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Jahn-teller distortions of SiH4+ and Si(CH3)4+
Chemical Physics 122 (1988) 233-245 North-Holland, Amsterdam
JAHN-TELLER
DISTORTIONS OF SiH; AND Si(CH&
Takako KUDO and Shigeru NAGASE Department of Chemistry, Faculty ofEducation,
Yokohama National University, Yokohama 240, Japan
Received 14 January 1988
In view of current interest in silane radical cations, the Jahn-Teller distortions of SiH: and Si(CH,)4+ to the Dzd, C3”, Clvr and C, structures are investigated by means of ab initio calculations with flexible basis sets and electron correlation. The C, structure is found to be the most stable in SiH4, as suggested in a recent theoretical study. On the other hand, the C3, structure is the most stable in Si( CHJ )$ , unlike the suggestion from the ESR study. This contrasts with the fragile C3, structure in SiH: . The relative stabilities (kcal/mol) of SiH: and Si(CH,): decrease in the order C,(O.O) > r&(8.5) >C&( 13.7) >Dz4(27.2) at the MP4 SDTQ/6-31+G(Zdf, 2p)//MP2/6-31G(d, p)+ZPC level and Cs,(0.0)>C,,(6.1)>C,(16.3) at MP2/6_31G(d)//HF/63 lG(d) +ZPC level, respectively. In both SiH: and Si( CH, )$, the CrVstructures are not energy minima but transition structures for the rearrangement to the most stable structures. An interesting finding is that Si(CH,): is much more stable to fragmentation than SiH: .
1. Introduction
It is well known that the methane radical cation, distortion from the tetrahedral Td symmetry of the neutral species to the lower Dzd, C3”, or C2” symmetry to have a nondegenerate ground state. For a long time, it was controversial which symmetry the ground state takes [ l-3 1. Now that a Czv ground-state structure is experimentally and theoretically established [ 1,2], it is natural that current effort is directed towards the heavier analogous XR: (X=Si [4-91, Ge [6,8,10-111, Sn [8,12-18],orPb [15]). Silane (SiH,) and its fragment ions have recently received special attention. The principal reason for this attention is because plasma chemical vapor deposition (CVD) processes are used as important sources of high-purity amorphous silicon. In these processes silane is decomposed by electric discharge. Appearance energies and ionization cross sections of SiH: and SiH: have repeatedly been investigated by means of the electron- and photon-impact dissociative ionization methods [ 19-26 1. However, the photoelectron [ 27-321 and photoionization [ 33-371 mass spectrometrical studies of silane have raised a growing interest in the intermediacy and role of the CH: , can undergo Jahn-Teller
0301-0104/88/$03.50 0 Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division )
silane radical cation, SiH: . The structure of SiH: was first investigated by Hartmann et al. [ 41 by means of one-center expansion calculations with a minimal basis set. They found that the square-planar D4,, structure is more stable than the C3” structure. In contrast, Gordon [ 51 calculated at the HF/4-31G level that the C& structure is the most stable and the relative stability decreases in the order Csv> Czv> DZd, unlike the case of CH: [ 2 ] . This ordering was also confirmed by Power et al. [7] by means of the HF/6-21G and CI/62 1G//HF/6-2 1G calculations. However, recent pseudopotential HF/DZP and CI/DZP calculations by Cabal101et al. [ 8 ] showed that the Czv structure is more stable than the Csv structure. Very recently, Pople and Curtiss calculated at the HF/6-3 1G* level that the C, structure is the most stable minimum on the SiH: potential energy surface [ 91. On the other hand, it is suggested from the ESR study by Walther and Williams [ 61 that the methyl-substituted radical cation, Si ( CH3 )2, has C2”symmetry rather than Csv symmetry. In view of the apparent discrepancies, we have undertaken the ab initio calculations of the Jahn-Teller distortions of SiHf and Si(CH3 )$ at higher levels of theory. Our primary concern is to resolve (i ) which
T. Kudo, S. Nagase / Jahn-Teller
234
symmetrical structure is the most stable, (ii) to what extent it is kinetically stable to fragmentation, and (iii) how the relative and kinetic stabilities are influenced by substituents. To this end, it will be shown that SiH: has C, symmetry in the ground state, as suggested by Pople and Curtiss [ 91, but is relatively unstable to fragmentation. On the other hand, Si( CH, )$ prefers CJv symmetry, unlike the experimental suggestion by Walther and Williams [ 61, and is kinetically more stable to fragmentation.
distortions of SiH+ and Si(CH,)”
diffuse sp functions on Si, double sets of d polarization functions on Si, double sets of p polarization functions on H, and a set off polarization functions on Si. Zero-point correction (ZPC) was made by using the HF/3-21G, HF/6-31G(d, p), and MP2/63 1G (d, p) harmonic vibrtational frequencies. In the following, the symbol “//” means “at the geometry of”.
3. Results and discussion 2. Computational details
3.1. SiH4+
The spin-restricted Hartree-Fock (RHF) method was used for closed-shell singlet states, while spin-unrestricted Hartree-Fock (UHF) calculations were carried out for open-shell doublets. The computed expectation values of the spin-squared operator ( S2) were in the range of 0.750-0.795 for all doublet species considered here: the relatively large values ( x0.79) were for the DZdstructure of SiH: and the Czv structure of Si(CH3)$. However, these are all close to the correct value of 0.750 for pure doublets. Geometries were optimized at the HF level with the split-valence 3-2 1G basis set [ 38,39 ] and the polarized 6-3 1G(d) and 6-3 1G (d, p) basis sets (which are also referred to as 6-3 lG* or 6-3 lG** ) [ 40 ] by means of the analytic energy gradients, and identified as equilibrium or transition structures by calculating analytically the Hessian matrices. To incorporate the effect of electron correlation, the HF/6-3 1G (d, p) geometries were reoptimized by using second-order Moller-Plesset perturbation theory (MP2) [41] and the 6-31G(d, p) basis set [40] for SiHz . The Hessian matrices were calculated by differentiating numerically the analytic first derivatives of the MP2 energies. Energies were improved by means of the MP theory #’ up to full fourth-order (MP4 SDTQ) [ 43 ] with the constraint that core-like orbitals were doubly OG cupied. The basis sets employed in these calculations were 6-31G(d), 6-31G(d, p), 6-31+G(2d, p), 631+G(2d, 2p), and 6-31+G(2df, 2p) [44]. The largest 6-3 1+ G (2df, 2p) basis set includes a set of
3.1.1. Structures Silane (SiH,) has a ‘A1 ground state in the tetrahedral Td form and the ground electron contiguration is (la, )2(2a, )‘(lt, )Y3al
Merller-Plesset
theory is described
in ref.
[ 42I.
I6
.
A lot of theoretical [ 39,40,45-501 and experimental [ 5 l-55 ] studies are already available for its geometry and vibrational frequencies. Table 1 compares the present calculations with some previous data. As shown in this table, the MP2/6-3 1G (d, p) geometry and frequencies are very close to the experimental values, compared with the HF/6-3 lG( d, p) values. In addition, the MP values are in good agreement with the CI values reported recently by Allen and Schaefer ]501. Ionization from the highest occupied 2t2 orbital to give SiH,+ leads to a three-fold degenerate state, 2T2, in the tetrahedral form. The energy for this vertical ionization was 12.83 eV at the MP4 SDTQ/631+G(2df,2p)//MP2/6-31G(d,p)levelandagrees very well with the CEPA value of 12.68 eV [ 561 #’ as well as the experimental value of 12.8 eV [ 27,291. According to the Jahn-Teller theorem [ 601, the degenerate 2T2 state can interact with the e and t2 vibrational modes and distort into some lower symmetry. Thus, the structures and relative energies of the lower DZdr C3”, C2”, and C, symmetries have extensively been investigated at several levels of theory [ 4,5,7-9 1, while it is surprising that the Hessian matrices have never been calculated to check if the structures are 42For
#’Third-order
12W2
the perturbation (12.3 eV), SCF (13.0 eV) and Xa (11.8 eV) values see refs. [ 57-591, respectively.
T. Kudo, S. Nagase / Jahn-Teller
distortions of SiH+ and Si(CH,)+
235
Table 1 Geometries and vibrational frequencies of SiH4 Method
r,(SiH) (A)
calculation CISD/DZP(Bl) ‘) CISDIDZP(B2) a) HF/6-31G(d, p) b, MP2/6-31G(d, p) ‘) experiment measured ( 1) (2) harmonic ( 1) (2)
1.4717 1.4755 1.4683 1.4726
a =)
1.4741
‘) g’
1.4806
Vibrational frequencies (cm-‘) vr(ar)
v2(e)
v,(tz)
vq(t2)
2334 2304 2379 2347
1022 1010 1066 1018
2337 2299 2357 2360
987 962 1032 974
2187 2186 2377 2268
974 972 975 960
2191 2189 2319 2273
914 913 945 929
‘) Ref. [50]. Bl: Si( 1ls7pld/6s4pld) and H(4slp/2slp). B2: Si( 12s9p2d/6s5p2d) and H(6s2p/4s2p). b, Ref. [47]. ‘) This work. d, Ref. [52]. ‘) Estimated r, from ref. [ 55] and frequencies from ref. [ 541. ‘) Ref. [53]. 8, r, from ref. [ 541 and predicted frequencies from ref. [ 501.
