Optimization Of Orbital Exponents Research Articles

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.

Linear Approximation of Basis Set Orbital Exponents for Isoelectronic Series of Atoms

The orbital exponents of Slater type atomic orbitals (AOs) in isoelectronic series of atoms may be approximated by the linear dependence on the nuclear charge using a technique developed for optimization of AO basis sets in Hartree–Fock–Roothaan calculations. This approach yields the analytical Hartree–Fock wave functions for any ion in the isoelectronic atomic series without optimization of orbital exponents. The approximated linear equations for atomic orbital basis sets of B, C, O, and F in the ground state are presented as an example.

Polarized basis sets for accurate predictions of molecular electric properties. Electric moments of the LiH molecule

A method for the determination of large polarized GTO/CGTO basis sets for the calculation of molecular properties is presented and illustrated by very accurate SCF and CAS SCF calculations of the dipole and quadrupole moments of the LiH molecule. Without any optimization of orbital exponents the GTO/CGTO HF SCF results are nearly the same as those recently obtained by the numerical integration of HF equations. The CAS SCF results, after rovibrational averaging, are in an excellent agreement with the available experimental data.