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~ near the "exact" equilibrium geometry, where Co 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.

Predictive abilities of scaled quantum-mechanical molecular force fields: application to 2-methylbuta-1,3-diene (isoprene)

“…The MP2(PC)/aug-cc-pVDZ scale factors were closer to unity than their HF/6-31G analogs [17,22,23]. The results of the present calculations and the most recent experimental vibrational data on both conformers of I are listed in Table 1.…”

“…Fortunately, these overestimations are systematic for analogous structural moieties. Solving such vibrational problems benefits dramatically from the Pulay scaling procedure, for which the theoretical background is given in [17]. The predictive abilities of this approach have been demonstrated also not only for isotopomers and rotational isomers like in the present article but for the relative compounds containing the isovalent heteroatoms of the 14 (IVA) group of the Mendeleyev Periodic Table (for example, see review in [30]).…”

“…The theoretical foundation for the Pulay scaling procedure we used in this analysis [16] has been given by Pupyshev et al [17].…”

The vibrational spectra (100–1500 cm−1) of a series of bicyclo[3.2.1]octanes assigned by means of scaled 3-21G ab initio harmonic force fields

“…Consequently, if more sophisticated basis sets are used, uniform scaling~will give more favorable results compared to this study, or may even be superior to nonuniform scaling (40). Some very recent theoretical work suggests that the Hartree-Fock-limit force field for a given molecule can be corrected with one factor only (41). HOWever, due to basis set truncation, calculations at the 3-21G level are significantly less accurate and require nonuniform scaling as demonstrated theoretically (41) and confirmed here.…”

The infrared spectrum of 2-methylaziridine from scaled abinitio force fields

“…suspicion that deficiencies in the structure are due to underlying deficiencies in the force field itself. It is well known that Hartree-Fock force fields are subject to a systematic, nearly constant, error (21), a theoretical rationalization of which has recently been presented (22). They are also subject to structure-related nonsystematic errors, which arise in part from deficiencies in the theoretical model (e.g., lack of electron correlation) but primarily from deficiencies in the basis set.…”