Nonempirical ab initio Methods. The Hartree-Fock Method

Meeting the conditions 1 and 2 is necessary for correct evaluation of the heat and the activation energy of a given reaction, the condition 3 has to be satisfied in order to reproduce the vibration spectrum and, consequently, the entropy and the isotopic effects while the conditions 3 and 4 are essential for the calculation of the true reaction path. 

Many modem quantum-mechanical methods, especially the semiempirical ones, have been devised with the specific aim of calculating some particular properties of molecular systems with the result that they adequately satisfy only one or two of the requirements mentioned. For this reason, the conclusions on reaction mechanisms obtained by such methods should be treated with a degree of caution. 

2 Nonempirical (ab initio) Methods. The Hartree-Fock Method 

Th6 theory and the analysis of calculational schemes of quantum chemistry have been dealt with in detail in a number of books [1-6] and review articles [7-12]. Here we give only a brief account of the main principles of the general theory of molecular orbitals (MO) that provides the basis for constructing the most important nonempirical methods of quantum chemistry. 

The MO approximation is based on the assumption that an individual spin orbital (pioc or (piP (where cpi is the function of space coordinates and a (m = 1/2) or P(nis= — 1/2) are the functions of spin coordinates) corresponds to each electron. The full wave function of a many-electron system ip in the Hartree-Fock approximation is written as a Slater determinant whose form provides for the property of antisymmetry of ip, required by the Pauli principle, with respect to the pairwise permutation of any electron 

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Nonempirical (ab initio) Methods. The Hartree-Fock Method Pxff is the bond order matrix ... 

The use of frozen orbitals, such as the bond orbitals connecting the quantum to the classical part of the system, can be extended to nonempirical quantum methods such as ab initio Hartree -Fock, post Hartree Fock, or DFT. In these cases, the overlap between atomic orbitals is taken into account and the orthogonality conditions are more difficult to fulfill. The mathematical formulation of the method has been developed in the original papers [26 28] and the process can be summarized as follows. 

The examples included in this chapter use some different theoretical models for the interpretation of, primarily. UPS valence band data, for pristine and doped systems as well as for the initial stages of interface formation for metals on conjugated molecules. Among the theoretical methods used in the examples are sem-iempirical Hartree-Fock methods such as the modified neglect of diatomic overlap (MNDO) [48,49] and Austin Model 1 (AMI) [50], the nonempirical valence effective Hamiltonian (VEH) pseudopotential method [51,52], ab initio Hartree-Fock techniques, and the local spin density (LSD) approximation [53,54],... 

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