364
J . Phys. Chem. 1988, 92, 364-367
basis of d functions. We wrote a code to find the population contribution to the dX2+,,z+,zcomponent and subtracted this from the total d population and added this to the s population. Table IV shows the d population without the x2 + y 2 + z2 component. As one can see from that table, the bent 2B2ground state of AuH2 is ionic with Au+H- polarity. The dipole moment of the bent 2B2 state is calculated to be 1.259 D at the d-MRSDCI levels of calculation. The dipole vector points in the +Z direction. The 2Ze+state has greater hydrogen population and less gold population, indicating greater ionic character although the dipole moment cancels out since this state is linear. The bent 2B2state has greater Au-H overlap population than the linear structure (22,+), indicating enhanced Au-H bonding in the bent state. The 2&,+ state, however, has a total Au gross population of 11.04, indicating that the charge separation is insignificant for this state. The d population of the various states is another property of considerable interest for transition metal hydrides. Only in the 2Zu+state is the d shell near complete (9.69 e). For the 2B2bent and 2Zg+linear states the d population deviates quite a bit from a closed-shell population. The contribution of the p orbital of Au is relatively small for the 22,,+state, as one can see from Table
IV, but somewhat more important for the 2Ze+ and 2B2states. 4. Conclusion In this investigation, we carried out CASSCF/CI calculations of low-lying electronic states of AuH2 with and without d correlation. The ground state of AuH2 was found to be a 2B2state with a bent structure, re(Au-H) = 1.62 A and Oe = 127’. Two linear states, namely 2Ze+and 2Zu+,were found within 0.3 eV, state being the lower of the two. The d correlation was the 22u+ found to be of considerable importance in calculating the energies but somewhat less important for the geometries. The bending potential energy surfaces of the 2B2and 2A1states are studied. These surfaces reveal that the excited A U ( ~ Patom ) would insert B ~ ) the A u ( ~ S )atom spontaneously into H2to form A u H ~ ( ~ while has to surmount a large barrier ((’AI); V, (planar) silasilene C,(’A, an )Az); VI, bent silasilene C,(’A”); VII, symmetry reduced trans-bent disilyne Cs(3A”);VIII, cis-bent disilyne C,()A,); and IX, symmetry reduced cis-bent disilyne C,()A”).
and GAuSSIANS~.” Because of the unusual structures investigated, the H F stability checks in GAUSSIANBZwere used to examine the stability of HF wave functions to internal and external perturbations.’*
Methods of Calculations To allow direct comparisons with the earlier results, the 631G(d,p) basis set proposed by Franc1 et al.”*” (denoted by 6-31G(d,p)F) is employed in some of our calculations. Geometry optimizations and single-point calculations have been carried out at the HF/6-3 1G(d,p) and MP4/6-3 l++G(d,p) levels, respectively. Our group has been using the original 6-31G(d,p) basis set for s i l i ~ o n . ’ ~ *Therefore, ’~ we use it as well in all of our calculations. Full optimized reaction space (FORS) MCSCF e n e r g i e ~ are ’ ~ also obtained a t the HF/6-3 1G(d,p) geometries. All valence orbitals are included in the active space (full valence (=FV) MCSCF). A smaller active space, which includes only four valence orbitals and four electrons (referred to as MCSCF(4,4)), is also employed in order to obtain certain optimized geometries of the SizH2molecule, as described in detail in the next section. S C F force fields were obtained by using analytical second derivatives, whereas those at the MCSCF level were calculated from finite differences of analytical gradients. Boys localized molecular orbitals (LMOs) with the 6-3 IG(d,p) basis set are used to interpret some of the electronic structures. The calculations were performed using the programs G A M E S S ’ ~
