The Hartree-Fock ground state potential energy curve for the carbon monoxide molecule is calculated using both the finite difference and the finite basis set methods. The results of calculations performed at ten internuclear separations are reported and a comparision is made of the calculated potential energy curves over the range of internuclear separations, 1.970-2.330 a0, around the experimental equilibrium value. Potential energy curve constants and spectroscopic constants are determined.

https://iopscience.iop.org/article/10.1088/0953-4075/27/21/008/pdf

A comparison of finite difference and finite basis set Hartree-Fock calculations for the ground state potential energy curve of CO

A comparison is made of the accuracy with which the total electronic energy can be calculated by using either the finite basis set approach (the algebraic approximation) or finite difference methods in calculations using the Hartree-Fock model for the ground (X1 Sigma +) state of the carbon monosulphide molecule. The CS molecule is considered as a prototype for systems containing atoms from different rows of the periodic table. The convergence of the calculations carried out within the algebraic approximation is monitored by employing systematically constructed basis sets of increasing size. The dependence of the finite difference calculations on the numerical grid employed is studied.

A comparison of finite basis set and finite difference methods for the ground state of the CS molecule

High-precision matrix Hartree-Fock calculations are reported for a series of five isoelectronic diatomic systems in their ground states. A universal even-tempered basis set of Gaussian-type functions is developed for the nitrogen molecule at its experimentally derived equilibrium nuclear separation and then used to parameterize the single-particle state functions in the matrix Hartree-Fock description of the neutral molecules CO and BF, and in the ions NO+ and CN- at their respective experimentally determined equilibrium geometries. The calculated energies are compared with the results of previously reported fully numerical calculations which were performed by using finite difference and/or finite element techniques and which are taken to define Hartree-Fock limit. Energies obtained using the universal even-tempered finite basis set expansion are well within what is usually regarded as 'chemical accuracy' of approximately 1 mHartree and are only in error by approximately 2.3, approximately 1.5, approximately 90, approximately 40 and approximately 140 mu Hartree for N2, CO, BF, NO+ and Cn-, respectively.

A universal basis set for high-precision molecular electronic structure studies

A finite difference Hartree–Fock program for atoms and diatomic molecules

A comparison is made of the accuracy with which the total electronic energy can be calculated by using either the finite basis set approach (the algebraic approximation) or finite difference methods in calculations using the Hartree-Fock model for the ground (X1Σ+) states of the Group IIIb fluorides: boron fluoride, aluminium fluoride and gallium fluoride molecules. The XF molecules, X = B, Al, Ga, are considered as a prototype for systems containing increasingly heavy atoms and numbers of electrons. The convergence of the calculations carried out within the algebraic approximation is monitored by employing systematically constructed basis sets of increasing size. The dependence of the finite difference calculations on the numerical grid employed is studied and it is found to be necessary to employ a multiple grid for the heaviest system, GaF, in order to achieve the target accuracy of 1 μE h for the total energy.

S. Wilson

Papers

Finite basis set versus finite difference and finite element methods