Variational nature of the frozen density energy in density-based energy decomposition analysis and its application to torsional potentials.

Abstract

The density-based energy decomposition analysis (DEDA) is the first of its kind to calculate the frozen density energy variationally. Defined with the constrained search formulation of density functional theory, the frozen density energy is optimized in practice using the Wu-Yang (WY) method for constrained minimizations. This variational nature of the frozen density energy, a possible reason behind some novel findings of DEDA, will be fully investigated in this work. In particular, we systematically study the dual basis set dependence in WY: the potential basis set used to expand the Lagrangian multiplier function and the regular orbital basis set. We explain how the convergence progresses differently on these basis sets and how an apparent basis-set independence is achieved. We then explore a new development of DEDA in frozen energy calculations of the ethane molecule, focusing on the internal rotation around the carbon-carbon bond and the energy differences between staggered and eclipsed conformations. We argue that the frozen density energy change at fixed bond lengths and bond angles is purely steric effects. Our results show that the frozen density energy profile follows closely that of the total energy when the dihedral angle is the only varying geometry parameter. We can further analyze the contributions from electrostatics and Pauli repulsions. These results lead to a meaningful DEDA of the torsional potential in ethane.