An ab initio study of SiC2 protonation

148 (1986) 33-43 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

Journal of Molecular Structure (Theochem)

AN AB INITIO STUDY OF Sic2 PROTONATION

J. R. FLORES,

Departamento

A. LARGO-CABRERIZO

and J. LARGO-CABRERIZO

de Quimica Fisica, Facultad de Ciencias, 47005.Valladolid

(Spain)

(Received 15 January 1986)

ABSTRACT Ab initio molecular orbital calculations have been carried out for SIC, and its protonated isomers at the Hartree-Fock and Mdller-Plesset levels of theory with different basis sets ranging in quality up to split-valence plus polarization. A linear structure is by far the most stable protonated isomer. The proton affinity of Sic, has also been computed with inclusion of zero-point vibrational energy contributions at the HF/6-31G* level. INTRODUCTION

For a long time silicon carbide was thought of, by analogy with the well known C3 molecule [ 1, 21, as a linear SiCC system. An ab-initio calculation reported by Green [ 31 supported this assumption. It was not until the development of two parallel works, one theoretical [ 41 and one experimental [ 51, that SiCz was shown to be a cyclic C,, molecule. The theoretical calculation, due to Grev and Schaefer [4], performed with a large basis set and inclusion of electron correlation at the CI level, predicted that the cyclic isomer lies about 5 kcal mol.’ below the linear one. In the experimental work, Michalopoulos et al. 153 showed that a correct assignment of the rotational structure in the visible spectrum of SiCz is only possible if CzV geometry is assumed. Following this work, Thaddeus et al. [6] have assigned some lines in the spectrum of an astronomical source as belonging to the CzV symmetric SiCz. Therefore, Sic? is not only the smallest ring system which contains a carbon-carbon triple bond (albeit a weak one) but it is also the only known cyclic species in interstellar space. Other theoretical studies have recently appeared. Pauzat and Ellinger [7] reported SCF and CI computations on linear SiCz and Oddershede et al. [8] carried out SCF and MBPT calculations on both isomers, concluding that the isomerization barriers between them are very small (less than 1.3 kcal mol.‘). Given its astrophysical significance, and the importance of the proton transfer reactions in space chemistry, we present in this paper a study of the protonated species of the SiCz molecule in order to investigate its behaviour in proton rich interstellar media. First, however, we will give the results obtained for the SiCz system at the HF level with three different basis sets to 0166.1280/86/$03.50

0 1986 Elsevier Science Publishers B.V.

34

check their adequacy in predicting molecular geometries and relative stabilities of the protonated isomers. We must stress that ab initio computations are valuable in the study of possible space molecular ions [9], mainly for those species whose experimental terrestrial observation is difficult. Well known examples are HCO’ [lo, 111 and N2H+ [12, 131. Other more recent examples can be quoted, such as the quantum mechanical calculation of rotational spectra for some molecular species [ 141, the CO protonation [15] and predictions of the vibrational frequencies for some molecular ions [ 161. COMPUTATIONAL

DETAILS

Ab initio Hartree-Fock molecular orbital calculations were done both on SiCp (for testing and comparison purposes) and its protonated species with the GAUSSIAN-82 program package [17]. Different basis sets were used: the minimal STO-3G; the split-valence 6-31G; the split-valence plus polarization 6-31G* [18, 191 which includes d-functions on heavy atoms; and, for the protonated species, the 6-31G** basis set, which also includesp-functions on the hydrogen atom [ 18, 191. Electron correlation effects were included through second-order M@ller-Plesset perturbation theory [20] , and extended to partial fourth order, including single, double and quadruple excitations [21] for the species involved in the proton affinity calculations. In correlation calculations, inner-shell molecular orbitals were not taken into account (“frozen core” approximation). Geometry optimizations were carried out using analytical gradient techniques [22 3 at the HF level. Finally, harmonic vibrational frequencies were analytically computed [23] at the HF/6-31G* level and scaled, when possible, with the empirical factor given by DeFrees and McLean [ 161 for this HartreeFock approximation. RESULTS

AND DISCUSSION

Testing the basis sets: study of Sic2 isomers The optimized geometrical parameters for the two SiCz isomers with CzV and C,, symmetries, corresponding to ‘A 1 and IX+ electronic states, respectively, are shown in Table 1. For the cyclic isomer, the STO-3G and 6-31G* results are in good agreement with the experimental values. A similar behaviour can be expected for the cyclic protonated forms. For the linear structure, we note that 6-31G* bond lengths are fairly similar to those obtained by Pauzat and Ellinger [7] at the HF/TZ + P level (r= 1.263 A, rsi+ = 1.672 A) while the 6-31G values are very close to the more reliable CI/TZ + P = 1.690 A). Thus it seems that the well parameters (r.Dc = 1.279 A, ret known effect of bond relaxation, which usually takes place when electron correlation is included, can be accounted for by using the 6-31G set at the

