For CrF 4 and MoF 4 , the tetrahedral configuration of nuclei in the electronic ... relative energies of the low-lying states generated by the partially filled d-shell of ... electrons on the orbitals Is 2 (F, Mo, W)0 2s 2, 2/o 6, 3s 2, 3p 6, 3d I~ (Mo, W), and 4s ... parameters, vibration frequencies, and relative energies of different states.
Journal of Stru,'tural Chemistry, Vol. 41, No. I, 2000
AB INITIO CALCULATIONS OF THE STRUCTURE AND SPECTRA OF CHROMIUM, MOLYBDENUM, AND TUNGSTEN TETRAFLUORIDES. NONTETRAHEDRAL MOLECULAR STRUCTURE OF WE 4 U D C 539.194
V. V. Siiznev and V. G. Solomonik
The prope•ies of MF 4 molecules ( M = Cr, Mo, W) are investigated by the restricted Hartree-Fock method using M61ler-Plesset second-order perturbation theory and by the second-order configuration hzteraction method using the m ulticonfiguration wave function derived in a complete active space approximation, in wide bases complemented with polarization d and f functions. Relativistic effective potentials are used to describe the core electrons. For CrF4 and MoF 4 , the tetrahedral configuration of nuclei in the electronic state of 3A 2 symmetry is energetically most favorable, in the WF4 molecule, the least-energy structure is a D2h structure in the singlet state 1A I. The D4h (IAlg) and Td (3A2) configurations in the WF4 molecule are higher on the energy scale than the ground state by 4 and 6305 cm-I and are saddle points. For all o f the analyzed configurations o f M F 4 molecules, the geometrical parameters, the vibrational spectra, and the energies of vertical electronic transitions are found. The chemical bonding is analyzed and a simple model is proposed to explain the vaeiation o f the relative energies o f states in the series CrF4 -.--->Mo F4 ---->WF4.
Gas-phase electron diffraction studies [1, 2] gave sets of effective geometrical parameters r~, of CrF 4 and MoF 4 molecules. In IR spectral investigations on C r F 4  and MoF 4  isolated in neon and argon matrices, three frequencies were assigned to CrF 4 [31 and one to M o F 4 [41. The enthalpies of formation of gaseous M o F 4 and WF 4 were obtained in mass spectral studies [5, 61. Q u a n t u m chemical calculations of the geometrical parameters, vibrational spectra, and vertical transition energies were performed for C r F 4 in [7, 8]. Thus the structure of CrF 4 is the best studied among MF 4 molecules (M = Cr, Mo, W). Structural data and hypotheses were also published for MoF4 [2, 4]. No structural data are available for W F 4. The symmetries and the relative energies of the low-lying states g e n e r a t e d by the partially filled d-shell of the metal atom are not treated anywhere except , where the electronic states of the CrF 4 molecule in the D4h configuration are considered. The aim of this work is a systematic study of the geometrical structure, vibrational spectra, and vertical transition energies in the series CrF4--->MoF4---->WF4.
APPROXIMATIONS U S E D AND DETAILS OF CALCULATIONS
All calculations were carried out with the G A M E S S program . The geometry optimization and vibration frequency calculations were performed numerically using symmetry coordinates from  and the procedures and programs described in [Ill. The atomic cores described with the aid of relativistic effective potentials [12, 13] included electrons on the orbitals Is 2 (F, Mo, W)0 2s 2, 2/o6, 3s 2, 3p 6, 3d I~ (Mo, W), and 4s 2, 4p 6, 4d I~ 4f 14 (W). The valence bases ( ~ = ~p) on the atoms F (31G), Mo(8s8p5d) -->[4s4p3dl, and W(7s7p5d) --->[4s4p3dl (contraction schemes: Mo - 4211/4211/311; W - - 411114111/311) were taken from [12, 13]. In all calculations, the basis on the F atom was Ivanovo State Chemical Engineering University. Translated from Zhumal Stmktumoi Khimii, Vol. 41, No. l, pp. 14-23, January-February, 2000. Original article submitted November 23, 1998. 0022-4766/00/4101-0011525.00 9
Kluwer Academic/Plenum Publishers
