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Circumstellar carbon-chain molecules. Prediction of the infrared spectrum of SiC4
Volume 164, number 5
CIRCUMSTELLAR
CHEMICAL PHYSICS LETTERS
22 December 1989
CARBON-CHAIN MOLECULES.
PREDICTION OF THE INFRARED SPECTRUM OF Sic, *
N. MOAZZEN-AHMADI
a and F. ZERBETTO b
a Herzberglnstitute ofAstrophysics. National Research Council of Canada, Ottawa, Ontario. Canada KlA OR6 b Division of Chemistry, National Research Council of Canada, Ottawa, Ontario, Canada, KIA OR6 Received 21 August 1989; in final form 3 October 1989
The infrared spectrum of Sic,, recently discovered in the circumstellar shell of the evolved star IRC+ 10216, is predicted ab initio at the MP2/6-31 lG(d) level of theory. A very intense asymmetric stretch is calculated to occur in an astrophysical window.
Carbon clusters have recently been subject of extensive experimental and theoretical investigations because of their relevance in astrochemistry and combustion processes [ 11. Despite numerous works carried out in the last few years, basic issues such as the structure of C4 and C,, with 12> 6, are still matter of controversy [ 2-41. Very recently, the linear chain molecule Cs has been detected [5-S] by infrared spectroscopy both in the laboratory and in the circumstellar shell of carbon star IRC+ 10216. This represented the first spectroscopic detection of gas phase Cs, which is now the largest pure carbon molecule to have been studied at high resolution. In December 1988, during the molecular line survey observation toward IRC+ 10216, Ohishi et al. [ 91 detected the rotational spectrum of a new carbon chain molecule Sic+ They suggested that a new series of carbon-chain molecules Sic, may be present in circumstellar and interstellar environments and the study of these molecules ought to elucidate the chemistry of silicon and carbon in such media. A step towards the understanding of the chemistry and dynamics of these atoms would be the detection of the infrared spectrum of the first known molecule containing both Si and C, and the calculation either from spectroscopic data or ab initio of its force field. In this note, we report ab initio calculations of the structure, force field, the harmonic infrared frequen-
*
Issued as NRCC No. 30763.
0009-2614/89/$
ties and the isotopic shifts of Sic4 with the purpose of facilitating its IR detection either in the laboratory or in space. The calculations were performed on an IBM 3090,’ 200VF mainframe, with the GAUSSIAN 86 program [ IO]. The basis sets used in this work were the 6-3 11G(d) [ 111 basis set for the carbon atoms and the ( 12s 9p) basis, contracted to [ 62 1111, 52 1111 s for the silicon atom [ 121. An additional set of d functions with exponent 0.450 was added on the silicon atom. This basis set was chosen because it was originally proposed for Moller-Plesset second-order (MP2 ) calculations, which is the level of theory used in this paper. All the 98 orbitals were included in the correlation correction to the energy and gradient. The molecular geometry was optimized constrained to be linear and only the ‘X state was considered. The force constants and the infrared intensities were obtained by numerical differentiation of MP2 energy gradient and MP2 dipole moments. In table 1, the calculated structural parameters are Table 1 Structural parameters (A) for the ‘Z state of Sic4 MP3/6-3IG(d) Sic, C:C2 C2CJ C,C,
1.689 1.275 1.303 1.278
a)
MP2/6-31 lG(d) 1.704 1.285 1.303 1.294
a1 Seeref. [9].
