19818
J. Phys. Chem. 1996, 100, 19818-19823
Density Functional Calculations on WH6 and WF6 Noppawan Tanpipat Molecular Simulations, Inc., 9685 Scranton Road, San Diego, California 92121
Jon Baker* Department of Chemistry & Biochemistry, UniVersity of Arkansas, FayetteVille, Arkansas 72701 ReceiVed: June 4, 1996; In Final Form: October 4, 1996X
We present the results of a computational study on both WH6 and WF6 using a relativistic pseudopotential on tungsten, comparing results at the HF and MP2 levels with density functional calculations using local (SVWN), nonlocal (BLYP), and hybrid HF-DFT (ACM) functionals. In agreement with the earlier allelectron HF study of Schaefer and co-workers (J. Chem. Phys. 1993, 98, 508), we find that the ground state geometry of WH6 is far from octahedral; instead, there are four low-lying structures of C3V (2) and C5V (2) symmetry. Barrier heights for interconversion of these isomers are low, indicating a highly fluxional molecule. In contrast, the octahedral structure appears to be the only stable species on the ground state potential energy surface of WF6. It derives its stability from the greater ionic character of the W-F bond compared to that of W-H.
Introduction In 1993, Schaefer and co-workers published an excellent theoretical paper on the structure of tungsten hexahydride (WH6).1 In it they investigated several different structures for WH6, covering a range of different symmetries, and concluded that the ground state structure was far from octahedral; indeed, the octahedral structure lay some 130 kcal/mol above the lowest energy structure found, which was a closed-shell triangular prism with C3V symmetry. Additionally, they found two other structuressboth characterized as minima by vibrational analysisslying very close energetically to the C3V ground state: an apex-capped C5V pentagonal pyramid and another, distorted, C3V structure. These results were apparently received with some skepticism,1 as the octahedral structure is the most favored based on the simple (and extremely useful) valence shell electron pair repulsion (VSEPR) model,2 and almost all other species of formula AB6 are octahedral. Although their work was very thorough, utilizing a number of quite large basis sets, it was essentially an all-electron study at the Hartree-Fock (HF) level only. Post-SCF calculations were done to account for correlation effects, but for the most part these were single-point calculations based on HF geometries. Because it is a third-row transition metal, relativistic effects should be important for tungsten, and although in a “note added in proof” Schaefer and co-workers carried out additional calculations using a tungsten relativistic effective core potential to account for these effects, it appears that the relativistic calculations were confined to the stable (minimum) structures only. Later in the same year, Albright and co-workers published a fairly comprehensive study of d0 ML6 and ML5 complexes,3 which included WH6 and which, in addition to the three minima noted above, predicted the existence of another C5V minimum, an umbrella-like structure in which all six hydrogen atoms were in the same hemisphere. This fourth minimum was apparently overlooked by the authors of ref 1. Albright’s study3 utilized a relativistic core potential on tungsten, and geometries were X
Abstract published in AdVance ACS Abstracts, November 15, 1996.
