−H

RH−H

ΔEGap

BE

DE

qm

cluster

PBE

MP2

PBE

MP2

PBE

MP2

PBE

PBE

PBE

H@H24− H@H24−a Be@H24 Mg@H24 B@H242− C@H24− N@H243− P@H243−b O@H242− S@H242− Se@H242− F@H24− Cl@H24− Br@H24− Cu@H24− Ag@H24− Au@H24− Zn@H24 Cd@H24

2.387 2.387 2.749 2.965 2.402 2.577 2.218 2.531 2.175 2.551 2.697 2.375 2.762 2.916 2.631 2.853 2.798 2.864 3.003

2.460 2.465 3.594 3.778 2.934 2.697 2.573 −b 2.192 2.576 2.723 2.396 2.794 3.045 3.412 3.250 2.819 3.424 3.393

0.762 0.762 0.755 0.755 0.776 0.761 0.785 0.788 0.779 0.778 0.776 0.759 0.758 0.758 0.766 0.763 0.762 0.754 0.753

0.746 0.745 0.738 0.738 0.744 0.745 0.748 −b 0.761 0.760 0.759 0.744 0.744 0.743 0.743 0.744 0.747 0.738 0.738

−3.16 −3.15 −1.11 −1.10 −4.19 −2.90 −19.98 −10.76 −11.17 −6.49 −5.49 −3.88 −2.79 −2.49 −2.88 −2.11 −2.63 −1.10 −0.96

−1.99 −1.83 −0.17 −0.30 −3.52 0.10 −13.19 −b −8.31 −4.57 −4.25 −3.10 −2.22 −1.89 −1.15 −1.70 −2.64 −0.29 −0.37

2.32 2.33 3.26 3.15 0.41 1.90 0.28 0.31 0.92 0.94 0.84 3.75 3.81 3.62 2.01 1.93 2.79 4.37 4.30

−0.64 −0.64 −0.96 −1.01 −0.73 −0.62 −0.70 −0.59 −0.78 −0.66 −0.61 −0.74 −0.64 −0.61 −1.11 −0.62 −0.70 −1.01 −0.90

−0.776 −0.774 0.131 0.170 −1.136 −0.570 −0.982 −1.684 −1.170 −1.395 −1.468 −0.855 −0.825 −0.834 −0.658 −0.710 −0.740 0.110 0.104

H@H24− was optimized using AVTZ basis set after removing one diffuse p and one diffuse d function from the AVTZ basis set and has been found to have negligible effect on the structure and properties of the H@H24− cluster. bP@H243− cluster could not be optimized by using the MP2 method. a

surface. Thus, the H@H24− cluster forms a very stable magic cluster with 26 electrons similar to the well-known Pb122− and Sn122− clusters and the M@C20 metallofullerenes. 80−82 Subsequently, to see the effect of substitution of H− with the Au− on the electronic structure of the parent H@H24− cluster, we have also included the molecular orbital pictures of Au@ H24− cluster in Figure 3, which reveal that the 3ag, 2ag, 2t1u, 1hg, and 1t2u MOs are very similar to the corresponding occupied MOs of the H@H24− cluster, except the 2hg orbitals, which correspond to the d orbitals of Au− ion. Here again 2t1u, 1hg, and 1t2u molecular orbitals correspond to s orbital of hydrogen molecules, while 3ag is a mixed molecular orbital contributed by s orbital of Au− and s orbital of hydrogen molecules. However, the 2ag occupied molecular orbital has very little contribution from the Au− ion. Thus, similar to H@H24−, the Au@H24− cluster forms a 26-electron system corresponding to closed shell electronic configuration, 1s21p61d102s22p6, and the gold− hydrogen analogy has been found to exist in this system. Similarly, both Cu@H24− and Ag@H24− clusters are found to be associated with 26-electron counts (Figure S1). Charge present on central atom might also play an important role for enhancing the bonding in these clusters. Therefore, to see the effect of charge, we have performed the charge calculation using the natural population analysis scheme. We observe higher and very similar charges on Au− (−0.740e) and H− (−0.776e) anion in Au@H24− and H@H24− clusters, respectively, using the PBE-D3/AVTZ method, as reported in Table 5. Thus, higher negative charge has led to more ioninduced dipole interaction in H@H24− cluster followed by Au@ H24− as compared to that in other coinage metal encapsulated clusters. Subsequently, to see whether the charge on the central atom or ion can actually affect the stability of clusters, we have studied the neutral atom as well as high negatively charged ion encapsulated clusters. It has been found that even the neutral