Results and Discussion Silasilene. BinkleyEand Luke et aL9 have concluded that the bent structure (VI) is the global minimum on the lowest triplet potential energy surface of Si2H2. The angle Si-Si-Y (Y is the midpoint between two hydrogen atoms in Scheme I) is about 160’. In this paper, Boys LMO’s are employed to interpret the bonding in this species. The center silicon atom appears to have roughly sp3 hybridization, while it is likely that there is no hybridization at the terminal silicon atom: Mulliken population analysis of the Si-H bond orbital gives an s:p ratio of 1:2.06 at the center silicon atom,I9 while the terminal silicon has nearly pure p character in the Si-Si LMO. The singly occupied orbitals are the 3p, orbital on the terminal Si atom and that one of the four roughly sp3 orbitals on the central silicon atom which does not participate in any chemical bond. The latter orbital is primarily a lone-pair orbital but interacts strongly with the 3p, orbital at the terminal silicon. It has s:p:d = 1:1.90:0.04, so that it is approximately an sp3 0rbita1.I~ The strong interaction with the vacant 3px orbital on the terminal Si atom forms a molecular orbital which becomes a n-orbital at the planar structure. The lowest 3Azstate of the planar structure (V) has a singly occupied a-orbital and a singly occupied 3p, (bz) orbital at the terminal silicon atom. In the planar structure, the terminal silicon L M O s still have nearly pure p character, while the center silicon consists of orbitals with intermediate hybridization (s:p:d = 1:1.68:O. 16 for the Boys LMO’s of the Si-H bonds. See ref 19). Our UHF/6-3 IG(d,p)F//UHF/6-3 lG(d,p)F (and UHF/6results show that the bent 3 l++G(d,p)F//UHF/6-31G(d,p)F) structure is lower in energy than the planar structure (not reported by Binkley* or Luke et aL9) by less than 1 kcal/mol. This is consistent with the weak A bonds between silicon atomsz0
(13) Koseki, S.; Gordon, M. S., manuscript in preparation. (14) Gordon, M. S. Chem. Phys. Lett. 1980, 76, 163. (15) (a) Ruedenberg, K.;Schmidt, M. W.; Gilbert, M. M.; Elbert, S . T. Chem. Phys. 1982, 71,41. (b) Ruedenberg, K.;Schmidt, M. W.; Gilbert, M. M. Chem. Phys. 1982, 71, 5 1 . (c) Ruedenberg, K.;Schmidt, M. W.; Gilbert, M. M.; Elbert, S. T. Chem. Phys. 1982, 71, 65. (16) (a) Dupuis, M.; Spangler, D.; Wendoloski, J. J. Program QGOI, National Resource for Computation in Chemistry Software Catalog; Lawrence Berkeley Laboratory: Berkeley, CA, 1980; p 60. (b) Schmidt, M. W.; Baldridge, K.K.;Boatz, J. A,; Koseki, S.; Gordon, M. S.; Elbert, S. T.; Lam, B. QCPE 1987, 7, 21 1.
(17) Binkley, J. S.;Frisch, M.; Ragavachari, K.;DeFrees, D. J.; Schlegel, H. B.; Whiteside, R.; Fluder, E.; Seeger,R.; Pople, J. A. GAUSSIAN82 Program; Carnegie-Mellon University; 1983 (unpublished). (18) (a) Seeger, R.; Pople, J. A. J . Chem. Phys. 1976,65,265. (b) Seeger, R.; Pople, J. A. J. Chem. Phys. 1977, 66, 3045. (19) Mulliken population analysis at the HF/6-31G(d,p) level gives an s:p:d ratio of 1:1.99:0.20 for sp’ orbitals of the SiH, molecule, 1:2.05:0.20 for sp’ orbitals of the Si,H, molecule, and 1:1.43:0.13 for sp2 orbitals of the 0 2 1 structure of the Si2H, molecule. (20) Gordon, M. S. In Molecular Structure and Energetics; Liebman, J. F., Greenberg, A,, Eds.; VCH: Deerfield Beach, FL, 1986.
and from analyses of SizHzreaction surfaces.13 In the present paper, we report new calculations on the triplet potential energy surface of Si2H2.