minima on the potential energy surface, except the recent study by Pople [ 9 ] on the C, structure. The DZd, C3”, CzV,and C, structures of SiH: are
a
Hb
I
H4
Hd’ \ Ha D2d
tib
c3v
.AHa
H?llia Cada)
C2v(b)
Fig. 1. The Dzdr CXv,Czy, and C, structures of SiH$
schematically displayed in fig. 1. The geometrical parameters optimized with the symmetry constraint at the HF/6-31G(d, p) and MP2/6-31G(d, p) levels are summarized in table 2. For comparison, previous results are also given in table 2. For the DZd and CzV structures, the HF/6-31G(d, p) geometries are very similar (within 0.027 A for lengths and 1” for angles) to the MP2/6-31G(d, p) geometries, suggesting that electron correlation has little effect on geometry optimization, as found in CH$ [ 2 1. However, this is not the case for the Cg, structure of SiH: ; the MP2 optimized SiH bond length ( 1.949 A) between the SiH3 and H moieties is 0.131 A shorter than the HF value (2.080 A). The same shortening of 0.13 1 A is also found in the pseudopotential HF/DZP and CI/DZP calculations by Cabal101et al. [ 81. As is apparent from the geometrical parameters in table 2, the C,, structure may .be regarded as a complex of SiH$ and H. An interesting finding is that two distinct structures, a and b, were located with CzVsymmetry constraint, as shown in fig. 1. Both have ‘Bi electronic states and give similar electron distributions. However, a and b differ in the spin density distributions. In a the spin density is almost localized on the silicon atom, while in b it is considerably delocalized onto the H, atoms in the H,H, bond. The main geometri-
T Kudo, S. Nagase /Jahn-Teller
236 Table 2 Optimized
geometrical
parameters
of the Dzd, Cs,,
distortions of SiH+ and Si(CH,)+
C,,(a), C,,(b), and C, structures of SiH: in A and degree DZP a’
6-31G(d,p)
6-21G
HF
MP2
HF
CI
SiH, H,SiH,
1.510 137.2
1.505 136.5
C 3” SiH, SiHb H,SiHb
2.080 1.455 92.5
1.949 1.456 92.9
2.073 1.460 93.4
1.942 1.472 93.2
1.646 1.448 0.848 2.750 29.9 143.5
1.625 1.447 0.875 2.742 31.2 142.6
1.660 1.452 0.884 2.767 30.9 144.7
1.679 1.462 0.897 2.790 31.0 145.2
b,
4-31G”
HF
HF
1.525 140.0
1.535 140.0
2.403 1.466 91.4
2.286 1.472 91.7
I .609 I .466 1.722 2.575 64.7 122.9
1.634 1.468 1.775
DZd
C&a) SiH, SiH, H,H, HbHb H,SiH. HbSiHb L(b) SiH, SiHb H,H. HbHb H,SiH, H,SiH,
1.563 1.452 1.471 2.575 56.1 124.9
65.8
C. SiH, SiHb SiH, H.Hb H,SiH, H,SiH, H,SiH, H,H,SiH, ‘) Ref. [S]. b, Ref. [7]. d, HF/6-31G*,ref. [9].
1.921 1.884 1.460 0.758 23.0 89.1 120.5 119.8
1.856 1.811 1.460 0.770 24.2 89.5 121.3 119.3
1.973 *’ 1.924 *’ 1.459 d’ 22.1 d’ 120.2 d’
‘) Ref. [5].
cal differences between a and b are characterized by the H&H, bond angles (~30” (a) versus 56” (b)) and H,H, bond lengths ( % 0.85 8, (a) versus 1.47 8, 0)). As is apparent from table 2, what was calculated at the HF/DZP and CI/DZP levels by Cabal101 et al. [ 8 ] is structure a while it is structure b that was located at the HF/4-3 1G level by Gordon [ 5 ] and the HF/6-2 1G level by Power et al. [ 7 1. As table 3 shows, a is z 7 kcal/mol ( x 5 kcal/mol after ZPC) more
stable than b at the HF/6-2 1G and HF/6-3 1G levels. This means that both Gordon and Power et al. failed to locate the more stable structure a at their calculational levels. In addition, we found that b has one imaginary b, frequency ( 10 16i cm- ’ at HF/6-2 1G and 971i cm-’ at HF/6-3 1G) and is a transition structure which leads to C3” symmetry. Upon addition of polarization functions, however, b becomes more stable than a, though it has still one imaginary frequency of 20 1i cm- ’ at the HF/6-3 1G(d) level, but
T. Kudo. S. Nagase / Jahn-Teller Table 3 Total (hartree)
and relative
(kcal/mol)
HF/6-21G + ZPC HF/6-3 1G + ZPC HF/6-3IG(d) +zpc HF/6-31G(d, p) + ZPC HF/6-31+G(2d, p) + ZPC MP2/6-31G(d, p) ‘) MP3/6-31G(d, p) b, MP4/6-3lG(d, p) b, +zpc
a) energies of C,,(a),
distortions of SiH+ and Si(CN,)+
C,,(b),
and the transition
structure
237
(TS) connecting
them
TS
L(a)
C,,(b)
-290.77222 -290.74513 - 290.78249 -290.75430 -290.81943 -290.78897 -290.83297 -290.80274 -290.83597 -290.80654 -290.93000 -290.94982 -290.95541 -290.92518
-290.76193 -290.73703 -290.77086 -290.74590 - 290.82264 - 290.79547 -290.83180 -290.80356 -290.83667 -290.80879 -290.92351 -290.94246 -290.94803 -290.91978
(6.5) (5.1) (7.3) (5.3) ( -2.0) ( -.4.1) (0.7) (-0.5) (-0.4) (- 1.4) (4.1) (4.6) (4.6) (3.4)
-290.76602
(10.3)
-290.81779
(1.0)
-290.83078 -290.80298
(1.4) (-0.2)
-290.92667 -290.94611 -290.95165 -290.92385
(2.1) (2.3) (2.4) (0.8)
a) Energies relative to C,,(a) in parentheses. ‘) Calculations on the HF/6-31G(d, p) geometries.
has only real frequencies at the HF/6-3 lG( d, p) or HF/6-31 +G(2d, p) levels; this suggests that Cabal101et al. also failed to calculate the more stable structure b at their HF/DZP level. As shown in fig. 2, we have managed to locate the transition structure connecting a and b at the HF level with several basis sets. As table 3 shows, a and b are separated by a small barrier. In order to examine the effect of electron correlation, we have carried out single-point MP2, MP3, and MP4 calculations on the HF optimized geometries. As shown in table 3, the energy of a is more intensely lowered by electron correlation than that of b, the former becoming more stable. In addition, electron correlation makes the transition state lie in energy below b, suggesting that b collapses to a without a barrier. To make this point clearer, structure b was reoptimized at the MP2/63 1G (d, p) level. As expected, b collapsed to a on the
Fig. 2. The HF/6-3 lG(d, p) optimized transition necting structures a and b in ii and degree.
structure
con-
MP2/6-31G(d, p) potential energy surface, and no stationary point was located which corresponded to b. Therefore, only structure a will be considered as the CzVstationary structure of SiH: in this paper. This contrasts with the fact that CH$ takes a b-like form in CaVsymmetry [ 2 1. On removal of the CzVsymmetry constraint, it was calculated that the SiH2 moiety is x0.25 8, further apart from the Hz moiety and is significantly rotated around the silicon atom at the HF and MP levels with the 6-31G(d, p) basis set. As table 2 shows, the resultant HF and MP optimized structures of C, symmetry are very similar to that calculated by Pople and Curtiss at the HF/6-31G* level except that electron correlation makes the distance between the SiHz and H2 moieties shorten by x 0.1 A. The presence of such a C, structure is again in contrast with the fact that the corresponding structure is absent in CH: . In the C, structure of SiH: , the SiHz and H2 portions are positively charged (0.818 e on Si) and essentially electroneutral, respectively, and have geometries very similar to those of the isolated SiH: and Hz. This allows one to represent the C, structure of SiH: as a complex of SiH: and Hz. It is interesting to note that the complex resembles in geometry the long-range potential well on the dissociation energy surface of the neutral silane ( SiH4+ SiHz + H2 ) [ 6 11. As is well known, the dissociation along the least-motion CIV path is symmetry forbidden according to the Wood-
238
T. Kudo, S. Nagase / Jahn-Teller
distortions of SiH + and Si(CH,)+
ward-Hoffmann rule [ 62 1, and therefore chooses a non-least motion path of C, symmetry with the progress of the reaction. The symmetry restriction would become less severe in radical processes. Nevertheless, the C, structure of SiHf is probably ascribable to the long distance between the SiH: and H2 moieties. 3.1.2. Relativestability Table 4 collects the total and relative energies of the Dzd, C3”, CzV, and C, stationary structures of SiH: calculated at the HF and MP levels with various basis sets. The harmonic vibrational frequencies calculated are summarized in table 5. At the HF level the most stable is the C, structure, as suggested by Pople and Curtiss [ 9 1. The DZd,C3”, Table 4 Total (hartree) and relative (kcal/mol)
a) energies of the C,, Czy, Ca,, and DZdstructures of SiH: a C,
calculations on the HF /6-31G(d, HF/6-31G(d, p) HF/6-31 +G(2d, p) HF/6-31 +G(2d, 2p) HF/6-31 +G(Zdf, 2p) +zpc b’ MP4 SDTQ/6-31G(d, p) MP4 SDTQ/6-31 +G(2d, p) MP4 SDTQ/6-31 +G(2d, 2p) MP4 SDTQ/6-31 +G(Zdf, 2p) +zpc b’
and C2”structures are about 35, 11, and 14 kcal/mol less stable than the C, structure, respectively, as shown in table 4. Within the HF approximation, the C3” structure is a4 kcal/mol more stable than the CzV structure, regardless of the basis sets employed. This finding conflicts with the fact that Cabal101et al. calculated the preference of CzVover CJVat the pseudopotential HF/DZP level in spite of their wrong location of the less stable structure of CzVsymmetry, as already pointed out. On the other hand, the order of decreasing stability C3”> CzV>Dzd is identical with that calculated by Gordon [ 5 ] and Power et al. [ 7 1. As the vibrational analyses in table 5 reveal, however, it was found at the HF level that the CzVand DZd stationary points have single (782i (b, ) cm- ’ ) and doubly degenerate (2234i (e) cm- ’ ) imaginary
p) geometries -290.85503 -290.85926 -290.86192 -290.86479 -290.83403 - 290.97004 -290.97795 -290.98858 -290.99829 -290.96753
calculations on the MP2/6-3 1G( d, p ) geometries MP2/6-31G(d, p) =) -290.95651 MP2/6-31G(d, p) -290.94618 MP2/6-31 +G(2d, p) -290.95260 -290.96135 MP2/6-31 +G(2d, 2p) -290.97026 MP2/6-31 +G(Zdf, 2p) MP3/6-31G(d, p) -290.96520 -290.97247 MP3/6-31 +G(2d, p) MP3/6-31G+(2d, 2p) -290.98256 MP3/6-31G+ (2df, 2p) -290.99215 -290.97050 MP4 SDTQ/6-31G(d, p) MP4 SDTQ/6-31 +G(2d, p) -290.97812 MP4 SDTQ/6-31 +G(2d, 2p) -290.98861 MP4 SDTQ/6-31 +G(2df, 2p) -290.99850 +ZPCd’ -290.96764 a) Energies relative to C, in parentheses. b, HF/6-31G(d, p) zero-point energies. ‘) All MOs are considered. d, MP2’/6-3lG(d, p) zero-point energies.