03.50 Q Elsevter Science Publishers B.V. (North-Holland)
517
Volume 164,number 5
22 December 1589
CHEMICALPHYSICSLETTERS
with those obtained at MP3/63 I G(d) level of theory [ 91. The MP2 bond lengths yielded a rotational constant B, of 1508 MHz, to be given and compared
Table 2 Calculated harmonic frequencies (cm-‘) mol ) for z8Si’2C4
compared with a B, experimental value of 1533.772 MHz. Due to the presence of low frequency bending vibration (see table 2), it is reasonable to expect Be to be smaller than B,,. The MP3 calculated value of
and intensities (km/
Table 3 Force field in internal coordinates (units are a-t/A*)
Z(w,) Z(w) C(w) Z(cJ,)
Frequency
Intensity
Description
2227 1837 1164 568
1808 0 50 15
CC asymmetric stretch CIC2-C& stretch Sic,-C2C3-C1C4 stretch Sic,-CzC, stretch
SK, C*C* GCZ CG
5.48166 0.05497 -0.07655 -0.10076
11.23575 0.47308 - 0.23074
10.47654 0.15961
404 236 82
4 12 0
C,C2C3 bend C&C& bend SiCICzC3C4 bend
SiCICl C, CZCS C&C,
0.08834 0.06587 -0.02590
0.41760 0.07090
0.14888
n!&) D!%) rI(w,)
10.45095
Table 4 Calculated isotopic shifts of the vibrational frequencies (in cm-‘)
28 13 12 12 12 28 12 13 12 12 2812121312 2s 12 12 12 13 28 13 13 12 12 28 13 12 13 12 28 13 12 12 13 28 12 13 13 12 28 12 13 12 13 28 12 12 13 13 28 12 13 13 13 28 13 12 13 13 28 13 13 12 13 28 13 13 13 12 28 13 13 13 13 3012121212 3013121212 30 12 13 12 3012121312 30 12 12 12 3013131212 30 13 12 13 3013121213 3012131312 3012131213 30 12 12 13 30 12 13 13 3013121313 30 13 13 12 30 13 13 13 3013131313
518
12 13 12
13 13 13 12
-11 -38 -29 -5 -48 -42 -16 -70 -43 -33 -74 ~-47 -54 -82 -88 0 -11 -38 -29 -5 -48 -43 -16 -70 -44 -33 -74 -47 -54 -82 -88
0
-26 -9 -25 -14 -37 -48 -40 -31 -22 -41 -46 -64 -50 -57 -72
-17 - 12 0 -15 -27 -17 -31 - 12 -26 -15 -26 -31 -41 -27 -42
-1 -4 -6 -1 -4 -6 -5 -7 -10 -10 -10 -7 -5 -11
-1 -26 -9 -26 - 15 -37 -49 -41 -32 -23 -42 -47 -65 -51 -51 -72
-4 -21 -15 -4 -18 -31 -21 -35 -15 -30 -18 -30 -35 -45 -31 -45
-10 -10 -11 -14 -16 -11 -14 -16 -15 -17 -20 -21 -20 -17 -15 -21
-2 -10 -3
0 0
-12 -5 -2 -14 -10 -3 -14 -5 -12 -16 -16
-4 -2 -3 -7 -5 -4 -2 -6 -6 -9 -5 -1 -9
0 -2 -10 -3
0 0 -1 -2 -1 -2 -I -I -1 -1 -2 -3 -2 -3
0 -3 0
0 -12 -5 -2 -14 -10 -3 -14 -5 -12 -16 -16
-1
-3
-4 -2 -3 -1 -5 -5 -2 -6 -6 -9 -5 -1 -9
0 -2 -1 -1 -1 -2 -2 -3 -1 -2 -1 -2 -3 -3 -2 -3
Volume 164. number 5
CHEMICAL PHYSICS LETTERS
1530 MHz is much closer to the observed Bn. The overall good agreement between the calculated and observed rotational constants, and the analogy with Cs, seem to exclude different isomers or electronic states than the one reported here. Upon diagonalization the calculated force field yields no imaginary frequencies, thus the linear structure is a minimum on the potential energy surface of SiC4, and the constrain to linearity was only a mean to save CPU time. In analogy with Cs the calculated IR frequencies and intensities (see table 2) show that only one mode is strongly IR active. The analysis of the normal mode description in Cartesian coordinates shows that it barely involves the silicon atom (coefficient of 0.026). This is hardly a surprise if one considers the force constant matrix (see table 3). since the Sic] force constant is about half the CC force constants. Since the MP2 frequencies are usually overestimated, a better estimate of the asymmetric stretch frequency can be obtained multiplying the calculated values by 0.93 to yield 2071 cm-’ [ 13,141. This frequency occurs in a region where the atmosphere is relatively transparent, a fact that ought to enable its experimental observation in space. The second most intense mode, 0~3,as is also the case for Cj [ 141, is much weaker than wl. It is described as a Sic, stretch vibrating out of phase with the C2CX and C3C4 stretches. Comparison of the calculated Sic, frequencies with those of C5 shows that the former are consistently lower. In particular the lowest bending frequency is calculated to be about 60% of its C5 counterpart. Since isotopic substitution of 28Sibarely affects it (see table 4), we ascribe its lower frequency to smaller bending constants; it is unfortunate that the force constants of C5 have not been published, so that a comparison is not possible. It is expected that this motion is more anharmonic than the corresponding motion for C, [ 151. The calculated isotopic shifts upon 13C substitution of 12Cand 3oSi substitution of 28Si are given in table 4. The resulting isotopic shifts for the two strongest IR active modes are almost all larger than the resolution attainable in a laboratory matrix isolation experiment and should therefore be of help in the identification of such spectra.