366 The Journal of Physical Chemistry, Vol. 92, No. 2, 1988
Koseki and Gordon
TABLE I Total Energies of Triplet Isomers Si2H2S
method and geometry state
disilyne
silasilene planar
bent
twisted
C2" A2
cs
c2
A"
HF HF + ZPE
0.0 0.0
-0.15 0.21
HF HF + ZPEb MP2 MP3 MP4SDQ MP4SDTQ
0.0 0.0 0.0 0.0 0.0 0.0
-0.15 0.21 1.90
HF HF + ZPE MCSCF" FV MC CSFs
0.0 0.0 0.0 0.0
-0.16 0.20 0.03 0.18 14916
7400
2.05 1.77 1.93
HF HF + ZPEb MP2 MP3 MP4SDQ
0.0 0.0 0.0 0.0 0.0
-0.15 0.21 2.05
MCSCFC
0.0 0.0
-0.11 0.02 14916
FV M C
CSFs
7400
cis-bent
c2,
B B, 6-3lG(d,p)F//UHF-6-3lG(d,p)F
trans-bent
c,
cs
c2 h
A"
A"
A"
19.03 6-3l++G(d,p)F//UHF/6-31G(d,p)F 19.06 14.15
13.96 13.62 12.71
6-3lG(d,p)//UHF/6-3 lG(d,p) 19.05 23.41
1 1.69
9.96
8.81
6-3l++G(d,p)//UHF/6-31G(d,p) 19.08 23.37 11.68
9.99
8.83
11.97 11.83
4.96 4.63 4.43
7.08 7.03 6.73
6-3lG(d,p)//MCSCF/6-31G(d,p)' 10.78 16.26 8.40 10.22 21.49 9.30 14900 7392 14784
4.60 2.49 7392
4.61 2.59 14784
11.32
10.16 14900
2.19
14.09
19.50 18.05
1.88
13.78
17.27
14.25
11.91
kcal/mol. see ref 10, 11, and 14. MP2, MP3, MP4SDQ, and MP4SDTQ energies do not include zero-point vibrational energies. Binkley (ref 8) reported the energy differences between bent silasilene and twisted disilyne obtained by using 6-3lG(d,p)F basis set at the UHF and MP4SDTQ levels. Other results are obtained in this study. bZPE = zero-point vibrational energy calculated by using the HF/6-3lG(d,p) method. MCSCF(4,4) calculations. See text. However, the inclusion of zero-point vibrational energies reverses the relative energies of these structures, even though the planar structure has one imaginary frequency (2292' cm-'(b,)) at the UHF/6-31G(d,p)F level (see Table I). The MP4SDTQ/631++G(d,p)F//UHF/6-31G(d,p)F energy of the planar structure is 1.9 kcal/mol lower than that of the bent one, even without zero-point vibrational energies. Identical results are obtained if the 6-31G(d,p) basis set is used for silicon as shown in Table I. Moreover, the MP2/6-3 lG(d,p) method predicts the planar structure, rather than the bent one, to be the minimum (Figure 2; the displacements along the bent and rocking motions lead to increases in the MP2 energy). Thus, the true minimum is apparently the planar structure, as reported by Lischka and Koehler6 and Kalcher et al.' In this study, FV MCSCF/6-31G(d,p) calculations were also carried out at the HF/6-31G(d,p) and small MCSCF/6-31G(d,p) geometries. The active space of the small MCSCF method includes the K and K* orbitals, and the lone-pair and 3p, orbitals of the terminal silicon (denoted MCSCF(4,4)/6-31G(d,p)). The numbers of electronic configurations generated by the FV MCSCF method are 7400 and 14916 for the planar and bent structures, respectively. The FV MCSCF energy difference between the bent and planar structures is very small (0.18 (HF) and 0.22 (MCSCF(4,4)) kcal/mol), with the planar structure lower in energy than the bent one. (The angle Si-Si-Y of the MCSCF(4,4) geometry is 169.4', as compared with 160' for the H F geometry.) Because small configuration mixing is found at both structures and the MP4SDTQ energies include electron correlation in the external space as well as that in the valence space, the MP4SDTQ results are probably more accurate than the FV MCSCF results. Disilyne. In our study, the U H F wave function for the 3B state of twisted disilyne (111, C2) is found to be unstable to internal perturbationi8 at the UHF/6-31G(d,p) level, while the wave functions for the other three isomers, IV (Ch('Ai)), V (C2JiA1)), and VI (C,(3A")) obtained by Binkley are stable. Therefore, the
2.280 (2.289)
H 2.306 12.301)
/
H
1.501
" -
--H
1.496 1.50 3)
H
105.9 (105.3)
2.398 (2.4321
H
'\(
112.5 (106.31
103.2 (98.5)
VIII.