35 TABLE 1 Geometrical parameters for the linear and cyclic isomers of Sic, in degrees) Parameter

r( Si-C) P(C-C) L CSiC

(distances in A, angles

C 1”

C,, STO-3G

6-31G

6-31G*

STO-3G

6-31G

6-31G*

Exp.*

1.633 1.255

1.694 1.278

1.671 1.270

1.821 1.267 40.7

1.926 1.273 38.6

1.837 1.253 40.0

1.812 1.250 40.4

sFrom ref. 5. TABLE 2 Energies (hartree) and energy differences (kcal mol”) between the two isomers of Sic, at the HF/SCF level Basis STO-3G 6-31G 6-31G*

WC,,)

E(C-v)

AE

-360.16477 -364.39406 -364.47769

-360.18954 -364.43384 -364.48159

+ 15.5 +25.0 +2.4

HF level. The geometrical parameters corresponding to the 6-31G* basis set are, in both cases, nearly identical to those obtained by Grev and Schaefer [4] with a very similar DZ + P basis. Energies and energy differences between both isomers are shown in Table 2. The energy difference obtained at the HF/6-31G* level of theory is very similar to that calculated by Grev and Schaefer [4] at the DZ + P (AE = 5.1 kcal mol-‘) and HF/DZ + PP (AE = 1.5 kcal mol-*) levels, and also to the HF result given by Oddershede et al. [8] (AE = 3.9 kcal mol-‘), always favourable to the linear form. Therefore, our best energetic results are, as could be expected, those obtained with the 6-31G* basis set, which behaves as well as the preceding sets for describing the Sic2 system. On the other hand, the STO-3G basis produces reasonable results and may be used to make cheap scans on the Si&H+ system potential-energy surface. The pro tona ted Sic&P

isomers

We studied, in principle, three possible minima in the Si&H+ potentialenergy surface: two linear forms, related with a linear SiCC linear isomer, with hydrogen bonding to silicon (CCSiH”) and carbon (SiCCH+), respectively; and a cyclic C?, form with a Si-H bond (CSiHC’). The optimized geometrical parameters obtained at the HF level are given in Table 3. The CIV cyclic structure (CSiHC+) appears in the optimization process as a

36 TABLE 3 Optimized geometries for the protonated species (distances in A, angles is degrees) Basis

STO-G 6-31G 6-31G* 6-31G**

SiCCH+ (C,,)

CSiHC+ (C,,)

CCSiH+ (C,)

r(CH)

r(CC)

r(SiC)

r(SiH) r(CC)

r(SiC)

r(SiH) r(CC)

r( Sic)

LCSiC

1.083 1.062 1.065 1.066

1.191 1.213 1.206 1.206

1.766 1.799 1.763 1.763

1.438 1.469 1.461 1.461

1.567 1.615 1.597 1.597

1.446 1.468 1.454 1.454

1.771 1.836 1.747 1.747

43.5 41.2 42.5 42.5

1.305 1.304 1.297 1.297

1.312 1.291 1.267 1.267

transition state rather than as a local minimum. An harmonic frequencies calculation, at the HF/STO-3G level of theory, on the corresponding optimized conformation predicts a complex frequency (v(&) = 509 i cm-‘) just as for the cyclic Sic? both at the HF/STO-3G (I@) = 610 i cm-‘) and the HF/6-31G* levels (see below, Table 6). However, it should be possible that this cyclic protonated isomer be a minimum in the exact potentialenergy surface, as cyclic SiCZ is, although it also presents a complex frequency in our HF calculation and in those carried out by Grev and Schaefer

[41*

The optimized geometries of different Sic&I+ isomers deserve brief comment. In both linear conformations, SiCCH’ and CCSiH+, the next bond to the X-H bond (X is C or Si, respectively) is shorter than the corresponding bond in the linear SiCC structure, whereas the remaining bond is lengthened. The cyclic conformer CSiCH+ is. much flattened by protonation, since it has a shorter Sk-C bond and a longer C-C bond than the corresponding nonprotonated cyclic species. The Si-H bond length is, at the most reliable HF/6-31G** level, fairly similar both in the linear CCSiH+ and the cyclic CSiHc” forms. Therefore, this bond appears to be very slightly affected by its environment. Differences in the optimized parameters corresponding to 6-31G* and 6-31G** basis sets are always within the accuracy limit of the optimization procedure. HF and MP2/6-31G** energies and energy differences between the protonated species are given in Table 4. It can be seen immediately that the most stable structure is the linear SiCCII+. This is in agreement with the fact that protonation usually takes place in the first row atom rather than in the second row one [25]. It must also be stressed that the cyclic structure CSMC” is lower in energy than the linear CCSiH+ (which is also silicon-protonated) at the HF/6-31G* and HF/6-31G** levels. But we must not forget that the inclusion of electron correlation is shown to be essential to predict cyclic SiCZ as more stable than the corresponding linear isomer [4,8] . Analysis of gross atomic populations [24] shows that in this two protonated species the silicon atom is more positively charged than in the SiCZ isomers. On the other hand, Green’s study of MgCz [26] shows the cyclic

