Solving the Independent-Particle Model via Nonunitary Transformation Based on Variational Coupled Cluster Singles

We propose an alternative new approach to obtain the Slater determinant ground state solution within an independent-particle approximation using the exponential ansatz for the wave function (Thouless theorem) and exact treatment in terms of variational coupled cluster singles. Although the resulting nonlinear equations formally represent nonterminating expansions, these can be reformulated to finite expansions in terms of the density matrix correction. The latter can be exactly calculated using a very simple recurrence relation within the occupied-occupied block, while the complementary occupied-virtual and virtual-virtual blocks are related and trivially obtained by subsequent matrix multiplications involving the amplitudes of the single-excitation operator. The density matrix is naturally idempotent in any step of the iterative procedure. Blocks of the density matrix are without any further change, apart from the sign, used in the orbital transformation matrix. The latter is not a unitary one, hence leading to nonorthogonal and unnormalized molecular orbitals. These are, however, biorthogonal and can be easily orthonormalized per blocks, if needed in the post-SCF calculations. Formulation is diagonalization free, and the implementation can be easily parallelized. Finally, the formulation provides a challenging way to the solution with "a priori" localized orbitals, a way toward a linear scaling algorithm.