−2.64 eV, respectively) are found to be different from the PBED3 calculated interaction energy values (−2.88, −2.11, and −2.63 eV, respectively), as reported in Table 5. Now it is important to analyze the molecular orbitals and corresponding energy level diagrams of all these clusters for obtaining further insights. Molecular orbital energy level diagram of H@H24− and X@H24− clusters (X = Au, Ag, Cu) depicted in Figure 2 reveal that the ag and t1u orbitals are the

Figure 2. Molecular orbital energy level diagram of X@H24− (X = H, Au, Ag, Cu) clusters as obtained by using the PBE-D3/AVTZ level of theory.

HOMO and LUMO, respectively, for all the clusters, except H@H24− cluster, for which the HOMO and LUMO are 2ag and 3ag, respectively. Molecular orbital plots for the H@H24− cluster shown in Figure 3 indicate that the 1t1u, 1hg, and 1t2u MOs have contributions from hydrogen molecules only, while remaining MOs 1ag and 2ag are contributed by the H− ion as well as surrounding hydrogen molecules. The 24 electrons from valence s orbital of 12H2 molecules and two electrons from H− anion together constitute the 26-electron system on the cluster 15040

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Figure 3. Comparison plot of molecular orbital pictures of H@H24− and Au@H24− clusters at PBE-D3/AVTZ level of theory.

to the Au@H24− cluster, all the halide ion encapsulated H24 clusters exhibit icosahedral geometry, except the I@H24− cluster, as reported in Tables 4 and 5. For the purpose of comparison we have reported the PBE-D3/def2-TZVPP calculated values in Table S4. Among all the halide encapsulated X@H24 (X = F−, Cl−, Br−) clusters, F@H24− has been found to be the most stable because of its higher interaction energy (−3.88 kcal mol−1) and larger HOMO− LUMO gap (3.75 eV) by using PBE-D3 method, as reported in Table 5. Subsequently, molecular orbital pictures of X@H24− clusters (X = F−, Cl−, Br−) reveal that all halide encapsulated clusters form closed shell systems with 30 electrons (Figure S4). Next, we studied the higher negatively charged chalcogenide and pnictide encapsulated X@H24 clusters (X = O2−, S2−, Se2−, N3−, P3−). All the X@H24 clusters are found to retain the icosahedral geometry of the parent H@H24− cluster. In N@H243− and O@H242− clusters, the calculated N−H and O−H bond lengths are found to be 2.218 and 2.175 Å, respectively, with a corresponding interaction energy value of −19.98 and −11.17 kcal mol−1 (per H2 molecule) at the PBED3/AVTZ level. Thus, we have observed a very strong bonding in N@H243− and O@H242− clusters as compared to that in all the remaining other clusters reported in Table 5. All the calculated results for X@H24 clusters shown in Table 5 clearly indicate that the interaction energy of H24 to an ionic core can be modulated significantly by replacing the central hydride ion with other metal and nonmetal ions. Thereafter, we studied the electronic behavior of chalcogenide and pnictide encapsulated X@H24 clusters by plotting their molecular orbital pictures, some of which are given in Figures S5 and S6. In the N@H243− cluster, 2t1u, 1t2u, 1hg, 3ag, 1t1u, and 2ag orbitals are the occupied molecular orbitals, which cumulatively form a 32-electron system. Similar to the N@ H243− cluster, the P@H243− cluster also forms a 32-electron system. In the O@H242− cluster, 2t1u, 1t2u, 1hg, 1t1u, snf 3ag orbitals are occupied, which forms a 30-electron system. Unlike