37 TABLE 4 Energiesand energy differences with respect to the most stable species Method

Species CCSiH+ (C,,)

CSiHC+ (C,,)

SiCCH+(C,,)

E (hartrees) HF/STO-3G HF/6-31G HF/6-31G* HF/6-31G** MP2/6-31G**a

-360.51183 -364.66225 -364.71669 -364.71748 -365.01668

-360.48634 -364.62090 -364.72662 -364.72756 -365.04769

-360.68746 -364.81682 -364.86103 -364.86307 -365.16609

AE (kcal mol-‘) HF/STO-3G HF/6-31G HF/6-31G* HF/6-31G** MP2/6-31G**a

110.2 96.4 91.2 91.4 93.8

126.2 122.3 85.0 86.0 74.3

0.0 0.0 0.0 0.0 0.0

aCalculationsmade at the HF/6-31G** geometries,usingthe “frozen-core” approximation.

isomer as the most stable at the HF approximation. This fact confirms that, when positive charge in the atom bounded to the CZ group increases (Mg is more electropositive than Si), the cyclic structure stability is favoured. However, HF/STO-3G and HF/6-31G energy differences between linear CCSiH+ and cyclic CSiHC+ are almost the same, as in the case of the corresponding non-protonated species. This implies that the role of polarization d-functions is more important here than in the non-protonated system. As for Sic&, the correlation energy obtained with the MP2/6-31G** approximation is clearly larger for the cyclic isomer than for the linear ones. MP4 (SDQ) results for cyclic SiCZ and linear SiCCH+ obtained to determine the proton affinity of silicon carbide (see Table 7) lead us to conclude that the protonated species stability order is not changed by the inclusion of higher order contributions in MP energy values. However, the cyclic-linear correlation-energy difference might be reduced a little bit by these contributions (say some 3 kcal mol-l). The most stable protonated isomer has a small dipole moment, p = 0.435 D at the HF/6-31G** level, which does not favour its possible radioastronomical detection. The study of other possible pro tona ted isomers The inadequacy of the HF method for describing the potential-surface regions which correspond to cyclic forms is a serious drawback in the study of possible cyclic isomers. We were particularly interested in a cyclic carbonprotonated form which might be, in principle, the most stable. Potentialsurface scanning at the HF/STG3G approximation produced a minimum (A)

si

I

c-c

:

:

C bl

\ 3

MP2/6-310** 0.0

as

I.0

16 .s:

Fig. 1. Energy profile curves along the reaction coordinate SiCCH+.

from cyclic CSiCH+ to linear

and a transition state (B) whose structures are shown in Fig. 1. They have, at this level, a very low energy difference (about 5.8 kcal mol-‘), but further MP2/STO-36 calculations on these two geometries showed a higher correlation energy for structure (B), leading to a correlation energy difference (about -7.9 kcal mol-l) which is large enough as to suppose that no extremes would possibly appear when more accurate approximations were used. Therefore, we did not make HF geometry optimizations with more extended basis sets and decided to assume the HF/STO-3G geometries for these two extremes. From these, we obtained the HF/STO-3G approximate reaction coordinate by making subsequent shifts on the potential surface in the direction pointed out by the eigenvector associated with the lowest eigenvalue of the actual Hessian matrix. All geometries obtained in each step were used to carry out HF/6-31G** and MP2/6-31G** calculations, the results being shown in Table 5. The C-H bond distance remained between 1.08 and 1.09 A and is not included in the Table (the particular values for the “minimum” and the “transition state” were 1.087 and 1.081 A, respectively).

