Hartree-Fock energy estimating

Two key pieces of theoretical data are required to obtain an empirical estimate of the correlation energy from the experimental data collected in the preceding section the total molecular Hartree-Fock energy and the relativistic corrections . It is implicit in the definition of the correlation energy presented in Eq. (1) that the total electronic energy ofa given molecule, Ef, may be divided into three constituent parts,... 

Until recently, only estimates of the Hartree-Fock limit were available for molecular systems. Now, finite difference [16-24] and finite element [25-28] calculations can yield Hartree-Fock energies for diatomic molecules to at least the 1 ghartree level of accuracy and, furthermore, the ubiquitous finite basis set approach can be developed so as to approach this level of accuracy [29,30] whilst also supporting a representation of the whole one-electron spectrum which is an essential ingredient of subsequent correlation treatments. 

We calculate the enthalpy of formation at 0 K as the difference between a H"(PF, g, OK) = -8.55 5.0 kcal mol" (1 ) and the selected value of 1.1 0.5 eV (25.366 kcal mol" ) for the electron affinity (EA) of PF. The value of EA refers to the vertical electron detachment process PF"(g) = PF(g) + e" and is taken from the molecular orbital study of O Hare 2). This value was obtained from Hartree-Fock energies and estimated corrections for correlation effects. The estimated uncertainty in EA is 0.5 eV which should be adequate to cover the possibility that the adiabatic value is lower than the vertical EA. Other theoretical predictions of EA include 2.55 eV ( ) and 1.4 eV (4). 

Figure 1. Total nonrelativistic multi-configuration Hartree-Fock energy, relativistic corrections (estimated as the difference between the multi-configuration Dirac-Hartree-Fock and Hartree-Fock energies) and correlation contributions (estimated from correlation energy density functional calculations) for the group 4 elements. The multi-configuration treatments were carried out with the atomic structure code GRASP [78] and correspond to complete active space calculations with the open valence p shell as active space. The nonrelativistic results were obtained by multiplying the velocity of light with a factor of 10 .

The effects of basis set truncation on the calculated correlation energy estimate are more pronounced than those for the matrix Hartree-Fock energy. Truncation with the tolerance increases the error in the second order correlation energy component by... 

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