S0022-3654(96)01633-4 CCC: $12.00
optimized at second order in Moller-Plesset perturbation theory (MP2);4 hence, it included both relativity and electron correlation. Apart from the additional minimum, optimized structures and relative energies were very similar to those found by Schaefer and co-workers,1 although not all of the structures mentioned in ref 1 were investigated. In particular, the octahedral structure was again found to be energetically very unfavorable. In this work we emulate the earlier studies,1,3 only using the latest density functional methods. Density functional theory (DFT) has become increasingly popular as a cost-effective and reliable means of accounting for correlation within the bounds of what is essentially a Hartree-Fock-like approach, at least within the implementation we have used for our calculations.5,6 DFT has now been extensively validated,5-9 and its accuracy and limitations are becoming more widely known. Although much of the validation has been on fairly small “organic-like” molecules, there have been several recent successes with organometallics, particularly with hybrid functionals.10,11 As well as DFT, we also carried out “traditional” Hartree-Fock and MP2 calculations, andsas per ref 3swe used a relativistic core potential on tungsten. (We use the potential developed by Ross et al.12) For the most part it is not possible to compare our results with experiment due to the almost total lack of hard experimental data on WH6, which is known to be unstable, if it exists at all. However, the related hexamethyltungsten, W(CH3)6, is knownsit was first synthesized by Shortland and Wilkinson in 197313sand electron diffraction studies have confirmed that gas phase W(CH3)6 is not octahedral; the experimental data are compatible with a D3h or a distorted C3V structure.14 We do compare the geometry and vibrational frequencies of WF6 with experiment. The main aim of this work is not to do a definitive study but to see whether the results obtained in the earlier studies1,3 for the structures and relative energies of WH6 are also found using density functional theory. Additionally, we explore the ground state potential energy surface (PES) in more detail by locating transition states for interconversion between the various minima found. © 1996 American Chemical Society
Density Functional Calculations on WH6 and WF6
J. Phys. Chem., Vol. 100, No. 51, 1996 19819
Computational Details All calculations were done with the TURBOMOLE program package15 modified to include a full range of DFT capability.6 As previously mentioned, we used an averaged relativistic effective core potential (AREP) on tungsten which had 60 electrons in the core and a 5s, 5p, 5d, 6s valence space represented by five s, five p, and four d functions, with a (2111/ 311/211) contraction scheme.12 For both hydrogen and fluorine we used the DZP basis of Schafer et al.16 We used three different density functionals in our study: the local SVWN functional (comprising Slater’s exchange term17 plus Vosko, Wilk, and Nusair’s18 parametrization of the exact uniform gas results of Ceperley and Alder19), the nonlocal BLYP functional (which combines Becke’s nonlocal correction20 to the Slater exchange with Lee, Yang, and Parr’s correlation functional21), and Becke’s original three-parameter approximation to the “adiabatic connection” formula (hereafter referred to as the adiabatic connection method, or ACM22). The latter is a hybrid HF-DFT functional which is a linear combination of several commonly used functionals and the “exact” HartreeFock exchange. Such hybrid functionals are the most accurate density functionals currently available.23 In addition to DFT, we also did standard Hartree-Fock and MP2 calculations. All stationary points, both minima and transition states, were located using the EF algorithm24 as implemented in the general purpose stand-alone optimization package OPTIMIZE.25 We used standard convergence criteria of 0.0003 au on the maximum gradient component and either an energy change from the previous cycle of less than 10-6 hartree or a maximum predicted displacement of less than 0.0003 au per coordinate. Stationary points were characterized at all levels of theory by vibrational analysis with a Hessian matrix determined by twopoint finite difference on the gradient. All systems were taken to be closed-shell singlets. Results Tungsten Hexahydride, WH6. We commenced our study on WH6 by considering the eight distinct stationary points found at the all-electron SCF level by Schaefer and co-workers,1 together with the additional minimum found by Albright,3 namely octahedral (Oh), trigonal prismatic (D3h), trigonal prismatic (C3V), distorted octahedral (C3V-B), distorted octahedral (C4V), edge-capped rhombic pyramid (C2V), face-capped rectangular pyramid (C2V-B), apex-capped pentagonal pyramid (C5V), and pentagonal umbrella (C5V-B). Diagrams of all these structures are shown in Figure 1. Starting more or less from the previously reported SCF geometries,1 we located similar structures at all levels of theory considered here, both standard ab initio and DFT. Energies of all stationary points found and their so-called “Hessian index” (the number of imaginary frequencies) are given in Table 1. Relative energies are shown in Table 2. Calculated geometrical parameters are shown in Table 3 along with values from ref 1 using basis set C, which is approximately double-zeta quality on tungsten and is the basis most comparable in quality to the one used in this work. The relative energies, energy ordering, and Hessian indices of the various WH6 structures are similar to those found in Schaefer’s study.1 In particular, the Oh structure lies relatively very high in energy, and the same three structuressC3V (2) and C5Vsform three low-lying minima. The “missing” C5V-B minimum is higher in energy than the other three minima; our MP2 and ACM relative energies for the four minima are in very good agreement with those reported in ref 3. There are some minor differences in energy ordering; for example, at the HF level the energy ordering in ref 1 is D3h > C4V > C2V whereas
Figure 1. All WH6 structures considered by Schaefer and co-workers in ref 1 plus the additional C5V umbrella structure from ref 3. The C5V-B, C3V-B, C5V, and C3V structures are minima; all other structures are second- or higher-order saddle points (Table 1; see text for more details).
