Theory of Electron-Pair Density Functions and Its Quantum Chemical Applications

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The motions of electron-pairs in atoms and molecules are described by the electron-pair intracule (relative motion) and extracule (center-of-mass motion) density functions. For atomic systems, these electron-pair densities are characterized by their spherical averages. The electron-pair densities are important probability density functions to understand the electron-electron interactions in atoms and molecules, but up to now we have neither sufficient knowledge about their theoretical structures nor practical applications to quantum chemical problems.The purpose of this research project has been to clarify the theoretical structure of the electron-pair density functions and to apply new results to various chemical and physical problems. The results of this research project during the two years are summarized as follows:(1) We introduced a generalized electron-pair density function. The intracule and extracule densities have been shown to be two particular cases of the density function. … More We have also shown that the second moments of the electron-pair densities satisfy a rigorous sum rule, which connects one- and two-electron properties of atoms and molecules.(2) We found that the electron-pair density values at the origin is specified by the electron-electron coalescence and counterbalance functions, and clarified the mathematical structures of these functions. Numerical results were reported for 102 atoms in their ground states.(3) We reported that the second moments of the intracule and extracule densities are rigorously connected to various physical properties, which were hitherto studies independently. The properties include electronic and nuclear kinetic energies, oscillator strength sums, nuclear mass correction energies, diamagnetic susceptibilities, and dipole polarizabilities.(4) The second moments of the intracule and extracule densities also clarify the statistical correlation of electrons in atoms and molecules. In the Hartree-Fock approximation, electrons in atoms are either negatively correlated or uncorrelated.(5) We have newly introduced the interelectronic angle density function which characterizes the spatial angular distribution of electrons and reported numerical results for atoms.(6) For the He, Li, and Be atoms in their ground states, the electron correlation effect on the electron-pair properties were examined. The results point out and correct the inconsistency in the literature values. Less