22 December 1989
In summary, we have presented calculations, at electron correlation level, of the structural parameter and the harmonic frequencies of the newly discovered carbon chain molecule Sic.+ These calculations find Sic4 to be, in the lowest ‘C state, linear and predict that a very intense CC asymmetric stretch occurs in an astrophysical window. We should like to thank Dr. K. Kawaguchi and Pr.P. Botschwina for preprints of their work. We also thank A.R.W. McKellar for helpful discussions.
References [ 1] W. Weltner Jr. and R.J. Van Zee, Chem. Rev. 244 ( 1989) 562. [2] D.E. Bemholdt, D.H. Magers and R.J. Bartlett, .I. Chem. Phys. 89 (1988) 3612. [3]M, Algranati, H. Feldman, D. Kella, E. Malkin and E. Mlklazky, J. Chem. Phys. 90 (1989) 4617. [4] K. Raghavachari and J.S. Binkley, I. Chem. Phys. 87 (1987) 2191; V. Parasuk and .I. Almlof, J. Chem. Phys. 9 1 ( 1989) 1137. [5]P,F. Bern&h, K.H. Hinkle and J.J. Kcady, Science 244 (1989) 562. [ 61 N. Moazzen-Ahmadi, A.R.W. McKellar and T. Amano, Chem. Phys. Letters 157 (1989) 1. [ 71 N. Moazzen-Ahmadi, A.R.W. McKellar and T. Amano, J. Chem. Phys. 91 (1989) 2140. [ 81 J. Heath, A. Coosky, M. Gruebele, C. Schmuttenmeyer and R.J. Saykally, Science 244 ( 1989) 564. [ 91 M. Ohishi, N. Kaifu, K. Kawaguchi, A. Murakami, S. Saito, S. Yamamoto, S. lshikawa, Y. Fujita, S. Shiratori and W.M. Irvme, Astrophys. J., submitted for publication. [lo] M.J. Frisch, J.S. Binkley, H.B. Schlegel, K. Raghavachari, C.F. M&us, R.L. Martin, J.J.P. Stewart, F.W. Bobrowicz, C.M. Rohlfing, L.R. Kahn, D.J. DeFrees, R. Seeger, R.A. Whiteside, D.J. Fox, E.M. Fleuder and J.A. Pople, GAUSSIAN 86, Carnegie-Mellon Quantum Chemistry Publishing Unit, Pittsburgh PA (1984). [ 111 R. Krishnan, J.S. Binkley, R. Seeger and J.A. Poplc, J. Chem. Phys. 72 (1980) 650. [ 121 A.D. McLean and G.S. Chandler, J. Chem. Phys. 72 (1980) 5639. [ 131 W.J. Hehre, L. Radom, P. van R. Schleyer and J.A. Pople, Ab initio molecular orbital theory (Wiley, New York, 1986 ). [ 141 J.M.L. Martin, J.P. Francois and R. Gijbels, J. Chem. Phys. 90 (1989) 3403. [15] P. Botschwina and P. Sebald, Chem. Phys. Letters 160 (1989) 485.
