Anharmonicity in compliance formalism: Potential constants and interaction coordinates

At the harmonic level, compliance constants are the inverse force constant matrix elements. In the present work, conversion of anharmonic force constants to compliance constants has been revisited and several new variants of the existing equations have been suggested. The reverse conversion of anharmonic compliance constants to force constants is addressed. The change in the internal coordinate (R-i) for constrained optimization is written as a monotonic polynomial function of the change in another chosen constrained internal coordinate (R-k) and the expansion coefficients extracted directly are the interaction coordinates (ICs). New expressions for computing the cubic and quartic anharmonic ICs using compliance constants are presented and the obtained numerical values are compared with the ICs extracted by the direct method. The work also highlights an effective way of extracting the diagonal harmonic and anharmonic compliance and force/relaxed force constants characterizing the bond in diatomic molecules and pseudo diatomic fragments in a molecule. The ability to compute the mentioned numerical values is likely to open up new possibilities for useful chemical applications.

Automated summary

This study revisits the conversion of anharmonic force constants to compliance constants and suggests new variants of existing equations. The reverse conversion of anharmonic compliance constants to force constants is addressed, and new expressions for computing cubic and quartic anharmonic ICs using compliance constants are presented. The ability to extract diagonal harmonic and anharmonic compliance and force constants may open up new possibilities for useful chemical applications.