Hartree-Fock theory derivative

A. Analytical Differentiation and Derivative Hartree-Fock Theory... 

The earlier derivative Hartree-Fock theory of Dykstra and Jasien is an equivalent procedure to the THDF approach described above for the static-field-only case. An alternate MO-based procedure developed by Sekino and... 

C. E. Dykstra and P. G. Jasien, Chem. Phys. Lett., 109,388 (1984). Derivative Hartree-Fock Theory to All Orders. 

S.-Y. Liu and C. E. Dykstra, ]. Phys. Chem., 91, 1749 (1987). Multipole Polarizabilities and Hyperpolarizabilities of AH and AjHn Molecules from Derivative Hartree-Fock Theory. 

Similar considerations apply to the electric dipole moment the derivatives of the dipole integrals can be easily obtained whilst the derivatives of the density matrix require the use of coupled Hartree-Fock theory (e.g. Gerratt and Mills, 1968). 

What does this mean We have replaced the non-local and therefore fairly complicated exchange term of Hartree-Fock theory as given in equation (3-3) by a simple approximate expression which depends only on the local values of the electron density. Thus, this expression represents a density functional for the exchange energy. As noted above, this formula was originally explicitly derived as an approximation to the HF scheme, without any reference to density functional theory. To improve the quality of this approximation an adjustable, semiempirical parameter a was introduced into the pre-factor Cx which leads to the Xa or Hartree-Fock-Slater (HFS) method which enjoyed a significant amount of popularity among physicists, but never had much impact in chemistry,... 

DERIVATION OF HARTREE-FOCK THEORY Equation (A.46) may be cast as a matrix equation... 

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