519
CIRCUMSTELLAR
CHEMICAL PHYSICS LETTERS
22 December 1989
CARBON-CHAIN MOLECULES.
PREDICTION OF THE INFRARED SPECTRUM OF Sic, *
N. MOAZZEN-AHMADI
a and F. ZERBETTO b
a Herzberglnstitute ofAstrophysics. National Research Council of Canada, Ottawa, Ontario. Canada KlA OR6 b Division of Chemistry, National Research Council of Canada, Ottawa, Ontario, Canada, KIA OR6 Received 21 August 1989; in final form 3 October 1989
The infrared spectrum of Sic,, recently discovered in the circumstellar shell of the evolved star IRC+ 10216, is predicted ab initio at the MP2/6-31 lG(d) level of theory. A very intense asymmetric stretch is calculated to occur in an astrophysical window.
Carbon clusters have recently been subject of extensive experimental and theoretical investigations because of their relevance in astrochemistry and combustion processes [ 11. Despite numerous works carried out in the last few years, basic issues such as the structure of C4 and C,, with 12> 6, are still matter of controversy [ 2-41. Very recently, the linear chain molecule Cs has been detected [5-S] by infrared spectroscopy both in the laboratory and in the circumstellar shell of carbon star IRC+ 10216. This represented the first spectroscopic detection of gas phase Cs, which is now the largest pure carbon molecule to have been studied at high resolution. In December 1988, during the molecular line survey observation toward IRC+ 10216, Ohishi et al. [ 91 detected the rotational spectrum of a new carbon chain molecule Sic+ They suggested that a new series of carbon-chain molecules Sic, may be present in circumstellar and interstellar environments and the study of these molecules ought to elucidate the chemistry of silicon and carbon in such media. A step towards the understanding of the chemistry and dynamics of these atoms would be the detection of the infrared spectrum of the first known molecule containing both Si and C, and the calculation either from spectroscopic data or ab initio of its force field. In this note, we report ab initio calculations of the structure, force field, the harmonic infrared frequen-
*
Issued as NRCC No. 30763.
0009-2614/89/$
ties and the isotopic shifts of Sic4 with the purpose of facilitating its IR detection either in the laboratory or in space. The calculations were performed on an IBM 3090,’ 200VF mainframe, with the GAUSSIAN 86 program [ IO]. The basis sets used in this work were the 6-3 11G(d) [ 111 basis set for the carbon atoms and the ( 12s 9p) basis, contracted to [ 62 1111, 52 1111 s for the silicon atom [ 121. An additional set of d functions with exponent 0.450 was added on the silicon atom. This basis set was chosen because it was originally proposed for Moller-Plesset second-order (MP2 ) calculations, which is the level of theory used in this paper. All the 98 orbitals were included in the correlation correction to the energy and gradient. The molecular geometry was optimized constrained to be linear and only the ‘X state was considered. The force constants and the infrared intensities were obtained by numerical differentiation of MP2 energy gradient and MP2 dipole moments. In table 1, the calculated structural parameters are Table 1 Structural parameters (A) for the ‘Z state of Sic4 MP3/6-3IG(d) Sic, C:C2 C2CJ C,C,
1.689 1.275 1.303 1.278
a)
MP2/6-31 lG(d) 1.704 1.285 1.303 1.294
a1 Seeref. [9].