metal encapsulated X@H24 clusters (X = Be, Mg, Zn, Cd) maintain the icosahedral geometry of the parent H@H24− cluster as true minima. Formation of neutral metal encapsulated clusters is supported by their negative interaction energy values, as reported in Table 5. However, we observe very small interaction between the neutral metal atom and the hydrogen molecules in X@H24 cluster as compared to that in other negatively charged clusters. Because of the valence−isoelectronic behavior of Be@H24 with H@H24− cluster, we have plotted the molecular orbital pictures of Be@H24 cluster (Figure S2) and found that 3ag, 1t2u, 1hg, 1t1u, and 2ag are the occupied molecular orbitals, among which 1t2u, 1hg, and 1t1u have contribution from s orbitals of 12H2 molecules, while 3ag and 2ag are mixed molecular orbitals, contributed by s orbital of Be and s orbital of hydrogen molecules. Thus, as expected, valence−isoelectronic Be@H24 cluster also forms a 26-electron system similar to the H@H24− cluster. Apart from the Be@H24 cluster, the remaining other neutral clusters, X@H24 (X = Mg, Cd), also form a 26-electron system, except Zn@H24, which obeys 36-electron system corresponding to 24 electrons from 12 H2 molecules and 12 electrons from valence 4s3d orbitals of the Zn atom. All the neutral metal atom centered X@H24 (X = Be, Mg, Zn, and Cd) clusters also possess a very high HOMO− LUMO gap, (3.26, 3.15, 4.37, and 4.30 eV, respectively) which again represents the stable nature of the corresponding clusters. Unlike other charged clusters, MP2 calculated X−H bonding strength in the neutral X@H24 (X = Be, Mg, Zn, and Cd) clusters has been found to be much weaker as compared to that of the PBE-D3 calculated X−H bond strength (Table 5). The calculated X−H bond length, HOMO−LUMO gap, and interaction energy values for X@H24 cluster (X = Be, Mg, Zn, Cd) are also included in Table 5, and the molecular orbital energy level diagram is presented in Figure S3. Because we have found the Au@H24− cluster to be stable, we further studied the halide ion encapsulated H24 clusters because of the existence of the gold−halogen analogy.44,45,83,84 Similar 15041

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Table 6. Calculated Values of X−H and H−H Bond Lengths (Å), Interaction Energy per H2 Molecule (BE in kcal mol−1), and Dispersion Energy Correction per H2 Molecule (DE in kcal mol−1) in H@H24−, H@H64−, and H@H88− Clusters at the PBE-D3/ AVTZ Level of Theory cluster −

H@H24 H@H64− H@H88−c

X−H1a

X−H2a

X−H3a

H1−H2b

H2−H3b

BE

DE

2.387 2.327 2.288

− 4.498 4.464

− − 5.413

− 2.773 2.755

− − 3.290

−3.16 −1.96 −1.74

−0.64 −0.67 −0.69

X−H1, X−H2, and X−H3 indicate the distance of central hydride ion to hydrogen molecules of first, second and third shells, respectively. bH1−H2 and H2−H3 represent the shortest distance between two hydrogen molecules between first−second and second−third shells, respectively. cAVTZ basis set for H atom after removing one diffuse p and one diffuse d function has been used to achieve SCF convergence. Removal of one p and d function is found to have negligible effect on the structure and properties of H@H24− cluster, as reported in Table 5. a

compared to the same in the C@H24− system (−2.90 kcal mol−1). We have provided all the calculated properties of B@ H242− and C@H24− clusters in Table 5. Electronic shell closing with different number of electrons for various X@H 24 icosahedral clusters reported here clearly indicate that both electronic shell closing and geometric shell closing are equally important10 for explaining the structure and stability of these systems. For the purpose of comparison, B3LYP-D3 and TPSSD3 calculated properties for X@H24 clusters (X = H−, F−, Cl−, Br−, Cu−, Ag−, Au−, Be, Mg, Zn, Cd, B2−, C−, N3−, P3−, O2−, S2−, and Se2−) are shown in Tables S5 and S6. We have also studied the H@H64− and H@H88− clusters because of the presence of their intense peak in the mass spectra of the Hn− cluster,40 next to the most intense peak of H@H24 − cluster. Similar to the H@H24− cluster, the icosahedral geometry has been found as a true minima geometry for the H@H64− and H@H88− systems, as reported in Table 6. For the purpose of comparison, corresponding PBED3/def2-TZVPP calculated values are given in Table S7. In the H@H64− cluster, 20 H2 molecules in a dodecahedral arrangement are found to reside at the 20 triangular faces of the icosahedral H@H24− cluster forming a second shell around the H− anion as intuitively proposed by Renzler et al.40 The bond length of the centered hydride anion with a hydrogen molecule of the first shell and second shell are 2.327 and 4.498 Å, respectively. Further addition of 12 hydrogen molecules in the H@H64− cluster leads to the formation of a third shell around the H− anion and forms a stable icosahedral H@H88− cluster. In the optimized icosahedral H@H88− cluster, 12 hydrogen molecules in the third shell occupy the 12 vertices of the inner first shell icosahedron of the H@H64− cluster. The distance between the central hydride ion and the hydrogen molecules of first, second, and third shells in the H@H88− cluster are found to be 2.288, 4.464, and 5.413 Å, respectively. Here, in the H@ H88− system, the distance between the centered hydride anion and hydrogen molecules of the first shell, that is H−H1 bond length (2.288 Å), is found to be the shortest, and the same has been found to be the longest in the H@H24− cluster (2.387 Å) among all three hydride-centered clusters, while intermediate H−H1 bond distance (2.327 Å) has been calculated in the H@ H64− system, which indicates that the strength of H−H1 bonding in the H@H64− system lies between the strength of H−H1 bonding in H@H88− and H@H24− systems. Moreover, the shortest value of H−H1 bond distance (2.288 Å) in the H@H88− system represents the strongest bonding between the central hydride ion and the hydrogen molecules of the first shell of the H@H88− system. Moreover, the larger value of H−H1 bond distance in H@H24− relative to H@H64− and H@H88− systems represents a comparatively weaker bonding between the hydride ion and the hydrogen atom of the first shell of the

