Dirac density matrix

These relations show that the Fock-Dirac density matrix is identical with the first-order density matrix, and that consequently the first-order density matrix determines all higher-order density matrices and then also the entire physical situation. This theorem is characteristic for the Hartree-Fock approximation. 

Fock-Dirac density matrix, 225-Framework, 379 Franck-Condon principle, 199 Free volume, 26, 27, 33... 

The determinant is best characterized by the associated Fock-Dirac density matrix.10... 

P is the first-order Fock-Dirac density matrix... 

The Fermi hole in turn is defined in terms of the idempotent Dirac density matrix ys(r, r ) of Eq. (36) where the orbitals < j(x) are solutions of the Har-... 

The field z(r [y]) thus defined is for the interacting system since the tensor involves the density matrix y(r,r ) of Eq. (6). With the field z(r [yj) derived similarly from the tensor tajj(r [ys])) written in terms of the idempotent Dirac density matrix > s( F) of Kohn-Sham theory, the field Z, (r) is then defined as... 

R. McWeeny, Phys. Rev., 126,1028 (1961). Perturbation Theory for the Fock-Dirac Density Matrix. 

McWeeny, R. (1962). Perturbation theory for the Fock-Dirac density matrix. Physical Review, 126,... 

The simplest measure of MO bond order is the Coul-son charge and bond-order matrix, which is essentially the Fock-Dirac density matrix for the minimal basis of occupied valence AOs. When the first-order density matrix is expressed in terms of its NAOs (keyword DMNAO), one obtains a generalization of Coulson s charge and bond-order matrix that exhibits many parallels to the expected Hiickel-like patterns, but can be evaluated for an arbitrarily high ab initio treatment (HF, DFT, or Cl)... 

This factorization of the 2-electron density in terms of the 1-electron p is peculiar to the 1-determinant approximation it means that in this approximation everything is determined by the function p(xi x[), which is often called the Fock-Dirac density matrix (Fock, 1930 Dirac, 1930 Lennard-Jones, 1931). It is in fact clear that the reduced density matrix... 

Show that the Fock-Dirac density matrix (5.3.7), for one determinant of orthonormal spin-orbitals, has the fundamental property... 

The first order Fock-Dirac density matrix is p. From this one constructs a zero order Hamiltonian. For a system of M-electrons, is defined as... 

---