Long range adiabatic potentials and scattering lengths for theEF, eandhstates of the hydrogen molecule

EXPONENTIALLY CORRELATED GAUSSIAN FUNCTIONS IN VARIATIONAL CALCULATIONS. THE EF1E*g STATE OF HYDROGEN MOLECULE*

“…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.…”

“…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][3][4][5][6][7][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.…”

“…All existing complete high-accuracy potentials of the EF state were obtained in this way [5,6,8]. Only in the last 10 years it was discovered that the ECG functions, which can easily be integrated analytically and therefore allow one to use larger and carefully optimized expansions without stability problems or prohibitive cost, can surpass the accuracy provided by the KW functions [9,22,23].…”

Vibrationally resolved ionization cross sections for the ground state and electronically excited states of the hydrogen molecule

“…As shown in section 2.2, these FCD are a prerequisite for the calculation of cross sections for the corresponding transitions. The potential curves of the six molecular states have been taken from [27], [28,29], [30], [31], [32,33] and [32,34], respectively. The potential curves of the ionic curves are from [15] and [35].…”

The variable phase method used to calculate and correct scattering lengths

“…We shall show how the Riccati equation can be used to predict corrections, to be applied to the calculated scattering length, that compensate for stopping the calculation at finite distance R c ; such corrections enable us to make calculations with smaller values of R c while maintaining desired accuracy [7,8,9].…”