39 TABLE 5 Geometrical parameters and energies of different points along the minimumenergy tion path where r is the distance along this path Energies (hartree)

Geometrical parameters r (a.u.) -0.159 O.OOob 0.159 0.318 0.477 0.636 0.794c 0.953 1.112 1.271 1.430 1.589 1.747

(A)

Sic (A)

LCCSi (“)

LCCH (“)

1.324 1.322b 1.320 1.317 1.311 1.302 1.28gc 1.277 1.263 1.256 1.252 1.248 1.244

1.769 1.777b 1.785 1.796 1.814 1.832 1.848= 1.865 1.892 1.922 1.948 1.977 2.009

130.8 124.4b 118.0 111.8 105.8 98.7 90.5c 82.4 74.1 70.1 67.8 65.5 63.3

110.2 116.6b 123.0 129.5 136.4 141.6 145.0= 148.4 150.1 152.0 153.4 154.8 156.2

cc

reac-

HF/STO-3G

-360.61319 61385 61322 61147 60882 60610 60460 60735 61639 62294 62717 63118 63448

a‘CFrozen-core” approximation was used. bGeometry CGeometry of the HF/STO-3G transition state.

HF/6-31G**

-364.79096 79195 79212 79170 79110 79101 79249 79724 80678 81368 81823 82262 82672

of the HF/STO-3G

MP2/6-31G’

-365.07034 07155 07251 07352 07512 07812 08462 09720 11498 12462 13017 13504 13933 minimum.

The curves in Fig. 1 give the energies relative to the corresponding value at the HF/STO-3G minimum as the distance along the reaction coordinate increases. It is readily seen that the extremes are still present at the HF/ 6.31G** level, although the energy difference is much lower and the transition state is closer to the minimum. As the bond between silicon and the non-protonated carbon is formed, the correlation energy increases, and the MP2/6-31G** curve does not present extremes. HF and MP2/6-31G** least-energy reaction paths were not used because they would require large amounts of computer time. Nevertheless, normal modes obtained from different levels of theory are fairly similar [27] ; in particular, those obtained at the HF/STO-3G and HF/6-31G* levels for cyclic SiCZ and SiCCH+ are almost identical Consequently, it can be expected that these reaction paths are essentially parallel to the HF/STO-3G one used here. Furthermore, force constants related to those geometrical parameters only slightly associated with the reaction coordinate are similar for structures (A) and (B) at the HF/STO-3G level. This means that there must be similar lowerings in energy for those structures if they were reoptimized at HF and MP2/6-31G** levels. Thus, the 6-31G** energy profiles can be expected to be very similar to the exact ones corresponding to these levels. On the other hand, the MP2/6-31G** correlation-energy difference between the HF/STO-3G extremes (about -7.9 kcal mol.‘) seems to be large enough to prevent the existence of such extremes in the exact reaction path. Although the problem cannot be considered as definitively solved, we

40

think that the results obtained are significant enough as to foresee the inexistence of an angular local minimum (structure A). On the other hand, it must be noted that its energy is much higher than that of linear SiCCH” (about 59 kcal mol-’ at the MP2/6-31G** level). The reaction coordinate was followed until structure (C) was reached. Here silicon can be considered as being bound to the non-protonated carbon (rs+c = 1.828 a). There is a fast energy decrease in both the HF and MP2 curves. Correlation energy always increases, increasing strongly at the beginning and slightly at the end. It seems clear that there is not any stable cyclic carbon-protonated isomer. A possible angular local minimum with silicon bounded to the nonprotonated carbon has been carefully searched both at HF and MP2/STO-3G levels (all MOs were included in the correlation computation) beginning from structure (C), but no extreme was found. There is a smooth variation in energy when going from structure (C) to the corresponding linear SiCCH+ isomer, especially when the SiCC angle goes beyond 130”. Calculation of SiC2 proton affinity

The general procedure for calculating heats of reaction from theoretical computations may be found in the paper by Snyder and Basch [28]. It may be assumed that the energy of a molecule can be separated in electronic, vibrational, rotational and translational contributions. Vibrational energy change is identified with zero-point vibrational energy variation (AZPVE). We have calculated harmonic frequencies at the HF/6-31G* level both for cyclic SiCz and the most stable protonated species, linear SiCCH”. The results are shown in Table 6, which also shows the scaled frequencies for the linear structure. The fifth normal mode for SiCCH+ is clearly related to that corresponding to the lowest frequency of linear Sic&. The latter is predicted by Pauzat and Ellinger [7] to increase from 125 cm-’ at the HF level to TABLE 6 Vibrational frequencies (cm-‘) for cyclic Sic, Normal mode description

and linear SiCCH’ Frequencya (cm-‘)

Sic,

v,(A,) v,(A,) r%(S,)

C-C stretching Si-CC stretching

1992 849 3381

SiCCH+

vs(e) vz(n) %(T) v*(e) v,(n)

C-H stretching C-C stretching CCH bending Si-CCH stretching SiCCH bending

3594 2255 934 755 194

aAnalytically computed at the HF/6-31G*

level. bScaled according to ref. 16.