complemented with the polarization d function with exponent ~ = 0.8 , and the basis on the d-metal atoms, with the f functions: one function with exponent ~ = 1.14 for Cr , and two uncontracted functions for Mo and W ( ~ = 0.89 and 0.41 for Mo; ~r 0.73 and 0.30 for W). The geometrical configurations of MF 4 molecules of Td, D4h, and D2d symmetries are considered (the latter, only for WF4). For the 3A 2 (Td), 3Big, lA t.e (D4h), and tA l (D2d) states of MF 4 molecules we obtained geometrical parameters, force fields, vibration frequencies, and IR intensities by the restricted Hartree-Fock (ROH F) method and using M611er-Plesset second-order (MP2) perturbation theory to include electron correlation effects. The vertical transition energies were calculated by the second-order configuration interaction (SOCI) method with the geometry optimized in the MP2 approximation. As the initial function in the SOCI method we used the multiconfiguration wave function derived by the MCSCF technique in a complete active space (CASSCF) approximation. In the CASSCF procedure, the inactive space consisted of 20 doubly occupied orbitals. The configuration functions of state were derived by placing two electrons on six active orbitals consisting predominantly of the ( n - 1)d and ns orbitals of the metal atom (n = 4, 5, 6 for Cr, Mo, and W, respectively). The remaining 84 orbitals comprised the secondary space. Thus, the wave function in the framework of C l symmetry contained 15 configurations in triplet energy calculations and 21 configuration in singlet energy calculations. The SOCI procedure took into account all single and double excitations of electrons into secondary space relative to the initial multiconfiguration wave function obtained in the CASSCF approximation. Thus the SOCI wave function consisted of 4005 and 4095 configurations in the triplet and singlet state energy calculations, respectively. DISCUSSION O F CALCULATION RESULTS The theoretical values of geometrical parameters, vibration frequencies, and relative energies of different states of MF 4 molecules are listed in Tables 1-3. Inclusion of electron correlation by the MP2 method leads to a theoretical value of Re(M-F) which is higher by 0.008 ,~ on the average and not more than by 0,016 ,~ (in CrF4). The R O H F calculated frequencies of normal vibrations are overestimated by 4-28% relative to the MP2 values for CrF 4 and MoF 4. The calculated relative energies of the planar D4h structures are lower when electron correlation is included, The greatest change is observed for the relative energy of the planar configuration in the singlet state (Table 1). The symmetry of the ground state of the WF 4 molecule also changes; in the ROHF approximation, the tetrahedral configuration (3A 2 state) possesses the least energy, whereas in the MP2 approximation (Tables 1 and 2) D ~ (IA l) is the main configuration and the T d (3A 2) structure corresponds to the saddle point on the potential surface. The experimental values of geometrical parameters and vibration frequencies are close to the MP2 calculated values (Table 1). Good agreement is also observed between the theoretical and experimental values of the isotopic frequency shifts of v~ (Av 3) and the relative intensities of bands (/3 : 14) in the IR spectrum of CrF 4 : Av3(52Cr- 5~
Av3(54Cr - 53Cr)
13 : 14
E x p e r i m e n t [31
MP2 c a l c u l a t i o n
The results of previous  calculations of the geometrical parameters and stretching frequencies of CrF4 by the density functional method agree with our MP2 calculated data. The deformation frequencies 0) 2 and o)4 calculated in [71 are much lower than our calculated values and than the experimental values obtained in . According to the results of MP2 and SOCI calculations, the tetrahedral configuration in the 3A2 state is energetically preferable for CrF 4 and MoF 4 molecules. In the WF 4 molecule, the least-energy configuration is D2d (IA1). The planar D4h (IA lg) structure of the WF 4 molecule corresponds to the saddle point on the pathway of the intramolecular rearrangement D~---)D4h ---~D~ (Fig. 1). The energy difference between the D ~ and D4h configurations in the singlet state of the WF4 molecule is only 4 c m - t. The deviation of the (FWF) angle from 180~ in the Dza configuration is only 5.6 ~ and Re(W-F) as well as vibration frequencies except 0)2 (Blu) do not change with respect to the parameters of the Dab structure (Table 2). Thus the WF 4 molecule in the ground state may be considered to be "quasiplanar." It seems that a spectrum calculation from the Blu vibrational mode requires a higher level of approximation than the harmonic oscillator approximation. Below we use the molecular parameters of WF 4 with a square configuration of nuclei (D4h symmetry). 12
TABLE 1, Geometrical Parameters, Vibration Frequencies (tO/), IR Band Intensities (Ai), and the Total (E) and Relative (h) Energies of the Configurations of M F 4 Molecules CrF4
Calculation ROHF MP2
Td, 3A2,-E Re(M-F) tol (A ~)
161 715 140 720 159 16384 1.8634 15971 1.8312
109 696 177 i 4087 1.8680 7887 1.8300
730 207 812
