J. Phys. Chem. 1990, 94, 6184-6196
6184
Trans Bendkrg at Double Bonds. Scrutiny of Various Rationales through Valence-Bond Analysis Georges Trinquier* and Jean-Paul Malrieu Laboratoire de Physique Quantique, C.N.R.S.U.R.A.505, UniuersitB Paul Sabatier, 31 062 Toulouse Cedex, France (Received: October 4 , 1989; In Final Form: January 17, 1990)
Trans bending at double bonds, a particular case of nonclassical distortions at multiple bonds, can be accounted for through two kinds of explanations, according to whether one considers a two-electron A bond or a four-electron u + A set. All kinds of explanations are reviewed and confronted to a valence-bond (VB) reading of CASSCF calculations performed on ethylene and its heavier analogues disilene, digermene,. and distannene. As a two-electron problem, the double bond is governed by its neutral and ionic A VB components R2X-XR2, R2X+--XR2, and R2X--+XR2, the trends of which can be deduced from the simple neutral and ionic fragments R3X, R3X+,and R3X-. From silicon to tin, any combination of these species induces a significant pyramidalization at the X center, stronger for the heavier elements. However, in the R2X=XR2 bonded system, a remaining A conjugation opposes this trend whatever X. As a four-electron problem, the double bond is analyzed through an orthogonal valence-bond (OVB) decomposition of a (four-electron, four-orbital) CASSCF wave function, with each carbene part XH2 contributing two electrons and its two orbitals nu and p,. For ethylene and disilene, the VB form n,p,n,p, (a,), corresponding to open-shell configurations at each XH2 parts, is always predominant whatever the bending angle 0. The (a3),corresponding to a singlet closed-shell configuration on both XH2 fragments, becomes increasingly VB determinant n;n; involved along the bending and stabilizes the trans-bent geometries through u-r mixing. For distannene, a crossing occurs between al and a3and, early in the bending, a3becomes the leading configuration. The case of digermene lies in between these two starting descriptions. The evolution of the weights of all the VB forms upon trans bending can be related to overlap factors. The resulting extent of trans bending is ultimately governed by a trend to restore a maximum occupation of the nu orbitals. The heavier the atom, the stronger this aptitude, as reflected by the singlet-triplet splittings in XH2.
Introduction Multiple bonds may be trans-bent distorted in their equilibrium geometries. The simplest examples are the trans-bent structures obtained from theoretical calculations on the heavier parent analogues of ethylene namely disilene,'-" digern~ene,~-' and distannene.8,9 For various substituted derivatives of these molecules, experimental structures are also known which confirm the phen o m e n ~ n . ~ * lVarious * ~ ~ explanations for the trans-bent geometries of double bonds have been proposed. A naive VB-like picture consists of figuring the trans-bent double bond as two interacting singlet carbene-like species.s*1ss16Clearly, a trans arrangement should be preferred for such an interaction since it actually builds two dative bonds, 1. Another efficient explanation makes use
1
2
of one-electron MO schemes where simple u-r mixing should ( I ) Krogh-Jespersen, K. J. Phys. Chem. 1982, 86, 1492. (2) Olbrich, G . Chem. Phys. Lerr. 1986, 130, 115. (3) Somasundran, K.;Amos, R. D.; Handy, N. C. Theor. Chim. Acta 1986, 70. 393; 1987, 72, 69. (4) Teramae, H. J. Am. Chem. SOC.1987, 109, 4140. ( 5 ) Trinquier, G.:Malrieu, J. P.; RiviEre, P. 1. Am. Chem. SOC.1982, 104, 4529. (6) Fjeldberg, T.; Lappert, M. F.; Schilling, B. E. R.; Seip, R.; Thorne, A. J . J . Chem. Soc., Chem. Commun. 1982, 1407. (7) Nagase, S.; Kudo, T. J. Mol. Strucf. (THEOCHEM) 1983, 103, 35. (8) Goldberg, D. E.; Hitchcok, P. B.; Lappert, M. F.; Thomas, K. M.; Thorne, A. J.; Fjeldberg, T.; Haaland, A.; Schilling, B. E. R. J. Chem. Soc., Dalton Trans. 1986, 2387. (9) Trinquier, G . J . Am. Chem. SOC.1990, 112, 2130. (10) Cowley, A. H. Polyhedron 1984, 3, 384. ( 1 1) Cowley, A. H. Acc. Chem. Res. 1984, 17, 386. (12) Raabe, G.; Michl, J. Chem. Rev. 1985, 85, 419. (13) Cowley, A. H.; Norman, N. C. Prog. Inorg. Chem. 1986, 34, 1. (14) West, R. Angew. Chem., Inr. Ed. Engl. 1987, 26, 1201. ( I 5) Davidson, P. J.; Harris, D. H.; Lappert, M. F. J . Chem. Soc.,Dalton Trans. 1976, 2268. (16) Trinquier, G . ; Malrieu, J. P . J. Am. Chem. Sot. 1987, 109, 5303.
0022-3654/90/2094-6 184$02.50/0
-
favor the planar trans-bent d i s t o r t i ~ n . ~Lastly, , ~ ~ even simpler rationalizations exist dealing with just the two A electrons of such a system. If one considers that the two ?r electrons are not strongly coupled (as UHF instabilities observed on disilene would ~ u g g e s t ) ~ then each R2X- part of the double bond may be seen as a radical and its local geometry is expected to be pyramidal, as the silyl, germyl, and stannyl radicals are. Conversely, the nonplanarity of the R2X- parts has been interpreted as being due to the trend of the R2X--group in the ionic resonant valence-bond forms R2X--+XR2 and R2X+--XR2.20 These ionic components are only important if the delocalization is large enough, which is somewhat in conflict with the preceding interpretation which assumes a weak, essentially diradicalar, A bond. One can see that these explanations can be divided into two groups, according to whether the double bond is considered as a four-electron set (a + 7~ bonds) or a two-electron set ( A bond). We would like, in this work, to review and discuss all these interpretations and to study them on more quantitative grounds from VB type considerations. Some time ago the authors proposed a VB-grounded model in which configuration 1 was assumed to be predominant in the trans-bent equilibrium structures whatever the heteroatom X.I6 In such modeling we assumed the existence of a crossing between the singlet-singlet pairing 1 and its triplet-triplet pairing counterpart which would lead to a classical planar (U r) double bond. That paper proved to be efficient in accounting for and predicting distortions although it was not grounded on real numerical valence-bond calculations. The present work reports quantitative orthogonal valence-bond (OVB) results for the bending surfaces in ethylene, disilene, digermene, and distannene (the case of diplumbene, linked to another problem, will be addressed el~ewhere).~ We thus hope to check whether and to what extent the crossing hypothesis is acceptable. More generally, the validity of all the various interpretations will be appraised. Z,18319
+
(17) Albright, T. A.; Burdett, J. K.; Wangbo, M . H. Orbital Interactions in Chemistry; Wiley: New York, 1985; p 166. See also Appendix I of ref 16. (18) Janoschek, B. R. Natunviss. Rundsch. 1984, 37, 486. (19) Horowitz, D. S.; Goddard, W. A. J. Mol. Sfruct. (THEOCHEM), 1988, 163, 207. (20) Pauling. L. Proc. Natl. Acad. Sci. 1983, 80, 3871.
0 1990 American Chemical Society
Trans Bending at Double Bonds
Our method is based on an OVB interpretation of a complete valence active space MCSCF calculation (CASCF) in a quite thorough basis set (double-zeta plus polarization), Le., on the best possible description of the nondynamical electronic correlation (internal to the valence shell). Such analysis is close to those developed by Robb and co-workers in their treatment of chemical reactivity.21.22 It demonstrates that correlation effects may be translated qualitatively in a simple and intuitive manner, provided that a VB language is used rather than invoking symmetry-adapted double excitations which do not have a direct chemical meaning. Among the various works that have contributed to the valencebond renewal over these last some have underlined the danger of using orthogonal VB instead of nonorthogonal VB analyses.25 We are aware of such risks and we might use nonorthogonal equivalent M O s defined from our CASSCF wave function, as it is frequently done in GVB calculations. The OVB procedure, however, has the advantage of avoiding overlap problems since it permits a unique partitioning of a correlated wave function in terms of its VB contributions. The use of a unique variational procedure should confer the required coherence to our comparisons along the group 14 series. The paper will successively consider the two ways of looking at double bonds: ( 1 ) focusing on the two A electrons over an independent well-behaved u skeleton; (2) treating simultaneously, and on an equal footing, the u and A bonds, focusing therefore on the four (u A ) interacting electrons. Within each of these two sections, we will first develop, briefly, the available explanations before examining their relevance in wave function analysis. All details about calculations and geometrical assumptions are given in the Appendix.