our calculations give C4V > C2V > D3h; note that all the DFT calculations predict the same ordering as Schaefer for these three structures. The major difference is with the second C2V structure considered in ref 1 (C2V-B), which wassapart from the four minimasthe lowest of the high-energy structures. We were unable to locate this species at all at the SCF level; all attempts collapsed to the D3h structure. We did find an equivalent structure at correlated levels, but geometrically this was quite different from that found by Schaefer and co-workers (see Table 3). The W-H bond lengths are much shorter than those reported in ref 1, and the large, almost linear H-W-H angle (172.1°) is some 30° less. Energeticallysapart from BLYPsthe C2V-B structure found in this work lies above the C2V and, for MP2 and SVWN, above the C4V as well.
19820 J. Phys. Chem., Vol. 100, No. 51, 1996
Tanpipat and Baker
TABLE 1: Energies and Hessian Indices of the Various WH6 Structures structure
HF
MP2
SVWN
BLYP
ACM
index
Oh D3h C4V C2V-B C2V C5V-B C3V-B C5V C3V
-70.135 314 -70.272 674 -70.264 843 not found -70.268 729 -70.265 411 -70.288 087 -70.306 512 -70.308 747
-70.420 113 -70.582 603 -70.593 392 -70.586 370 -70.592 181 -70.607 613 -70.621 176 -70.629 890 -70.632 800
-70.673 362 -70.888 309 -70.909 758 -70.906 491 -70.929 255 -70.952 955 -70.959 542 -70.959 577 -70.963 446
-70.829 047 -71.026 210 -71.026 671 -71.028 561 -71.028 154 -71.053 806 -71.066 741 -71.082 561 -71.082 825
-70.946 007 -71.139 638 -71.148 268 -71.149 481 -71.151 147 -71.180 633 -71.191 661 -71.199 967 -71.202 385
3 2 2 2 0 0 0 0
TABLE 2: Relative Energies of the Various WH6 Structures (kcal/mol) structure
HF
MP2
SVWN
BLYP
ACM
Oh D3h C4V C2V-B C2V C5V-B C3V-B C5V C3V
108.8 22.6 27.5
133.5 31.5 24.7 29.1 25.5 15.8 7.3 1.8 0.0
182.0 47.2 33.7 35.7 21.5 6.6 2.4 2.4 0.0
159.2 35.5 35.2 34.1 34.3 18.2 10.1 0.2 0.0
160.9 39.4 34.0 33.2 32.2 13.6 6.7 1.5 0.0
25.1 27.2 13.0 1.4 0.0
Comparing our geometries for the other structures with those reported previously,1 we find a similar picture in all cases. There are, of course, differences in the actual geometrical parameters, but overall things are very much the same. Note that in almost every case BLYP W-H bond lengths are longer than with any other theoretical method. The tendency of the BLYP functional to predict bond lengths that are too long is well-known.6,23 Our general conclusion is that the major predictions made in the previous studiessat both the HF1 and MP23 levelssregarding the structures and relative energetics of stationary points on the WH6 potential energy surface also hold for a range of density functionals. Consequently, they are likely to be true. The four nonoctahedral minima found for WH6 are very close in energy. In all our calculations the energy ordering is C5V-B > C3V-B > C5V > C3V, with the last two extremely close energetically (at most a couple of kcal/mol) and the C3V-B and, especially, the C5V-B structure lying somewhat higher (except at the local SVWN level where all four minima lie within ≈6 kcal/mol of each other). We have carried out additional calculations to locate transition states for interconversion between these four different minima. We found five different transition states linking the four minima. For each structure vibrational analysis gave one, and only one, imaginary frequency. Diagrams of the transition structures are shown in Figure 2, total energies in Table 4, energies relative to the four minima in Table 5, and geometrical parameters in Table 6. A