242 880 128 21489 1.7186 32741 !.7033
195 856 140 19687 1.7343 22632 !.7128
D4h, IA 1,~.h
Calculation ROHF MP2
D4h, 3BI~ h Re(M-F)
to2 (E) to3 (F2) A3 A4
105 564 143 10129 1.8722 1825 1.8274
69 554 147 7804 1.8783 -6301 1.8287
aE given in au; internuclear distances Re, in ,~; toi, h in c m - l ; Ai in km/mole, bRg parameter . CRg parameter . a . e . TABLE 2. Results of MP2 Calculations of the Geometrical Parameters, Vibration Frequencies, Intensities of IR Bands, and Relative Energies of the D4h and D2d Configurations of the W F 4 Molecule Property D4h, IA lg D2d, IA 1
D4~, 1Aig D ~ , 1A i
D4h, IA lg D2d, IA 1 Property
326 (Big)~,e) (B 325 (BII 705 705 (B21
149 (A2.)1152 (B.I
728 (E u) 728 (E) 1215 (G) 218 (E)
D4h, IA Ig D ~ , IA 1
TABLE 3. Relative Energies (AE a, cm- 1) of Low-Lying Electronic States of M F 4 Molecules State
Td configuration (2e) 2
(2e) 1(5t2) 1
(2e) t (5t2) I
2 ! 467
TABLE 3 (Continued) I
D4h configuration 19687
(4a lg) l(2e,~) 1
(2blg) l(2eg) 1
(4a lg)l(3b2x) 1
(4a Ig) l(2eg) l
(4a i ~,)l(2blg) I
IBlg lB2g IBlg
(2big) l(2e~) 1
(4alg) 1(2blx) l
a For the D4h configuration, the relative energy of the aF electronic state was found from the relation AE(C~F) = [EMP2(aFref) 3A2)] + [EsocI(aF) - Esocl(aFref)], where EMP2 and ESOC! are the total energies found in the MP2 and SOC! approximations. For CTre f we took the and IA Ig states for the triplet and singlet states, respectively.
A decrease in the relative energy of the planar square configuration C r F 4 ----)MoF4 ----~WF4 (Tables 1 and 3), changing the symmetry of the ground state in the W F 4 molecule, is one of the most interesting features. Stabilization of the planar structure in this group of compounds is probably associated with the peculiarities of the electronic structure of MF 4.
2 0 - h,cm-1
0 a, deg
Fig. I. Potential function of the out-of-plane deformation of the WF 4 molecule corresponding to the intramolecular rearrangement in the singlet state.
Fig. 2. Electron density maps on the highest occupied MO of the W F 4 molecule. The bold lines denote the boundaries of electron density corresponding to the values of 0.001, 0.01, and 0.1. The solid straight bold lines connect the nuclei of the F and W atoms; the dashed straight bold lines are the projections of the lines connecting the nuclei of F and W on the plane of the drawing, a - - X Y plane; b, c, d - - cyd plane.
For the effective core potentials chosen, the electronic configurations in the 3A ~ (Td) and IA1,r (D4h) states of MF 4 molecules may be recorded as follows: 3A2 - - ]corel (lal)2(lt2)6(2al)2(2t2)6(~2)6(3al)2(le)4i4t2)6(ltl)6(2e)2; IA lg - - [core] (lalg) 2( le,)4(la2u) 2(2a lg)2( lb2.~)2(2eu)a(2b2g)2(3alg)2( lblg)2( leg)a(3eu)4(2a2u)2(4eu)4( lblu)2( I a2g)2(4alg) 2. The MO composition analysis and the Mulliken population analysis showed that the main contribution to the filled orbitals in both tetrahedral and planar configurations is from the 2s, 2p orbitals of fluorine atoms or the ( n - l ) s , ( n - l)p orbitals of the d-metal atom. The highest occupied MO ( H O M O ) (Fig. 2) may be considered to be nonbonding. The major contribution to HOMO is made by the orbitals of the d-metal atom. In the T d configuration, the d_2 and dx.,_yZatomic orbitals (AO) are predominant in the doubly degenerate (2e) H O M O ; in the D4h configuration, the d_z AO predominates in the HOMO of 4alg symmetry. The lowest unoccupied MO (5t 2 for T d and 2er 2bl. ~. and 362.e for D4h) also have prevailing contributions from the corresponding orbitals of the d-metal atom. Thus the MO composition analysis indicates that in MF 4 molecules the electron density is transferred from the ns and partly from the ( n - l)d orbitals of the d-metal atom to the ligands. Electron density redistribution in MF 4 molecules is judged more clearly from full and difference electron density maps. We constructed electron density maps for both geometrical configurations under analysis, T d (3A 2) and D4h(IA Ig), of the WF 4 molecule (Fig. 3). The difference electron densities of WF a were estimated from the total density by subtracting the electron densities of the W and F 15
Fig. 3. Total (a, c) and difference (b, d) electron density maps of the WF 4 molecule. The solid lines correspond to the positive values of difference electron density; the dashed lines, to the negative ones; the bold lines correspond to zero density points. The straight lines connect the nuclei of the F and W atoms; a and b - - T d ( 3 A 2 ) , a d plane, c and d - - D 4 h ( I A l g ) , X Y plane.