+
A Two-Electron Problem: The A Bond Built on a
Framework A. Available Rationalizations. I . Diradical Character. From a criterion grounded on unrestricted Hartree-Fock calculations, the Si=Si double bond has been suggested to be of significantly diradical ~ h a r a c t e r .Actually, ~ disilene H2Si=SiH2 undergoes a Hartree-Fock symmetry-breaking of spin-density-wave type, which is characteristic of a strongly correlated situation, Le., of a weak bond. The so-defined diradical character is, however, small ( ~ 2 % ) .According to this picture, disilene can be seen as two weakly coupled silyl groups, H2Si-SiH2. Bearing in mind that the SiH3 radical is pyramidal,2631 one may understand the trans bending as a result of the intrinsic tendency of the -SiH2 groups to pyramidalize, to the detriment of A bond formation. The preference for trans bending over cis bending would result from ( I ) evident repulsive effects between the SiH2 groups and (2) a larger overlap between the two mono occupied hybrids when they are in a trans conformation, which favors electronic delocalization.'' Within this philosophy, the planarity of ethylene would come from the planarity of the methyl radical. Note, however, that most substituted methyl radicals are actually pyramidal.32 u
(21) McDoual, J. J. W.; Robb, M. A. Chem. Phys. Lett. 1987,132,319. (22)Robb, M. A.; Bernardi, F. In New Theoretical Concepts for Understanding Organic Reactions; BertrBn, J., Csizmadia, 1. G.,Eds.; NATO AS1 Series C, Vol. 267; Kluwer Academic: Dordrecht, 1989;p 101. (23)Epiotis, N. D.Lect. Notes Chem. 1982,29,1. Epiotis, N. D. Lect. Notes Chem. 1983,34, I. Epiotis, N. D. N o w . J . Chim. 1988, 1 1 , 231. Epiotis, N. D. N o w . J . Chim. 1988,1 1 , 257. Epiotis, N. D. Nouo. J . Chim.
1988,I/, 303. (24)Shaik, S.S.In New Theoretical Concepts for Understanding Organic reactions; Bertran, J., Csizmadia, 1. G.,Eds.; NATO AS1 Series C, Vol. 267; Kluwer Academic: Dordrecht, 1989;p 165. (25)Ohanessian, G.;Hiberty, P. C. Chem. Phys. Lett. 1987,137,437. (26)Sakurai, H.;Murakami, M.; Kumada, K. J . Am. Chem. SOC.1969, 91,519. (27)Brook, A. G.;Duff, J. M. J . Am. Chem. SOC.1969,91,2119. (28)Goddard, W. A.; Harding, L. B. Annu. Reu. Phys. Chem. 1978,29, 363. (29)Ellinger, Y.; Pauzat, F.; Barone, V.; Douady, J.; Subra, R. J . Chem. Phws. 1980. 72. 6390. 130) Luke,-B. T.; Pople, J. A.; Krogh-Jespersen, M. 9.; Apeloig, Y.; Chandrasekhar, J.; Schleyer, P. v. R. J . Am. Chem. Soc. 1986,108,260 and references therein. (31)Selmani, A.; Salahub, D. R. Chem. Phys. Leit. 1988,146,465.
The Journal of Physical Chemistry, Vol. 94, No. 16, 1990 6185 The planarity of substituted ethylenes would then be interpreted by the strength of the C=C A bond which, being much larger than that of a Si=Si T bond, would restore the planarity of an intrinsic pyramidal group, say -CMe2.33 An outline of this type of explanation has been illustrated in d i ~ t a n n e n e , ' the ~ , ~pyram~ idalization of SnH3 radical being interpreted in terms of "uconjugation".36 2. Role ofthe Ionic VB Components. The trans bending in distannene H2Sn=SnH2 has also been explained as being due to the role of ionic valence-bond components.20 Since SnH3- is strongly pyramidal, the doubly bonded molecule would retain this pyramidalization as a consequence of its ionic components H2Sn+--SnH2. This interpretation faces some comments: (1) C H c also is pyramidal, whereas ethylene remains planar. (2) The ionic VB components are less and less important when going from ethylene to distannene (see below). (3) The XH2+- group, for its part, would force a planar structure. A satisfactory and entire explanation must therefore take into account the trends of all VB components and their coupling. Let us point out, lastly, that the .explanations through the intrinsic geometrical trends of the H2X- or H2X-- fragments are interrelated to one another. It is expected that the more pronounced the pyramidalization of the radical XH,, the larger that of the anion XHC, and the lesser the resistance to pyramidalization of the cation XH3+. B. Valence-Bond Analyses. Within a A two-electron scheme, the simplest way of taking into account A electronic correlation is to perform a two-configuration MCSCF calculation, which is a two-electron two-orbital complete active space (CAS) MCSCF treatment, regarding the two electrons of the A bond \k =
xao - pa(*+n*)2
Such a procedure will define, within reasonable basis sets, the two best valence orbitals A and A * . Combining them enables one to define a set of two orthogonal atomic-like orbitals, essentially centered on the left and right atoms, respectively:
These localized orbitals are as close as possible to the pz atomic orbitals centered on atoms A and B. They can be used to reexpress the multiconfigurational wave function which, omiting its u part, will be written \k =
XIAiil
- pl**;;sI
(32)(a) Ethyl radical: Dobbs. K. D.; Hehre, W. J. Organometallics 1986, 5, 2057. (b) tert-Butyl radical: Krusic, P. J.; Meakin, P. J. Am. Chem. Soc. 1976,98,230.Lisle, J. 9.; Williams, L. F.; Wood,D. E. J . Am. Chem. SOC. 1976,98,227. Overill, R. E. Mol. Phys. 1980,41, 119. Paddon-Row, M. N.; Houk, K. N. J . Am. Chem. Soc. 1981,103,5046. Bonnazzola, L.; Leray, N.; Roncin, J. R. J . Am. Chem. Soc. 1977,99,8348. Dyke, J.; Jonathan, N.; Lee, E.; Morris, A.; Winter, N. Phys. Scr. 1977, 16, 197. Houle, F. A.; Beauchamp, J. L. J . Am. Chem. Soc. 1979,101,4067.Pacansky, J.; Dupuis, M. J . Chem. Phys. 1978,68,4276;1979,71,2095.Pacansky, J.; Coufal, H. J . Chem. Phys. 1980,72,5285.Yoshimine, M.; Pacansky, J. J. Chem. Phys. 1981,74,5468. Percival, P. W.;Brodovitch, J. C.; b u n g , S.K.; Yu, D.; Kiefl, R. F.; Luke, G. M.; Venkateswaran, K. Chem. Phys. 1988, 127, 137. (c) Other radicals: Krusic, P. J.; Bingham, R. C. J . Am. Chem. SOC.1976,98, 230. (33)Quite in this spirit, the nonplanarity of the silyl radical and of the fluorine-substituted methyl radicals were suggested to be responsible for strains in planar silaethylene and tetrafluoroethylene, which should induce their reduced *-bond energy and enhanced reactivity." (34)(a) Bernett, W.A. J . Org. Chem. 1969,34,1772. (b) Cherry, W.; Epiotis, N.; Borden, W. T. Ace. Chem. Res. 1977,I O , 167. (35)Dewar, M. J. S.; Grady, G.L.; Kuhn, D. R.; Men, K. M. J . Am. Chem. SOC.1984,106,6773. (36)Dewar, M. J. S. J. Am. Chem. SOC.1984, 106,669.