2.342 (2.328) 1.510 (1.514)
cPv(3131)
1.489
(1.5151 (91.7)
(126.51
IX Cs(3A")
Figure 3. MCSCF(4,4)/6-3lG(d,p) optimized geometries of triplet didynes. Bond length is in angstroms and bond angle is in degrees. The geometric parameters in parentheses are obtained at the HF/6-3 IG(d,p)
level. S C F calculations on the twisted structure may not be reliable. Binkley considered the trans-bent and cis-bent structures for triplet acetylene and found that they are not minima on the triplet potential energy surface of C2H2. However, he did not report such structures for triplet disilyne. According to our UHF/6-3 lG(d,p) results (See Table I and Figure 3), the 3A, state is the lowest triplet in the trans-bent C2, structure (I1 in Figure 1) of Si2H,. This state is higher in energy than the 3A" state in the trans-bent C, structure (VII) by only 1 kcal/mol, but the former is more stable than the latter at the correlated levels as shown in Table I. The
Lowest Triplet Potential Energy Surface of Si2H2
The Journal of Physical Chemistry, Vol. 92, No. 2, 1988 361 1
SCHEME I1
* e
W
5
'i
,\d
(c2h)
,
O O
, , , , , , , , , , , , , ,
90
180
Dihedral Angle [degree] Figure 4. Potential energy surface for rotation about the H-Si-Si-H dihedral angle of triplet disilyne. 'A, state is apparently lower in energy than the 'B state of the twisted structure (C,) obtained by Binkley at both U H F and MP4SDTQ levels. Unfortunately, the U H F solution for the 'A, state is unstable to internal perturbation as well. In our study, the cis-bent C2, structure (VIII) has 'BI as its lowest triplet state. This state is about 12 (UHF) or 6 (MP4SDQ) kcal/mol higher than the 'A" state in the cis-bent C, structure IX (Table I). This 'A'' state is also lower in energy than the 'B state of twisted disilyne. However, the U H F wave function for this state is unstable to internal perturbation. Thus, the U H F results on triplet disilyne may be unreliable. At our UHF/6-31G(d,p) level, the character of the Si-H bonds in twisted disilyne is s:p:d = 1:2.57:0.23,obtained from the average between the (Y and 0LMOs. This suggests that the Si-H bonds are nearly pure p orbital, rather than sp', at the silicon atom at this computational 1 e ~ e l . l As ~ shown in Scheme 11, the four lone-pair orbitals and the two Si-H bonds are placed at the sterically stable staggered positions in this structure. The least stable structure along the internal rotation path of the Si-Si bond should have an H-Si-Si-H dihedral angle of about 120°, because the four lone-pair orbitals and the two Si-H bonds are then in their eclipsed positions. Actually, our MCSCF calculations predict an angle of about looo, as shown in Figure 4. This smaller angle is caused by the stronger repulsive interactions among the lone-pair orbitals than those between the Si-H bonds. The four lone-pair orbitals might be energetically close to each other, suggesting that large configurational mixing may occur in the 'B state of the twisted structure. The 7b, 8a, 8b, and 9a orbitals correspond to the four lone-pair orbitals. According to our FV MCSCF/6-3lG(d,p)//UHF/6-31G(d,p) results, which include 14900 electronic configuration state functions, the 'B state should be described mainly by a linear combination of the following two electronic configurations: (core) (sa),( 6b)2(7a)2(7b)2(8a) I (8b) (core) (6a)2(6b)2(7a)2(7b) (8a) (8b)2 The occupation numbers of the natural orbitals, 7b, 8a, 8b, and 9a, are 1.843, 1.012, 0.994, and 0.148. This may be the source of the internal instability in the SCF wave function for this state. It seems to be important to consider the influence of electron correlation upon geometric structures in such cases. Because it is rather time consuming to carry out geometry optimizations at the FV MCSCF/6-3 lG(d,p) level, the MCSCF active space used to reoptimize the geometries includes only four valence orbitals (denoted MCSCF(4,4)/6-3lG(d,p)) which correspond to the four lone-pair orbitals in the twisted structure. The optimized geometries of the cis-bent (VIII, IX), twisted (111), and trans-bent (11) structures are shown in Figure 3. The C, cis-bent VI11 has two imaginary frequencies which correspond to the rotation about the Si-Si bond and the deformation to the
