Antisymmetrized wave function, electronic structure calculations

Both formal analysis and computational developments associated with DFT can be carried over intact to nDFT. For example, the exact two-particle ground-state density, no(x), can be determined through a constrained search [34] for that many-particle, properly symmetrized or antisymmetrized wave function, with symmetry imposed with respect to ordinary particles, which yields n0 and also minimizes the many-particle energy, T + Vpp, where Vpp denotes the interparticle interaction in two-particle space. Essentially any method developed within a single-particle application of DFT for the study of electronic structure can, with appropriate technical modifications, be extended to two-, or rc-particle states. The use of multiple-scattering theory to calculate fully correlated two-particle densities in solids will be given in a future publication. 

Later, J. C. Slater showed that the Hartree equations can be obtained if the variation principle is applied to a product of spin orbitals. The Russian theoretical physicist Vladimir A. Lock pointed out that certain symmetry conditions are not obeyed in the Hartree method, of which the most important one is the antisymmetric property of the total wave function. The variation principle was now applied to an antisymmetrized product of spin orbitals, that is, a Slater determinant. This is a fnndamen-tal method in electronic structure calculations and is referred to as the Hartree-Fock method or simply Hartree-Eock. ... 

The application of quantum-mechanical methods to the prediction of electronic structure has yielded much detailed information about atomic and molecular properties.13 Particularly in the past few years, the availability of high-speed computers with large storage capacities has made it possible to examine both atomic and molecular systems using an ab initio variational approach wherein no empirical parameters are employed.14 Variational calculations for molecules employ a Hamiltonian based on the nonrelativistic electrostatic nuclei-electron interaction and a wave function formed by antisymmetrizing a suitable many-electron function of spatial and spin coordinates. For most applications it is also necessary that the wave function represent a particular spin eigenstate and that it have appropriate geometric symmetry. 

Figures 1 and 2 depict our calculated band structures for the all- rans conformations of unsubstituted polysilane and poly(dimethylsilane). Because the reflection plane containing the silicon nuclei in the all- rans conformations commutes with the operations of the one-dimensional translation group, all one-electron wave functions will be either symmetric (a-like) or antisymmetric (7T-like) with respect to this reflection operation. Thus the bands in Figures 1 and 2 are labeled with solid lines or dashed lines, which indicate that the corresponding one-electron wave functions are a-like or 7T-like, respectively.

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