6186 The Journal of Physical Chemistry, Vol. 94, No. 16, 1990
Trinquier and Malrieu
Defining two neutral and ionic orthogonal valence-bond determinants as 1 PAP^- + p e g )
@N
=
@I
= %(PAPA
2
1
-
+ PBZ)
40
-
30
-c
IO
-
and defining the CI coefficients a and p such as 1 a = -(A
2’12
+ p)
1
P=5 0- F ) leads to a final expression of \k as \k = a@N+ pa, The quantities a2and p2 define the weights of the neutral and ionic orthogonal valence-bond (OVB) components. As long as the molecule is planar, the pA and pB orbitals are pz-type atomic orbitals centered on atoms A and B, respectively. When the system distorts, the pA and pB orbitals take some s component and become sxpY hybrids with more and more s component as the bending occurs, 3. In that case, the “x” system
3
no longer involves pure ptype orbitals but two hybrids, orthogonal to the u skeleton, so that the x reasoning applies to these hybrid orbitals as well. Notice that as long as the pyramidalization does not exceed 6 N 5 4 O (which is beyond our equilibrium geometries), these orbitals are in between p and sp3 hybrids and keep therefore a strong p character. The evolutions of the weights a2and p2 upon bending have been calculated within DZd basis sets for the various X=X bonds of group 14. The corresponding curves are drawn in Figure 1 (for details on geometries and calculations, see the Appendix). The neutral character of the T bond becomes somewhat larger when it involves heavier elements. On the other hand, the pyramidalization increases, to a small extent, this neutral character. Both remarks might seem to question the interpretation of the trans bending in terms of a supposedly predominant role of the ionic VB structures.20 In order to check the validity of these interpretations in terms of intrinsic trends of the -XH2 and -XHC fragments, a three-step procedure will be followed: ( I ) We will first examine the pyramidalization of isolated XH3 groups in their various ionicities XH,, XH3+, and XH,-. (2) We will then calculate an average potential V(6) from the pyramidalization potential curves of these isolated fragments weighted according to various neutral/ionic character ratios (including the one obtained from the CAS-SCF calculation with the x-active space):
(3) It will be examined, last, how well this sum fits with the calculated trans-bending potential for the bound H2X=XH2 molecule. The potential curves for the XH3 species are calculated at the S C F level, keeping constant the X-H distances along pyramidalization. Despite these constraints, the pyramidalization angles for the radicals and anions are reasonable, as can be seen in Table 111 of the Appendix. The methyl radical is found to be planar while the silyl, germyl, and stannyl radicals are found to be pyramidal. The corresponding energy variations upon pyramidal-
0
0
40
20
60
80
8 (deg) Figure 1. % ’ weights of the ionic V B forms upon pyramidalization, as obtained from two-configuration MCSCF calculations (*-active space CASSCF) on ethylene and its heavier analogues. The arrows indicate equilibrium bending for disilene, digermene, and distannene from left to right.
ization of these radicals are plotted in the lower curves, labeled r, of Figures 2-5 for CH, to SnH,, respectively. In these figures, two XH, species are summed for our purpose, and the curves r represent the potential obtained from relation 1 when a = 1 (a2 = 100%). Note also in these figures that the pyrmidalization angle 6 for XH3 is defined according to the familiar definition used for H2X=XH2, 4. This angle is related to the HXH valence angles
4
a in C3,XH, XH or the pseudo C3,part of H2X=XH2, through the relation cos a COS 6 = cos ( a / 2 )
As expected from simple VSEPR arguments, the cations XH3+ are always largely destabilized by the pyramidalization while the anions XH3- are always largely stabilized by the pyramidalization. What is less obvious is the variation of the sum VXH + + VXH,under the bending. As mentioned, this is the key !or testing Pauling’s interpretation.20 These sums, Le., V(6) of relation 1 with p = 1 (p2 = loo%), are plotted in the upper curves, labeled i, of Figures 2-5 for CH3 to SnH,, respectively. Only for CH3 pyramidalization destabilizes the cation more than it stabilizes the anion, so that curve i of Figure 2 exhibits no minimum. For the other groups SiH,, GeH,, and SnH,, the stabilization brought by the pyramidalization of the anion overcompensates the de-
The Journal of Physical Chemistry, Vol. 94, No. 16, 1990 6187
Trans Bending at Double Bonds
I
40
H,Si=SiH2
20
30
10
-E
-
:
20
1 m
1m
Y
Y
-
0
W
a
0
W
a
10
-10
0
20
40
60
80
0
20
40
e
8(deg)
Figure 2. Energy curves upon pyramidalization of two isolated CH3 groups. r, radicals; i, anion + cation; ri. sum of r and i, properly weighted. These three curves correspond to potential (1) with a2= 100% (r), f12 = 100% (i), and a2/f12 = 70/30(ri). The curve labeled mc figures the actual energy variation upon trans pyramidalization of the CH2 groups in H2C=CH2. The shaded area pictures the n-delocalization
effects.
60
80
weg)
Figure 3. Energy curves upon pyramidalization of two isolated SiHl groups. r, radicals; i, anion cation: ri, sum of r and i, properly weighted. These three curves correspond to potential (1) with a2= 100% (r), f12 = 100% (i), and a2/P2= 80/20 (ri). The curve labeled mc figures the actual energy variation upon trans pyramidalization of the SiH2 groups in H2Si=SiH2. The shaded area pictures the *-delocalization
+
effects.
stabilization brought by that of the cation, so that curves i of Figures 3, 4,and 5 do exhibit a minimum along the pyramidalization. Note that these minima (V(O), = 100%) are less deep than those of curves r (V(O), a2 = 100%). The explanation of the trans bending in H2X=XH2 through geometrical preferences of the ionic forms20 happens to work in spite of the unjustified restriction of the wave function to its ionic components. Since both curves r and i in Figures 3-5 exhibit a minimum for some pyramidalization angle, the explanations through the intrinsic trends of radicals (a2= 100%) or ionic contributions (02= 100%) are in fact closely related. In this respect, carbon can be seen as the only exception in group 14, with a planar preference for both the methyl radical and the sum of methyl cation plus methyl anion. Going a step further would combine a 50/50 partitioning in relation 1 (a= 4 = 1/42). This would mimic a 17-SCF treatment which gives equal importance to the neutral and ionic forms. The corresponding potential curves would be exactly halfway between curves r and i in Figures 2-5. Such a 50/50 partitioning is, however, unrealistic and a step further is to weight V(8) according to more reasonable values of a2and 02,such as those obtained from the *-active space MCSCF calculation. Near the equilibrium bending, such treatment gives ionic weights of p2 N 30% in H2CH=CH2, o2 20% in H2Si=SiH2 and H2Ge=GeH2, and o2 N 18% in H2Sn=SnH2. The so-weighted V(8)curves are plotted in Figures 2-5 as the second curves from the bottom, labeled ri. Since in all cases neutral VB character prevails, these curves are closer to the bottom radical curves r than to the ionic curves i. So far, these energy variations are computed as weighted sums of the energy variations of two separate XH3 fragments. We now come to the comparison between the curves ri and the actual *-active space MCSCF calculations on the real H2X=XH2 molecules in which the X-X link allows delocalization of the “an electrons on the two centers. These curves are drawn and labeled
o2
MC in Figures 2-5. For ethylene, as expected from the large “T” interaction, the MC curve rises steeply and is always above all the other potential curves. In the three other cases, the ?r MC curve is always above the ri curve. This means that pyramidalization at X in H2X=XH2 is always less than what could be expected from the proper combination of the trends of the radicals, cations, and anions of two isolated XH, fragments. This difference, pictured by the shading in Figures 2-5, originates in the “p,-p,” conjugation. This effect is expected to be very large in ethylene, quite significant for disilene, and smaller for digermene and distannene. The loss of A delocalization energy under trans bending is measured by the shaded areas in the figures. The pyramidalization induced by the geometrical trends of the corresponding radical and ions of the XR, group is therefore partly counterbalanced in R2X=XR2 by the loss of conjugation occurring between the singly occupied sxpY hybrids of the pseudo-?r system. This conjugation is less and less strong when these hybrids are borne by silicon, germanium, or tin atoms, respectively. The structure results from two opposing forces: the *-bond delocalization which prefers planarity but becomes less and less efficient when the atoms become heavier, and the intrinsic trends of the -XR2 fragments to pyramidalize which increases for heavy elements. The model might be further formalized by adding to eq 1 a term corresponding to the loss of conjugation energy which is a function of O and is proportional to the strengths of the 17 bond. Such improvement would be pertinent for the study of the behavior of group 14 heteropolar double bonds. Lastly, note that the success of the model proposed in ref 20 in terms of ionic structures is partly due to a lucky cancellation between two neglects: ( I ) the role of the neutral VB structures, which would increase pyramidalization, and (2) the coupling between neutral and ionic components (Le., the electron delocalization in the T bond) which favors planarity.