C 2”
C 3”
DZd
-290.83297 -290.83588 -290.83843 -290.84179 -290.81156 -290.95541 -290.96269 - 290.97270 -290.98383 - 290.95360
(13.8) (14.7) (14.7) (14.4) (14.1) (9.2) (9.6) ( 10.0) (9.1) (8.7)
-290.83793 -290.84311 -290.84481 -290.84744 -290.82076 -290.94192 -290.95106 -290.96116 -290.97134 -290.94466
(10.7) (10.1) (10.7) (10.9) (8.3) (17.6) (16.9) (17.2) (16.9) (14.4)
-290.80067 -290.80428 -290.80522 -290.80839 -290.78555 -290.92471 -290.93364 -290.94303 -290.95497 -290.93213
(34.1) (34.5) (35.6) (35.4) (30.4) (28.4) (27.8) (28.6) (27.2) (22.2)
-290.94072 -290.93013 -290.93624 -290.94471 -290.95472 -290.94992 -290.95694 -290.96665 -290.97744 -290.95549 -290.96281 -290.97292 -290.98405 -290.95410
(9.9) (10.1) (10.3) (10.4) (9.8) (9.6) (9.7) (10.0) (9.2) (9.4) (9.6) (9.8) (9.1) (8.5)
-290.93132 -290.92076 -290.92862 -290.93655 -290.94583 -290.93778 -290.94655 -290.95622 -290.96636 -290.94247 -290.95157 -290.96176 -290.97226 -290.94580
(15.8) (16.0) (15.0) (15.6) (15.3) (17.2) (16.3) (16.5) (16.2) (17.6) (16.7) (16.8) (16.5) (13.7)
-290.90790 -290.89701 -290.90448 -290.91178 -290.92203 -290.91781 -290.92638 -290.93525 -290.94662 -290.92474 -290.93363 -290.94295 -290.95481 -290.92423
(30.5) (30.9) (30.2) (31.1) (30.3) (29.7) (28.9) (29.7) (28.6) (28.7) (27.9) (28.7) (27.4) (27.2)
T. Kudo. S. Nagase / Jahn-Teller Table 5 Harmonic
vibrational
frequencies
HF
MP2
4197 2489 2427 1116 951 805 701 631 183
4025 2461 2393 1197 920 878 731 690 252
239
’ ) of SiH: calculated with the 6-3 1G (d, p ) basis set C Z”
C,
a’ a” a’ a’ a’ a’ a” a’ a”
(cm-
distortions of SiH + and Si(CH,)+
a, b2 a, b, a, aI bz a, b,
C 3” HF
MP2
2843 2551 2467 1777 1221 916 794 701 7821
2635 2532 2439 1790 1287 937 788 739 607i
frequencies, respectively, and are not the minima on the HF potential energy surface of SiW . The vibrational mode of the imaginary frequency of the Czv structure corresponds to distortion to C, symmetry, while those of the DZd structure lead to distortion to C3” symmetry. On going from the HF to MP levels, the Dzd structure possesses only real vibrational frequencies but the Czv structure has still a single b, imaginary frequency of 607i cm-‘, as shown in table 5. As calculated at the HF level, the DZd structure is the most unstable also at the MP level, the most stable being the C, structure, as shown in table 4. However, electron correlation reverses the relative stability of the C3”and Czv structures, the latter becoming = 7 kcal/ mol more stable than the former at any levels of MP calculations. The similar energy difference favoring C2” over CJv was also calculated at the pseudopotential CI/DZP level by Cabal101et al., while Power et al. calculated that C2” is 4.8 kcal/mol less stable even at the CI/6-21G//HF/6-21G level, probably because they did not locate correctly the Czv structure. As table 4 shows, the relative energies at the MP level are almost insensitive to the basis sets, the order of perturbation, and geometries employed. The most reliable energies at the MP4 SDTQ/6-3 1 + G (2df, 2p)//MP2/6-31G(d, p) level yield the relative stability (kcal/mol) which decreases in the order C,(0.0)>C2,(9.1)>CJ,(16.5)>D2,(27.4). Zeropoint correction (ZPC) made with the MP2/63 1G( d, p) harmonic vibrational frequencies yields a final prediction of C,(0.0)>C2v(8.5)>Cj,( 13.7) > Dzd( 27.2) for the relative stability of SiH: . This
e a, e a, a, e
D2d HF
MP2
2521 2455 1013 908 452 415
2481 2408 974 875 679 370
e a, b2 b, e a, bz
HF
MP2
1697 2183 1968 969 2234i 763 750
2536 2185 2012 938 844 786 743
provides an interesting contrast with the fact that in CH: the Czv structure is the most stable energy minimum and the relative stability (kcal/mol) decreases in the order Cz,(0.0)>D,,(2.6)>C,,(12.3) at the MP4 SDTQ/6-31 +G(2df, 2p)//MP2/6_31G(d, p) level. 3. I. 3. Ionization energies Table 6 summarizes the adiabatic ionization energies of SiH4 calculated at various levels of theory. The adiabatic ionization energies assigned in the various early spectroscopic studies are in the range of 11.5-l 4 eV but are suggested to be probably below 11.8 eV [ 27-321. The present calculated values of 12.09 (DZd), 11.50 (C,,), and 11.28 (C,,) eV at the MP4 SDTQ/6_31+G(2df, 2p)//MP2/6_31G(d, p)+ ZPC level may suggest that the experimentally assigned values are the adiabatic ionization to the Cs, structure. On the other hand, it is noteworthy that the adiabatic ionization energy (10.91 eV) calculated for the most stable C, structure coincides perfectly with the peak at 1 l.OO? 0.02 eV observed in the very recent photoionization mass spectroscopic study [ 371. 3.1.4. Kinetic stability In most photoionization [ 33-371 and guided ion beam [63] studies, only the fragment ions such as SiH,+ and SiH: have very frequently been detected instead of the parent radical cation, SiHa . In order to assess the kinetic stability of SiH$ , we have investigated the fragmentation processes of the most stable C, as well as the second most stable C,, minimum
T. Kudo, S. Nagase / Jahn-Teller
240
distortions ofSiH + and Si(CH,)+
Table 6 Adiabatic ionization potentials (eV) of SiH4 calculated on the MP2/6-3lG(d,
HF/6-3lG(d, p) HF/6-31 +G(Zdf, 2p) MP2/6-3lG(d, p) a) MP2/6-3lG(d, p) MP2/6_3l+G(2df, 2p) MP3/6-3lG(d, p) MP3/6-31 +G(Zdf, 2p) MP4 SDTQ/6-3lG(d, p) MP4 SDTQ/6-31 +G(Zdf, 2p) +ZPCb’
p) geometries
C,
C2”
C3”
DZd
10.24 10.17 10.70 10.69 10.84 10.74 10.94 10.75 10.96 10.91
10.83 10.77 11.13 11.13 11.26 11.16 11.34 11.16 11.35 11.28
10.69 10.63 11.39 11.38 11.50 11.49 11.64 11.51 il.67 11.50
11.71 11.69 12.03 12.03 12.15 12.03 12.18 12.00 12.15 12.09
‘) All MOs are considered. b, MP2/6-3lG(d, p) zero-point energies.
structure. The energies and structures of the fragment ions are summarized in table 7. First examined is the dissociation of the CsVstructure which leads to the formation of SiH$ and H, ‘A, SiH$ (&,)+‘A,,
SiH,+ (D3,,)+H.
This reaction was calculated to be 10.2 kcal/mol endothermic at the MP4 SDTQ/6-31 +G(2df, 2p) //MP2/6-3 1G( d, p) level. Zero-point correction made with the MP2/6-3 lG(d, p) frequencies decreases the endothermicity to 8.3 kcal/mol. These values are larger than the HF/4-3 1G value ( 1.7 kcal /mol) calculated by Gordon [ 5 ] but are rather close to the CI/DZP value (8.5 kcal/mol) calculated by Cabal101et al. [ 81. In order to check whether or not there is an energy barrier for the dissociation, we chose the distance (R) between SiH: and H as the reaction coordinate and optimized all other geometrical parameters for several selected values of R. Fig.
3 shows the changes in the potential energy as a function of R. Upon going from SiH: (C,, ) to SiH$ + H, the energy increases monotonously, there being no barrier for the dissociation. This means that the dissociation of the CsVstructure is only hindered by a small amount of energy ( x 8 kcal/mol). In addition, it was found that the C,, structure collapses to the C, structure with a slight barrier ( 1.06 kcal/mol at MP2/6-3 1G (d, p ) ) via a transition structure shown in fig. 4; the barrier decreases to -0.01 kcal/ mol and almost disappears at the MP4 SDTQ/6-3 1 + G( 2df, 2p)//MP2/6-31G(d, p) level. Thus, we have next investigated the dissociation of the most stable C, structure of SiH$ which leads to SiH,+ and Hz,
Table 7 The MP4 SDTQ/6-3 1+G(2df, 2p) total energies (hartree) calculated at the MP2/6-3lG(d, p) optimized (8, and degree) of the frament ions
SiHZ (Dx, ) SiHZ (C,, 1 H2 H
Total energy ‘)
Structure
-290.45778 (-290.43439) -289.80724 (-289.79424)
SiH= 1.455 SiH= 1.469 L HSiH = 120.0 HHc0.734
- 1.16863 -0.49823
(- 1.15813)
a) In parentheses are values corrected by MP2/6-31G(d, p) zeropoint energies.
Fig. 3. Potential energy curves for the dissociations of the Cx, and C. structures of SiHJ as a function of R at the MP4 SDTQ/631 +G(Zdf, 2p)//MP2/6-3lG(d, p) level.
T. Kudo, S. Nagase/ Jahn-Teller distortionsof SiH+ and Si(CH,)+
241
MP3/6-31G(d)//HF/6_31G(d) level. Theselarger endothermic energies suggest that SiF,’ is more kinetically stable. At this point, it is interesting to note that the spectra of SiF: have frequently been detected in the recent spectroscopic studies [ 65-681. 3.2. Si(CH,)t
167,Y Fig. 4. The MP2/6-31G(d, p) optimized transition structure connecting the C, and Cfv structures in A and degree.
‘A’ SiH$ (C,)+*A,
SiH2+(C,,)+‘C,’
H,(D,,)
.
