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Ideas of Quantum Chemistry P61

Ideas of Quantum Chemistry P61 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. | 566 10. Correlation of the Electronic Motions 3. The wave function for the H molecule positions of nuclei a and b 0 0 0 and R 0 0 respectively in the form of a single Slater determinant built of three spinorbitals i r a pi r a a 2 Vi r fi a 3 V2 r a a 1 is the doubly occupied bonding and ç 2 is the singly occupied antibonding one . If ri R2 0 0 ai 2 r2 0 0 0 2 2 a 2 then the probability density of finding electron 3 is a almost zero on nucleus a b almost zero on nucleus b c equal to 0 everywhere d proportional to ç 2l2. 4. A Hartree-Fock function a correlates the positions of all electrons b correlates the positions of electrons with the same spin coordinates c correlates the positions of electrons with opposite spin coordinates d does not correlate the positions of electrons since in the Hartree-Fock method electron correlation is not accounted for. 5. The Brillouin theorem says that H is the Hamiltonian T0 is the Hartree-Fock function 1 is a singly and 2 a doubly excited Slater determinant a 0lH i 0 if all the spinorbitals are orthogonal b i H i 0 c 2lH i 0 d W i 0. 6. In the Coupled Cluster method T is the cluster operator 0 is the Hartree-Fock wave function the wave function a is ÿ cxp T T0 b does not vanish in infinity c contains only single and double excitations d is ÿ cxp T T0 and ensures size consistency. 7 MRPT- Tf thp nniic-lnr P I 0 0 l and Ô v l 0 0 l p 0 form thp . MBrl. JJ the projector p ÿ0 ÿ0 1 and Q - i ÿn ÿn I ÿn form the complete orthonormal set then a PQ i b P Q 2 i c P Q ih d Q exp P . 8. The Mpller-Plesset method MP2 is a a variational method with two variational parameters b a perturbation theory with unperturbed wave function in the form of a Gaussian geminal c a perturbation theory with the energy computed through the second order d a Ritz method limited to double excitations. 9. To calculate the exact correlation energy a it is enough to have the expansion in singly excited Slater determinants b it is enough to know the Hartree-Fock .