O@H242− cluster, S@H242− and Se@H242− clusters form a 32electron system. In these two clusters, we have found contribution from their inner s orbital. Thus, all the studied chalcogenide and pnictide encapsulated X@H24 clusters form very stable closed shell systems. Subsequently, we calculated the charges on chalcogenides and pnictogenides using a natural population analysis scheme and found a negative charge of −0.982e and −1.170e on N and O in N@H243− and O@H242− clusters, respectively. This result indicates that the extent of charge transfer from the central ion to the peripheral hydrogen molecules is higher, which leads to larger ion-induced dipole interaction. The calculated charge on N (−0.982e) and P (−1.684e) central ion in N@H243− and P@H243− systems, respectively, shows that more than one atomic charge (out of formal charge of −3) has not been located on central ions (Table 5). This lowering in charge on the central ion clearly signifies that some of the negative charge has been transferred from the ionic core (N3− and P3−) to hydrogen atoms of hydrogen molecule in the N@H243− and P@H243− systems. Therefore, large charge transfer from the ionic core of the N@ H243− and P@H243− systems leads to a very strong interaction between the ionic core and hydrogen molecules in these systems, which ultimately gives rise to the extremely large interaction energy values. Similarly, in chalcogenide encapsulated clusters, namely O@H242−, S@H242−, and Se@H242−, charge located on the respective central ion is calculated to be −1.170, −1.395, and −1.468e, which are found to be approximately more than 0.5−0.8e lower as compared to the actual initial charge of −2 on O2−, S2−, and Se2− ions. Thus, in O@H242−, S@H242−, and Se@H242− systems again we have found significant charge transfer from the ionic core to the hydrogen molecules. This large charge transfer results in a stronger interaction between the central ions (O2−, S2−, and Se2−) and hydrogen molecules in O@H242−, S@H242−, and Se@H242− systems, which can be perceived from their more negative binding energy values. Apart from electronically closed shell systems, we have also studied the electronically open shell B@H242− and C@H24− icosahedral clusters with all real frequency values, which are associated with three unpaired electrons corresponding to a half-filled HOMO. This finding is analogous to the “magnetic super atom” reported recently.7 Moreover, in the B@H242− system, charge present on the ionic core is calculated to be −1.136e, which is again found to be significantly lower as compared to the actual charge on the central ion (B2−). Thus, similar to the N@H243− systems, very strong interaction has been found in the B@H242− system because of more charge transfer from the ionic core to the hydrogen molecules within the B@H242− cluster. Consequently, we have found significantly more negative interaction energy (−4.19 kcal mol−1) even for the open shell B@H242− system as 15042