This reaction is 14.2 kcal/mol endothermic at the MP4 SDTQ/6-31 +G(2df, 2p)//MP2/6-31G(d, p) level. However, it becomes 9.6 kcal/mol endothermic after the MP2/6-3 1G (d, p ) zero-point energies are included. These values are much smaller than the value of 61.6 kcal/mol (53.9 kcal/mol after ZPC) calculated at the same level by us for the corresponding dissociation of the most stable C2” structure in CH,+. To examine whether the dissociation of SiH: (C, ) is hindered by a significant energy barrier, the distance (R) between the silicon atom in SiH: and the midpoint of the H-H bond in H2 was taken as the reaction coordinate and the potential energy changes were calculated as a function of R. These results are also shown in fig. 3. As characterized by the monotonous energy increasing, the energy required for the dissociation of the C, structure of SiH, is = 10 kcal/mol. As is apparent from these calculations, SiH: is relatively unstable to fragmentation in a kinetic sense. This certainly makes it considerably difficult to confirm experimentally the intermediacy of SiH$ . The kinetic unstability of SiH: may result from the relatively weak Si-H bonds. Thus, the hydrogens in SiH: were all replaced by fluorine atoms because it is known that Si-F bonds are unusually strong [ 641. In the preliminary calculations of SiFz , the C, structure, rather resembling the &-like structure, was found to be the most stable. The dissociations into SiF: +F and SiF: +F2 were calculated to be 19.5 and 129.3 kcal/mol endothermic, respectively, at the
3.2. I. Structures Tetramethylsilane, Si ( CH3) 4, has Td symmetry in the ground state, as shown in fig. 5. Its electron configuration is (core)(4a,)2(3t2)6(5a,)2(4t2)6(le)4(lt,)V5t*Y.
As mentioned in the introduction, the solid-state ESR study shows that the radical cation adopts CzV symmetry. Thus, we first optimized the structure with CzV symmetry constraint. The resultant optimized structure is shown in fig. 6. As characterized by the long C,-C, bond length of 2.8 12 A, the CzVstructure is rather similar to structure b located in CzVsymmetry for SiH$ . In several ways, we searched for the second CzVstructure which has the smaller C,-C, bond length and resembles structure a in SiH: . However, we were unable to locate the second CzVstructure which might be represented as a product for the ad-
Fig. 5. The HF/6-31G(d) optimized Td structures of Si(CH3)4 in A and degree. The total energy is - 447.4 1355 hartree and it is -448.02265 hartree at the MP2/6-3lG(d)//HF/6-31G(d) level.
242
Fig. 6. The HF/6-31G(d) Si(CH,)$ in 8, and degree.
T. K&o, S. Nagase /.lahn-Teller
optimized
CZy structure
of
dition of the dimethylsilylene cation radical (Si(CH,)T) totheC-Cbondofethane (C2H6).As demonstrated in the study of SiH: , CZVstructures are liable to undergo distortion to CsVand C, structures, respectively. Therefore, we next searched for the stationary points of C3” or C, symmetry. Fig. 7 shows the optimized CsV structure of Si( CH3 )$ . As the geometrical parameters show, the
distortions of SiH + and Si(CH,)+
CJ, structure may be regarded as a complex of the trimethylsilyl cation (Si ( CH3 ) 3’ ) and methyl radical (CH,). This is also supported from the spin and charge density distributions: the spin density is almost localized with 0.974 eon the carbon atom in the CH3 moiety while the great amount of positive charge ( + 1.090 e) is on the silicon atom in the Si(CH3)3 moiety. The Si ( CH3 ) 3 and CH3 moieties are 2.4 11 A apart in the C3” structure. This distance is 0.517 8, (27.3%) longer than that (1.894 A) in the neutral Si( CH,)4 ( Td) . However, the lengthening is considerably small compared with the corresponding value of 0.763 A (51.7 %) calculated at the same level on going from SiH4 ( Td) to SiHZ ( C3”). According to this, the Si (CHr ): moiety in Si ( CH3 )$ is less deformed than the SiH: moiety in SiH$ . Also located is the C, structure. As fig. 8 shows, it is quite different from the C, structure of SiH: . The C, structure of Si (CH3 )4’ can be best regarded as a weak complex of Si ( CH3 ) $ and C2H6. In this open C, structure, the positively charged silicon atom of Si (CH, ): is bound to one of the negatively charged carbon atoms of CzH6 as much as 3.08 1 A away and makes an angle of 159.2“ with the C-C bond of CzH6 to avoid steric repulsion. Fig. 9 shows the optimized structures of the fragment ions Si( CH3 ): and Si( CH3 )$ . These fragment ions have CJh and C2 symmetry, respectively, in the most stable conformations. 3.2.2. Relative and kinetic stability Table 8 compares the total and relative energies of the CZV,C3”, and C, structures of Si(CH3 )$ calculated at the HF/6-3lG(d) and MP2/6-31G(d)
C,CbSiCc=
Fig. 7. ‘The HF/6-31G(d) Si ( CHJ )z in A and degree.
optimized
C,,
structure
of
61.7
Fig. 8. The HF/6-31G(d) in 8, and degree.
optimized C, structure of Si(CH,):
T. Kudo, S. Nagase / Jahn-Teller
n
T
a
C
v
CSiCHa=
58.2
CSiCHb=
-59.1
CSiCHc=
179.6
Fig. 9. The HF/6-31G(d) optimized Si(CH,):(Cg,,)andSi(CH3):(Cz)inAanddegree.
structures
of
/ /HF/6-3 1G ( d ) levels. At both levels, the CsVstructure is the most stable unlike the SiH,+ case and the CzVstructure is the second most stable. The Cs, structure is 13.3 kcal/mol more stable than the CzVstruc-
243
distortions of SiH + and Si(CH,)+
ture at the HF level. Electron correlation decreases the energy difference but its effect is too small to reverse the relative stability unlike the SiW case. Because of the size of the molecule, we calculated the vibrational frequencies at the HF/3-21G level. According to the vibrational analyses, the CsV and C, structures are the energy minima, but the Czy structure has a single imaginary frequency of 1167i(b, ) cm- I. The vibrational mode of the great imaginary frequency corresponds to distortion to the most stable Cs, structure: the CzV structure is a transition structure for the conformational interconversion from one C3”to the other C3” structures. As table 8 shows, the barrier for the interconversion is 6.3 kcal/mol (6.1 kcal/mol after ZPC) at the MP2 level. This small barrier rather suggests that there is a considerably rapid dynamical equilibrium, C3V+C2V~C3V,and it may blur the experimental spectra. The more sophisticated calculations may be required for the exact evaluation of the small barrier height. However, it is instructive to remember that relative energies at the MP level are almost independent of the basis sets (including d functions), the order of perturbation, and geometries, as demonstrated in the SiH: system. In this view, we conclude that the CJ, structure should be observed at low temperatures. At this point, it is instructive to note that Cs, structures are suggestedforC(CH,)t [69],Sn(CH,)$ [13,15],and Pb ( CHs )a [ 15 ] at 4.2,77, and 85 K, respectively. As table 8 shows, the C, structure of Si ( CHJ )a is the most unstable and is 13.7 kcal/mol ( 16.3 kcal/ mol after ZPC) more unstable than the CfVstructure at the MP2 level. As expected from the weak complex character, the C, structure is very subject to the decomposition into Si(CH,)$ and C2H6; the energy
Table 8 Total (hartree) and relative 31G(d) basis set
(kcal/mol)
‘) energies of Si(CHp ): calculated
HF C 3” C 2” C, Si(CH,)$ Si(CH,)Z ‘) Values in parentheses. b, HF/3-2 1G zero-point
+CH3 +CzH6
energies.
-447.10757 -447.08634 -447.08151 -447.08681 -447.07598
on the HF/6-3
MP2 (0.0) (13.3) (16.4) (13.0) (19.8)
-447.68776 -447.67778 -447.66585 -447.65690 -447.65525
lG(d)
optimized
MP2+ZPC (0.0) (6.3) (13.7) (19.4) (20.4)
-447.53338 -447.52372 -447.50740 -447.50803 -447.49804
geometries
b, (0.0) (6.1) (16.3) (15.9) (22.2)
with the HF/6-
244
i? Kudo, S. Nagase/ Jahn- Teller distortionsof SiH + and Si(CH,)+
required for this decomposition is only 6.7 kcal/ mol (5.9 kcal/mol after ZPC) at the MP2 level, as shown in table 8. On the other hand, the dissociation of the most stable Csv structure into Si ( CH3 ) : and CHJ is calculated to be 19.4 kcal/mol ( 15.9 kcal/ mol after ZPC) endothermic at the MP2 level. This endothermic energy is more than three times greater than that calculated at the same level for the corresponding dissociation of SiH: ( Cfv ), suggesting that tetramethyl substitution makes silane radical cations much less fragile.
Acknowledgement
All calculations were carried out at the Computer Center of the Institute for Molecular Science with the GAUSSIAN 82 [ 711 program in IMS Computer Center library program package. This work was supported in part by a grant from the Ministry of Education, Science, and Culture in Japan.
References
3.2.3. Ionization energies The adiabatic ionization energies of the C3”, C2”, and C, structures of Si ( CH3 )4 were calculated to be 9.11,9.38,and9.71eV(9.01,9.27,and9.72eVafter ZPC), respectively, at the MP2/6_31G(d)//HF/631G(d) level. These are close to the values of 9.42 [ 701 and 9.6 [ 221 eV assigned experimentally. The calculated and experimental values are e2.0 eV smaller than those of SiH,+. This is ascribable to the rising of the HOMO energy levels upon going from SiH, (-13.2eV)toSi(CH3)4(-11.4eV). 4. Concluding remarks In an attempt to resolve several discrepancies in the Jahn-Teller distortion of silane radical cations of current interest, we have performed the ab initio calculations of SiHa and Si ( CH3 ) .$ at higher levels of theory. The C, structure is the most stable minimum in SiHa and the relative stability decreases in the order C, > C2”> C3”> D2+ It is found that the Czv structure is a transition structure which leads to the C, structure while the second most stable Csv minimum structure collapses to the C, structure almost without a barrier. The adiabatic ionization to the most stable C, structure is predicted to be at 10.9 1 eV. However, it should be noted that the C, structure is relatively unstable to the fragmentation into SiH$ and Hz. On the other hand, the C3” structure is the most stable in Si ( CH3 )2. The Czv structure is again a transition structure. Two equivalent Cj, structures are easily interconvertible via the Czy transition structure. Interesting is that Si(CH3 )z is more stable to fragmentation than SiH: . The C, structure is also located in Si ( CHs ) a. However, it is much more unstable than the Cjv structure and decomposes easily.