Trinquier and Malrieu
6188 The Journal of Physical Chemistry, Vol. 94, No. 16, 1990 H&e=GeH,
H$n=SnH,
20
10
-E"
1 s
Y
o
v
w
4
-10
r -20
I 0
20
0
60
40
40
60
l 3
e (deg)
e (deg) Figure 4. Energy curves upon pyramidalization of two isolated GeH, groups. r, radicals; i, anion + cation; ri, sum of r and i, properly weighted. These three curves correspond to potential (1) with a* = 100% (r), = 100% (i), and a2/B2= 80/20 (ri). The curve labeled mc figures the actual energy variation upon trans pyramidalization of the GeH2 groups in H2Ge=GeH2.The shaded area pictures the r-delocalization effects.
A Four-Electron Problem: The Double Bond as Two Interacting Carbenic Fragments A . Available Rationalizations. 1. Avoided Crossing between Two Leading VB Configurations. While CH2 has a triplet nspr ground state, stabler than the singlet n: state by 9 k~al/mol,~' the heavier analogues have a singlet ground state with a singlet-triplet separation ( U s T ) of 18-20 kcal/mol for SiH2,38and 22-24 kcal/mol for GeH239and SnH2.@ A classical planar u + s double bond is built from triplet carbenes, 5. Carter and
5
20
I
6
Goddard have pointed out that the bond strengths of planar double bonds built from singlet carbenes might be rationalized easily by considering that these carbenes have to be promoted first to their excited triplet states.4' (37) (a) Shavitt, 1. Tetrahedron 1985, 41, 1531. (b) Schaefer 111, H.F. Science 1986, 231, 1100. (c) Bunker, P. R.; Jensen, P.; Kraemer, W. P.; Beardsworth, R. J . Chem. Phys. 1986, 85, 3724. (d) Bauschlicher, C. W.; Taylor, P. R. J . Chem. Phys. 1986.85.6510. (38) (a) Gordon, M. S. Chem. Phys. Lett. 1985, 114, 348. (b) Selmani, A.; Salahub, D. R.J . Chem. Phys. 1988.89, 1529. (c) Balasubramanian, K.; McLean, A. D. J . Chem. Phys. 1986.85, 51 17. (39) (a) Philips, R. A.; Buenker, R. J.; Beardsworth, R.; Bunker, P. R.; Jensen, P.; Kraemer, W. P. Chem. Phys. Lett. 1985, 118.60. (b) Pettersson, L. G. M.; Siegbahn, P. E. M. Chem. Phys. 1986, 105, 355. (40) (a) Balasubramanian, K. Chem. Phys. Lett. 1986, 127. 585. (b) Balasubramanian, K . J . Chem. Phys. 1988, 89, 5731.
Figure 5. Energy curves upon pyramidalization of two isolated SnH, groups. r, radicals; i, anion cation; ri, sum of r and i, properly weighted. These three curves correspond to potential (1) with a2= 100% (r), p2 = 100%(i), and = 82/18 (ri). The curve labeled mc figures the actual energy variation upon trans pyramidalization of the SnH, groups in H,Sn=SnH2. The shaded area pictures the r-delocalization effects.
+
Following the same idea, we suggested elsewherei6 that the trans-bent double bonds might be considered as being built from the interaction of two singlet carbenoids XR2, the delocalization taking place from the nu lone pairs of a XR2 group toward the empty pr orbital of its partner, 6. In the trans-bent structure, the nuA2nug2valence-bond component is assumed to be predominant, with delocalization tails leading to ionic configurations of the type nuAnaB2P*B. A simple modelization of that type of interaction enabled us to propose a rule of occurrence of the distortion: the trans-bent structure would prevail when the following inequality is satisfied
where CAEsTis the sum of the singlet-triplet splittings of the two XR2 fragments, and E,+, is the X=X bond energy (e.g., 172-179 kcal/mol for C=€$2 70-80 kcal/mol for Si=Si$3 60-65 kcal/mol for Ge=Ge or S ~ = S I I ...). ,~~ A crucial point in that approach is the assumption of an avoided crossing between the nuA2nuB2VB configuration built from singlet carbenoids and the naAPrAnuAP,B triplet pairing embodied in the U ~ T : configuration of the normal double-bond structure. In other words, the n,A2n,B2 VB form was assumed to be dominant in the trans-bent conformation. To obtain inequality (3), we had to further assume that the two singlet carbenoids might be brought to the equilibrium distance re in a 90°-bent conformation without significant repulsion, the pr orbitals remaining empty. On the other hand, the trans-wagging angle 0 was expected to remain around 4 5 O , while this angle actually takes different values in the experimentally known or accurately calculated trans-bent structures. Finally, the model did not rule out the possibility of double (41) Carter, E. A,; Goddard, W. A. J . Phys. Chem. 1986, 90, 998. (42) Carter, E. A.; Goddard, W. A. J . Am. Chem. SOC.1988, 110,4077. (43) Kutzelnigg, W. Angew. Chem., In?.Ed. Engl. 1984, 23, 272.
The Journal of Physical Chemistry, Vol. 94, No. 16, 1990 6189
Trans Bending at Double Bonds minima, one planar and one trans bent. Actually, all calculations have shown, up to now, that, as soon as the real minimum is trans-bent the planar structure is only a saddle point and not a secondary minimum on the potential energy surface. Conversely no trans-bent secondary minimum has ever been identified when the planar structure is found to be a real minimum. In spite of all these rather crude hypotheses, the model happens to work for all the current nonconjugated double bonds.I6 2. Molecular Orbital u-A Mixing. An extended Huckel calculation is able to predict the trans-bent geometry of digermene, despite its elementary physical content. Such methods mainly include two elements: (1) the orbital energies (and therefore the nu - pI energy differences in XR,); (2) the electronic delocalization, essentially ruled by overlap factors. The interpretation goes through the u-A mixing permitted by the trans The A molecular orbital mixes with a low-lying u* orbital. The larger the difference between the energies of nu an p, in XR2, the closer the T and u* MO’s, as has been shown analytically in a simplified treatment.44 The trans-bent distortion weakens the bonds = n,A
A
= PIA + PIE
+
lu)(ul
+ lu*)(u*l+
IA)(*I
+
I?r*)(A*l
is applied on the fragment orbitals (noted nl, n2, pl, and p2 starting from now, for clarity):
In’, ) = Pinl) 111’2)
determinants
confian eracv nature 6‘
neutral
2
neutral
1
neutral
1
neutral
4
ionic
4
ionic
2
diionic
4
neutral
4
neutral
4
ionic
4
ionic
+ nuE
d
built from the fragments orbitals, but the A-u* mixing, acting as a perturbation, stabilizes the energy of the T bond. Simple trigonometric dependence of these two factors led again to condition (3) and to a measure of the extent of pyramidalization through estimates of wagging angle, inversion barrier, and force constants as a function of the two parameters X U s Tand The agreement of these quantities with experiment is only qualitative but it is satisfactory, if one remembers the uncertainties regarding the two imput parameters AESTand E,+,. This predictive ability may seem to favor the u-A mixing scheme over the avoided crossing model but we will see now, through the quantitative orthogonal valence-bond analysis which follows, that both schemes are closely related. B. Valence-Bond Analysis. I . Procedure. The four electrons of the u A double bond roughly occupy the same region of space. They need therefore to be correlated. A consistent and simple way to do so is to perform a four-electron four-orbital complete-active-space MCSCF calculation (CAS-SCF), as proposed by Ruedenberg 10 years ago.4S From the four-orbital set u,u*.A,A* it is easy to build the 11 determinants which will be involved in the multiconfigurational CAS-SCF wavefunction. Such calculations, performed within DZd basis sets, provide quite satisfactory results regarding the potential curves for the bending (see the Appendix for details on the calculation). To perform a local VB-like reading of that part of the wave function, we shall project the nu and pI orbitals of the isolated fragments A and B onto the subspace of the four active MO’s u,u*,A,x*. For doing so, a projector P on these active orbitals, defined as P=
TABLE I: The 11 Classes of Determinants Defining the Four-Electron Valence-Bond Description of the Double Bond degen- VB states of
= Plnd
IP’l) = PIPI) IP’2) = PlP2) These projections are then symmetrically orthogonalized through the S-’l2procedure, leading to an orthonormal set: In”l,n”2,~”l,p”21= S-1/21n’l,n’2,p’l,p’2) (44) Malrieu, J. P.; Trinquier, G. J . Am. Chem. Soc. 1989, 111, 5916. (45) Cheung, L. M.; Sundberg, K. R.; Ruedenberg, K. J . Am. Chem. Soc. 1978, 100, 8024.
