Handy-Schaefer vector

Let us summarize. The calculation of Cl first anharmonicities requires no storage or transformation of second and third derivative two-electron integrals, but the full set of first derivative MO integrals is needed. One must construct and transform one set of effective density elements for third derivative integrals and 3M — 6 sets of effective densities for second derivative integrals. In addition to the 3N — 6 MCSCF orbital responses k(1) and the Handy-Schaefer vector Cm needed for the Hessian, the first anharmonicity requires the solution of 3JV — 6 response equations to obtain (1). 

When the orbital rotational parameters are not contained in the variational space, the orbital responses through order 2n + 1 formally appear in the equations that determine the energy to order 2n + 1. However, Handy and Schaefer (1984) pointed out that the orbital responses dU) for j > n always appear in expressions such as where a(l) is some vector whose... 

The block of vacant-occupied CPHF coefficients f/ of Eq. (2.20), which depend on the specific perturbation a, may be eliminated by using the interchange (Z-vector) method of Handy and Schaefer [20], properly extended to the PCM framework [21] ... 

However, instead of solving the coupled Hartree-Fock equations for all components a of the field. F, i.e. with the molecular orbital integrals b dj... (j>j) as the right-hand side, one can solve one set of coupled Hartree-Fock equations for the so-called Z-vector (Handy and Schaefer, 1984), with this second type of Lagrangian, as... 

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