TAILIEUCHUNG - Ideas of Quantum Chemistry P39

Ideas of Quantum Chemistry P39 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. | 346 8. Electronic Motion in the Mean Field Atoms and Molecules we derive the Euler equation for this problem from 8i . 0. In fact it is the Fock equation expressed in orbitals31 F 1 i 1 j i 1 closed-shell Fock operator where are the orbitals. The Fock operator is defined for the closed shell as F 1 h 1 2J 1 - K 1 where the first term see eq. is the sum of the kinetic energy operator of electron 1 and the operator of the interaction of this electron with the nuclei in the molecule the next two terms . Coulombic J and exchange K operators are connected with the potential energy of the interaction of electron 1 with all electrons in the system and they are defined slightly differently than before for J and K operators32 via the action on any function x of the position of electron 1 MO MO 1 2J 1 x 1 2j7i 1 x 1 E2 dV2 2 i 2 x 1 2 21 dV2 r i 2 2x 1 i 12 K 1 x 1 12Ki 1 x 1 2 f dV2 P 2 x 2 Pi 1 i 1 i 1 r12 where integration is now exclusively over the spatial coordinates33 of electron 2. Factor 2 multiplying the Coulombic operator results as the reader presumably guessed from the double occupation of the orbitals. Interpretation of the Coulombic operator The Coulombic operator is nothing else but a calculation of the Coulombic potential with the opposite sign as created by all the electrons Fig. at the position of 31 After a suitable unitary transformation of orbitals analogous to what we have done in GHF case. 32Because we have orbitals here and not spinorbitals. 33 Simply the summation over the spin coordinates has already been done when deriving the equation for the mean value of the Hamiltonian. The Fock equation for optimal spinorbitals 347 Fig. . Point-like electron 1 interacts with the total electron density shown as electron cloud with density M 2p 2 . To compute the interaction energy the total electron density is chopped into small cubes. The interaction energy of electron 1 with one of such cubes of volume dV2 containing .

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