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The Journal of Physical Chemistry C hydrogen molecules in H@H24− system as compared to that in the H@H88− system followed by the H@H64− system. Consequently, we found significant increase in bonding between the central hydride anion with hydrogen molecules of first shell in the H@H88− cluster followed by the H@H64− cluster as compared to that in the H@H24− cluster. This increase in bonding with the central hydride ion has occurred to minimize the repulsion between the hydrogen molecules of the first, second, and third shells. However, in both H@H64− and H@H88− clusters, interaction energy and HOMO−LUMO gap are found to be somewhat smaller. Thus, from the smaller HOMO−LUMO gap and less negative interaction energy per hydrogen molecule of H@H64− and H@H88− clusters as compared to that in H@H24− clusters, we have found that the H@H24− system is more stable as compared to H@H64− and H@H88− clusters. These findings are in complete agreement with the experimentally observed mass spectra of Hn− clusters (n = 5−130).40 Molecular orbital pictures of H@H64− and H@ H88− clusters depicted in Figures S7 and S8, respectively, clearly indicate that these two clusters are associated with the shell closing corresponding to 66 and 90 electrons, respectively. Finally, we studied atom- or ion-centered X@H64− and X@ H88− clusters. We found that among all the atom- or ioncentered clusters, only a few possess the icosahedral geometry as the stable geometry with real frequency values. Among coinage metal-centered clusters, Au− and Cu− ions form a stable X@H64− cluster with Au−H and Cu−H bond length values of 2.739 and 2.604 Å, respectively. Moreover, halide ioncentered H64 clusters are also observed to form an icosahedral X@H64− structure. In contrast, we found only B@H882− and S@H882− to have icosahedral geometry with real frequency values. PBE-D3/AVTZ calculated bond length values, HOMO−LUMO gap, charge, and interaction energies for X@H64− and X@H88− clusters are given in Table 7, and the corresponding values calculated using PBE-D3/def2-TZVPP are reported in Table S8 for the sake of comparison. From

Table 7 one can see that in the Au@H64− cluster, the HOMO− LUMO gap and charge on the Au− are very close to the corresponding values in the H@H64− cluster. Thus, the Au@ H64− cluster has been found to show analogous behavior with the H@H64− cluster. Moreover, among all the clusters, H@ H64− and F@H64− clusters possess more negative interaction energy of −1.96 and −2.31 eV, respectively, as compared to other ion-centered X@H64 (X = Au−, Cu−, C−, Cl−, Br−) clusters. In all the halide-centered X@H64− (X = F, Cl, Br) clusters, very high value of HOMO−LUMO gap (in the range of 3.86−3.62 eV) has been found. Existence of X---H interaction (between X and H2 molecule), H---H interaction (between two neighboring H2 molecules), as well as H−H interaction (within one H2 molecule) is clearly evident from the presence of bond critical points (BCPs) from the electron density plots and Laplacian of electron density plots of H@H24−, H@H64−, and H@H88− systems obtained by using the PBE-D3/AVTZ level of theory (Figure 4) by employing the atoms-in-molecule approach.85,86 For all the X@ H24 (X = H−, Be, Mg, N3−, O2−, S2−, F−, Cu−, Ag−, Au−, and Cd) clusters, we have calculated the values of electron density [ρ], Laplacian of electron density [∇2ρ], local energy density [Ed], local kinetic energy density [G(r)], and the ratio of electron kinetic energy density to the electron density [G(r)/ρ] at the PBE-D3/def2-TZVPP level of theory as reported in Table S9. According to Boggs criteria,86 bond critical point (BCP) with high electron density (ρ > 0.1) and negative value of ∇2ρ represent strong covalent interaction, whereas BCP with less electron density (ρ < 0.1) and positive value of ∇2ρ indicate a noncovalent nature of bonding of that particular bond. In all the X@H24 clusters, the H−H interaction (within a H2 molecule) is found to be of A, B, C type covalent interaction as they satisfy the Boggs criteria [ρ > 0.1, ∇2ρ < 0, Ed < 0 and G(r)/ρ < 0] of the A, B, C covalent type of bonding, while all X---H interactions are found to be D type (weak noncovalent) interaction because the BCP between X---H satisfies the criteria of D type noncovalent interaction, namely, ∇2ρ > 0, |Ed| < 0.005, and G(r)/ρ < 0. From all the above results and discussions it is clear that weak interactions are involved in the X@H24−, X@H64−, and X@H88− clusters. Therefore, it is interesting to study the effect of the dispersion correction in the binding energy of all the studied clusters. We have found that the dispersion corrections have significantly improved the accuracy of the results, and the cost associated with the dispersion correction calculations are found to be negligible. In the present studied systems, the interaction energy values are found to be controlled by ioninduced dipole interaction via charge transfer from the ionic core to the hydrogen atom of the hydrogen molecules, which gives rise to the interaction between the central ion and the hydrogen molecules. Here, apart from the ion−molecule interactions, we have also observed the ion-induced dipole type of interaction between hydrogen molecules within the X@ H24 systems. Moreover, molecule−molecule interactions are also present between neighboring hydrogen molecules, which are expected to contribute to the dispersion interaction. Among all the studied systems, the effect of the dispersion correction to BE is found to be larger in Cu@H24− and in all the neutral X@ H24 (X = Be, Mg, Zn, Cd) systems, as reported in Table 5. For all the systems considered in this work, we have reported the values of dispersion correction to the binding energy in Tables 5−7. Naturally, dispersion effect should have played an important role, and that is clearly evident from the difference

