Determination of electronic excitation energies within the doubly occupied configuration interaction space by means of the Hermitian operator method.

In this work, we formulate the equations of motion corresponding to the Hermitian operator method in the framework of the doubly occupied configuration interaction space. The resulting algorithms turn out to be considerably simpler than the equations provided by that method in more conventional spaces, enabling the determination of excitation energies in N-electron systems under an affordable polynomial computational cost. The implementation of this technique only requires to know the elements of low-order reduced density matrices of an N-electron reference state, which can be obtained from any approximate method.

Variational determination of ground and excited-state two-electron reduced density matrices in the doubly occupied configuration space: A dispersion operator approach.

This work implements a variational determination of the elements of two-electron reduced density matrices corresponding to the ground and excited states of N-electron interacting systems based on the dispersion operator technique. The procedure extends the previously reported proposal [Nakata et al., J.

Variational reduced density matrix method in the doubly-occupied configuration interaction space using four-particle N-representability conditions: Application to the XXZ model of quantum magnetism.

This work deals with the variational determination of the two-particle reduced density matrix (2-RDM) and the energy corresponding to the ground state of N-particle systems within the doubly occupied configuration interaction (DOCI) space. Here, we impose for the first time up to four-particle N-representability constraint conditions in the variational determination of the 2-RDM matrix elements using the standard semidefinite programming algorithms. The energies and 2-RDMs obtained from this treatment and the corresponding computational costs are compared with those arisen from previously reported less restrictive variational methods [D.

Variational reduced density matrix method in the doubly occupied configuration interaction space using three-particle -representability conditions.

Ground-state energies and two-particle reduced density matrices (2-RDMs) corresponding to -particle systems are computed variationally within the doubly occupied configuration interaction (DOCI) space by constraining the 2-RDM to satisfy a complete set of three-particle -representability conditions known as three-positivity conditions. These conditions are derived and implemented in the variational calculation of the 2-RDM with standard semidefinite programming algorithms. Ground state energies and 2-RDMs are computed for N, CO, CN, and NO molecules at both equilibrium and nonequilibrium geometries as well as for pairing models at different repulsive interaction strengths.