Optimization of basis sets for isoelectronic series of closed-shell atoms in Hartree-Fock-Roothaan calculations

Calculations of the Energies of the Excited States of Open-Shell Atoms in the Hartree-Fock Approximation

“…In this connection, we deal with the problem of conventional minimization. We note that the expression for energy (5) and conditions (6) are similar to the relations in Roothaan's theory for one open shell [6,8]. Therefore, all the subsequent calculations are actually repetitions of what was performed earlier within the scope of the Roothaan method [6,7].…”

“…These methods involve proven conditions and a high rate of convergence and rigorous criteria for termination of the computation, which makes it possible to find a solution for a many-electron problem in the LCAO approximation (orbital coefficients and exponents of atomic orbitals) with any given accuracy. To realize the minimization algorithms of the first and second orders, expressions were obtained in the framework of the Hartree-Fock-Roothaan method for calculating the energy derivatives of the system with respect to optimized parameters [5,6] such as the elements of density matrices, which are constructed from orbital coefficients, and the exponents of atomic orbitals. In the present article, this approach is extended to the Roothaan-Hartree-Fock atomic theory [9, 10] (the Roothaan-Bagus method), which allows one to calculate atoms with several open shells.…”

“…These methods allow one to carry out optimization only with a limited accuracy and require enormous expenditures of computer time. In [5][6][7], with in the framework of the classical Roothaan method [8], a method is developed for solving the HartreeFock equations for many-electron systems with closed and open shells; the method is based on the contemporary methods of minimization of the functions of many variables. These methods involve proven conditions and a high rate of convergence and rigorous criteria for termination of the computation, which makes it possible to find a solution for a many-electron problem in the LCAO approximation (orbital coefficients and exponents of atomic orbitals) with any given accuracy.…”

“…The first two terms in (5) (5). To apply the methods of minimization in order to find the matrices D c λ and D o λ as well as optimum values of orbital exponents, it is necessary to calculate the energy derivatives with respect to these parameters.…”

Numerical Research of Materials Crystal Lattice Parameters Based on Rare-Earth Metals

“…Regardless of several attempts to accelerate the calculations by Hartree-Fock method [4][5][6], there are still reasons according to which the calculations of real crystals are difficult. It is a well-known fact that even 1 mm³ volume crystal contains an immense amount of atoms, which excludes the possible calculations of realworld samples.…”