A generalized self‐consistent‐field procedure in the improved BCS theory

Abstract

The basic ideas of the Improved Bardeen–Cooper–Schrieffer (IBCS) approach to the first‐ and second‐order Reduced Density Matrices (1‐ and 2‐RDM) are briefly reviewed. The molecular orbital occupations $\left\{ {\rho _q } \right\}$ are expressed by means of new quantities $\left\{ {\gamma _q } \right\}$, which, satisfying a trigonometric relation, guarantee the non‐idempontent condition. Thus, a variational method is introduced to determine $\left\{ {\rho _q } \right\}$, involving only an unconstrained minimization which may be performed using a conjugate gradient technique. A new effective Hamiltonian $\hat V$ which is composed of the Coulomb, exchange and exchange‐time inversion operators is also presented. It leads exactly to equations of Hartree–Fock type, however, the electronic field includes now an arbitrary number of orbitals and fractional occupation numbers. Accordingly, a generalized self‐consistent‐field method is proposed: the iterative procedure is repeated until convergence is reached for the actual density matrix.