schematic of the potential energy surface is depicted in Figure 3. The first transition state we looked for was that linking the two C3V minima. These two minima are structurally closely related, and one can imagine a “rotation” of the top half, say, of the tungsten atom along with three of the hydrogen atoms such that the W-H bonds change from eclipsed (in C3V) to staggered (C3V-B). This can theoretically be accomplished by a motion that retains the C3 axis. The transition state for this interconvertion was located fairly easily and did indeed have C3 symmetry. It lies energetically very close (within around 3 kcal/mol) to the C3V-B minimum (see Table 5). The barrier height correlates well with the “rotation” angle for the various levels of theory (Tables 5 and 6). The two C5V minima can be interconverted maintaining full symmetry by bending all five symmetry-equivalent W-H bonds simultaneously, and Albright and co-workers have suggested that the transition state does indeed have C5V symmetry, at least
TABLE 3: Geometrical Parameters for the Various Structures of Tungsten Hexahydride (Bond Lengths in Å, Bond Angles in deg; See Figure 1 for Atom Labeling) parameter
HF
rWH1 (r1) rWH4 (r2) ∠H1WH3 ∠H5WH6
MP2
SVWN
BLYP
ACM
ref 1
1.712 1.647 112.7 63.3
Trigonal Prismatic (C3V) 1.691 1.701 1.715 1.635 1.655 1.669 114.5 116.7 114.5 60.3 60.7 62.4
1.699 1.649 115.5 61.6
1.708 1.652 116.1 62.2
rWH1 (r1) rWH2 (r2) ∠H1WH2
1.732 1.666 113.9
Pentagonal Pyramid (C5V) 1.718 1.726 1.735 1.654 1.672 1.685 114.8 116.0 115.0
1.722 1.666 115.4
1.733 1.669 115.7
rWH1 (r1) rWH5 (r2) ∠H2WH3 ∠H4WH6
Distorted Octahedral (C3V-B) 1.716 1.684 1.686 1.708 1.632 1.623 1.643 1.656 119.9 119.0 116.9 118.8 60.9 59.5 61.7 61.5
1.689 1.636 118.2 61.5
1.700 1.640
rWH1 (r1) rWH2 (r2) ∠H1WH2
Pentagonal Umbrella (C5V-B) 1.615 1.618 1.634 1.643 1.671 1.645 1.662 1.680 67.7 64.3 63.5 65.4
1.625 1.660 64.6
rWH1 (r1) rWH3 (r2) rWH5 (r3) ∠H1WH2 ∠H3WH4 ∠H5WH6
Edge-Capped Rhombic Pyramid (C2V) 1.794 1.777 1.794 1.802 1.791 1.637 1.632 1.656 1.669 1.647 1.664 1.645 1.668 1.679 1.662 152.2 154.5 160.1 155.6 157.5 61.6 60.4 63.9 64.2 63.2 118.5 113.7 110.8 115.0 113.6
1.814 1.641 1.672 160.9 64.0 113.3
rWH1 (r1) rWH3 (r2) ∠H1WH2 ∠H3WH4 ∠H3WH5
Face-Capped Rectangular Pyramid (C2V-B) 1.715 1.731 1.746 1.728 1.674 1.689 1.705 1.685 139.7 152.2 137.9 144.1 86.2 82.5 87.2 86.8 66.5 68.6 67.0 66.8
1.868 2.053 172.1 69.9 21.4
62.7
rWH1 (r1) rWH6 (r2) rWH5 (r3) ∠H1WH2
1.877 1.667 1.669 121.1
Distorted Octahedral (C4V) 1.839 1.830 1.849 1.665 1.707 1.720 1.655 1.678 1.686 124.6 125.4 123.5
1.845 1.693 1.670 123.9
1.925 1.681 1.671 122.7
rWH1 (r1) ∠H3WH6
1.714 75.9
Trigonal Prismatic (D3h) 1.708 1.730 1.737 76.9 77.5 76.9
1.722 76.9
1.724 77.3
rWH1 (r1)
1.784
Octahedral (Oh) 1.777 1.817 1.816
1.804
1.804
for the equivalent rearrangement in CrH6.3 However, the C5V stationary point is not a true transition state; it lies energetically quite high (over 80 kcal/mol above the C5V-B minimum at SVWN) and has at least three imaginary frequencies. Examination of the vibrational modes for the C5V-B structure reveals that all the low modes are 2-fold degenerate, and the first totally symmetric mode has a fairly high frequency; this strongly suggests the existence of lower-energy symmetry-breaking pathways. The true transition state has Cs symmetry, and the C5V-B T C5V rearrangement takes place by bending down one of the symmetry-equivalent W-H bonds in the C5V-B structure (to become the axial bond in the C5V structure) with the other bonds rearranging themselves to form the five equivalent