atoms in the 7S [5d56s 1] and 2p [2s22pS] states, respectively. In Fig. 3b and d, one can clearly see regions of redundant electron density. The regions are nearly spherical in form with the center displaced relative to the nucleus of the fluorine atom. The results of the total and difference electron density calculations together with MO composition and Mulliken population analyses data indicate that the chemical bonds in the given class of compounds are ionic. Consequently, the MF 4 molecule may be represented as the central ion M 4+ surrounded by F- anions, i.e, as [M 4+ I[F- ]4. In the ionic system [M 4+ ]IF- ]4, the F- anion possesses a filled valence L-shell. In the metal cation M4+ , the inner ( n - l)s and ( n - l)p shells are also filled. Therefore, the ground state and the nearest states of the molecules must arise from the states generated by the partly filled ( n - l)d 2 shell of the M 4+ central cation. Figure 4 shows the correlation diagram between the ionic and molecular electronic levels of two geometrical configurations (tetrahedron and square). For the levels of the free ion we used the results of the SOCI calculation of the electronic spectrum of the Cr 4+ cation. As would be expected in conformity with Hund's rules, the least-energy state is 3F. Other states of the Cr 4+ free ion are higher than the ground state by 15,024 (1D), 18,090 (3p), 24,307 (IG), and 55,948 cm- I (Is)" The ground state of the tetrahedral configuration of MF 4 molecules (Table 2 and Fig. 4) correlates with the 3F ground state of the M 4+ ion. The ground state of the square structure of the CrF 4 molecule is also generated by the 3F state of the Cr 4+ cation. However, in MoF,~ and WF 4, the energetically preferable IA lg state of the D4h configuration results from the excited 1D state of the cation. Moreover, in passing from CrF 4 to WF 4, the relative 16
D4h c o n f i g u r a t i o n
T d configuration
, ' ~
45 40 "--
," , : , : ~ - - "
~A , - -
'E 3 0
,'," ; ,,,
i ' , '
y ~ ~
C r F4 MoF 4 WF 4 ~ ....... ". ""-3Tt 9 ".. -
.. : ' : :
~ '~l ~
' ~ 'o*
', il ~ '~ m l
~ ' - .
s% _ _ . "
~ " 9" o" , ~ "
t~ t g "B'm~
o~ " " " ~ , "
. ; , ~ m , ' , - ~ , ; 3p . f : ," , ~ ' , ~ ' 1 , ' ~ " " "1 , -*",, '~ ~1', t ~ ' ~ - 4 -h ,:"
- -~ -~
I ~ 3 F [,'1
,' ~.*'. j,. . . . . . . . . . . . . I I
Fig. 4. Correlation diagram of the electronic states of the M 4+ ion and the MF 4 molecule.