the fragments
‘The six determinants belong to three different categories; see 7,8, 9.
These new orbitals span the same active space but keep a local character. This is why, in the following, we shall delete the double prime index and label them n and p despite their tail on the neighbor group. Notice that when the trans bending takes place, they will follow the orientation of the XH2 groups which bear them, as would do the strictly localized atomic or fragment n and p orbitals. The CAS-SCF wave function \k may then be rewritten as a linear combination \k = XCiOi of determinants Oi corresponding to all possible electron distributions of the four electrons in these four projected orbitals n,, n2, p,, and p2. These determinants can be gathered into 11 types which are listed in Table I. The seven first ones, OIto 07,have nonzero coefficients in the wave function of the planar conformation. O8- O,,,on the other hand, involve an odd number of A electrons. They cannot contribute to the wave function for a planar arrangement but they will be responsible for the u-A mixing since they have either one or three electrons in the n orbitals or in the p orbitals. Among the seven first types, CP, and O4 must be considered separately since they involve four n or four p electrons, respectively. Their contribution to the planar form wave function is zero in the S C F description which is by definition n2p2(Le., u2& It remains small in the CAS-SCF wave function since they only appear through the double excitations ( A u * ) and ~ (u A * ) which ~ are of weak importance. With these tools in hand, let us start with a look at the valence-bond content of the wave function in the planar form. 2. The Planar Double Bond. The weights of determinants Oi in the wave function of planar ethylene, disilene, digermene, and distannene are listed in Table 11. The largest weight is brought of space part nlp,n2p2,with one by the neutral determinants 01,
-
-
Trinquier and Malrieu
6190 The Journal of Physical Chemistry, Vol. 94, No. 16, 1990
1
TABLE 11: Weights (76) of the VB Determinants for the Planar 0.8
t
0.4
-
Form of Ethylene and Its Heavier A~logues
SCF'
C,H,
Si2HI
Ge2H1
Sn2H4
21 17 0.1
24 18 0.5
25
26
18
18
0.6
0.9
38 II 0.02 0.01 29
42
+7
12.5 12.5 0 25 12.5 0 0 25 25 12.5
0.2 0.02 30 15 3
43 10 0.2 0.02 29 15 3
45 IO 0.5 0.02 29 14 2
x(neutra1) x(ionic)
37.5 62.5
49
52 48
53 47
55 45
91, 91s +IC
91
a2
93 94 95 @6
18
4 51
IO
S
'This V B decomposition of an uncorrelated wave function is common to the four planar olefins. electron per orbital. These are divided into three types according to their spin distribution. The determinants ai,,7, engage one
7
8
-
-0.4
-
9
pair of ab electrons in both the u and u bonds with each atom bearing two electrons of the same spin, thus satisfying Hund's rule (each fragment being in a 3B1state). They have the largest contribution. Determinants 8, also permit electronic delocalization between the carbenes along both the u and a bonds, but they no longer satisfy atomic Hund's rule and have therefore a somewhat smaller contribution to the correlated wave function. Finally, determinants 9, in which the two electrons of both bonds are of the same spin, do not permit any delocalization at all in the planar geometry. They have therefore no component in the classical u2a2single determinantal description and remain of negligible contribution after CI. Another important neutral configuration in the planar geometry ), each fragment bears two electrons in the is a2( I I , ~ ~ ,in~ which same n or p orbital. By adding the weights of CPI and @2 one finally obtains a weight around 50% for the neutral forms (see Table 11), while the corresponding weights in a S C F noncorrelated wave function would be only 37.5% for all compounds, by definition. A u-only correlated wave function, on the other hand, yields a reduced weight of the neutral forms (see above). Comparing these numbers shows the tendency of electronic correlation-especially the correlation between the cr and a electrons-to restore the mean neutrality of the fragments or, in other words, to diminish the fluctuation of the number of electrons they bear. This is why the weights of the ionic forms are reduced. Because the u bond is stronger (Le., more delocalized) than the a bond, a, (n12plp2),which implies a u charge transfer, has a larger weight than 0 6 (nlp12n2)which implies a ?r charge transfer. Both had the same weight, 25%, in the SCF wavefunction. Regarding the difference along the series from carbon to tin, the double bond appears to be more and more neutral, which reflects a lesser delocalization between the fragments. Notice from the evolution of @6 in Table 11 that the delocalization becomes weaker and weaker in the x bond. As expected, the electronic correlation reduces the weights of doubly ionic configurations a, from 12.5% in the SCF wave function to 3-4% in the CAS-SCF one. Note that the configuwhich has four electrons in the u bonds and which is ration 03, brought about by the (u u * ) double ~ excitation, has a very small weight in the planar geometry, while it is expected to play a large part in the nonplanar deformation, as is discussed next. 3. Effect of Trans Bending on the Wave Function. The evolution of the weights of the 1 1 VB configurations under bending, as they will appear in the next figures, may look terribly complex,
-
-0.2
0
30
60
90
Figure 6. Overlap upon trans bending for the n, and p1 orbitals of two methylenes in the geometry of ethylene.
with opposite and nonuniform behaviors. We claim, however, that if one traces the leading physical effects, these variations may be rationalized quite simply. This is the object of the following development. The electronic delocalization between the two XH2 fragments is expected to follow approximately the evolution of the overlap between the nonorthogonal fragment orbitals n l and pI with nz and p2. In Figure 6, these overlaps are plotted upon trans bending for two CH, fragments in the geometry of ethylene, with the n, orbitals being defined close to sp2 hybrids (see the Appendix for details). The overlap S,, = (nlln2) between the n, hybrids decreases and changes its sign for % = 75'. A similar evolution is obtained for the overlap S, = ( pIIp2)between the two pr atomic orbitals, with the change of sign occurring for a smaller bending angle % N 45'. Lastly, the overlap S,, = (n,lpz) = -(n21p,) between the n and p orbitals increases from zero to a maximum value near 6 = 55'. Of course, the exact position of the zero and maxima of the overlaps S,, and S,, depend on the nature of the n hybrid and may therefore vary with the XH, fragments. However, the intensities of any n n, p p, n p, and p n charge transfers are expected to roughly follow the trends of the corresponding overlap given in this figure. When the trans bending takes place, the configurations aito @, will have modified contributions and the configurations a8to previously absent, will now play their part. The evolution of the relative weights for ethylene, disilene, digermene, and distannene are given in Figures 7-10, respectively. For clarity we have split the determinants into two sets according to whether they involve neutral or ionic forms. Except for distannene which appears as an exception and will require a special interpretation, the neutral determinants remain the most important ones, despite some oscillations. A deeper examination of the coefficients of 91A-@,c enables one to understand these amplitude variations. In alA,delocalization remains possible from both the n and p orbitals of an XH2 group to the n and p orbitals of its partner delocalization from nl can only take place whatever %,lo. In toward nz and not pz for spin prohibition reasons;similarly, electron transfer from p, can only occur toward p2 and not n2, 11.