Density Functional Calculations on WH6 and WF6
J. Phys. Chem., Vol. 100, No. 51, 1996 19821
TABLE 4: Energies of the Various WH6 Transition States (See Text for More Details) C3V T C5V ) TS-Cs C3V T C3V-B ) TS-C3 C5V T C5V-B ) TS-Cs* C5V T C5V ) TS-C2V C3V-B T C3V-B ) TS-C1 transition state
HF
MP2
SVWN
BLYP
ACM
TS-C2V TS-C1 TS-Cs* TS-C3 TS-Cs
-70.277 624 -70.268 823 -70.261 378 -70.286 655 -70.299 385
-70.588 559 -70.593 777 -70.601 677 -70.618 770 -70.621 859
-70.898 272 -70.910 374 -70.945 086 -70.952 726 -70.950 082
-71.031 877 -71.028 242 -71.046 869 -71.064 350 -71.073 026
-71.147 779 -71.151 247 -71.173 279 -71.187 258 -71.190 326
TABLE 5: Relative Energies of the Low-Lying WH6 Minima and Transition States (kcal/mol) structure
HF
MP2
SVWN
BLYP
ACM
TS-C2V TS-C1 TS-Cs* C5V-B TS-C3 C3V-B TS-Cs C5V C3V
19.5 25.0 29.7 27.2 13.9 13.0 5.9 1.4 0.0
27.8 24.5 19.5 15.8 8.8 7.3 6.9 1.8 0.0
40.9 33.3 11.5 6.6 6.7 2.4 8.4 2.4 0.0
32.0 34.3 22.6 18.2 11.6 10.1 6.1 0.2 0.0
34.3 32.1 18.3 13.6 9.5 6.7 7.6 1.5 0.0
equatorial bonds. The barrier is small (less than 5 kcal/mol) at all levels of theory (see Table 5). The C3V minimum can be rearranged to the C5V by bending up one of the “upper” W-H bonds (r1) while at the same time pushing the other two down and forcing out the other three W-H bonds (r2) (see Figure 1). This distortion can be accomplished with retention of a Cs plane which includes the W-H bond being bent up (r1) and one of the “lower” W-H bonds (r2) and bisects the other two pairs of C-H bonds. The transition state linking these two minima has Cs symmetry. The rearrangement is fairly facile, requiring 6-8 kcal/mol relative to the C3V minimum and even less relative to the C5V (see Table 5). Despite some effort, we were unable to locate a transition state directly linking the C5V and C3V-B structures. We note that a similar motion to the one that effects the C3V T C5V rearrangement must be accompanied by a “twist” or rotation in order to convert the C3V-B structure to C5V as here the W-H bonds are staggered (as opposed to eclipsed in the C3V structure); any twist in the C3V-B structure is likely to lead directly to the C3V. During our attempts to find this transition state, however, we located two other stationary points, one with C2V and the other with C1 symmetry, which analysis indicated were the transition states for “direct” hydrogen scrambling in the C5V and C3V-B structures, respectively. We did not search for transition states linking either of the C3V minima with the C5V-B. The motion effecting hydrogen scrambling in the C5V structure, i.e., interchanging the axial and an equatorial hydrogen, starts by bending down the axial hydrogen while at the same time bending up one of the equatorial hydrogens; this motion preserves a Cs symmetry plane containing the two “bending” hydrogens and the tungsten atom. The transition state occurs when both these hydrogens have bent to the same extent, so to speak, and both W-H bonds are the same length. This results in the appearance of another Cs plane in the transition state, bisecting the two moving hydrogens (bonds W-H1 and W-H2 in Figure 2)swhich are now formally equivalentsand including all four of the remaining W-H bonds. Continuing past the transition state removes the second Cs plane and completes the rearrangement. We thus have C5V symmetry at the minimum f Cs during the first “half” of the reaction f C2V at the transition state f Cs during the second “half” of the reaction f C5V at the (H-scrambled) minimum.
