TAILIEUCHUNG - Ideas of Quantum Chemistry P41

Ideas of Quantum Chemistry P41 shows how quantum mechanics is applied to chemistry to give it a theoretical foundation. The structure of the book (a TREE-form) emphasizes the logical relationships between various topics, facts and methods. It shows the reader which parts of the text are needed for understanding specific aspects of the subject matter. Interspersed throughout the text are short biographies of key scientists and their contributions to the development of the field. | 366 8. Electronic Motion in the Mean Field Atoms and Molecules Each of these matrices is square of the rank M . F depends on c and this is why it is a pseudo-eigenvalue equation . The Hartree-Fock-Roothaan matrix equation is solved iteratively a we assume an initial c matrix . also an initial P matrix often in the zero-th iteration we put P 0 as if there were no electron repulsion b we find the F matrix using matrix P c we solve the Hartree-Fock-Roothaan equation see Appendix L p. 984 and obtain the M MOs we choose the N 2 occupied orbitals those of lowest energy d we obtain a new c matrix and then a new P etc. e we go back to a . The iterations are terminated when the total HF energy more liberal approach or the coefficients c less liberal one change less than the assumed threshold values. Both these criteria ideally fulfilled may be considered as a sign that the output orbitals are already self-consistent. Practically these are never the exact solutions of the Fock equations because a limited number of AOs was used while expansion to the complete set requires the use of an infinite number of AOs the Hartree-Fock total energy in such a case would be called the Hartree-Fock limit energy . limit After finding the MOs hence also the HF function in the SCF LCAO MO approximation we may calculate the total energy of the molecule as the mean value of its Hamiltonian. We need only the occupied orbitals and not the virtual ones for this calculation. The Hartree-Fock method only takes care of the total energy and completely ignores the virtual orbitals which may be considered as a kind of by-product. PRACTICAL PROBLEMS IN THE SCF LCAO MO METHOD Size of the AO basis set NUMBER OF MOs The number of MOs obtained from the SCF procedure is always equal to the number of the AOs used. Each MO consists of various contributions of the same basis set of AOs the apparent exception is when due to symmetry the coefficients at some AOs are equal to zero . For double occupancy M

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