Quantum chemistry of many-electron systems: high-priority aspects

The review generalizes the studies devoted to the development of a new quantum chemistry method representing an alternative to the Hartree–Fock approximation. Based on the hypothesis of prohibition of equipotential surfaces, which clarifies the physical sense of the Pauli exclusion principle, and taking account of the condition for antisymmetrical wave function of the triplet state (3S) of He atom, the Hartree–Fock approximation is inappropriate for a priori determination of the nodal surfaces of many-electron wave functions (MWFs) for the test systems traditionally used in quantum chemistry, namely, excited triplet state of H₂ molecule and the ground electronic states of Li atom and LiH molecule. The nodal surfaces of the wave functions corresponding to the minimum basis set of Slater orbitals in the Hartree–Fock approximation are constructed and analyzed. An alternative to the Hartree–Fock approximation is provided by the MWF quantum chemical method being developed by the authors. In the MWF method, the nodal surfaces for H₂(³Σ _u ^v ) and Li(²S) are specified a priori. Some aspects of geometric interpretation of the Pauli exclusion principle are discussed. Unlike the MWF method, the Hartree–Fock approximation is unsuitable for taking account of the dependence of the MWF nodal surfaces on the nuclear charges and on correlation effects related to the motion of electrons with antiparallel spins because such nodal surfaces are predefined by the mathematical properties of Slater determinants rather than by physically clear and more practically valuable algebraic products of electrostatic potential differences.