Table 7. Calculated Values of X−H Bond Length (Å), Interaction Energy per H2 Molecule (BE in kcal mol−1), Dispersion Energy Correction per H2 Molecule (DE in kcal mol−1), HOMO−LUMO Energy Gap (ΔEGap in eV), and Charge on the X Atom in X@H64 (X = H−, Au−, Cu−, C−, F−, Cl−, Br−) and X@H88 (X = H−, B2−, S2−) Clusters at the PBE-D3/AVTZ Level of Theory cluster

X−H

BE

ΔEGap

charge

DE

H@H64− Au@H64− Cu@H64− C@H64− F@H64− Cl@H64− Br@H64− H@H88−a B@H882−a B@H882−a,b S@H882−a S@H882−a,c

2.327 2.739 2.604 2.515 2.340 2.723 2.877 2.288 2.278 2.315 2.443 2.450

−1.96 −1.76 −1.82 −1.87 −2.31 −1.83 −1.71 −1.74 −4.52 −4.52 −3.04 −3.03

2.16 2.75 1.83 1.99 3.86 3.81 3.62 2.29 0.28 0.27 0.71 0.70

−0.752 −0.718 −0.614 −0.543 −0.855 −0.824 −0.833 −0.723 −0.445 −0.435 −1.297 −1.297

−0.67 −0.71 −0.86 −0.69 −0.72 −0.67 −0.66 −0.69 −0.78 −0.78 −0.72 −0.72

a AVTZ basis set for H atoms after removing one diffuse p and one diffuse d function has been used to achieve SCF convergence. bAVTZ basis function for B after removing one diffuse d and one diffuse f function. cAVTZ basis function for S after removing one diffuse f function.

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Figure 4. Electron density (a, c, e) and Laplacian of electron density (b, d, f) plots of H@H24−, H@H64−, and H@H88− clusters as obtained by using PBE-D3/AVTZ level of theory. Blue and green points represent the bond critical points and ring critical points, respectively.

0.07 kcal mol−1 using def2-TZVPP and AVTZ basis sets, respectively. Similarly in F@H24− and C@H24− clusters, BSSE values are found to be smaller (0.08 and 0.10 kcal mol−1) using larger size AVTZ basis set as compared to the same using smaller size def2-TZVPP basis set (1.56 and 0.66 kcal mol−1). In the Be@H24 cluster, BSSE values are calculated to be very small (0.02 and 0.03 kcal mol−1) using both def2-TZVPP and AVTZ basis sets, respectively. Therefore, in the case of large size AVTZ basis set, we have found almost negligible basis-set superposition error as compared to the error calculated using a relatively small def2-TZVPP basis set in X@H24 (X = H−, C−, F−) systems. This is one of the reasons for the difference in the interaction energy as calculated by using different basis sets. Thus, apart from the basis set limit, the negligible BSSE for X@ H24 systems calculated using AVTZ basis set again shows the suitability of AVTZ basis set for the calculation of all the studied atom- or ion-centered hydrogen clusters.

in the bond distance (R) and interaction energy (BE) values calculated with and without dispersion correction as reported in Tables S4 and S10, respectively. The bond distance between the central atom or ion and hydrogen molecules (R) has been found to be longer and the interaction energy (BE) value is found to be less negative without employing dispersion correction in PBE/def2-TZVPP level of theory as compared to the corresponding values calculated at the dispersion corrected PBE-D3/def2-TZVPP level of theory, as shown in Tables S4 and S10. Because the interaction energy of the studied systems is found to be basis set dependent, we have calculated the basis set superposition error for a few smaller X@H24 systems (X = H−, Be, C−, F−) by using GAMESS software.74 Here, we have used a counterpoise method for calculating the BSSE71−73 with two different basis sets, namely, def2-TZVPP and larger size aug-cc-pVTZ (AVTZ) for the X@H24 systems (X = H−, Be, C−, F−). In the H@H24− cluster, BSSE is found to be 1.36 and 15044

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determining the geometries of the X@H24− systems. The calculated values of interaction energy using CCSD and CCSD(T) methods are given in Table 8.