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JAHN-TELLER
DISTORTIONS OF SiH; AND Si(CH&
Takako KUDO and Shigeru NAGASE Department of Chemistry, Faculty ofEducation,
Yokohama National University, Yokohama 240, Japan
Received 14 January 1988
In view of current interest in silane radical cations, the Jahn-Teller distortions of SiH: and Si(CH,)4+ to the Dzd, C3”, Clvr and C, structures are investigated by means of ab initio calculations with flexible basis sets and electron correlation. The C, structure is found to be the most stable in SiH4, as suggested in a recent theoretical study. On the other hand, the C3, structure is the most stable in Si( CHJ )$ , unlike the suggestion from the ESR study. This contrasts with the fragile C3, structure in SiH: . The relative stabilities (kcal/mol) of SiH: and Si(CH,): decrease in the order C,(O.O) > r&(8.5) >C&( 13.7) >Dz4(27.2) at the MP4 SDTQ/6-31+G(Zdf, 2p)//MP2/6-31G(d, p)+ZPC level and Cs,(0.0)>C,,(6.1)>C,(16.3) at MP2/6_31G(d)//HF/63 lG(d) +ZPC level, respectively. In both SiH: and Si( CH, )$, the CrVstructures are not energy minima but transition structures for the rearrangement to the most stable structures. An interesting finding is that Si(CH,): is much more stable to fragmentation than SiH: .
1. Introduction
It is well known that the methane radical cation, distortion from the tetrahedral Td symmetry of the neutral species to the lower Dzd, C3”, or C2” symmetry to have a nondegenerate ground state. For a long time, it was controversial which symmetry the ground state takes [ l-3 1. Now that a Czv ground-state structure is experimentally and theoretically established [ 1,2], it is natural that current effort is directed towards the heavier analogous XR: (X=Si [4-91, Ge [6,8,10-111, Sn [8,12-18],orPb [15]). Silane (SiH,) and its fragment ions have recently received special attention. The principal reason for this attention is because plasma chemical vapor deposition (CVD) processes are used as important sources of high-purity amorphous silicon. In these processes silane is decomposed by electric discharge. Appearance energies and ionization cross sections of SiH: and SiH: have repeatedly been investigated by means of the electron- and photon-impact dissociative ionization methods [ 19-26 1. However, the photoelectron [ 27-321 and photoionization [ 33-371 mass spectrometrical studies of silane have raised a growing interest in the intermediacy and role of the CH: , can undergo Jahn-Teller
0301-0104/88/$03.50 0 Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division )
silane radical cation, SiH: . The structure of SiH: was first investigated by Hartmann et al. [ 41 by means of one-center expansion calculations with a minimal basis set. They found that the square-planar D4,, structure is more stable than the C3” structure. In contrast, Gordon [ 51 calculated at the HF/4-31G level that the C& structure is the most stable and the relative stability decreases in the order Csv> Czv> DZd, unlike the case of CH: [ 2 ] . This ordering was also confirmed by Power et al. [7] by means of the HF/6-21G and CI/62 1G//HF/6-2 1G calculations. However, recent pseudopotential HF/DZP and CI/DZP calculations by Cabal101et al. [ 8 ] showed that the Czv structure is more stable than the Csv structure. Very recently, Pople and Curtiss calculated at the HF/6-3 1G* level that the C, structure is the most stable minimum on the SiH: potential energy surface [ 91. On the other hand, it is suggested from the ESR study by Walther and Williams [ 61 that the methyl-substituted radical cation, Si ( CH3 )2, has C2”symmetry rather than Csv symmetry. In view of the apparent discrepancies, we have undertaken the ab initio calculations of the Jahn-Teller distortions of SiHf and Si(CH3 )$ at higher levels of theory. Our primary concern is to resolve (i ) which
T. Kudo, S. Nagase / Jahn-Teller
234
symmetrical structure is the most stable, (ii) to what extent it is kinetically stable to fragmentation, and (iii) how the relative and kinetic stabilities are influenced by substituents. To this end, it will be shown that SiH: has C, symmetry in the ground state, as suggested by Pople and Curtiss [ 91, but is relatively unstable to fragmentation. On the other hand, Si( CH, )$ prefers CJv symmetry, unlike the experimental suggestion by Walther and Williams [ 61, and is kinetically more stable to fragmentation.
distortions of SiH+ and Si(CH,)”
diffuse sp functions on Si, double sets of d polarization functions on Si, double sets of p polarization functions on H, and a set off polarization functions on Si. Zero-point correction (ZPC) was made by using the HF/3-21G, HF/6-31G(d, p), and MP2/63 1G (d, p) harmonic vibrtational frequencies. In the following, the symbol “//” means “at the geometry of”.
3. Results and discussion 2. Computational details
3.1. SiH4+
The spin-restricted Hartree-Fock (RHF) method was used for closed-shell singlet states, while spin-unrestricted Hartree-Fock (UHF) calculations were carried out for open-shell doublets. The computed expectation values of the spin-squared operator ( S2) were in the range of 0.750-0.795 for all doublet species considered here: the relatively large values ( x0.79) were for the DZdstructure of SiH: and the Czv structure of Si(CH3)$. However, these are all close to the correct value of 0.750 for pure doublets. Geometries were optimized at the HF level with the split-valence 3-2 1G basis set [ 38,39 ] and the polarized 6-3 1G(d) and 6-3 1G (d, p) basis sets (which are also referred to as 6-3 lG* or 6-3 lG** ) [ 40 ] by means of the analytic energy gradients, and identified as equilibrium or transition structures by calculating analytically the Hessian matrices. To incorporate the effect of electron correlation, the HF/6-3 1G (d, p) geometries were reoptimized by using second-order Moller-Plesset perturbation theory (MP2) [41] and the 6-31G(d, p) basis set [40] for SiHz . The Hessian matrices were calculated by differentiating numerically the analytic first derivatives of the MP2 energies. Energies were improved by means of the MP theory #’ up to full fourth-order (MP4 SDTQ) [ 43 ] with the constraint that core-like orbitals were doubly OG cupied. The basis sets employed in these calculations were 6-31G(d), 6-31G(d, p), 6-31+G(2d, p), 631+G(2d, 2p), and 6-31+G(2df, 2p) [44]. The largest 6-3 1+ G (2df, 2p) basis set includes a set of
3.1.1. Structures Silane (SiH,) has a ‘A1 ground state in the tetrahedral Td form and the ground electron contiguration is (la, )2(2a, )‘(lt, )Y3al
Merller-Plesset
theory is described
in ref.
[ 42I.
I6
.
A lot of theoretical [ 39,40,45-501 and experimental [ 5 l-55 ] studies are already available for its geometry and vibrational frequencies. Table 1 compares the present calculations with some previous data. As shown in this table, the MP2/6-3 1G (d, p) geometry and frequencies are very close to the experimental values, compared with the HF/6-3 lG( d, p) values. In addition, the MP values are in good agreement with the CI values reported recently by Allen and Schaefer ]501. Ionization from the highest occupied 2t2 orbital to give SiH,+ leads to a three-fold degenerate state, 2T2, in the tetrahedral form. The energy for this vertical ionization was 12.83 eV at the MP4 SDTQ/631+G(2df,2p)//MP2/6-31G(d,p)levelandagrees very well with the CEPA value of 12.68 eV [ 561 #’ as well as the experimental value of 12.8 eV [ 27,291. According to the Jahn-Teller theorem [ 601, the degenerate 2T2 state can interact with the e and t2 vibrational modes and distort into some lower symmetry. Thus, the structures and relative energies of the lower DZdr C3”, C2”, and C, symmetries have extensively been investigated at several levels of theory [ 4,5,7-9 1, while it is surprising that the Hessian matrices have never been calculated to check if the structures are 42For
#’Third-order
12W2
the perturbation (12.3 eV), SCF (13.0 eV) and Xa (11.8 eV) values see refs. [ 57-591, respectively.
T. Kudo, S. Nagase / Jahn-Teller
distortions of SiH+ and Si(CH,)+
235
Table 1 Geometries and vibrational frequencies of SiH4 Method
r,(SiH) (A)
calculation CISD/DZP(Bl) ‘) CISDIDZP(B2) a) HF/6-31G(d, p) b, MP2/6-31G(d, p) ‘) experiment measured ( 1) (2) harmonic ( 1) (2)
1.4717 1.4755 1.4683 1.4726
a =)
1.4741
‘) g’
1.4806
Vibrational frequencies (cm-‘) vr(ar)
v2(e)
v,(tz)
vq(t2)
2334 2304 2379 2347
1022 1010 1066 1018
2337 2299 2357 2360
987 962 1032 974
2187 2186 2377 2268
974 972 975 960
2191 2189 2319 2273
914 913 945 929
‘) Ref. [50]. Bl: Si( 1ls7pld/6s4pld) and H(4slp/2slp). B2: Si( 12s9p2d/6s5p2d) and H(6s2p/4s2p). b, Ref. [47]. ‘) This work. d, Ref. [52]. ‘) Estimated r, from ref. [ 55] and frequencies from ref. [ 541. ‘) Ref. [53]. 8, r, from ref. [ 541 and predicted frequencies from ref. [ 501.