Scaled frequencyb (cm-‘)

3235 2030 841 680

41

838 cm-’ at the CI level. Therefore, it is possible that the v5(.rr)value is too low and, consequently, is not scaled. Anyway, our results are quite similar to those obtained at the same level of theory by DeFrees and McLean [ 161 for the analagous molecular ion, C3H+, except for the uq(u) frequency lowering which is mainly associated with the Si-CCH stretching. Cyclic SiCz presents a complex frequency very similar in magnitude to that found by Grev and Schaeffer in their finite differences calculations at the HF/DZ + P level (v(B,) = 328 i cm-‘) [4]. The results of the frequency calculations performed by Grev and Schaeffer [4] at the two configuration SCF levels and the peculiarity of this molecule led us to avoid the presentation of any scaled frequency for it. Electronic energy was calculated for both species by using MtillerPlesset theory up to fourth order. The 6-31G* and 6-310”” basis sets were used for SiCz and SiCCW, respectively, at the corresponding HF optimized geometries. Results arising from the HF approximation with different basis sets are also given in Table 7. AE,,, corresponds to the difference between correlation energies of protonated and non-protonated species. It is really seen that the correlation energy is higher in cyclic SiCz than in linear SiCCI-P by 3.6 kcai mol-’ at the MP4(SDQ)/6-31G ** level. This value is consistent with the behaviour of correlation energy in SiCz isomers. In order to calculate the proton affinity, we assimilated the complex frequency of cyclic SiCz to a rotational degree of freedom. The final formula is PA(T) = -A&,,

-AZPVE

+ 712 RT

For the protonated species, we used the non-scaled frequencies. The zeropoint vibrational energy is higher for the protonated species (12.7 kcal mol-‘) than for the cyclic species SiCz (4.1 kcal mol-‘). The effect of AZPVE is, therefore, to lower the proton affinity. Results are given in Table 7 with PA(T) values calculated at T = 298.15 K. TABLE 7 Energies (hartree), electronic and correlation energy differences (kcal mol-I), and proton affinities (kcal mol-‘) at different levels of theory Method HF/STO-3G HF/6-31G HF/6-31G* HF/6-31G** MP2* MP3* MF4( SDQ)*

JWG (Cd -360.16477 -364.39406 -364.47769 -364.7904ab -364.80184b -364.80836b

E( SiCCH+ (C,,)) -360.68746 -364.81682 -364.86103 -364.86307 -365.16609c -36S.1808Bc -366.18808c

*Calculations made at the HF geometry. b6-31G* was used.

AE,

6.1 4.0 3.6

AE-

PA,,,

-328.0 -264.7 -240.6 -241.8 -235.7 -237.8 -238.3

321.5 258.1 234.0 235.3 229.2 231.3 231.8

basis set was used. C6-31G** basis set

42

There is a certain amount of convergence in HF and post-HF results. When the basis set is expanded, a lowering in HF proton affinities takes place. The MP2 level seems to overestimate AE,,, because the MP3 and MP4(SDQ) results are very close and are significantly lower. In this case, vibrational normal modes with very low frequencies are found and, therefore, it is not strictly correct to separate vibration and rotation. This problem may cause an error in proton affinity determination. Sic* has a very high proton affinity; it is greater than the corresponding to neutral precursors (Hz and CO) of some of the most important interstellar protonated species, H+3and HCO’ (PAH2 (300) = 101.3 kcal mol-‘, PAco(300) = 141.9 kcal mol-’ to give HCO’ [15] ). Consequently, if there is no kinetic hinderance, Sic* must react in proton-rich interstellar media to give SiCClI+ as the principal product. CONCLUSION

The SiCZ molecule presents a very high proton affinity and must be able to produce the linear carbon-protonated ion SiCCI-Pthrough proton exchange reactions. The linear and possible cyclic silicon-protonated forms are clearly higher in energy. We have not found any stable cyclic carbon-protonated form. On the other hand, dissociative recombination of SiCCH+ (an electron is caught and bond breaking takes place) might lead in principle [29] to the linear metastable isomer SiCC as the main product. In other words, the SiCC form can be produced not only by isomerization of cyclic SiCZ, as suggested by Pauzat et al. [7], but also through the so-called secondary synthesis [ 281 in proton-rich interstellar media. ACKNOWLEDGEMENTS

We would like to thank Prof. J. Bertran and his group at the Universidad Autonoma de Barcelona (Spain) for their kindly help in some computations. REFERENCES 1 2 3 4 5 6 7 8 9 10 11

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