TABLE 6: Selected Geometrical Parameters for the Four Transition States of Tungsten Hexahydride (Bond Lengths in Å, Bond Angles in deg; See Figure 2 for Atom Labeling) parameter
HF
MP2
SVWN
BLYP
ACM
1.717 1.661 120.0 59.8 39.3
1.701 1.643 120.0 59.1 35.4
rWH1 (r1) rWH4 (r2) ∠H2WH2 ∠H4WH5 τH1WH4a
1.721 1.636 119.9 59.9 41.8
C3V-B T C3V (C3) 1.692 1.701 1.628 1.651 120.0 119.9 57.9 58.6 37.5 31.6
rWH1 (r1) rWH2 (r2) rWH3 (r3) rWH4 (r4) ∠H1WH2 ∠H1WH3 ∠H1WH4 ∠H2WH3 ∠H2WH4
1.616 1.731 1.655 1.695 92.4 61.4 66.3 67.5 132.9
C5V-B T C5V (Cs) 1.615 1.637 1.672 1.682 1.637 1.657 1.657 1.673 87.1 87.0 59.2 59.3 60.8 59.7 61.5 59.6 122.9 120.6
1.645 1.706 1.672 1.694 89.0 60.8 61.9 61.9 124.6
1.627 1.685 1.653 1.674 87.7 59.8 61.2 61.0 123.1
rWH1 (r1) rWH2 (r2) rWH3 (r3) rWH5 (r4) ∠H1WH2 ∠H3WH4 ∠H5WH6 ∠H1WX
1.710 1.672 1.704 1.723 65.6 34.7 113.9 131.2
C3V T C5V (Cs) 1.716 1.724 1.643 1.664 1.658 1.675 1.673 1.688 90.8 91.7 89.6 89.4 83.4 85.9 130.1 133.0
1.735 1.680 1.686 1.704 90.0 89.4 86.3 130.4
1.721 1.660 1.668 1.686 90.8 89.6 85.5 131.6
rWH1 (r1) rWH3 (r2) rWH5 (r3) ∠H1WH2 ∠H3WH4 ∠H5WH6
1.683 1.756 1.681 120.0 153.5 63.8
C5V T C5V (C2V) 1.677 1.696 1.749 1.775 1.672 1.689 119.5 118.6 154.2 158.7 64.1 65.7
1.703 1.782 1.701 119.7 156.5 65.8
1.688 1.768 1.683 119.3 157.1 64.9
rWH1 (r1) rWH2 (r2) rWH3 (r3) rWH4 (r4) rWH5 (r5) rWH6 (r6) ∠H1WH2 ∠H1WH3 ∠H2WH3 ∠H4WH5 ∠H4WH6 ∠H5WH6 ∠H2WH6 ∠H2WH4
1.776 1.803 1.665 1.654 1.628 1.664 151.7 87.4 106.4 61.8 69.8 59.7 87.0 75.2
C3V-B T C3V-B (C1) 1.693 1.735 1.823 1.816 1.654 1.674 1.649 1.668 1.647 1.675 1.653 1.674 146.5 152.5 72.9 73.3 120.6 119.3 59.5 61.8 72.6 71.3 55.7 54.7 72.6 73.7 97.0 90.6
1.778 1.815 1.681 1.679 1.668 1.680 154.6 84.5 108.0 64.0 69.4 58.0 82.9 76.9
1.767 1.804 1.664 1.659 1.644 1.664 156.5 84.5 107.7 63.1 68.4 57.5 83.6 75.8
a τ is the (dihedral) angle the “top” WH has to be rotated to bring 3 H1 above (eclipsed) to H4. τ is 0° (eclipsed) in the C3V minimum and 60° (staggered) in the C3V-B.
The final transition state found, which had C1 symmetry, appears to be that for “direct” hydrogen scrambling in the C3V-B structure. As depicted in Figure 2, the hydrogen atom labeled H2 is moving from the “top” to the “bottom” of the structure, with atom H6 “replacing” it.