minima on the potential energy surface, except the recent study by Pople [ 9 ] on the C, structure. The DZd, C3”, CzV,and C, structures of SiH: are
a
Hb
I
H4
Hd’ \ Ha D2d
tib
c3v
.AHa
H?llia Cada)
C2v(b)
Fig. 1. The Dzdr CXv,Czy, and C, structures of SiH$
schematically displayed in fig. 1. The geometrical parameters optimized with the symmetry constraint at the HF/6-31G(d, p) and MP2/6-31G(d, p) levels are summarized in table 2. For comparison, previous results are also given in table 2. For the DZd and CzV structures, the HF/6-31G(d, p) geometries are very similar (within 0.027 A for lengths and 1” for angles) to the MP2/6-31G(d, p) geometries, suggesting that electron correlation has little effect on geometry optimization, as found in CH$ [ 2 1. However, this is not the case for the Cg, structure of SiH: ; the MP2 optimized SiH bond length ( 1.949 A) between the SiH3 and H moieties is 0.131 A shorter than the HF value (2.080 A). The same shortening of 0.13 1 A is also found in the pseudopotential HF/DZP and CI/DZP calculations by Cabal101et al. [ 81. As is apparent from the geometrical parameters in table 2, the C,, structure may .be regarded as a complex of SiH$ and H. An interesting finding is that two distinct structures, a and b, were located with CzVsymmetry constraint, as shown in fig. 1. Both have ‘Bi electronic states and give similar electron distributions. However, a and b differ in the spin density distributions. In a the spin density is almost localized on the silicon atom, while in b it is considerably delocalized onto the H, atoms in the H,H, bond. The main geometri-
T Kudo, S. Nagase /Jahn-Teller
236 Table 2 Optimized
geometrical
parameters
of the Dzd, Cs,,
distortions of SiH+ and Si(CH,)+
C,,(a), C,,(b), and C, structures of SiH: in A and degree DZP a’
6-31G(d,p)
6-21G
HF
MP2
HF
CI
SiH, H,SiH,
1.510 137.2
1.505 136.5
C 3” SiH, SiHb H,SiHb
2.080 1.455 92.5
1.949 1.456 92.9
2.073 1.460 93.4
1.942 1.472 93.2
1.646 1.448 0.848 2.750 29.9 143.5
1.625 1.447 0.875 2.742 31.2 142.6
1.660 1.452 0.884 2.767 30.9 144.7
1.679 1.462 0.897 2.790 31.0 145.2
b,
4-31G”
HF
HF
1.525 140.0
1.535 140.0
2.403 1.466 91.4
2.286 1.472 91.7
I .609 I .466 1.722 2.575 64.7 122.9
1.634 1.468 1.775
DZd
C&a) SiH, SiH, H,H, HbHb H,SiH. HbSiHb L(b) SiH, SiHb H,H. HbHb H,SiH, H,SiH,
1.563 1.452 1.471 2.575 56.1 124.9
65.8
C. SiH, SiHb SiH, H.Hb H,SiH, H,SiH, H,SiH, H,H,SiH, ‘) Ref. [S]. b, Ref. [7]. d, HF/6-31G*,ref. [9].
1.921 1.884 1.460 0.758 23.0 89.1 120.5 119.8
1.856 1.811 1.460 0.770 24.2 89.5 121.3 119.3
1.973 *’ 1.924 *’ 1.459 d’ 22.1 d’ 120.2 d’
‘) Ref. [5].
cal differences between a and b are characterized by the H&H, bond angles (~30” (a) versus 56” (b)) and H,H, bond lengths ( % 0.85 8, (a) versus 1.47 8, 0)). As is apparent from table 2, what was calculated at the HF/DZP and CI/DZP levels by Cabal101 et al. [ 8 ] is structure a while it is structure b that was located at the HF/4-3 1G level by Gordon [ 5 ] and the HF/6-2 1G level by Power et al. [ 7 1. As table 3 shows, a is z 7 kcal/mol ( x 5 kcal/mol after ZPC) more
stable than b at the HF/6-2 1G and HF/6-3 1G levels. This means that both Gordon and Power et al. failed to locate the more stable structure a at their calculational levels. In addition, we found that b has one imaginary b, frequency ( 10 16i cm- ’ at HF/6-2 1G and 971i cm-’ at HF/6-3 1G) and is a transition structure which leads to C3” symmetry. Upon addition of polarization functions, however, b becomes more stable than a, though it has still one imaginary frequency of 20 1i cm- ’ at the HF/6-3 1G(d) level, but
T. Kudo. S. Nagase / Jahn-Teller Table 3 Total (hartree)
and relative
(kcal/mol)
HF/6-21G + ZPC HF/6-3 1G + ZPC HF/6-3IG(d) +zpc HF/6-31G(d, p) + ZPC HF/6-31+G(2d, p) + ZPC MP2/6-31G(d, p) ‘) MP3/6-31G(d, p) b, MP4/6-3lG(d, p) b, +zpc
a) energies of C,,(a),
distortions of SiH+ and Si(CN,)+
C,,(b),
and the transition
structure
237
(TS) connecting
them
TS
L(a)
C,,(b)
-290.77222 -290.74513 - 290.78249 -290.75430 -290.81943 -290.78897 -290.83297 -290.80274 -290.83597 -290.80654 -290.93000 -290.94982 -290.95541 -290.92518
-290.76193 -290.73703 -290.77086 -290.74590 - 290.82264 - 290.79547 -290.83180 -290.80356 -290.83667 -290.80879 -290.92351 -290.94246 -290.94803 -290.91978
(6.5) (5.1) (7.3) (5.3) ( -2.0) ( -.4.1) (0.7) (-0.5) (-0.4) (- 1.4) (4.1) (4.6) (4.6) (3.4)
-290.76602
(10.3)
-290.81779
(1.0)
-290.83078 -290.80298
(1.4) (-0.2)
-290.92667 -290.94611 -290.95165 -290.92385
(2.1) (2.3) (2.4) (0.8)
a) Energies relative to C,,(a) in parentheses. ‘) Calculations on the HF/6-31G(d, p) geometries.
has only real frequencies at the HF/6-3 lG( d, p) or HF/6-31 +G(2d, p) levels; this suggests that Cabal101et al. also failed to calculate the more stable structure b at their HF/DZP level. As shown in fig. 2, we have managed to locate the transition structure connecting a and b at the HF level with several basis sets. As table 3 shows, a and b are separated by a small barrier. In order to examine the effect of electron correlation, we have carried out single-point MP2, MP3, and MP4 calculations on the HF optimized geometries. As shown in table 3, the energy of a is more intensely lowered by electron correlation than that of b, the former becoming more stable. In addition, electron correlation makes the transition state lie in energy below b, suggesting that b collapses to a without a barrier. To make this point clearer, structure b was reoptimized at the MP2/63 1G (d, p) level. As expected, b collapsed to a on the
Fig. 2. The HF/6-3 lG(d, p) optimized transition necting structures a and b in ii and degree.
structure
con-
MP2/6-31G(d, p) potential energy surface, and no stationary point was located which corresponded to b. Therefore, only structure a will be considered as the CzVstationary structure of SiH: in this paper. This contrasts with the fact that CH$ takes a b-like form in CaVsymmetry [ 2 1. On removal of the CzVsymmetry constraint, it was calculated that the SiH2 moiety is x0.25 8, further apart from the Hz moiety and is significantly rotated around the silicon atom at the HF and MP levels with the 6-31G(d, p) basis set. As table 2 shows, the resultant HF and MP optimized structures of C, symmetry are very similar to that calculated by Pople and Curtiss at the HF/6-31G* level except that electron correlation makes the distance between the SiHz and H2 moieties shorten by x 0.1 A. The presence of such a C, structure is again in contrast with the fact that the corresponding structure is absent in CH: . In the C, structure of SiH: , the SiHz and H2 portions are positively charged (0.818 e on Si) and essentially electroneutral, respectively, and have geometries very similar to those of the isolated SiH: and Hz. This allows one to represent the C, structure of SiH: as a complex of SiH: and Hz. It is interesting to note that the complex resembles in geometry the long-range potential well on the dissociation energy surface of the neutral silane ( SiH4+ SiHz + H2 ) [ 6 11. As is well known, the dissociation along the least-motion CIV path is symmetry forbidden according to the Wood-
238
T. Kudo, S. Nagase / Jahn-Teller
distortions of SiH + and Si(CH,)+
ward-Hoffmann rule [ 62 1, and therefore chooses a non-least motion path of C, symmetry with the progress of the reaction. The symmetry restriction would become less severe in radical processes. Nevertheless, the C, structure of SiHf is probably ascribable to the long distance between the SiH: and H2 moieties. 3.1.2. Relativestability Table 4 collects the total and relative energies of the Dzd, C3”, CzV, and C, stationary structures of SiH: calculated at the HF and MP levels with various basis sets. The harmonic vibrational frequencies calculated are summarized in table 5. At the HF level the most stable is the C, structure, as suggested by Pople and Curtiss [ 9 1. The DZd,C3”, Table 4 Total (hartree) and relative (kcal/mol)
a) energies of the C,, Czy, Ca,, and DZdstructures of SiH: a C,
calculations on the HF /6-31G(d, HF/6-31G(d, p) HF/6-31 +G(2d, p) HF/6-31 +G(2d, 2p) HF/6-31 +G(Zdf, 2p) +zpc b’ MP4 SDTQ/6-31G(d, p) MP4 SDTQ/6-31 +G(2d, p) MP4 SDTQ/6-31 +G(2d, 2p) MP4 SDTQ/6-31 +G(Zdf, 2p) +zpc b’
and C2”structures are about 35, 11, and 14 kcal/mol less stable than the C, structure, respectively, as shown in table 4. Within the HF approximation, the C3” structure is a4 kcal/mol more stable than the CzV structure, regardless of the basis sets employed. This finding conflicts with the fact that Cabal101et al. calculated the preference of CzVover CJVat the pseudopotential HF/DZP level in spite of their wrong location of the less stable structure of CzVsymmetry, as already pointed out. On the other hand, the order of decreasing stability C3”> CzV>Dzd is identical with that calculated by Gordon [ 5 ] and Power et al. [ 7 1. As the vibrational analyses in table 5 reveal, however, it was found at the HF level that the CzVand DZd stationary points have single (782i (b, ) cm- ’ ) and doubly degenerate (2234i (e) cm- ’ ) imaginary
p) geometries -290.85503 -290.85926 -290.86192 -290.86479 -290.83403 - 290.97004 -290.97795 -290.98858 -290.99829 -290.96753
calculations on the MP2/6-3 1G( d, p ) geometries MP2/6-31G(d, p) =) -290.95651 MP2/6-31G(d, p) -290.94618 MP2/6-31 +G(2d, p) -290.95260 -290.96135 MP2/6-31 +G(2d, 2p) -290.97026 MP2/6-31 +G(Zdf, 2p) MP3/6-31G(d, p) -290.96520 -290.97247 MP3/6-31 +G(2d, p) MP3/6-31G+(2d, 2p) -290.98256 MP3/6-31G+ (2df, 2p) -290.99215 -290.97050 MP4 SDTQ/6-31G(d, p) MP4 SDTQ/6-31 +G(2d, p) -290.97812 MP4 SDTQ/6-31 +G(2d, 2p) -290.98861 MP4 SDTQ/6-31 +G(2df, 2p) -290.99850 +ZPCd’ -290.96764 a) Energies relative to C, in parentheses. b, HF/6-31G(d, p) zero-point energies. ‘) All MOs are considered. d, MP2’/6-3lG(d, p) zero-point energies.