Apart from the interaction energy, we have also checked the basis set dependence of charges in the various small size systems. For this, we have calculated the charges on various central atom or ion(s) as well as on the hydrogen atoms of hydrogen molecules in X@H24 clusters using the natural population analysis scheme. For the charge calculation we have used PBE-D3 method with three different basis sets, namely, def2-TZVPP, def2-QZVPP, and AVTZ. Subsequently, using different basis sets, we have found change in the charges, mainly on the central atom or ions in almost all the X@H24 systems; however, charge on the hydrogen atoms has been found to be similar using three different basis sets. Among all the clusters, change in the charges on the central ion in B@H242−, N@ H243−, and P@H243− clusters are found to be higher as compared to that in other clusters, as shown in Table S11. Thus, all three B@H242−, N@H243−, and P@H243− clusters are found to be more basis set dependent. Moreover, the charges on the hydrogen atoms of the hydrogen molecules in B@H242−, N@H243−, and P@H243− clusters are found to be higher using all three different basis sets. However, in all other clusters, very small charge has been found to be present on the hydrogen atoms of the hydrogen molecules. Therefore, considerable amount of charge redistribution has been found in B@H242−, N@H243−, and P@H243− clusters as compared to that in other clusters. We have found significant incongruity in the interaction energy, obtained from the MP2 and DFT-D3 methods, as reported in Tables 2 and 5; therefore, we have performed single-point CCSD and CCSD(T) calculations for the few smaller systems to check whether the MP2 results have been actually converged with respect to the inclusion of electron correlation. All the CCSD and CCSD(T) calculations60−62 have been done using MOLPRO 201263 with AVTZ basis set. For all the considered X@H24 systems (X = H−, Be, F−, Cu−, Au−, B2−, C−, O2−), two different optimized geometries obtained at the PBE-D3/AVTZ and MP2/AVTZ level of theory have been taken as initial geometry for single-point CCSD and CCSD(T) calculations. For the H@H24− system, interaction energy calculated using CCSD(T) is found to be −1.94 and −1.98 kcal mol−1 using PBE-D3/AVTZ and MP2/ AVTZ level optimized geometry, respectively, which are found to be very close to the MP2 calculated interaction energy value of −1.99 kcal mol−1. However, CCSD calculated interaction energies are found to be −1.72 and −1.77 kcal mol−1, for the H@H24− system with the PBE-D3 and MP2 optimized geometries, respectively. For other systems like F@H24− and O@H242−, CCSD(T) calculated interaction energies are also found to be very close to the corresponding MP2 calculated values. Similarly, in the Be@H24 system, the interaction energy value obtained from CCSD(T) calculation (−0.16 kcal mol−1) using MP2/AVTZ optimized geometry has been found to be very close to the MP2 calculated interaction energy (−0.17 kcal mol−1). On the other hand, CCSD(T) interaction energy (0.36 kcal mol−1) calculated using PBE-D3/AVTZ optimized geometry is found to be slightly different. Similarly for other X@H24 clusters, MP2 calculated interaction energies are found to be closer with the single-point CCSD(T) calculated interaction energy values, indicating that the MP2 method is quite adequate as far as the effect of electron correlation is concerned. All the calculated results reveal that for a particular system both PBE-D3 and MP2 optimized geometries lead to very similar CCSD(T) interaction energy values, indicating that both PBE-D3 and MP2 methods are quite suitable for

Table 8. Calculated Values of Interaction Energy per H2 Molecule (BE in kcal mol−1) of X@H24 (X = H−, Be, B2−, C−, O2−, F−, Cu−, and Au−) Clusters at MP2/AVTZ, CCSD/ AVTZ, and CCSD(T)/AVTZ Levels of Theory PBE-D3/AVTZ geometry

