Reduced Two-Electron Interactions in Anharmonic Molecular Vibrational Calculations Involving Localized Normal Coordinates

Abstract

Spatially localized vibrational normal mode coordinates are shown to reduce the importance of calculating the full set of two-electron terms in the molecular electronic Schrodinger equation. Electron correlation and dispersion interactions become less significant in (E,E)-1,3,5,7octatetraene vibrational self-consistent field calculations when displacing remote atoms along multiple coordinates. Electron correlation interactions between spatially remote modes are also found to be less important compared to their corresponding uncorrelated interaction terms. Attenuation of the Coulomb operator indicates that the two-electron terms between remote electrons become less important for accurately describing the strongly contributing mode-coupling terms between sets of localized vibrational modes.

Static Electron Correlation in Anharmonic Molecular Vibrations: A Hybrid TAO-DFT Study

“…PES sampling can be restricted to just nuclear second derivatives of the energy around an equilibrium geometry (the harmonic approximation), and the remaining anharmonic PES terms can be evaluated in the basis of normal coordinates along which the harmonic vibrations become independent. When anharmonic terms are included only up to the fourth-order nuclear derivatives, this is termed a quartic force field, or QFF, and further reductions are often made by only including derivatives that involve a specified number of different coordinates, termed an n -mode representation ( n MR), or by changing the coordinates to find more disconnected terms that enable further reductions to be safely made. − …”

“…When anharmonic terms are included only up to the fourth-order nuclear derivatives, this is termed a quartic force field, or QFF, and further reductions are often made by only including derivatives that involve a specified number of different coordinates, termed an n -mode representation ( n MR), 35 or by changing the coordinates to find more disconnected terms that enable further reductions to be safely made. 36 − 57 …”