- - -
-
Thre Journal of Physical Chemistry, Vol. 94, No. 16, 1990 6191
Trans Bending at Double Bonds
10
12
11
Therefore, the weight of this configuration will decrease drastically in the region 6' N 60° where both (nlln2) and (pllp2) overlaps become small. Actually, the weights of alBfollow this trends as can be seen from the differences between the aIAand alA+ 0,s curves in Figures 7-10. On the contrary in 0 ,which ~ had a negligible weight at 0 =,'O electron delocalization may take place from n, to p2 and n2 to p, as soon as the geometry is bent, 12. The weights of this configuration go through a maximum amplitude for 6' N 60'. Here also for clarity we did not plot aIc in Figures 7-10 but this curve can be deduced from the and curves. Except for tin, the configuration may therefore be considered as the leading one, whatever be the value of 6'. Assuming a generative role for the a,, set, which are the two basic spin-paired configurations used as starting point in a H a r t r e F o c k determinant, it becomes possible to rationalize the 6'-dependence of the other configurations. alAand aIB, acting as a first generation, will generate all the other configurations by successive charge transfer n n, p p, n p, or p n, each having a &dependent amplitude. Figure 11 summarizes such a genealogy. The second generation includes ionic determinants resulting from single-electron jumps from a,, and alp a5and 0 6 are generated by n n and p p charge transfers, respectively. a5has the larger amplitude and presents a minimum around 70' where S,, = 0 while Osbecomes zero at 6' N 50' where Sp,N 0 (see Figure 7). Ol0 and allresult from GI, by p n and n p charge transfers, respectively. They start from a zero contribution at 6' = 0' to reach a maximum amplitude around 6' N 60' where these charge transfers have larger amplitudes since S,, is maximum. Starting from these ionic configurations, a new single charge transfer leads to a third generation of neutral determinants whose weights will be weaker. a2is obtained from asand a6 by n n and p p transfers. Its amplitude decreases from 0 = ,'O exhibiting two minima corresponding to the nullity of the S,,S,, product. as(resp. a9)is obtained from as,a69 and al0(resp. all).It is clear from the genealogic tree that their coefficient should behave as (S,,, + S,,) S,, and therefore cancel for both 6' = 0' and 0 = 60°,as occurs. a3and result from al0and allby p n and n p electron jumps, respectively, so that their amplitude is governed by the factor S,:. The neutral configuration ale, which for clarity reasons only appears in Figures 7-10 as the difference between and aIA aIB, is obtained from al0 and allthrough n p and p n charge transfers. Its weight along the bending hence varies as S!:, as already discussed. The doubly ionic configuration a 7 , omitted for clarity in Figure 11, would belong to that generation and is reached from any of the singly ionic configurations of generation 2. Its weight depends on the products S,,S, S,: and is almost constant as can be seen in the corresponjing figures. Since @ ] A and alB are the leading neutral components of the classical u + A double bond description, their maintained leading role under the trans bending of ethylene and disilene supports the idea that trans bending simply adds u--P mixing to the classical double bond and excludes the avoided-crossing scheme. This genealogy rationalizes the complex behavior of the amplitudes of the various configurations of the MCSCF wave function and it is quite encouraging to see that such a rather complex ab initio wave function may be qualitatively understood in terms of overlap between orbitals and energy differences. The general picture is the same for disilene as for ethylene, with one dramatic difference only: while the n p and p n charge transfers were equally probable in C2H4, which results in analogous amplitudes for the two determinants of the couples (a3,a4), (@*,a9), and ( @ l o , @ l l ) , see Figure 7, the n p charge transfers have lesser amplitude than the p n ones in disilene. This is due to the large energy difference between the n, and pI orbitals in SiH2 and is
+
+
- - - - -
-
-
-
- - -+ +
- - -
therefore linked to its singlet-triplet separation. As a consequence, ala, which has an n3p occupation, will become much more important than allwhich has a np3 occupation. Similarly, in the next generation, aswill have a larger amplitude than a9since these determinants involve n3p and np3 space parts, respectively. The contrast is even more pronounced between 03(n4) and a4(p4) which had similar amplitudes in ethylene (compare Figures 7 and 8). Let us now consider the case of distannene. A striking feature in Figure 10 is the vanishing of and the rise of a3,resulting in a crossing near 0 i= 60'. Even before, near 6' N 50°, which is close to the calculated equilibrium bending, the weight of alA alBbecomes smaller than that of a3. Quite obviously, the genealogy proposed in Figure 11 no longer holds. Due to the leading role of a3(what was also assumed in the avoided-crossing model)I6 an alternative genealogy may be proposed, taking a3as the first generation (Figure 12). The second generation is obtained from through n p transfers and involves only ionic determinants of type ala, which have a large component in the wave function (see Figure 10). The third generation involve aIA, ale, and as,and two other generations are needed to include all determinants. This analysis supports the idea that for distannene the avoided crossing model of ref 16 is more relevant than the U--P mixing scheme. Digermene appears as an intermediate case since a3becomes of larger importance than aIA+ alBin some part of the curve (0 = 60'-80') which is beyond the equilibrium structure. The discussion about the relevance of u-A mixing versus the avoided crossing interpretations may be pushed further from energy considerations. In the UT mixing model, the zeroth-order p and n n description is the u A double bond with p delocalization effects. It may be concentrated in a linear combination of neutral a,,, aIB and ionic O5 and a6:
+
-
-
+
-
+ @ @ , B + 705 + 6 @ 6 (4) In the avoided crossing model, one starts from aP3 and considers \k,zpz
=
aa1A
-
the n p delocalizations in the zeroth-order description, based therefore on a3and al0only: \k,4
=
+ palo
&'a3
(5)
The energies resulting from these orthogonal multiconfigurational wave functions, and obtained through partial diagonalizations, are plotted for disilene and distannene in Figure 13, which also includes the full CASSCF energies. These curves confirm that a crossing does occur between the two zeroth-order states. When going from silicon to tin, the energy gap between \kn2,z and \k,l is reduced at the origin (0 = 0') and the crossing occurs for a smaller bending angle. Whereas the equilibrium takes place before the crossing in disilene, it occurs clearly beyond the crossing in distannene. Again, this contrast supports the idea that for disilene the u-A mixing stabilizes a classical double bond while for distannene this model breaks down in favor of a qualitative change of the wave function, now dominated by the singlet carbenoids. So far the two qualitative models have been rather opposed but there is a way to formulate the observed trends in a less contrasted fashion. Since the trans bending is linked to an increasing tendency to occupy the n orbitals to the detriment of the p ones, one can attempt to group the determinants according to their n/p occupation. To summarize this, we have gathered them into three groups: ( I ) those having a n2p2occupation (2) the configurations having three or four electrons is n, and therefore one or zero electrons in p:
(3) the configurations having three or four electrons in p, and therefore one or zero electrons in n: p3'4 = {*4?*9,*1II
6192 The Journal of Physical Chemistry, Vol. 94, No. 16, 1990
Trinquier and Malrieu
50
40
30 ap
ECD .-
t
m
>
20
‘.
0
.I--.
30
90
60
Figure 7. Trans bending in ethylene. Weights of the VB determinants in the CASSCF wave function. Left: neutral determinants. Right: ionic determinants. The determinants are defined in Table I.
=O
j
\ - 0
90
60
e
e
dog
deg
Figure 8. Trans bending in disilene. Weights of the V B determinants in the CASSCF wave function. Left: neutral determinants. Right: ionic determinants. The determinants are defined in Table I.
