Calculation of electronic excited states of molecules using the Helmholtz free-energy minimum principle

We show that the Helmholtz free-energy variational principle is the physical principle underlying the ensemble variational theory formulated in seminal papers by Theophilou and by Gross, Oliveira, and Kohn. A method of calculating electronic excitations of atoms and molecules is then proposed, based on the constrained minimization of the free energy. It involves the search for the optimal set of Slater determinant states to describe low electronic excitations and, in a second step, the search for optimal rotations in the space spanned by these states. Boltzmann factors are used as weights of states in the ensemble since for these the free energy achieves a minimum. The proposed method is applied to the Be atom and LiH and BH molecules. The method captures static electron correlation but naturally lacks dynamic correlation. To account for the latter, we describe short-range electron-electron interaction with a density functional, while the long-range part is still expressed by a wave-function method. Using the example of the LiH molecule, we find that the resulting method is able to capture both static and dynamic electron correlations.