19822 J. Phys. Chem., Vol. 100, No. 51, 1996
Tanpipat and Baker
Figure 3. Schematic of the WH6 potential energy surface showing all four minima and five transition states. The energy ordering is based on ACM relative energies (Table 5) with MP2 values in parentheses. Figure 2. Transition states on the WH6 potential energy surface. The dummy atom X in TS-Cs bisects the W-H5 and W-H6 bonds; it defines the ∠H1WX angle shown in Table 6. TS-C3 shows a top view looking down the C3 axis (see text for more details).
A schematic of the potential energy surface for WH6 in the region of the four minima is shown in Figure 3. All four minima are readily interconvertible, although the C5V-B structure is more difficult to reach than the other three. The C3V structure is the global minimum. At the ACM level the barrier for rearrangement to the C5V structure is 7.6 kcal/mol and to the C3V-B structure 9.5 kcal/mol; the C5V T C5V-B barrier is 16.8 kcal/ mol. The corresponding values at the MP2 level are 6.9, 8.8, and 17.7 kcal/mol, respectively. Barriers for “direct” hydrogen scrambling are higher: 32.8 (26.0) kcal/mol in the C5V structure and 25.4 (17.2) kcal/mol in the C3V-B (ACM with MP2 in parentheses). Thus, scrambling of the hydrogen atoms is more easily accomplished via isomer interconversion than by a singlebarrier pathway that starts and ends at the same isomer. These values are of course only approximate due to the nature of our calculations; additionally, they do not include zero-point effects (which are in fact only minor). The WH6 PES is very rich structurally, and we have not reported here all the second and higher order saddle points that we located during the course of our investigation. Tungsten Hexafluoride, WF6. For our study of WF6 we considered the same structures that were found for WH6. However, only the Oh, D3h, and C5V structures survived to give definite stationary points, with the Oh structure clearly the globalsin fact the onlysminimum (however, see below). The C3V-B, C4V, and C2V structures all collapsed to Oh, the C5V-B structure collapsed to C5V, and the C3V structuresthe global minimum for WH6scollapsed to D3h. Energies and Hessian indices for the three stationary points located on the WF6 potential energy surface are given in Table 7, with relative energies in Table 8 and geometrical parameters in Table 9. We also show calculated vibrational frequencies
for the octahedral (minimum) structure, together with experimental values, in Table 10. As noted above, octahedral WF6 is the global minimum. The C5V structure lies energetically some 50 kcal/mol above the Oh minimum and is a second-order saddle point. At all levels of theory except for MP2 the D3h structure has one imaginary frequency and seems to be the transition state for fluorine scrambling, i.e., for conversion of one Oh structure to another with some of the fluorine atoms switched. The Oh f D3h f Oh conversion can be achieved by a simple rotation about one of the 3-fold axes. The predicted barrier height is around 9.5 kcal/mol. At the MP2 level the D3h structure appears to be a minimum. In the absence of any other supporting data, we regard this prediction as an artifact of the MP2 method. A number of cases are known for which MP2 predicts the existence of spurious minima; e.g., the C2V transition state for the F + HF reaction was found to be a shallow minimum at the MP2 level,28 and we may have a similar situation here. Vibrational frequencies for gas-phase WF6 have observed using IR spectroscopy by McDowell and Asprey.27 These authors also report estimated harmonic frequencies. As can be seen from Table 10, uncorrected frequencies at the HF level are in excellent agreement with McDowell and Asprey’s estimated harmonic values. None of the correlated methods are anywhere near as good, which is somewhat surprising. The very good agreement for the harmonic frequencies is almost certainly related to the fact that the HF W-F bond length is also in excellent agreement with experiment (Table 9). All of the correlated methods predict a W-F bond that is too long; this might be an artifact of the effective core potential. Why should WH6 distort from octahedral symmetry while WF6 does not? Albright and co-workers have outlined the necessary conditions for distortion in octahedral d0 ML6 complexes, the driving force for which derives from secondorder Jahn-Teller stabilization resulting from a mixing of the
Density Functional Calculations on WH6 and WF6
J. Phys. Chem., Vol. 100, No. 51, 1996 19823
TABLE 7: Energies and Hessian Indices of the Various WF6 Structures
a
structure
HF
MP2
SVWN
BLYP
ACM
index
C5V D3h Oh
-663.612 117 -663.686 504 -663.701 633
-665.190 582 -665.257 646 -665.276 859
-662.991 854 -663.054 009 -663.068 200
-666.783 096 -666.845 731 -666.863 100
-666.657 231 -666.721 872 -666.737 028
2 1a 0
Except MP2 where the D3h structure is a minimum.
