Astron. Astrophys. 333, 1007-1015 (1998)

Appendix

All calculations have been performed at increasing levels of Moller-Plesset perturbation theory, namely MP2, MP3, and MP4 using Gaussian 92 (Frisch et al. 1992). First, investigations were carried out at the MP2 level using a double-zeta basis set extended by polarization functions (6-31G(d,p)). To obtain accurate electronic energies, single point calculations were performed at the MP4SDTQ/6-311 + + G(3df,3pd) theoretical level using MP2/6-31G(d,p) optimized geometries. These are full fourth order perturbation calculations, including contributions from single, double, triple, and quadruple excitations and employing a triple-zeta basis set extended by polarization and diffuse functions; such basis sets are known to give a large flexibility to the one-particle space approaching the so-called Hartree-Fock limit. The character of each stationary point (either minimum energy, for which all vibrational frequencies are real, or saddle point, characterized by one imaginary frequency) has been confirmed by vibrational analysis at the MP2/6-31G(d,p) theoretical level.

The optimized reaction path considered is C approaching ammonia along its axis. Relative energies have been corrected for zero-point vibrational energy (ZPE) using carefully scaled vibrational wave numbers. The MP2 scaling factor has been deduced from our previous theoretical study of the HCN, HNC, systems (Talbi et al. 1996). It is equal to 0.969 and has been applied to all molecules studied here.

When indicated, energies have been corrected for spin contamination from higher spin states using an approximate spin projection method, whose description can be found in Schlegel (1986).

Knowing from our past experience that basis set superposition errors (BSSE) (Boys & Bernardi 1970; Liu & McLean 1989) are less than one Kcal/mol (DeFrees et al. 1990, Talbi et al. 1996), they have been neglected in view of the large energy differences involved by the processes studied here.

Since previous theoretical studies (DeFrees & McLean 1985) have shown that calculated rotational constants are much closer to experimental values when third-order perturbation theory is used rather than second-order or fourth-order, the MP3/6-311 + + G(d,p) level has been used for their determination. We have calculated rotational constants for all structures corresponding to either potential minima or saddle points along the lowest potential energy surface leading to H₂ NC (¹ A₁)/HCNH (), since they are required as input for dynamics calculations. For this surface, the final MP4SDTQ calculations have been done using both MP2/6-31G(d,p) and MP3/6-311 + + G(d,p) geometries as a test of energy stability with respect to geometry. A comparison of the MP4SDTQ/6-311 + + G(3df,3pd) calculations obtained using MP2/6-31G(d,p) and MP3/6-311 + + G(d,p) optimized geometries (Table 2) shows energy differences smaller than 0.2 Kcal/mol. These negligible differences justify the use of the MP2/6-31G(d,p) optimized geometries for the ² and ⁴ surfaces.

© European Southern Observatory (ESO) 1998

Online publication: April 28, 1998

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