Density matrices and iterative natural modals in vibrational structure theory

ABSTRACT

It is demonstrated how the second-quantisation formulation of multi-mode dynamics leads to expressions for vibrational density matrices. The properties and different representations of these matrices are discussed. Diagonalising the one-mode density matrices defines a set of natural modals for each vibrational mode. The theory and first implementation of the iterative natural modals (ItNaMo) method for correlated vibrational structure models is presented. In the ItNaMo method, natural modals are used as basis functions for a subsequent correlated calculation. This optimisation of the one-mode basis is repeated until the changes in the basis functions become sufficiently small. Ground-state and excited-state energy calculations are presented for water, formaldehyde and ethylene. It is shown that using optimised coordinates for the water calculation makes the occupation numbers converge to zero much faster and thereby allows for large reductions in the required number of basis functions. For the higher-order wave-function models the ItNaMo method results in smaller energy errors compared to full vibrational configuration interaction and thereby facilitates a more accurate description of the wave function.

KEYWORDS:

• Density matrix
• natural orbitals
• vibrational-structure theory

Acknowledgments

O.C. acknowledges support from the Lundbeck Foundation, the Danish e-infrastructure Cooperation (DeiC), and the Danish Council for Independent Research through a Sapere Aude III grant (DFF - 4002-00015).

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. These correction terms can be fitted to the SOP form.

Additional information

Funding

Lundbeck Foundation; Danish e-infrastructure Cooperation (DeiC); Danish Council for Independent Research through a Sapere Aude III grant [grant number DFF 4002-00015].