03.50 Q Elsevter Science Publishers B.V. (North-Holland)
517
Volume 164,number 5
22 December 1589
CHEMICALPHYSICSLETTERS
with those obtained at MP3/63 I G(d) level of theory [ 91. The MP2 bond lengths yielded a rotational constant B, of 1508 MHz, to be given and compared
Table 2 Calculated harmonic frequencies (cm-‘) mol ) for z8Si’2C4
compared with a B, experimental value of 1533.772 MHz. Due to the presence of low frequency bending vibration (see table 2), it is reasonable to expect Be to be smaller than B,,. The MP3 calculated value of
and intensities (km/
Table 3 Force field in internal coordinates (units are a-t/A*)
Z(w,) Z(w) C(w) Z(cJ,)
Frequency
Intensity
Description
2227 1837 1164 568
1808 0 50 15
CC asymmetric stretch CIC2-C& stretch Sic,-C2C3-C1C4 stretch Sic,-CzC, stretch
SK, C*C* GCZ CG
5.48166 0.05497 -0.07655 -0.10076
11.23575 0.47308 - 0.23074
10.47654 0.15961
404 236 82
4 12 0
C,C2C3 bend C&C& bend SiCICzC3C4 bend
SiCICl C, CZCS C&C,
0.08834 0.06587 -0.02590
0.41760 0.07090
0.14888
n!&) D!%) rI(w,)
10.45095
Table 4 Calculated isotopic shifts of the vibrational frequencies (in cm-‘)
28 13 12 12 12 28 12 13 12 12 2812121312 2s 12 12 12 13 28 13 13 12 12 28 13 12 13 12 28 13 12 12 13 28 12 13 13 12 28 12 13 12 13 28 12 12 13 13 28 12 13 13 13 28 13 12 13 13 28 13 13 12 13 28 13 13 13 12 28 13 13 13 13 3012121212 3013121212 30 12 13 12 3012121312 30 12 12 12 3013131212 30 13 12 13 3013121213 3012131312 3012131213 30 12 12 13 30 12 13 13 3013121313 30 13 13 12 30 13 13 13 3013131313
518
12 13 12
13 13 13 12
-11 -38 -29 -5 -48 -42 -16 -70 -43 -33 -74 ~-47 -54 -82 -88 0 -11 -38 -29 -5 -48 -43 -16 -70 -44 -33 -74 -47 -54 -82 -88
0
-26 -9 -25 -14 -37 -48 -40 -31 -22 -41 -46 -64 -50 -57 -72
-17 - 12 0 -15 -27 -17 -31 - 12 -26 -15 -26 -31 -41 -27 -42
-1 -4 -6 -1 -4 -6 -5 -7 -10 -10 -10 -7 -5 -11
-1 -26 -9 -26 - 15 -37 -49 -41 -32 -23 -42 -47 -65 -51 -51 -72
-4 -21 -15 -4 -18 -31 -21 -35 -15 -30 -18 -30 -35 -45 -31 -45
-10 -10 -11 -14 -16 -11 -14 -16 -15 -17 -20 -21 -20 -17 -15 -21
-2 -10 -3
0 0
-12 -5 -2 -14 -10 -3 -14 -5 -12 -16 -16
-4 -2 -3 -7 -5 -4 -2 -6 -6 -9 -5 -1 -9
0 -2 -10 -3
0 0 -1 -2 -1 -2 -I -I -1 -1 -2 -3 -2 -3
0 -3 0
0 -12 -5 -2 -14 -10 -3 -14 -5 -12 -16 -16
-1
-3
-4 -2 -3 -1 -5 -5 -2 -6 -6 -9 -5 -1 -9
0 -2 -1 -1 -1 -2 -2 -3 -1 -2 -1 -2 -3 -3 -2 -3
Volume 164. number 5
CHEMICAL PHYSICS LETTERS
1530 MHz is much closer to the observed Bn. The overall good agreement between the calculated and observed rotational constants, and the analogy with Cs, seem to exclude different isomers or electronic states than the one reported here. Upon diagonalization the calculated force field yields no imaginary frequencies, thus the linear structure is a minimum on the potential energy surface of SiC4, and the constrain to linearity was only a mean to save CPU time. In analogy with Cs the calculated IR frequencies and intensities (see table 2) show that only one mode is strongly IR active. The analysis of the normal mode description in Cartesian coordinates shows that it barely involves the silicon atom (coefficient of 0.026). This is hardly a surprise if one considers the force constant matrix (see table 3). since the Sic] force constant is about half the CC force constants. Since the MP2 frequencies are usually overestimated, a better estimate of the asymmetric stretch frequency can be obtained multiplying the calculated values by 0.93 to yield 2071 cm-’ [ 13,141. This frequency occurs in a region where the atmosphere is relatively transparent, a fact that ought to enable its experimental observation in space. The second most intense mode, 0~3,as is also the case for Cj [ 141, is much weaker than wl. It is described as a Sic, stretch vibrating out of phase with the C2CX and C3C4 stretches. Comparison of the calculated Sic, frequencies with those of C5 shows that the former are consistently lower. In particular the lowest bending frequency is calculated to be about 60% of its C5 counterpart. Since isotopic substitution of 28Sibarely affects it (see table 4), we ascribe its lower frequency to smaller bending constants; it is unfortunate that the force constants of C5 have not been published, so that a comparison is not possible. It is expected that this motion is more anharmonic than the corresponding motion for C, [ 151. The calculated isotopic shifts upon 13C substitution of 12Cand 3oSi substitution of 28Si are given in table 4. The resulting isotopic shifts for the two strongest IR active modes are almost all larger than the resolution attainable in a laboratory matrix isolation experiment and should therefore be of help in the identification of such spectra.
