Excitation energies with linear response density matrix functional theory along the dissociation coordinate of an electron-pair bond in N-electron systems

Time dependent density matrix functional theory in its adiabatic linear response formulation delivers exact excitation energies omega(alpha) and oscillator strengths f(alpha) for two-electron systems if extended to the so-called phase including natural orbital (PINO) theory. The Lowdin-Shull expression for the energy of two-electron systems in terms of the natural orbitals and their phases affords in this case an exact phase-including natural orbital functional (PILS), which is non-primitive (contains other than just J and K integrals). In this paper, the extension of the PILS functional to N-electron systems is investigated. With the example of an elementary primitive NO functional (BBC1) it is shown that current density matrix functional theory ground state functionals, which were designed to produce decent approximations to the total energy, fail to deliver a qualitatively correct structure of the (inverse) response function, due to essential deficiencies in the reconstruction of the two-body reduced density matrix (2RDM). We now deduce essential features of an N-electron functional from a wavefunction Ansatz: The extension of the two-electron Lowdin-Shull wavefunction to the N-electron case informs about the phase information. In this paper, applications of this extended Lowdin-Shull (ELS) functional are considered for the simplest case, ELS(1): one (dissociating) two-electron bond in the field of occupied (including core) orbitals. ELS(1) produces high quality omega(alpha) (R) curves along the bond dissociation coordinate R for the molecules LiH, Li-2, and BH with the two outer valence electrons correlated. All of these results indicate that response properties are much more sensitive to deficiencies in the reconstruction of the 2RDM than the ground state energy, since derivatives of the functional with respect to both the NOs and the occupation numbers need to be accurate. (C) 2014 AIP Publishing LLC.