On the Accurate Wavefunction of H2+

Abstract

For hydrogen molecular ion, it is shown that the James function is an approximation to the more general Guillemin and Zener wavefunction. From IsO" and 2pO", Guillemin and Zener orbitals, a correlated wavefunction of H2 is constructed. It contains all the terms which occur in the James and Coolidge wavefunction for H. molecule. The proposed function for H2 is dealt with in parts so as to study the contributions from configuration interaction and the correlation factor to the total binding energy of the H2 molecule.

An accurate pair potential function for diatomic systems

“…(5). As shown in Tables 1 and Figure. 1(b), the three-parameter model potential [10] for the ground-state H þ 2 agrees well with the most accurate data [13,14] for a set of parameters (a ¼ 1:0511106; b ¼ 0:91703424; c ¼ 2:25) [10]. This shows that the three parameters a; b and c can be properly adjusted so that contributions of both the polarization and exchanging energies can be accounted for in an much efficient way, thereby achieving in effect the same goal as that of using a larger basis set (e.g., 6-311++G (3df,2pd)) in the trial wave function of H þ 2 [10].…”

“…As shown in Tables 1 and Figure 1(b) and (c), the five-parameter model potential for the ground-state H þ 2 agrees well with the most accurate data [13,14] for a set of parameters (a ¼ 0:95; b ¼ 0:669; c ¼ 0:965; n ¼ 6:0, and f ¼ 0:11). To be noted, R e and dissociation energy D e ¼ E 1 À E min (the minimum energy E min ¼ EðR ¼ R e ÞÞ are fitted to the most accurate data: [13] 1.0574 Å and 0.10263 Hartree, respectively.…”

“…Thus, if one increases the basis set size (for example, including polarization and even diffuse functions in the trial function), then the potential curve of the ground-state H þ 2 should be improved significantly in all the regions of R. In Figure 1a, we demonstrate the effect of basis set size by using Hartree-Fock (HF) method implemented in the GAUSSIAN 09 electronic structure package [16]. It is seen that the numerical potential curve for the ground-state H þ 2 is greatly improved and approaching to the most accurate data [13,14] as the basis size is increased from GAUSSIANtype basis set 3-21G (2 sets of GAUSSIAN functions in the valence region), to 6-31G (d,p) (including polarization p and d functions), and then to 6-311+G (3df,2pd) (including 2p and 1d polarization functions and diffuse functions) [16].…”

“…It reads an energy minimum E min ¼ À0:56483 Hartree at an equilibrium internuclear distance R e ¼ 1:323 Å, and satisfies the necessary criteria and characteristics for building a good diatomic potential [10]. In comparison with accurate data [13,14], this analytical potential-energy curve Eq.…”

“…If the first-order exchange energy ð1Þ exch is used, the energy of the (3df,2pd) (dark green). The filled dots are the most accurate data [13,14]. The equilibrium distance Re and minimum energy Emin in the three-and five-prameter model potentials are fitted to 1.0574 Å and À0.60263 Hartree, respectively.…”