energies decrease for other singlet states as well (Fig. 4). The stabilization of the low-spin states observed in the series CrF4 ---~MoFa---)WF4 is explained in ligand filed theory  by the greater strength of the field, breaking the LS bond between the odd electrons of M 4+ . In this case, the energetically preferable configuration and electronic state may be determined by using the simple electrostatic model that takes into account only two types of interaction: I) repulsion o f electrons lying on the partly filled d-shell of the central ion from the electronic shells of the ligands (hereafter "d-shell-ligand repulsion"); 2) repulsion between the electronic shells of ligands (hereafter "ligand-ligand repulsion"). The least energy of ligand-ligand repulsion is achieved in the tetrahedral configuration. In the field of T d symmetry, the fivefold degenerate d-orbitals of the free cation are split; the d.2 and dx2_ p orbitals are transformed according to the doubly degenerate irreducible representation e; the d~:~, da:, and d~ orbitals, according to the triply degenerate representation t 2. In MF 4 molecules, these AO predominate in the 2e (Fig. 2a, b) and 5t 2 MO. For the partly filled d2-shell of the cation, the least energy of the d-shell-ligand repulsion in the tetrahedral configuration is achieved when two electrons occupy the doubly degenerate 2e MO since the electron density on the 2e MO (Fig. 2) is maximally remote from the electronic shells of ligands. This is confirmed by the results of electronic spectrum calculations for MF 4 molecules (Table 3, Fig. 4); the states obtained for the occupied 5t 2 MO lie much higher on the energy scale than the ground state 3A2. In the planar square structure, the degenerate d orbitals are split in the field of D4h symmetry according to the following scheme: the d_z, dx2_ ,,2, and d ~ orbitals are transformed according to the a].~, bl,~. and b2g representations, respectively; the d~-z and d ~ orbitals, according to the doubly degenerate representation eg. In MF 4 molecules, these d orbitals are predominant in the 4alg, 2bl ~ 3b2~. and 2eg MO. The form of the d.= (Fig. 2c), dx:, and d~ orbitals, unlike that of the dx2_ ~ and d~. orbitals, is such that the major part of electron density is concentrated outside the ((~h) plane of the molecule. Therefore, occupation of the dx2_ ,/. and d_~, orbitals, whose major electron density is in the o h plane, must be less favorable because of the increasing energy of d-shell-ligand repulsion. This assumption is confirmed by the data of Table 2 showing that the states with occupied 4a]g and 2eg MO are energetically preferable for the Dab configuration. A comparison o f the electron density maps of the 2e (T d) and 4alg (D4h) MO presented in Fig. 2 shows that the distance from the electron density maximum on the given orbital to the ligand nucleus is maximal in the ]A Ig state of the planar configuration. In this case, the energy of d-shell-ligand repulsion is minimal. Thus the d-shell-ligand repulsion decreases and the ligand-ligand repulsion increases when the geometrical configuration of nuclei changes 17
from tetrahedral to square (T d ---rD4h) and the electronic state changes accordingly. In the CrF 4 molecule, the increasing energy of ligand-ligand interaction due to the T d ----~D4h transition prevails over the decreasing d-shell-ligand repulsion energy. Therefore, the tetrahedral structure is the main type of structure in the CrF 4 molecule. Moreover, the energy of d-shell-ligand interaction in C r F 4 seems to be lower than the energy of electron interaction in the d-shell o f Cr 4+ . Thus the ligand field effect on the Cr 4§ cation in the CrF 4 molecule is not so high, and the high-spin triplet states are energetically preferable in both the T d and D4h configurations. On passing from C r F 4 to MoF 4 and then to WF 4, the d-shell-ligand interaction becomes to prevail over the ligand-ligand interaction. T h e increased contribution of the former interaction in the series CrF 4---)MoF4 ---~WF4 may be explained by the extension o f the d orbitals in space. The values of rmax which define the distance from the nucleus of the cation to the electron density maximum on the d orbital may serve as a measure of this extension. We calculated rmax using the electron densities on the d-shell obtained in CASSCF calculations for the ground state of the free M 4+ cations. A comparison between rmax (0.23 for Cr 4+ , 0.50 for Mo 4+ , and 0.58/~ for W 4+ ) and the internuclear distances Re(M-F) shows that the increments of rmax in the series Cr 4+ ---~Mo4+ ---~W4+ are greater than those of Re(M-F) in the series CrF 4 ----)MoF4----).wF 4. Consequently, in passing from CrF 4 to WF 4, the distance from the electron density maximum on the highest occupied MO to the ligand decreases in the tetrahedral configurations (3A2) and increases in the planar square structures (IA lg)" In the framework of our model, this tendency means that in the series CrF 4 - ~ M o F 4 ---)WF4 the d-shell-ligand repulsion increases in the tetrahedral configuration and decreases in the square configuration. The energy gain due to the decreased d-shell-ligand repulsion in the T d---~D4h transition in this series must prevail over the energy loss due to the growing ligand-ligand repulsion. Hence, the planar square configuration with the IA lg state must be stabilized in passing from CrF 4 to WF 4. Apart from explaining the electronic structure of the MF 4 molecule considered here, the proposed model possesses the predictive ability. For example, when fluorine is replaced by a heavier analog (chlorine, bromine, iodine) from the same group of the periodic table, one can expect that the role of the d-shell-ligand repulsion will decrease and the tetrahedral structure with the 3A 2 state will prevail in chromium, molybdenum, and tungsten chlorides, bromides, and iodides. Hence the WF 4 molecule with a planar (or quasiplanar) nuclear configuration and the singlet electronic state is an exceptional occurrence among subgroup V1B element tetrahalides. To verify the above assumptions it would be interesting to perform further experimental and theoretical studies on the structure and spectra of tungsten tetrahalides.
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