PHYSICAL REVIEW A VOLUME 48, NUMBER 1 JULY 1993 Dipole moment, polarizability, and their derivatives for the SiC molecule Marcos A. Castro and Sylvio Canuto* Departamento de Fisica, Universidade Federal de Pernambuco, 50732-910 Recife, Pernambuco, Brazil (Received 9 July 1992; revised manuscript received 8 October 1992) The dipole moment and the polarizability of the SiC molecule are calculated by using the coupled cluster with double-substitution approximation with partial inclusion of single and triple substitutions. Their respective derivatives with respect to the internuclear separation are also reported within the many-body-perturbation-theory scheme to fourth order limited to double and quadruple substitutions. PACS number(s): 31. 20. Tz, 31. 90. + s, 35. 20.My The SiC molecule in its ground state was detected for the first time by Cernicharo et al. [1] and is predicted to be present in abundance in dense interstellar clouds [2] and to be an important component of stellar atmosphere [3]. The identification of SiC [1] is supported by the com- parison of a number of millimeter-wave rotational lines detected, both in the laboratory and in space, with ab ini- tio calculated spectroscopic constants [4]. Now the in- frared spectrum is expected to be observed. Since ir in- tensities are proportional to the square of the derivative of the dipole moment with respect to the internuclear separation, it is important to have available theoretical values of these properties. There are many calculations including the electron-correlation effects on the spectro- scopic constants of SiC [4 — 6] but no calculations of the electric properties have been reported. In this work we present theoretical values for the dipole moment and po- larizability of the SiC molecule and their derivatives with respect to the internuclear separation. Dipole moments and polarizabilities are very impor- tant quantities in the study of phenomena concerned with intermolecular forces in gases and liquids and optical phenomena in general [7]. However, accurate theoretical values of these properties are difficult to obtain [8], as can be noted by some recent calculations for atomic [9] and molecular [10, 11] systems, because they are very sensitive to the effects of electron correlation. Also, 1arge basis sets with many diffuse functions are necessary. Many cal- culations of electric properties have been performed within the fourth-order many-body perturbation theory [MBPT(4)], yielding satisfactory results. The need for higher-order terms of the perturbation expansion occurs when the MBPT series is slowly convergent, exemplified by multiconfigurationa1 reference state or, for open-shell systems, high spin contamination of the unrestricted Hartree-Fock (UHF) reference [12]. It is known as well that the calculation of dipole moments frequently shows problems of convergence, the CO molecule being a good example [11]. The ground state of SiC is theoretically predicted and consistent with a (rr o') II state [1, 4]. Our preliminary self-consistent-field (SCF) calculations show that the spin contamination of the UHF reference determinant is fairly high ( ( S ) = 2. 5 ) and decreases only slightly (by 0. 1) in MBPT(2). Therefore theoretical calculations of the electric properties of SiC demand ex- tensive treatment of the electron-correlation effects or a better starting reference configuration. An eScient way to handle electron correlation is to use the coupled-cluster (CC) method [13], and it has been shown that the coupled cluster with single and double (CCSD) substitution has a great capacity to eliminate spin contaminations [12]. An important point in CC cal- culation is the selection of the excitation models. This is usually done on the basis of the accuracy required and the computational cost involved. The coupled cluster with double-substitution (CCD) approximation [13 — 15] is correct to fourth order in many-body perturbation theory in the double- and quadruple-substitution space [Dg- MBPT(4)] and includes significant higher-order terms. But CCD may not be effective in reducing spin contam- inations in all cases. For more accurate results the in- clusion of single and triple substitutions is necessary. The full inclusion of iterated single and triple substitu- tions in the CC scheme (CCSDT) for SiC is very expen- sive and beyond the limits of reasonable computational resources. The partial inclusion of the single and triple substitutions can be performed by using the CCD ampli- tudes [16] [CCD+ ST(CCD)]. The CCD+ ST(CCD) ap- proximation handles the contributions of single and triple substitution more properly [16, 17] than MBPT(4), where single and triple substitution may also be extracted to give CCD+ST(4). The CCD+ST(CCD) approximation could be considered of an accuracy intermediate between CCD+ST(4) and the fully iterated CCSDT approxima- tions. There does not seem to be a systematic analysis of the performance of CCD+ ST(CCD) in reducing spin contamination of the UHF reference state. For that matter, a superior approximation would be CCSD+T(CCSD), but this code is not generally available [18]. We find this CCD+ST(CCD) a good compromise model for the present investigation. It is correct to fifth order in the terms resulting from the interaction of dou- ble excitations and single and triple excitations, and some terms are included to all orders, viz, those involving the interactions of higher-order double excitations with sin- gle and triple excitations [16]. In this work we report results of calculations of the di- pole moment and the polarizability of the SiC molecule. Both will be calculated in the CCD+ST(CCD) approxi- mation. Their respective derivatives with respect to the 1050-2947/93/48(1)/826(3)/$06. 00 826 1993 The American Physical Society