Hartree-Fock theory ground state

Multiconhgurational methods have been particularly successful in studies of transition metal complexes, both for ground state and excited states. This is an area where the alternative methods are few. Many open shells with varying values of the spin together with many close lying electronic states (not only singly excited) makes it difficult to use simple methods like Density Functional Theory, or other methods which assume a Hartree-Fock like ground states. 

Note that the frequency calculation produces many more frequencies than those listed here. We ve matched calculated frequenices to experimental frequencies using symmetry types and analyzing the normal mode displacements. The agreement with experiment is generally good, and follows what might be expected of Hartree-Fock theory in the ground state. ... 

The problem has now become how to solve for the set of molecular orbital expansion coefficients, c. . Hartree-Fock theory takes advantage of the variational principle, which says that for the ground state of any antisymmetric normalized function of the electronic coordinates, which we will denote H, then the expectation value for the energy corresponding to E will always be greater than the energy for the exact wave function ... 

Moller-Plesset perturbation theory (MPPT) aims to recover the correlation error incurred in Hartree-Fock theory for the ground state whose zero-order description is Moller-Plesset zero-order Hamiltonian is the sum of Fock operators, and the zero-order wave functions are deteiminantal wave functions constructed from HF MOs. Thus the zero-order energies are simply the appropriate sums of MO energies. The perturbation is defined as the difference between the sum of Fock operators and the exact Hamiltonian ... 

Subsequently Chang, Pu, and Das72 carried out a many-body calculation of a for the ground state of lithium and compared the results with Hartree-Fock theory. Their Bruckner-Goldstone method is illustrative of many other calculations. The w-particle hamiltonian... 

From all this one must conclude that the determinantal and second-quantized formulations should be regarded as a poor man s group theory which, while convenient, hides the basic freeon dynamics. These fermion methods have the additional disadvantage that their antisymmetric fermion functions are not normally pure spin (freeon) states so that spin-projection may be required. A method for avoiding (approximately) spin projection is the employment of the variation principle to approximate the ground state e. g., unrestricted Hartree-Fock theory. Finally the use of the fermion formulations has lead to the spin paradigm as a replacement for the more fundamental freeon dynamics. 

For most applications, the external potential operator v reduces to a local potential v(r), and the Hohenberg-Kohn theory is valid for the ground state. The present derivation follows exactly the logic of standard Hartree-Fock theory. It is not restricted to ground states and remains valid for fractional occupation numbers. 

Table 3. Total ground-state energies of noble gas and closed s-subshell atoms as determined within Slater theory, the Work-interpretation Pauli-correlated approximation, and Hartree-Fock theory. The negative values of the energies in atomic units are quoted...

Fig. 6. Ground-state energy differences (in ppm) of Slater theory and the Work-interpretation Pauli-correlated approximation with respect to Hartree-Fock theory...

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