The weights of these three subsets of determinants under trans bending are plotted in Figures 14. The bending always reduces the n2p2occupation probability. While in ethylene the n p and p n transfer processes are equally probable, the latter prevails more and more for heavier elements, illustrating the tendency to
-
-
restore a n2 occupation in XH2-in other words to preserve the singlet ground state in XH2-as far as this remains compatible with the electronic delocalization which cements the X=X bond. See in Figure 14 how the n3tl weights increase while the p334weights decrease along the series from H2C=CH2 to H2Sn=SnH2. See
Trans Bending at Double Bonds
"he Journal of Physical Chemistry, Vol. 94, No. 16, 1990 6193
50
40
$10
30 a9
E
.-m
t
m 5
20
,.
10
0
0
30
\
&.
e
'.
60
90
deg
Figure 9. Trans bending in digermene. Weights of the VB determinants in the CASSCF wave function. Left: neutral determinants. Right: ionic determinants. The determinants are defined in Table I.
-
ap c m
.-
t
m
>
Figure 10. Trans bending in distannene. Weights of the VB determinants in the CASSCF wave function. Left: neutral determinants. Right: ionic determinants. The determinants are defined in Table I.
also the neat change of rule from digermene to distannene. The role of the n2n2 configuration a3on the trans-bending phenomenon may be evaluated simply by removing it from the list of determinants in the C1. The resulting potential curves are plotted on the left part of Figure 15, the right part of which reports the full MCSCF curves. Trans bending would occur even without
a3,but its extent and stabilization energy would be grossly underestimated, especially for tin. Conclusion The present quantitative valence-bond analyses made it possible to illustrate how fragments tend to preserve their idiosyncrasies.
The Journal of Physical Chemistry, Vol. 94, No. 16, 1990
6194
2nd generation
(ionic)
Figure 1 1 . Generation of the VB configurations from
1st generation
alaand aIB.
9
(neutral)
Inp
2nd
generation
(ionic)
3rd
generation
(neutral)
4th
generation
(ionic)
5 t h generation
Trinquier and Malrieu
(neutral )
Figure 12. Generation of the VB configurations from 9,. 9 2
H,Sn=SnH,
H,SI =SiH,
insufficient to prevent pyramidalization in weaker bonds built from heavier elements. The u + A fragments XR2 which compose the u A double bond RzX: :XR2 also tend to preserve one of their major characteristics: their singlet ground state when X = Si, Ge, or Sn. To do so, they will tend to choose a trans-bent arrangement which largely favors the corresponding singlet n: configurations by minimizing the pair-pair repulsion while authorizing n: p/ electronic delocalization between the partners.& This propensity is counteracted by the normal intrabond delocalization effects between the two XR2 fragments which in turn favors the nap, configurations on each fragment (or n2p2global occupation for the whole system) and a planar arrangement. In other words, the u + A delocalization effects oppose the tendency of the XR2 fragments to keep their singlet ground states and consequently a trans-bent arrangement. For the four-electron analysis of the double bond, two limiting models may be considered. In the first one, the pairing of two n,p, open-shell XR, fragments remains predominant even for significant bending. The involvement of :n configurations in the VB function is made possible through u-A mixing and leads to a stabilization of the trans-bent geometries. The second model assumes a crossing between two dominant VB configurations along the trans-bending coordinate. Beyond a certain value of the trans-wagging angle 0, the wave function generated from the pairing of singlet configurations 11,231: (aP3) becomes of lower energy than that generated from the pairing of open-shell con-
+
-9 4
-
-9 6
9 8 0
30
60
1) rdeg )
90
0
30
60
0
90
(degl
Figure 13. The MCSCF energy variation as compared with the energies eq 4) or 9, ( q n 4 , associated with two starting descriptions, from a, (qnv eq 5). Left, disilene; right, distannene.
An interesting feature is that this view applies both to fragments, obtained by mentally breaking the A bonds on a general u skeleton, and to the real fragments, Le., a group of atoms totally isolated from their neighbors. In a pure 9 reasoning, the A fragments.constituting a double bond R,X-XR2 are analogous to two R3X groups. Such radicals have an intrinsic tendency to pyramidalize when X = Si, Ge, or Sn, as have the mean resonant ionic forms R3X+ which are of lower weight in the wavefunction. This trend to depart from planarity is damped by the delocalization which occurs between the two adjacent A electrons in the doubly bonded system. This A delocalization is more or less strong depending on the atoms, but it always opposes the pyramidalization trends. It prevails, for instance, in tetramethylethylene but remains
(46) For a general discussion on cis-bending in olefins see ref 19, and Trinquier, G.; Malrieu, J. P. In The Chemistry of Double-Bonded Functional Groups; Patai, S . , Ed.; Wiley Interscience: New York, 1989; Supplement A, Vol. 2. See also: Hrovat, D. A.; Bordcn, W. T. J. Am. Chem. Soc. 1988, 110, 4710. Borden, W. T. Chem. Reo. 1989, 89, 1095.
Trans Bending at Double Bonds
The Journal of Physical Chemistry, Vol. 94, No. 16. 1990 6195 Ge
Sn Sn
0
e (deg)
(deg)
30
2, 0
60
(deg)
90
0
&
30
e
60
I
90
(deg)
Figure 14. Valence-bond decomposition upon trans bending, gathering the determinants into three classes according to their n / r distribution of electrons. From left to right: ethylene, disilene, digermene, and distannene.
I
40
TABLE I V SCF-DZd-Calculated Geometries for Ethylene and Its Heavier Analogues (in A and d e ) X=X X-H HXH O=(XX,HXH) HZC=CHZ 1.322 1.084 116.6 0 H2Si=SiH2 2.115 1.461 115.7 0 H2Ge=GeH, 2.322 1.557 108.8 38.1 H2Sn=SnH2 2.716 1.733 102.9 49.4
30
We should emphasize, lastly, the advantages of the procedures used in this work. They made it possible to understand and interpret each of the VB forms. The transcription of a complete valence active space MCSCF wave function (Le., the best internally correlated one) into an OVB language appears to be an efficient tool for understanding correlated wave functions and for managing the accuracy/interpretability couple.
20
--
5 0
Y
10
w
4
Acknowledgment. We thank Drs. Alejandro Ramirez and Jean-Pierre Daudey for assistance in the programming and computing parts.
0
-1 0
-20 40
20
0
20
40
60
80
e (deg) Figure 15. Calculated relative energies upon trans bending for ethylene, disilene, digermene, and distannene. Right, four-electron CASCF treatment; left, after removing the configuration a3 from the corresponding CI. TABLE 111: SCF-Calculated Valence Angles and Barriers to Planarity in XH, Radicals and Anions C Si Ge Sn HXHg AH, 120 111 110 109 96 96 96 XHS104 AE,lb AH, 8 8 11 XHI12 36 37 '40 a
In degrees.
In kcal/mol.
figurations nap,nap, + ale)so that the former becomes predominant in the wave function. This pattern was assumed when the semiquantitative rules developed in ref 16 were derived. According to the present results it is valid stricto sensu for distannene only but the rules related to relation 3 remain general since they may also be obtained from the other limit namely the u-?r mixing scheme.44 The first model clearly holds for ethylene and disilene while the second holds for distannene. The case of digermene lies in between, both descriptions being usable as starting points.
Appendix I. General. The S C F calculations were performed with the PSHONDOG algorithm4' which introduces the effective core potentials of Durand and Barthelat" into the HONDO pr0gram.4~ For tin, part of the relativistic effects (mean relativistic effects, described through the mass-velocity and Darwin terms) are included For the calculations on the XH3 in the core pse~dopotential.~~ radicals, the U H F version of the program was used. The DZd basis sets used are of double-zeta type, augmented by a set of d functions on the group 14 atoms, with exponents qd = 0.8, 0.50, 0.25, and 0.2 for C, Si, Ge, and Sn atoms, respectively. All scannings along 0 were made with at least one calculation every loo, with more points in some minima regions. The curves were then smoothed with cubic splines functions. The MCSCF calculations were performed with the program described in ref 51. 2. X H 3 Groups and T-CASSCF Calculations. The folding curves for the XH3 groups were calculated with the X-H bond lengths kept constant. These are therefore nonadiabatic curves which overestimate the barriers to planarity in the radicals and anions. The following X-H bond lengths were taken: C-H = l.lI(;Si-H=1.5A;Ge-H=1.54A;Sn-H= 1.7%r. TheSCF calculated HXH angles and barriers to planarity for the radical and anions are listed in Table 111. All angles are sound but some (47) Pelissier, M.; Komiha, N.; Daudey, J. P. J . Comput. Chem. 1988, 9, 298. (48) Durand, Ph.; Barthelat, J. C. Theor. Chim. Acta 1975, 38, 283. (49) Dupuis, M.; King, H. F. J . Chem. Phys. 1978, 68, 3998. (50) Barthelat, J. C.; Pelissier, M.; Durand, Ph. Phys. Rev. A 1981, 21, 1773. (51) Carbo, R.; Domingo, L.; Peris, J. J. Adu. Quantum Chem. 1982, I S , 215. (52) Marquez, A.; Gonzalez, G.G.;Fernandez Sanz, J. Chem. Phys. 1989, 138, 99.
