Accurate ab initio prediction of molecular geometries and spectroscopic constants, using SCF and MP2 energy derivatives

Abstract

The evaluation of analytic gradients and higher derivatives has had a tremendous impact on quantum chemistry. Although self-consistent field (SCF) first derivatives and higher derivatives are now routinely evaluated as ‘black-box’ procedures, derivatives of correlated wavefunctions are not. It is argued in the following that the least sophisticated correlated method, Møller–Plesset second-order perturbation theory (MP2), can be treated so efficiently that first and second derivatives can be viewed as a ‘black-box’ procedure with the same limitations as the SCF first and second derivatives themselves.

Discussed in this paper are the methods for MP2 geometry optimisation, evaluation of MP2 harmonic frequencies and prediction of i.r. intensities. Recent progress is reported which enables calculations with very large basis sets. Such calculations are reported for H₂O, NH₃ and CH₄, where it is found that the MP2 large-basis ‘limit’ gives bond lengths within 0.003 Å and bond angles within 0.5° of experimental values. Harmonic frequencies at this MP2 ‘limit’ are typically within 2% of experimental values, and i.r. intensities are much improved over SCF values. A previously suggested problem concerning the CH₄ equilibrium bond length is also discussed and resolved.

The evaluation of analytic third and fourth derivatives of the SCF energy is also discussed. Calculations with a DZP basis are reported for H₂O, NH₃ and CH₄, and values are given for vibration–rotation constants α^(B)_r, anharmonic constants x_rs, vibrationally averaged corrections to bond lengths r_g–r_e, and also (ν_r–ω_r), the difference between fundamental and harmonic frequencies. For nearly all these values there is good agreement with the available experiment data (typically within 10%).

The conclusion of this work is that ab initio chemistry can now provide very accurate predictions of equilibrium geometries and harmonic frequencies using Møller–Plesset second-order perturbation theory (MP2). Furthermore, SCF cubic and quartic force constants can provide a good description of the anharmonic potential. Together these theoretical techniques yield an accurate full description of quadratic, cubic and quartic interactions, providing the high-resolution spectroscopist with important data on a very wide class of molecules. In addition, as the theoretical techniques are suitably formulated for vector processing, the potential applications using supercomputers instead of scalar mainframes moves from small to large molecules.