Mixed second and third energy derivatives from auxiliary density perturbation theory^†

^†This work is dedicated to the memory of Prof. Dr. Dieter Cremer, an outstanding scientist and wonderful colleague.

Abstract

The working equations for the calculation of mixed second- and third-order energy derivatives in the framework of auxiliary density functional theory are presented. The perturbations with respect to nuclear displacements and external homogeneous electric field components are calculated with auxiliary density perturbation theory. The presented energy derivative working equations were implemented in deMon2k and validated by vibrational spectra simulations within the double harmonic approximation. The effect of the auxiliary functions on the IR and Raman spectra simulation were analysed for the C₆₀ fullerene. As applications, vibrational spectra of icosahedral carbon fullerenes with up to 540 atoms are calculated without employing symmetry constraints.

GRAPHICAL ABSTRACT

Keywords:

• Auxiliary density functional theory
• auxiliary density perturbation theory
• frequency analysis
• double harmonic approximation
• fullerenes

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

^† This work is dedicated to the memory of Prof. Dr. Dieter Cremer, an outstanding scientist and wonderful colleague.

Additional information

Funding

This work was financially supported by the Consejo Nacional de Ciencia y Tecnología (CONACyT) projects [grant numbers CB252658 and GIC268251]. R.D.V. gratefully acknowledges a CONACyT PhD fellowship [grant number 347383]. Some of the presented calculations were performed on the HPC resources Xiuhcoatl of Cinvestav, Mexico and Cedar of Compute Canada.