J . Phys. Chem. 1990, 94, 6196-6201
6196
barriers are largely overestimated. The 7-MCSCF pyramidalization curves of H2X=XH2 were also performed, keeping the X-X and X-H bond lengths constant (C=C = 1.34 A; Si=Si = 2.236 A; G e = G e = 2.364 A; Sn = Sn = 2.65 A; C-H = 1.085 A; Si-H = 1.475 A; Ge-H = 1.557 A; Sn-H = 1.733 A). For the sake of geometrical consistency with the energy curves of the XH3 groups, the HXH and HXX valence angles in H2X=XM2 are taken at 120' in the starting planar geometry and are varied according to relation 2 as the molecule is bent. 3. u K CASSCF Calculations. The 1 I-configuration MCSCF calculations were performed with all bond lengths kept constant and HXH angles kept close to their MCSCF optimized values. Consequently, in Figure 15 the optimum bending angles are correct (6 = 36', 42', and 50' for disilene, digermene, and distannene, respectively) but the barriers to planarity (the depths of the wells) are overestimated. The geometries were selected as follows. For ethylene, experimental and accurately calculated geometries are available. For disilene, MCSCF-calculated geometries are a ~ a i l a b l e .For ~ digermene and distannene, we first determined a DZd-SCF geometry (given in Table IV), and then we reoptimized the X=X bond lengths at the MCSCF level. We selected these X=X bond lengths, slightly shortened in order to compensate the effects of nonadiabaticity along the bending curves. Finally, the following parameters (in angstroms and degrees) were used: CC = 1.34, C H = 1.085, HCH = 118.0, SiSi = 2.236, SiH = 1.475, HSiH = 111.8, GeGe = 2.364, GeH = 1.557, HGeH = 108.9, SnSn = 2.728, SnH = 1.733, HSnH = 102.9. One can find in the literature more refinedly calculated geometries and barriers to planarity. For disilene, the best calculations including correlation effects predict a wagging angle 0 of 33-36°.3*4and a barrier to Dlanaritv of 0.5-1.5 k ~ a l / m o l . ~For ~'~ digermene, taking the DZd-Lptimizk geometry for the DZhplanar and CZhtrans-bent forms, one gets a barrier to planarity of 3.6
+
kcal/mol at a CI level5 Using a DZP basis set changes very little this value (3.2 k ~ a l / m o l ) . ~Most calculations converge toward a value of 38-40' for the bending angle 0.s,8*9 For distannene, the SCF-DZd geometry has been determined for the planar form (SnSn = 2.536 A, SnH = 1.701 A, HSnH = 114.7'). Starting from the C,, and D2 geometries, the following energy differences were calculated: SCF, 9.7 kcal/mol; MCSCF, 10.9 kcal/mol; CI(CIPSI), 10.5 kcal/mol. The same adiabatic differences, using SCF-DZP geometries (i.e., further including p orbitals on hydrogen) were calculated at SCF, 9.2 kcal/mol; CI(CIPSI), 9.4 k ~ a l / m o l .In ~ ref 8 the adiabatic barrier to planarity is calculated at the S C F level at 6.2 kcal mol. Most calculations predict a bending angle of 46-49°.8*9. In summary, we would say that the present state of theoretical treatments predict the following bending parameters for the parent molecule (in degrees and kcal/ mol) :
l
disilene digermene distannene
trans-wagging angle
barrier to planarity
33-36 38-40 46-50
0.5-1.5 3-4 8-10
4 . Ouerlap Curves. The overlaps in Figure 6 were calculated between 2p, atomic orbitals and n, hybrids sxpY, built from Slater orbitals centered on carbon atoms distant by 1.34 A. We used the FMO analysis possibilities offered by the ICON version of the EHT program.s3 By setting the H, of the hydrogen Is orbital to an arbitrarily high value (999 eV), one gets an hybrid with 20% s character, which was used in Figure 6. The Slater exponents for the carbon atoms were taken at 1.625 for both the 2s and 2p orbitals. Other hybridizations were tried for the n, hybrid. This mainly results in a vertical translation of the S,, curve. (53) Hoffmann, R. J . Chem. Phys. 1963, 39, 1397.
Vibrational Analysis of an Electronic Emission Spectrum of 32SF2and 34SF2 Robert J. Glinski,* C. Douglas Taylor, and Frank W. Kutzler Department of Chemistry, Tennessee Technological University, Cookeville, Tennessee 38505 (Received: October 4 , 1989: In Final Form: January 23, 1990)
An electronic emission spectrum of SF2 extending from 5500 to 8500 %, is observed during the reactions of F2 with CS2, OCS, and sulfur vapor. Long vibrational band progressions of 355 i 2 cm-l and short progressions of 838 f 2 cm-' are definitively assigned to v2/1 and vl", respectively. Isotopic substitution of CS2with sulfur-34 has allowed a tentative assignment of the third ground-state frequency, Y; = 817 f 6 cm-I, and the electronic origin, 18 123 f IO00 cm-I. Ground-state frequencies and their isotopic shifts compared very well with those obtained in infrared absorption experiments by other workers. Estimates of the anharmonicities of the ground-state frequencies are presented. Weak bands lying 243 6 cm-l to the blue of the strongest bands are ascribed to the v i frequency. Results of first principles electronic energy calculations are presented, showing that two low-lying singlet electronic states are in the energy range of this emission spectrum. A discussion is presented relating the possible activity of the asymmetric stretch and the nature of the excited electronic state. The true multiplicities of the electronic states are undetermined and unaddressed. Reaction of CS2 with F2 produces SF,* together with an unknown feature displaying overlapping vibrational bands, 310 f 30 cm-l apart, extending from 7000 A into the near-infrared region. Reaction of F2 with SO2 produced no detectable chemiluminescence between 3000 and 8800 A.
*
Introduction The spectroscopy of sulfur difluoride has been studied by microwave,] infrared?~~ REMPI? and photoelectron spectroscopic5 (1) Kirchoff, W. H.; Johnson. D. R.;Powell, F. X . J. Mol. Spectrosc. 1973, 48. 157. Endo, Y.; Saito, S . ; Hirota, E.; Chikaraishi, T. J . Mol. Spectrosc. 1979. 377, 222. (2) Haas, A.; Willner, H. Spectrochim. Acta 1978, 34A, 541. (3) Deroche, J.-,C.; Burger, H.; Schulz, P.; Willner, H. J . Mol. Spectrosc. 1981, 89. 269. Willner, H. 2. Anorg. Allg. Chem. 1981, 117. 481.
0022-3654/90/2094-6196$02.50/0
methods, but direct observation of its lower lying electronic excited states by optical methods has not been reported. Isotopic substitution of CS2 in its chemiluminescent reaction with F2 has been used in this laboratory to demonstrate that SF2* produces one of the chemiluminescence featurese6 In this paper, we present (4) Johnson, R. D. 111; Hudgens, J. W. J . Phys. Chem. 1990, 94, 3273. ( 5 ) De Leeuw, D. M.; Mooyman, R.; De Lange, C. A. Chem. Phys. 1978.
34, 281. ( 6 ) Glinski, R. J.; Taylor, C. D. Chem. Phys. Lett. 1989, 155, 511.
0 1990 American Chemical Society
