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Ideas of Quantum Chemistry P57

Ideas of Quantum Chemistry P57 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. | 526 10. Correlation of the Electronic Motions function o i.e. rhf - When one spinorbital is replaced the resulting determinant is called singly excited when two - doubly excited etc.46 47 The virtual spinorbitals form an orthonormal basis in the virtual space Appendix B p. 895 . If we carry out any non-singular linear transformation cf. p. 396 of virtual spinorbitals each new n-tuply excited Slater determinant becomes a linear combination of all old n-tuply excited determinants and only n-tuply excited ones.48 In particular the unitary transformation preserves the mutual orthogonality of the n-tuply excited determinantal functions. Thus the total wave function 10.20 is a linear combination of the known Slater determinants we assume that the spinorbitals are always known with unknown c coefficients. The name of the CI methods refers to the linear combination of the configurations rather than to the Slater determinants. CSF configuration A configuration CSF i.e. Configuration State Function is a linear combination of determinants which is an eigenfunction of the operators S2 and Sz and belongs to the proper irreducible representation of the symmetry group of the Hamiltonian. We say that this is a linear combination of the spatial and spin symmetry adapted determinants. Sometimes we refer to the spin-adapted configurations which are eigenfunctions only of the S2 and Sz operators. The particular terms in the CI expansion may refer to the respective CSFs or to the Slater determinants. Both versions lead to the same results but using CSFs 46In the language of the second quantization see Appendix U p. 1023 the wave function in the CI method has the form the 0 function is a Slater determinant which does not necessarily need to be a Hartree-Fock determinant co 0 cpP4 a 0 cpq i4P4 a6 0 higher excitations 10.22 where c are the expansion coefficients the creation operators q4 p4 . refer to the virtual spinorbitals p q . and the annihilation operators a b . refer to occupied .