22 December 1989
In summary, we have presented calculations, at electron correlation level, of the structural parameter and the harmonic frequencies of the newly discovered carbon chain molecule Sic.+ These calculations find Sic4 to be, in the lowest ‘C state, linear and predict that a very intense CC asymmetric stretch occurs in an astrophysical window. We should like to thank Dr. K. Kawaguchi and Pr.P. Botschwina for preprints of their work. We also thank A.R.W. McKellar for helpful discussions.
References [ 1] W. Weltner Jr. and R.J. Van Zee, Chem. Rev. 244 ( 1989) 562. [2] D.E. Bemholdt, D.H. Magers and R.J. Bartlett, .I. Chem. Phys. 89 (1988) 3612. [3]M, Algranati, H. Feldman, D. Kella, E. Malkin and E. Mlklazky, J. Chem. Phys. 90 (1989) 4617. [4] K. Raghavachari and J.S. Binkley, I. Chem. Phys. 87 (1987) 2191; V. Parasuk and .I. Almlof, J. Chem. Phys. 9 1 ( 1989) 1137. [5]P,F. Bern&h, K.H. Hinkle and J.J. Kcady, Science 244 (1989) 562. [ 61 N. Moazzen-Ahmadi, A.R.W. McKellar and T. Amano, Chem. Phys. Letters 157 (1989) 1. [ 71 N. Moazzen-Ahmadi, A.R.W. McKellar and T. Amano, J. Chem. Phys. 91 (1989) 2140. [ 81 J. Heath, A. Coosky, M. Gruebele, C. Schmuttenmeyer and R.J. Saykally, Science 244 ( 1989) 564. [ 91 M. Ohishi, N. Kaifu, K. Kawaguchi, A. Murakami, S. Saito, S. Yamamoto, S. lshikawa, Y. Fujita, S. Shiratori and W.M. Irvme, Astrophys. J., submitted for publication. [lo] M.J. Frisch, J.S. Binkley, H.B. Schlegel, K. Raghavachari, C.F. M&us, R.L. Martin, J.J.P. Stewart, F.W. Bobrowicz, C.M. Rohlfing, L.R. Kahn, D.J. DeFrees, R. Seeger, R.A. Whiteside, D.J. Fox, E.M. Fleuder and J.A. Pople, GAUSSIAN 86, Carnegie-Mellon Quantum Chemistry Publishing Unit, Pittsburgh PA (1984). [ 111 R. Krishnan, J.S. Binkley, R. Seeger and J.A. Poplc, J. Chem. Phys. 72 (1980) 650. [ 121 A.D. McLean and G.S. Chandler, J. Chem. Phys. 72 (1980) 5639. [ 131 W.J. Hehre, L. Radom, P. van R. Schleyer and J.A. Pople, Ab initio molecular orbital theory (Wiley, New York, 1986 ). [ 141 J.M.L. Martin, J.P. Francois and R. Gijbels, J. Chem. Phys. 90 (1989) 3403. [15] P. Botschwina and P. Sebald, Chem. Phys. Letters 160 (1989) 485.
519