Harmonic force field: An approximate relationship between the exact nonrelativistic and the Hartree–Fock limit values of the force constants

Abstract

A theoretical background to the scaling procedure used for correcting molecular force constants computed at the Hartree–Fock (HF) level is presented, in which scaling is considered as an empirical simulation of the effect of electron correlation. Using a variational formalism for the analytical first and second derivatives, it is shown that a successful scaling requires (i) relatively large exact excitation energies; (ii) a singlet‐stable solution for the HF ground state; and (iii) molecular orbitals that can be well localized for the ground electronic state. The relationship between the exact nonrelativistic and HF limit values of the quadratic force constants has been investigated when the above conditions are satisfied. A single multiplicative (scale) factor is required at this limit and its value is approximately C 2 0 near the ‘‘exact’’ equilibrium geometry, where C 0 is the coefficient of the HF determinant in a complete configuration interaction expansion. This approach requires a moderate size of the molecules investigated. A specific numerical example is considered.