Abstract
Publisher Summary This chapter deals with the formal problem of reducing molecular orbital calculations to expressions involving one- and two-electron integrals over the spatial coordinates, with coefficients determined by the group theoretical properties of the spin functions and the electronic permutations. This problem is encountered, for example, when one undertakes to write the expectation value of the Hamiltonian for a given anti-symmetrized spin-orbital product, and in that particular case, the answer is well-known. The focus is on wave functions, which are constructed to be eigenfunctions of the spin, and shall consider the reduction of expressions not only for the energy and other spin-free one- and two-electron operators, but also for general one- and two-electron spin-dependent operators, such as the spin density or the Fermi contact interaction. It has been shown as how a spin-projected single-determinantal wave function based on different spatial orbitals for different spins can be related to the matrix representation method, and it is shown, how to calculate expectation values of both spin-free and spin-dependent operators.
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