Summary
TABLE 8: Relative Energies of the Various WF6 Structures (kcal/mol) structure
HF
MP2
SVWN
BLYP
ACM
C5V D3h Oh
56.2 9.5 0.0
54.1 12.1 0.0
47.9 8.9 0.0
50.2 10.9 0.0
50.1 9.5 0.0
TABLE 9: Geometrical Parameters for the Various Structures of Tungsten Hexafluoride (Bond Lengths in Å, Bond Angles in deg; See Figure 1 for Atom Labeling) parameter
HF
rWF1 (r1) rWF2 (r2) ∠F1WF2
BLYP
ACM
1.781 1.872 100.5
Pentagonal Pyramid (C5V) 1.818 1.807 1.838 1.908 1.891 1.926 100.0 100.2 100.2
1.809 1.896 100.3
rWF1 (r1) ∠F3WF6
1.838 78.3
Trigonal Prismatic (D3h) 1.872 1.857 1.889 78.4 78.5 78.4
1.862 78.4
rWF1 (r1)
1.833
Octahedral (Oh) 1.868 1.855 1.886
1.858
a
MP2
SVWN
expta
Acknowledgment. The authors thank Drs. J. T. Golab and M. Green of AMOCO for suggesting this study and for encouragement in its early stages. 1.832
References and Notes
Reference 26.
TABLE 10: Calculated and Experimental Frequencies for Octahedral Tungsten Hexafluoride (cm-1) mode
HF
MP2
SVWN
BLYP
ACM
obsa
harm.a
a1g t1u eg t2g t1u t2u
807 738 695 326 252 118
737 669 625 326 269 153
731 712 663 290 221 112
688 672 621 286 223 114
735 706 658 300 229 115
772 ( 1 713 ( 1 678 ( 1 320 ( 1 252 ( 1 129 ( 2
791 ( 12 733 ( 7 693 ( 8 330 ( 10 253 ( 8 136 ( 13
a
In summary, our DFT calculationsswhich incorporate both relativistic effects and electron correlationsstrongly support previous predictions1,3 that the ground state geometry of WH6 is far from octahedral. Instead, there are four low-lying minima having C3V (2) and C5V (2) symmetry, with one of the C3V structures likely to be the global minimum. Barrier heights for interconversion of the four minima are low, indicating that WH6 is a highly fluxional molecule. In contrast the octahedral structure appears to be the only stable species on the ground state potential energy surface of WF6. The barrier height for scrambling of the fluorine atomssvia a D3h transition statesis around 9.5 kcal/mol, suggesting that WF6 too is highly fluxional at room temperature.
Reference 27.
t1u HOMO and t2g LUMO in these systems.29 The conditions are as follows: (i) For steric reasons, the ligand must not be bulky (distorted geometries are often sterically much more demanding than Oh). (ii) The t2g-t1u energy gap should be small; this situation is favored when the ligands are strong σ donors, possess little or no π-donating capability, and the metal is not too electropositive. (iii) The metal-ligand bond should be covalent. Essentially all of these conditions are satisfied in WH6. In WF6, on the other hand, the W-F bonds are much more ionic due to the highly electronegative fluorine atoms; additionally, fluorine is a weaker σ donor than hydrogen as well as being a mild π donor. All these factors favor the octahedral structure. A rough idea of the charge distribution in WH6 and WF6 is provided by a simple Mulliken population analysis.30 For the octahedral geometry the Mulliken charge on the tungsten atom in WH6 is only +0.3 with a charge of -0.05 on each hydrogen, indicating a highly covalent bond. In contrast, the Mulliken charges in WF6 are +2.88 on tungsten and -0.48 on fluorine, clearly, as expected, much more ionic. Recently attempts have been made to explain the unusual geometries of simple metal hydrides (such as WH6) using concepts from approximate valence bond theory31 and invoking sdn hybridization.32 Such methods apparently predict at least qualitatively the same four minima for WH6 obtained by ab initio computations.32
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