Excited States of the Hydrogen Molecule

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. 

We shall next consider whether or not the antisymmetric eigenfunction Hl for two hydrogen atoms (Equation 29b) would lead to an excited state of the hydrogen molecule. The perturbation energy is found to be... 

Low-Lying Excited States of the Hydrogen Molecule in Cylindrical Harmonic Confinement... 

The low-lying excited states of the hydrogen molecule conhned in the harmonic potential were studied using the configuration interaction method and large basis sets. Axially symmetric harmonic oscillator potentials were used. The effect of the confinement on the geometry and spectroscopic constants was analyzed. Detailed analysis of the effect of confinement on the composition of the wavefunction was performed. 

The simplest molecular system exhibiting effects of electron correlation is the hydrogen molecule. For this molecule the explicitly correlated wave function has been applied in the early days of quantum mechanics (James and Coolidge, 1933), It was later generalised by Kolos and Wolniewicz (Kcrfos and Wolniewicz, 1965) and successfully used to solve variety of problems in the ground and excited states of the hydrogen molecule. This wave function, called there the Kolos-Wolniewicz function (Kolos and Wolniewicz, 1965) is assumed in the form of an expansion ... 

For excited states of the hydrogen molecule the quality of theoretical results are... 

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. 

J.M.H. Lo, M. Klobukowski, G.H.F. Diercksen, Low-lying excited states of the hydrogen molecule in cylindrical harmonic confinement, Adv Quantum. Chem. 48 (2005) 59-89. 

Light emission in collisions of He with H2 was studied37 for a He-beam energy of llOOeV. The apparatus has been described in the foregoing section. Emission from excited states of the hydrogen atom was found to be much stronger than emission from excited He-states which could not be detected at all. No emission from excited states of the hydrogen molecule could be found.86,37... 

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.

The shapes for the wavefunctions are shown in Figure 9-4. The result for the ground-state of a hydrogen molecule is similar to that for a H2 molecule. There will be an additional electron and it will be placed in the a orbital of opposite spin with the other electron. When higher order diatomic molecules or excited states of the hydrogen molecule are considered, then p atomic orbitals will combine to form molecular orbitals. When the 2p atomic orbitals overlap, a 0 bond is formed that is symmetric about the inter-nuclear axis. The two 2pz molecular orbital wavefunctions are as follows. ... 

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