Angular momentum in molecular quantum mechanical integral evaluation

摘要: Abstract Solid-harmonic derivatives of quantum-mechanical integrals over Gaussian transforms scalar, or radial, atomic basis functions create angular momentum about each center. Generalized Gaunt coefficients limit the amount cross differentiation for multi-center to ensure that does not affect total momentum. The generalized satisfy a number other selection rules, which are exploited in new computer code computing forces analytic density-functional theory based on robust and variational fitting Kohn–Sham potential. Two-center exponents defined four more solid-harmonic differentiations matrix elements. Those can either build up centers give molecular potential-energy surfaces, thus order greater than considered. These 4- j two-center used compute first all involving triplet at once. First factors contracted with corresponding part linear-combination-of-atomic-orbitals density matrix. This intermediate quantity is then reused nuclear attraction integral function fit potential muffin-tin-like, but analytic, Slater–Roothaan method allows molecules dissociate into atoms having any desired energy, including experimental electronic energy. energy stationary respects precisely agree previous tests small molecules. During geometry optimization an icosahedral C 720 fullerene these transforming them via coefficient takes sixty percent time. same could be identical fashion Slater-type numerical radial orbitals.