Structure of free complement wavefunction for the ground and the first excited state of helium atom

We review the fundamental ideas of free complement (FC) method through its application on both ground and first excited states of helium atom. We have found that lower energies can be obtained with fewer number of terms in the FC expansion of the ground state wavefunction. In this case, the optimization of orbital exponents was not necessary for achieving spectroscopic accuracy, especially at higher orders where the structure of the FC wavefunction converges to that of the exact one. We have discovered that permanents naturally appear in the FC expansion of the first triplet excited state wavefunction. Including permanents in the FC expansion is shown to be energetically important for the first triplet excited state of helium atom whereas it is not computationally favorable at higher orders. Finally, considering the group theoretical properties of the symmetric group [Formula: see text] and using immanants, a compact and more elegant form for the FC expansion of the first triplet excited state of the helium atom is achieved.

A NEW FORMULA FOR THE EVALUATION OF THE IONIZATION ENERGY BASED ON THE ORBITAL EXPONENTS OF THE ATOMS OF 118 ELEMENTS OF THE PERIODIC TABLE

We propose a simple approach for the calculation of the ionization potentials of atoms in terms of their orbital exponents. The prescription is simple and utilizes only the simple Bohr equation with some modifications. We have pointed out that the atomic first ionization energy not only depends on the principal quantum number (n) but also on the azimuthal quantum number (l) of the orbital (n, l) on which the electron of interest is present. The formalism is tested through the calculation of the atomic ionization potentials of 118 elements of the periodic table. The orbital exponent values for 118 elements of the periodic table are computed following the suggestions of Reed. The calculated numerical results for a number of atoms are shown to agree quite well with their experimental counterparts. To perform the validity tests of the present scale of ionization potential, various physico-chemical properties of the atoms are also correlated on the basis of the computed ionization potential data. It is found that the stability of the half filled configuration depends on the orbital (n, l) on which the electron is present. The expressed periodic behavior and correlation of the most important physico-chemical properties of elements suggest that the present method of evaluation of the ionization potential of the atoms is quite a successful venture.

On The Computation Of Two-Center Coulomb Integrals Over Slater Type Orbitals Using The Poisson Equation

In this paper, a new analytical formula has been derived for the two-center Coulomb integrals over Slater type orbitals using the Poisson equation. The obtained results from constructed computer program for the presented formula have been compared with the available literature and it is seen that the efficiency of the presented algorithm for a wide range of quantum numbers, orbital exponents and internuclear distances is satisfactory.

Evaluation of Two-Center Overlap Integrals Over Slater-Type Orbitals Using Fourier Transform Convolution Theorem

Analytical expressions are presented for two-center overlap integrals over Slater-type orbitals using Fourier transform convolution theorem. The efficiency of calculation of these expressions is compared with those of other methods and good rate of convergence and great numerical stability is obtained for wide range of quantum numbers, orbital exponents and internuclear distances.