D. Van Neck

We propose an approach to the electronic structure problem based on noninteracting electron pairs that has similar computational cost to conventional methods based on noninteracting electrons. In stark contrast to other approaches, the wave function is an antisymmetric product of nonorthogonal geminals, but the geminals are structured so the projected Schrödinger equation can be solved very efficiently. We focus on an approach where, in each geminal, only one of the orbitals in a reference Slater determinant is occupied. The resulting method gives good results for atoms and small molecules. It also performs well for a prototypical example of strongly correlated electronic systems, the hydrogen atom chain.

Inspired by the wavefunction forms of exactly solvable algebraic Hamiltonians, we present several wavefunction ansatze. These wavefunction forms are exact for two-electron systems; they are size consistent; they include the (generalized) antisymmetrized geminal power, the antisymmetrized product of strongly orthogonal geminals, and a Slater determinant wavefunctions as special cases. The number of parameters in these wavefunctions grows only linearly with the size of the system. The parameters in the wavefunctions can be determined by projecting the Schrödinger equation against a test-set of Slater determinants; the resulting set of nonlinear equations is reminiscent of coupled-cluster theory, and can be solved with no greater than O (N⁵) scaling if all electrons are assumed to be paired, and with O (N⁶) scaling otherwise. Based on the analogy to coupled-cluster theory, methods for computing spectroscopic properties, molecular forces, and response properties are proposed.

The G-condition for the N-representability of the two-electron reduced density matrix is tightened by replacing the semidefiniteness constraint with the true upper and lower bounds of the G-type Hamiltonian operator. The lower bound is not easily computed (in contrast to the sharp P- and Q-conditions), but maps onto a well-known integer programming problem. The sharp-G, sharp-P, and sharp-Q conditions are just three members of a much broader class of conditions based on exactly solvable model Hamiltonians.

Single-particle overlap functions and spectroscopic factors are calculated on the basis of the one-body density matrices (ODM) obtained for the nucleus ¹⁶O employing different approaches to account for the effects of correlations. The calculations use the relationship between the overlap functions related to bound states of the (A-1)-particle system and the ODM for the ground state of the A-particle system. The resulting bound-state overlap functions are compared and tested in the description of the experimental data from (p,d) reactions for which the shape of the overlap function is important.