MP2/AVTZ geometry

cluster

MP2

CCSD

CCSD(T)

CCSD

CCSD(T)

H@H24− Be@H24 B@H242− C@H24− O@H242− F@H24− Cu@H24− Au@H24−

−1.99 −0.17 −3.52 0.10 −9.11 −3.10 −1.15 −2.64

−1.72 0.57 −1.77 −1.85 −8.80 −3.12 0.01 −1.15

−1.94 0.36 −2.40 −2.03 −9.53 −3.29 −0.53 −1.50

−1.77 −0.11 −a −1.93 −8.80 −3.13 −0.60 −1.21

−1.98 −0.16 −a −2.08 −9.69 −3.31 −0.87 −1.55

a

Interaction energy could not be calculated by using CCSD/AVTZ and CCSD(T)/AVTZ methods for the optimized MP2/AVTZ geometry of the B@H242− cluster.

4. CONCLUDING REMARKS We have theoretically determined and confirmed the icosahedral structure of H@H24−, H@H64−, and H@H88− clusters associated with all real vibrational frequencies by using dispersion corrected density functional theory with the PBE-D3 method. Some of the smaller systems have been calculated using the MP2/aug-cc-pVTZ method and were found to provide interaction energies which are very close to the CCSD(T)/aug-cc-pVTZ computed values. Among all the clusters, the H@H24− cluster is found to be the most stable corresponding to its higher HOMO−LUMO gap and higher interaction energy. The H@H24− cluster forms a magic cluster corresponding to 26 electrons with 1s21p61d102s22p6 closed shell electronic configuration, similar to plumbaspherene and stannaspherene clusters.80,81 Moreover, we have predicted various atom- or ion-centered new clusters, X@H24 (X = F−, Cl−, Br−, Cu−, Ag−, Au−, Be, Mg, Zn, Cd, B2−, C−, N3−, P3−, O2−, S2−, Se2−). Similar to H@H24− clusters, coinage metalcentered Au@H24−, Ag@H24−, and Cu@H24− clusters and neutral metal-centered Be@H24, Mg@H24, and Cd@H24 clusters form a stable 26-electron icosahedral system with large HOMO−LUMO gap. Among all these clusters, only F−, Cl−, Br−, Au−, and Cu− anions are capable of forming X@H64− icosahedral clusters with real frequency values. Moreover, in the X@H64 cluster HOMO−LUMO gap has been found to be slightly higher while interaction energy has been found to be lower as compared to that in X@H24 clusters (X = F−, Cl−, Br−). Furthermore, we have observed the strongest bonding in pnictide encapsulated clusters followed by chalcogenide encapsulated clusters, corresponding to their extremely high interaction energy as compared to that in any other atom- or ion-centered cluster. This is due to the higher negative charge on the central atom, which in turn increases the extent of ioninduced dipole interaction. Among all the pnictogenides and chalcogenides, only S2− forms a stable icosahedral S@H882− cluster with real frequency values. Apart from the closed shell systems, we have also found stable open shell B@H242−, C@ H24−, C@H64−, and B@H882− clusters in icosahedral geometry 15045

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The Journal of Physical Chemistry C

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with higher HOMO−LUMO gap and reasonable interaction energy values. All the calculated results indicate that it may be possible to investigate some of the predicted systems experimentally, in particular, the singly charged anion systems by using suitable techniques.20,40 Indeed, the new hydrogen clusters predicted in the present work, aiming at bridging the gap between the molecular form and solid form of hydrogen, would be interesting for experimental investigations.



ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b02877. Bond length, interaction energy, optimized XYZ coordinates, charge distributions of various structures at PBE-D3, B3LYP-D3 TPSS-D3 and PBE levels, HOMO− LUMO gap values, AIM properties, molecular orbital pictures and molecular orbital energy levels of X@H24 clusters (PDF)



AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: 0091-22-25505151. ORCID

Tapan K. Ghanty: 0000-0001-7434-3389 Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS The authors gratefully acknowledge the generous support provided by their host institution, Bhabha Atomic Research Centre, Mumbai. The authors thank Computer Division, BARC for providing computational facilities. We thank Dr. A. K. Nayak, Shri R. K. Rajawat, and Dr. P. D. Naik for their continuous encouragement. M.J. thanks Homi Bhabha National Institute for the Ph.D. fellowship in Chemical Sciences.



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