EXPONENTIALLY CORRELATED GAUSSIAN FUNCTIONS IN VARIATIONAL CALCULATIONS. THE EF STATE OF HYDROGEN MOLECULE*

The Born-Oppenheimer (BO) potential energy curve, the adiabatic and the relativistic corrections for the EF state of the hydrogen molecule are calculated for the internuclear distances ranging from 0.01 to 20 bohr. 600-term variational expansions of exponentially correlated Gaussian (ECG) functions are used. The BO energies and the adiabatic corrections are more accurate than previously reported and the relativistic calculations confirm existing literature values. 1. I N T R O D U C T I O N * Dedicated to the memory of Professor Jacek Rychlewski EXPONENTIALLY CORRELATED GAUSSIAN FUNCTIONS IN VARIATIONAL CALCULATIONS. THE EF STATE OF HYDROGEN MOLECULE* The EF state of the hydrogen molecule is the lowest excited state having the same symmetry as the ground state. Its most striking feature is the potential energy curve with two deep and well separated minima, resulting from the avoided crossing of two diabatic states, E and F [1]. The united atom configuration is S (ls2s). The dominant configuration for the inner part of the potential is (1sσg2sσg), whereas in the outher part of the energy curve the (2pσ u ) 2 configuration is contributing the most to the wave function, although the (1sσg2sσg) and (1sσg) 2 configurations are also present. Finally, the state dissociates onto H (1s) + H(2s). AS a result of the two-minimum potential, two separate band systems can be observed in certain energy regions. The EF state has drawn significant interest and a number of variational calculations of increasing accuracy has been reported over the last 40 years [2-8]. The current most accurate electronic energy was obtained in 1999 by Orlikowski et al. [8], who used a 443-term expansion of the Kołos-Wolniewicz-type (KW) wave function [3] and evaluated also the adiabatic corrections. At R = 1.5 bohr, the Born-Oppenheimer (BO) energy of Ref. [8] is, however, over 0.3 μhartree higher than the older result [9] obtained by the present authors as a test of our exponentially correlated Gaussian (ECG) package. In the present paper we extend our ECG calculation to the complete BO energy curve of the EF state and calculate the adiabatic and relativistic corrections. The aim of this work is twofold. Firstly, to generate new and more accurate benchmark results. Secondly, to test the performance of our correction 80 J. Komasa and IV. Cencek packages. We use the direct perturbation theory (DPT) of Kutzelnigg [10] and Rutkowski [11] in relativistic calculations and the Bom-Handy approach [12-14] to adiabatic corrections, both methods never used before in studies of excited states of the hydrogen molecule. 2. M E T H O D OF C A L C U L A T I O N 2.1. B o r n O p p e n h e i m e r energy The electronic wave function used in this work is expressed in the form of the linear combination of properly symmetrized two-electron basis functions, ψk