Excited States of the Hydrogen Molecule-ion

Excited States of the Hydrogen Molecule-ion.—We have discussed (Sec. 42a) one of the excited electronic states of the hydrogen molecule-ion, with a nuclear-antisymmetric wave function formed from normal hydrogen-atom functions. This is not a stable state of the molecule-ion, inasmuch as the potential function for the nuclei does not show a minimum. 

Calculations of potential functions for other excited states, many of which correspond to stable states of the molecule-ion, have been made by various investigators,1 among whom Teller, Hylleraas, and Jaff6 deserve especial mention. 

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Pauling and Sherman, loc. cit. (4). Calculations of the bonding power of 2 -2p hybrid orbitals have been reported also by R. S. Mulliken, J. Chem. Phys. 19, 900, 912 (1951). C. A. Coulson and G. R. Lester, Trans. Faraday Soc. 51, 1605 (1955), have made calculations for excited states of the hydrogen molecule-ion that agree reasonably well with the postulate that the strength S of an orbital determines its bond-forming power. 

Figure 20.3 The Born-Oppenheimer Energy of the Ground State and Rrst Excited State of the Hydrogen Molecule Ion as a Function of Internuclear Distance.

Excited states of the hydrogen molecule may be formed from a normal hydrogen atom and a hydrogen atom in various excited states.2 For these the interelectronic interaction will be small, and the Burrau eigenfunction will represent the molecule in part with considerable accuracy. The properties of the molecule, in particular the equilibrium distance, should then approximate those of the molecule-ion for the molecule will be essentially a molecule-ion with an added electron in an outer orbit. This is observed in general the equilibrium distances for all known excited states but one (the second state in table 1) deviate by less than 10 per cent from that for the molecule-ion. It is hence probable that states 3,4, 5, and 6 are formed from a normal and an excited atom with n = 2, and that higher states are similarly formed. 

The electronic quantum state ofthe pair H,ls> H+>= in> remains invariant at all distances. The electron transfer will not take place in a direct manner because the electronic parity is equal for both channels. The interconversion process requires aTS with parity -1. Among the states available to a system decomposable in one electron and two protons (or proton deuterium, etc) there are the hydrogen molecule ion species. The first electronic excited state (leu) ofthe molecular ion H2+ provides an "intermediate" (Q-state) for the interconversion once angular momentum conservation rules are fulfilled. The state (lau) is found above the in> and out> states leading to resonance in the cross section. This state may either relax to the (lrg) state yielding the hydrogen molecule ion and emitting a photon as this state is 2.8eV below dissociation, or it may take the product channels. This is a FC-like process. The reaction (27) is a prototype of electron transfer (ET). Thus, for any ET reaction whose in> and out> asymptotic electronic states share the same parity, the actual interconversion would require the mediation of a TS. 

The interaction of two alkali metal atoms is to be expected to be similar to that of two hydrogen atoms, for the completed shells of the ions will produce forces similar to the van der Waals forces of a rare gas. The two valence electrons, combined symmetrically, will then be shared between the two ions, the resonance phenomenon producing a molecule-forming attractive force. This is, in fact, observed in band spectra. The normal state of the Na2 molecule, for example, has an energy of dissociation of 1 v.e. (44). The first two excited states are similar, as is to be expected they have dissociation energies of 1.25 and 0.6 v.e. respectively. 

In view of the large size of the valine molecule, our calculations (Kaplan et al., 1983) were carried out on a minimal basis of 51 Slater orbitals in the MO LCAO approximation using the method described in Sections II, C, and III, B, 1. We have taken into account 608 singly excited states of the ion (valine-He)+. The results of calculations for valine on a minimal basis were corrected with regard to the results of calculation of the influence of the basis length on the excitation probabilities of the fragments that are shown enclosed in boxes in Fig. 9 (the rest of the molecule was replaced by a hydrogen atom). 

II is mainly ionic in character and function IV completely so, representing the interaction of H+ and H-. Of these IV corresponds to a known state, the first electronically excited state of the molecule. As might have been anticipated from the ionic character of the wave function, the state differs in its properties from the other known excited states, having r, = 1.29 A and v, = 1358 cm-1, whereas the others have values of rt and v, close to those for the normal hydrogen molecule-ion, 1.06 A and 2250 cm-1. The calculations of Zener and Guillemin and of Hylleraas have shown that at the equilibrium distance the wave function for this state involves some contribution from wave functions for one normal and one excited atom (with n = 2,1 = 1), and with increase in Tab this contribution increases, the molecule in this state dissociating into a normal and an excited atom. 

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