C 2”
C 3”
DZd
-290.83297 -290.83588 -290.83843 -290.84179 -290.81156 -290.95541 -290.96269 - 290.97270 -290.98383 - 290.95360
(13.8) (14.7) (14.7) (14.4) (14.1) (9.2) (9.6) ( 10.0) (9.1) (8.7)
-290.83793 -290.84311 -290.84481 -290.84744 -290.82076 -290.94192 -290.95106 -290.96116 -290.97134 -290.94466
(10.7) (10.1) (10.7) (10.9) (8.3) (17.6) (16.9) (17.2) (16.9) (14.4)
-290.80067 -290.80428 -290.80522 -290.80839 -290.78555 -290.92471 -290.93364 -290.94303 -290.95497 -290.93213
(34.1) (34.5) (35.6) (35.4) (30.4) (28.4) (27.8) (28.6) (27.2) (22.2)
-290.94072 -290.93013 -290.93624 -290.94471 -290.95472 -290.94992 -290.95694 -290.96665 -290.97744 -290.95549 -290.96281 -290.97292 -290.98405 -290.95410
(9.9) (10.1) (10.3) (10.4) (9.8) (9.6) (9.7) (10.0) (9.2) (9.4) (9.6) (9.8) (9.1) (8.5)
-290.93132 -290.92076 -290.92862 -290.93655 -290.94583 -290.93778 -290.94655 -290.95622 -290.96636 -290.94247 -290.95157 -290.96176 -290.97226 -290.94580
(15.8) (16.0) (15.0) (15.6) (15.3) (17.2) (16.3) (16.5) (16.2) (17.6) (16.7) (16.8) (16.5) (13.7)
-290.90790 -290.89701 -290.90448 -290.91178 -290.92203 -290.91781 -290.92638 -290.93525 -290.94662 -290.92474 -290.93363 -290.94295 -290.95481 -290.92423
(30.5) (30.9) (30.2) (31.1) (30.3) (29.7) (28.9) (29.7) (28.6) (28.7) (27.9) (28.7) (27.4) (27.2)
T. Kudo. S. Nagase / Jahn-Teller Table 5 Harmonic
vibrational
frequencies
HF
MP2
4197 2489 2427 1116 951 805 701 631 183
4025 2461 2393 1197 920 878 731 690 252
239
’ ) of SiH: calculated with the 6-3 1G (d, p ) basis set C Z”
C,
a’ a” a’ a’ a’ a’ a” a’ a”
(cm-
distortions of SiH + and Si(CH,)+
a, b2 a, b, a, aI bz a, b,
C 3” HF
MP2
2843 2551 2467 1777 1221 916 794 701 7821
2635 2532 2439 1790 1287 937 788 739 607i
frequencies, respectively, and are not the minima on the HF potential energy surface of SiW . The vibrational mode of the imaginary frequency of the Czv structure corresponds to distortion to C, symmetry, while those of the DZd structure lead to distortion to C3” symmetry. On going from the HF to MP levels, the Dzd structure possesses only real vibrational frequencies but the Czv structure has still a single b, imaginary frequency of 607i cm-‘, as shown in table 5. As calculated at the HF level, the DZd structure is the most unstable also at the MP level, the most stable being the C, structure, as shown in table 4. However, electron correlation reverses the relative stability of the C3”and Czv structures, the latter becoming = 7 kcal/ mol more stable than the former at any levels of MP calculations. The similar energy difference favoring C2” over CJv was also calculated at the pseudopotential CI/DZP level by Cabal101et al., while Power et al. calculated that C2” is 4.8 kcal/mol less stable even at the CI/6-21G//HF/6-21G level, probably because they did not locate correctly the Czv structure. As table 4 shows, the relative energies at the MP level are almost insensitive to the basis sets, the order of perturbation, and geometries employed. The most reliable energies at the MP4 SDTQ/6-3 1 + G (2df, 2p)//MP2/6-31G(d, p) level yield the relative stability (kcal/mol) which decreases in the order C,(0.0)>C2,(9.1)>CJ,(16.5)>D2,(27.4). Zeropoint correction (ZPC) made with the MP2/63 1G( d, p) harmonic vibrational frequencies yields a final prediction of C,(0.0)>C2v(8.5)>Cj,( 13.7) > Dzd( 27.2) for the relative stability of SiH: . This
e a, e a, a, e
D2d HF
MP2
2521 2455 1013 908 452 415
2481 2408 974 875 679 370
e a, b2 b, e a, bz
HF
MP2
1697 2183 1968 969 2234i 763 750
2536 2185 2012 938 844 786 743
provides an interesting contrast with the fact that in CH: the Czv structure is the most stable energy minimum and the relative stability (kcal/mol) decreases in the order Cz,(0.0)>D,,(2.6)>C,,(12.3) at the MP4 SDTQ/6-31 +G(2df, 2p)//MP2/6_31G(d, p) level. 3. I. 3. Ionization energies Table 6 summarizes the adiabatic ionization energies of SiH4 calculated at various levels of theory. The adiabatic ionization energies assigned in the various early spectroscopic studies are in the range of 11.5-l 4 eV but are suggested to be probably below 11.8 eV [ 27-321. The present calculated values of 12.09 (DZd), 11.50 (C,,), and 11.28 (C,,) eV at the MP4 SDTQ/6_31+G(2df, 2p)//MP2/6_31G(d, p)+ ZPC level may suggest that the experimentally assigned values are the adiabatic ionization to the Cs, structure. On the other hand, it is noteworthy that the adiabatic ionization energy (10.91 eV) calculated for the most stable C, structure coincides perfectly with the peak at 1 l.OO? 0.02 eV observed in the very recent photoionization mass spectroscopic study [ 371. 3.1.4. Kinetic stability In most photoionization [ 33-371 and guided ion beam [63] studies, only the fragment ions such as SiH,+ and SiH: have very frequently been detected instead of the parent radical cation, SiHa . In order to assess the kinetic stability of SiH$ , we have investigated the fragmentation processes of the most stable C, as well as the second most stable C,, minimum
T. Kudo, S. Nagase / Jahn-Teller
240
distortions ofSiH + and Si(CH,)+
Table 6 Adiabatic ionization potentials (eV) of SiH4 calculated on the MP2/6-3lG(d,
HF/6-3lG(d, p) HF/6-31 +G(Zdf, 2p) MP2/6-3lG(d, p) a) MP2/6-3lG(d, p) MP2/6_3l+G(2df, 2p) MP3/6-3lG(d, p) MP3/6-31 +G(Zdf, 2p) MP4 SDTQ/6-3lG(d, p) MP4 SDTQ/6-31 +G(Zdf, 2p) +ZPCb’
p) geometries
C,
C2”
C3”
DZd
10.24 10.17 10.70 10.69 10.84 10.74 10.94 10.75 10.96 10.91
10.83 10.77 11.13 11.13 11.26 11.16 11.34 11.16 11.35 11.28
10.69 10.63 11.39 11.38 11.50 11.49 11.64 11.51 il.67 11.50
11.71 11.69 12.03 12.03 12.15 12.03 12.18 12.00 12.15 12.09
‘) All MOs are considered. b, MP2/6-3lG(d, p) zero-point energies.
structure. The energies and structures of the fragment ions are summarized in table 7. First examined is the dissociation of the CsVstructure which leads to the formation of SiH$ and H, ‘A, SiH$ (&,)+‘A,,
SiH,+ (D3,,)+H.
This reaction was calculated to be 10.2 kcal/mol endothermic at the MP4 SDTQ/6-31 +G(2df, 2p) //MP2/6-3 1G( d, p) level. Zero-point correction made with the MP2/6-3 lG(d, p) frequencies decreases the endothermicity to 8.3 kcal/mol. These values are larger than the HF/4-3 1G value ( 1.7 kcal /mol) calculated by Gordon [ 5 ] but are rather close to the CI/DZP value (8.5 kcal/mol) calculated by Cabal101et al. [ 81. In order to check whether or not there is an energy barrier for the dissociation, we chose the distance (R) between SiH: and H as the reaction coordinate and optimized all other geometrical parameters for several selected values of R. Fig.
3 shows the changes in the potential energy as a function of R. Upon going from SiH: (C,, ) to SiH$ + H, the energy increases monotonously, there being no barrier for the dissociation. This means that the dissociation of the CsVstructure is only hindered by a small amount of energy ( x 8 kcal/mol). In addition, it was found that the C,, structure collapses to the C, structure with a slight barrier ( 1.06 kcal/mol at MP2/6-3 1G (d, p ) ) via a transition structure shown in fig. 4; the barrier decreases to -0.01 kcal/ mol and almost disappears at the MP4 SDTQ/6-3 1 + G( 2df, 2p)//MP2/6-31G(d, p) level. Thus, we have next investigated the dissociation of the most stable C, structure of SiH$ which leads to SiH,+ and Hz,
Table 7 The MP4 SDTQ/6-3 1+G(2df, 2p) total energies (hartree) calculated at the MP2/6-3lG(d, p) optimized (8, and degree) of the frament ions
SiHZ (Dx, ) SiHZ (C,, 1 H2 H
Total energy ‘)
Structure
-290.45778 (-290.43439) -289.80724 (-289.79424)
SiH= 1.455 SiH= 1.469 L HSiH = 120.0 HHc0.734
- 1.16863 -0.49823
(- 1.15813)
a) In parentheses are values corrected by MP2/6-31G(d, p) zeropoint energies.
Fig. 3. Potential energy curves for the dissociations of the Cx, and C. structures of SiHJ as a function of R at the MP4 SDTQ/631 +G(Zdf, 2p)//MP2/6-3lG(d, p) level.
T. Kudo, S. Nagase/ Jahn-Teller distortionsof SiH+ and Si(CH,)+
241
MP3/6-31G(d)//HF/6_31G(d) level. Theselarger endothermic energies suggest that SiF,’ is more kinetically stable. At this point, it is interesting to note that the spectra of SiF: have frequently been detected in the recent spectroscopic studies [ 65-681. 3.2. Si(CH,)t
167,Y Fig. 4. The MP2/6-31G(d, p) optimized transition structure connecting the C, and Cfv structures in A and degree.
‘A’ SiH$ (C,)+*A,
SiH2+(C,,)+‘C,’
H,(D,,)
.