C, structure IX. The C, cis-bent IX has no imaginary frequency, so that the A" state is still the lowest cis-bent triplet. The twisted structure has C, symmetry and the MCSCF(4,4) force field is positive definite. The trans-bent structure has C2, (11) (rather than C, (VIII)) symmetry, although the potential energy surface is very flat (243 cm-I) along the b, mode. The MCSCF(4,4) force constant matrix is positive definite. Interestingly, the M P energy differences (based on the U H F wave functions) are similar to the MCSCF values. There are quantitative differences, but the energetic order predicted at the M P levels still correctly predicts the most stable structure, even though the U H F wave functions are unstable to internal perturbation. Figure 4 illustrates the potential energy surface for rotation about the Si-Si bond of triplet disilyne at the MCSCF(4,4)/631G(d,p) level. There are three local minima, the cis-bent (C,), twisted (C2),and trans-bent (C2h) structures, as described above. The energy barrier for the rotation from the trans-bent structure to the cis-bent one is about 11 kcal/mol. There is a very small energy barrier (less than 1 kcal/mol) between the cis-bent and twisted structures. The C2structure for twisted disilyne is deformed to CI (corresponding to a bifurcation) as the dihedral angle becomes small. This smaller barrier might disappear at higher computational levels (e.g., FV MCSCF/6-31G(d,p)), because it is caused by a strong avoided crossing with a higher electronic state and external correlation may be important. The FV MCSCF/6-3lG(d,p)//MCSCF(4,4)/6-31G(d,p) energies of these three structures are listed in Table I. The numbers of electronic configuration state functions are 14 784 (cis-bent C,), 14 900 (twisted), and 7392 (trans-bent c2h). The relative energies of these structures are almost the same as those obtained by the MCSCF(4,4) method. Therefore, it is concluded that the c 2 h trans-bent structure is the most stable triplet disilyne and that the C, cis-bent structure is also a minimum on the triplet potential energy surface of Si2H2. It is not clear that twisted disilyne is a minimum. The global minimum on the triplet surface appears to be planar silasilene, with the c,h trans-bent structure higher in energy by only 2.5 kcal/mol.
Conclusion Although bent silasilene has previously been reported to be the global minimum on the triplet potential energy surface of Si2HZ, planar silasilene is found in the present work to be more stable than bent silasilene by about 2 kcal/mol in this study. The trans-bent (CZh), rather than the twisted, structure is predicted to be the most stable as triplet disilyne and is only 3-4 kcal/mol higher than planar silasilene. The cis-bent structure (C,) for triplet disilyne is also found to be a minimum on the triplet potential energy surface, so that it should be observable. Apparently, the M P methods based on U H F wave functions can be employed to estimate energy differences, even though the U H F wave functions are unstable to internal perturbation. Acknowledgment. This work was supported by grants from the National Science Foundation (CHE86-40771) and the Air Force Office of Scientific Research (AFOSR 87-0049). We are indebted to Dr. Michael W. Schmidt for several helpful discussions. All calculations were performed on an IBM 3081D at the North Dakota State University Computer Center, a VAX 11/750 minicomputer (purchased with the aid of AFOSR grant 84-0428), and a microVAX I1 minicomputer (purchased with the aid of NSF grant CHE-8511697). Computer time was also made available on the CRAY XMP48 at the San Diego Supercomputer Center through the N S F grant. Registry No. Si,H,, 36835-58-2.