This reaction is 14.2 kcal/mol endothermic at the MP4 SDTQ/6-31 +G(2df, 2p)//MP2/6-31G(d, p) level. However, it becomes 9.6 kcal/mol endothermic after the MP2/6-3 1G (d, p ) zero-point energies are included. These values are much smaller than the value of 61.6 kcal/mol (53.9 kcal/mol after ZPC) calculated at the same level by us for the corresponding dissociation of the most stable C2” structure in CH,+. To examine whether the dissociation of SiH: (C, ) is hindered by a significant energy barrier, the distance (R) between the silicon atom in SiH: and the midpoint of the H-H bond in H2 was taken as the reaction coordinate and the potential energy changes were calculated as a function of R. These results are also shown in fig. 3. As characterized by the monotonous energy increasing, the energy required for the dissociation of the C, structure of SiH, is = 10 kcal/mol. As is apparent from these calculations, SiH: is relatively unstable to fragmentation in a kinetic sense. This certainly makes it considerably difficult to confirm experimentally the intermediacy of SiH$ . The kinetic unstability of SiH: may result from the relatively weak Si-H bonds. Thus, the hydrogens in SiH: were all replaced by fluorine atoms because it is known that Si-F bonds are unusually strong [ 641. In the preliminary calculations of SiFz , the C, structure, rather resembling the &-like structure, was found to be the most stable. The dissociations into SiF: +F and SiF: +F2 were calculated to be 19.5 and 129.3 kcal/mol endothermic, respectively, at the
3.2. I. Structures Tetramethylsilane, Si ( CH3) 4, has Td symmetry in the ground state, as shown in fig. 5. Its electron configuration is (core)(4a,)2(3t2)6(5a,)2(4t2)6(le)4(lt,)V5t*Y.
As mentioned in the introduction, the solid-state ESR study shows that the radical cation adopts CzV symmetry. Thus, we first optimized the structure with CzV symmetry constraint. The resultant optimized structure is shown in fig. 6. As characterized by the long C,-C, bond length of 2.8 12 A, the CzVstructure is rather similar to structure b located in CzVsymmetry for SiH$ . In several ways, we searched for the second CzVstructure which has the smaller C,-C, bond length and resembles structure a in SiH: . However, we were unable to locate the second CzVstructure which might be represented as a product for the ad-
Fig. 5. The HF/6-31G(d) optimized Td structures of Si(CH3)4 in A and degree. The total energy is - 447.4 1355 hartree and it is -448.02265 hartree at the MP2/6-3lG(d)//HF/6-31G(d) level.
242
Fig. 6. The HF/6-31G(d) Si(CH,)$ in 8, and degree.
T. K&o, S. Nagase /.lahn-Teller
optimized
CZy structure
of
dition of the dimethylsilylene cation radical (Si(CH,)T) totheC-Cbondofethane (C2H6).As demonstrated in the study of SiH: , CZVstructures are liable to undergo distortion to CsVand C, structures, respectively. Therefore, we next searched for the stationary points of C3” or C, symmetry. Fig. 7 shows the optimized CsV structure of Si( CH3 )$ . As the geometrical parameters show, the
distortions of SiH + and Si(CH,)+
CJ, structure may be regarded as a complex of the trimethylsilyl cation (Si ( CH3 ) 3’ ) and methyl radical (CH,). This is also supported from the spin and charge density distributions: the spin density is almost localized with 0.974 eon the carbon atom in the CH3 moiety while the great amount of positive charge ( + 1.090 e) is on the silicon atom in the Si(CH3)3 moiety. The Si ( CH3 ) 3 and CH3 moieties are 2.4 11 A apart in the C3” structure. This distance is 0.517 8, (27.3%) longer than that (1.894 A) in the neutral Si( CH,)4 ( Td) . However, the lengthening is considerably small compared with the corresponding value of 0.763 A (51.7 %) calculated at the same level on going from SiH4 ( Td) to SiHZ ( C3”). According to this, the Si (CHr ): moiety in Si ( CH3 )$ is less deformed than the SiH: moiety in SiH$ . Also located is the C, structure. As fig. 8 shows, it is quite different from the C, structure of SiH: . The C, structure of Si (CH3 )4’ can be best regarded as a weak complex of Si ( CH3 ) $ and C2H6. In this open C, structure, the positively charged silicon atom of Si (CH, ): is bound to one of the negatively charged carbon atoms of CzH6 as much as 3.08 1 A away and makes an angle of 159.2“ with the C-C bond of CzH6 to avoid steric repulsion. Fig. 9 shows the optimized structures of the fragment ions Si( CH3 ): and Si( CH3 )$ . These fragment ions have CJh and C2 symmetry, respectively, in the most stable conformations. 3.2.2. Relative and kinetic stability Table 8 compares the total and relative energies of the CZV,C3”, and C, structures of Si(CH3 )$ calculated at the HF/6-3lG(d) and MP2/6-31G(d)
C,CbSiCc=
Fig. 7. ‘The HF/6-31G(d) Si ( CHJ )z in A and degree.
optimized
C,,
structure
of
61.7
Fig. 8. The HF/6-31G(d) in 8, and degree.
optimized C, structure of Si(CH,):
T. Kudo, S. Nagase / Jahn-Teller
n
T
a
C
v
CSiCHa=
58.2
CSiCHb=
-59.1
CSiCHc=
179.6
Fig. 9. The HF/6-31G(d) optimized Si(CH,):(Cg,,)andSi(CH3):(Cz)inAanddegree.
structures
of
/ /HF/6-3 1G ( d ) levels. At both levels, the CsVstructure is the most stable unlike the SiH,+ case and the CzVstructure is the second most stable. The Cs, structure is 13.3 kcal/mol more stable than the CzVstruc-
243
distortions of SiH + and Si(CH,)+
ture at the HF level. Electron correlation decreases the energy difference but its effect is too small to reverse the relative stability unlike the SiW case. Because of the size of the molecule, we calculated the vibrational frequencies at the HF/3-21G level. According to the vibrational analyses, the CsV and C, structures are the energy minima, but the Czy structure has a single imaginary frequency of 1167i(b, ) cm- I. The vibrational mode of the great imaginary frequency corresponds to distortion to the most stable Cs, structure: the CzV structure is a transition structure for the conformational interconversion from one C3”to the other C3” structures. As table 8 shows, the barrier for the interconversion is 6.3 kcal/mol (6.1 kcal/mol after ZPC) at the MP2 level. This small barrier rather suggests that there is a considerably rapid dynamical equilibrium, C3V+C2V~C3V,and it may blur the experimental spectra. The more sophisticated calculations may be required for the exact evaluation of the small barrier height. However, it is instructive to remember that relative energies at the MP level are almost independent of the basis sets (including d functions), the order of perturbation, and geometries, as demonstrated in the SiH: system. In this view, we conclude that the CJ, structure should be observed at low temperatures. At this point, it is instructive to note that Cs, structures are suggestedforC(CH,)t [69],Sn(CH,)$ [13,15],and Pb ( CHs )a [ 15 ] at 4.2,77, and 85 K, respectively. As table 8 shows, the C, structure of Si ( CHJ )a is the most unstable and is 13.7 kcal/mol ( 16.3 kcal/ mol after ZPC) more unstable than the CfVstructure at the MP2 level. As expected from the weak complex character, the C, structure is very subject to the decomposition into Si(CH,)$ and C2H6; the energy
Table 8 Total (hartree) and relative 31G(d) basis set
(kcal/mol)
‘) energies of Si(CHp ): calculated
HF C 3” C 2” C, Si(CH,)$ Si(CH,)Z ‘) Values in parentheses. b, HF/3-2 1G zero-point
+CH3 +CzH6
energies.
-447.10757 -447.08634 -447.08151 -447.08681 -447.07598
on the HF/6-3
MP2 (0.0) (13.3) (16.4) (13.0) (19.8)
-447.68776 -447.67778 -447.66585 -447.65690 -447.65525
lG(d)
optimized
MP2+ZPC (0.0) (6.3) (13.7) (19.4) (20.4)
-447.53338 -447.52372 -447.50740 -447.50803 -447.49804
geometries
b, (0.0) (6.1) (16.3) (15.9) (22.2)
with the HF/6-
244
i? Kudo, S. Nagase/ Jahn- Teller distortionsof SiH + and Si(CH,)+
required for this decomposition is only 6.7 kcal/ mol (5.9 kcal/mol after ZPC) at the MP2 level, as shown in table 8. On the other hand, the dissociation of the most stable Csv structure into Si ( CH3 ) : and CHJ is calculated to be 19.4 kcal/mol ( 15.9 kcal/ mol after ZPC) endothermic at the MP2 level. This endothermic energy is more than three times greater than that calculated at the same level for the corresponding dissociation of SiH: ( Cfv ), suggesting that tetramethyl substitution makes silane radical cations much less fragile.
Acknowledgement
All calculations were carried out at the Computer Center of the Institute for Molecular Science with the GAUSSIAN 82 [ 711 program in IMS Computer Center library program package. This work was supported in part by a grant from the Ministry of Education, Science, and Culture in Japan.
References
3.2.3. Ionization energies The adiabatic ionization energies of the C3”, C2”, and C, structures of Si ( CH3 )4 were calculated to be 9.11,9.38,and9.71eV(9.01,9.27,and9.72eVafter ZPC), respectively, at the MP2/6_31G(d)//HF/631G(d) level. These are close to the values of 9.42 [ 701 and 9.6 [ 221 eV assigned experimentally. The calculated and experimental values are e2.0 eV smaller than those of SiH,+. This is ascribable to the rising of the HOMO energy levels upon going from SiH, (-13.2eV)toSi(CH3)4(-11.4eV). 4. Concluding remarks In an attempt to resolve several discrepancies in the Jahn-Teller distortion of silane radical cations of current interest, we have performed the ab initio calculations of SiHa and Si ( CH3 ) .$ at higher levels of theory. The C, structure is the most stable minimum in SiHa and the relative stability decreases in the order C, > C2”> C3”> D2+ It is found that the Czv structure is a transition structure which leads to the C, structure while the second most stable Csv minimum structure collapses to the C, structure almost without a barrier. The adiabatic ionization to the most stable C, structure is predicted to be at 10.9 1 eV. However, it should be noted that the C, structure is relatively unstable to the fragmentation into SiH$ and Hz. On the other hand, the C3” structure is the most stable in Si ( CH3 )2. The Czv structure is again a transition structure. Two equivalent Cj, structures are easily interconvertible via the Czy transition structure. Interesting is that Si(CH3 )z is more stable to fragmentation than SiH: . The C, structure is also located in Si ( CHs ) a. However, it is much more unstable than the Cjv structure and decomposes easily.
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