Rotationally inelastic collisions between a diatomic molecule in a 2S+1Σ electronic state and a 2S atom: The optimal choice for the total‐J representation

1985 ◽  
Vol 83 (10) ◽  
pp. 5060-5067 ◽  
Author(s):  
Gregory C. Corey ◽  
Millard H. Alexander
Keyword(s):  
Electronic State ◽  
Diatomic Molecule ◽  
Optimal Choice ◽  
Inelastic Collisions

Potential Energy Surfaces

1996 ◽  
Author(s):  
Tomas Baer ◽  
William L. Hase
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Electronic State ◽  
Diatomic Molecule ◽  
Potential Energy Surfaces ◽  
Energy Surface ◽  
Electronic States ◽  
Dissociation Energies ◽  
State Potential ◽  
Energy Surfaces

Properties of potential energy surfaces are integral to understanding the dynamics of unimolecular reactions. As discussed in chapter 2, the concept of a potential energy surface arises from the Born-Oppenheimer approximation, which separates electronic motion from vibrational/rotational motion. Potential energy surfaces are calculated by solving Eq. (2.3) in chapter 2 at fixed values for the nuclear coordinates R. Solving this equation gives electronic energies Eie(R) at the configuration R for the different electronic states of the molecule. Combining Eie(R) with the nuclear repulsive potential energy VNN(R) gives the potential energy surface Vi(R) for electronic state i (Hirst, 1985). Each state is identified by its spin angular momentum and orbital symmetry. Since the electronic density between nuclei is different for each electronic state, each state has its own equilibrium geometry, sets of vibrational frequencies, and bond dissociation energies. To illustrate this effect, vibrational frequencies for the ground singlet state (S0) and first excited singlet state (S1) of H2CO are compared in table 3.1. For a diatomic molecule, potential energy surfaces only depend on the internuclear separation, so that a potential energy curve results instead of a surface. Possible potential energy curves for a diatomic molecule are depicted in figure 3.1. Of particular interest in this figure are the different equilibrium bond lengths and dissociation energies for the different electronic states. The lowest potential curve is referred to as the ground electronic state potential. The primary focus of this chapter is the ground electronic state potential energy surface. In the last section potential energy surfaces are considered for excited electronic states. A unimolecular reactant molecule consisting of N atoms has a multidimensional potential energy surface which depends on 3N-6 independent coordinates. For the smallest nondiatomic reactant, a triatomic molecule, the potential energy surface is four-dimensional (three independent coordinates plus the energy). Since it is difficult, if not impossible, to visualize surfaces with more than three dimensions, methods are used to reduce the dimensionality of the problem in portraying surfaces. In a graphical representation of a surface the potential energy is depicted as a function of two coordinates with constraints placed on the remaining 3N-8 coordinates.

Exact formula for the dipole moment of a one-electron diatomic molecule

1985 ◽  
Vol 401 (1821) ◽  
pp. 373-392 ◽  
Keyword(s):  
Dipole Moment ◽  
Electronic State ◽  
Diatomic Molecule ◽  
Recursion Relation ◽  
Energy Eigenvalue ◽  
Exact Formula ◽  
Electronic Energy ◽  
Moment Function ◽  
Expectation Values ◽  
Feynman Theorem

It is shown that the dipole moment function, μ ( R , Z a , Z b ), for an arbitrary bound electronic state of a one-electron diatomic molecule, with inter-nuclear distance R and atomic numbers Z a , Z b may be expressed exactly in terms of the separation eigenconstant C and the electronic energy eigenvalue W of the Schrödinger equation by means of the Hellmann-Feynman theorem and a new recursion relation. The formula is used to investigate the behaviour of μ in the vicinity of the united atom and when the nuclei are far apart. The generalization required to extend the relation to other expectation values is derived in an appendix.

scholarly journals Infra-red investigations of molecular structure. Part II.—The molecule of nitric oxide

1929 ◽  
Vol 124 (794) ◽  
pp. 453-464 ◽  
Keyword(s):  
Electronic State ◽  
Diatomic Molecule ◽  
Band Spectrum ◽  
Electric Moment ◽  
Electronic Band ◽  
Hydrogen Halides ◽  
Direct Measurements ◽  
Infra Red ◽  
Band Spectra ◽  
Vibration Rotation

There have been few attempts at the resolution of the vibration-rotation bands of a diatomic molecule. In 1919 Imes was successful with the bands of three of the hydrogen halides, work which was later extended by Colby and Meyer; Czerny proved the existence of a doublet due to HI, but the weakness of the absorption prevented more detailed study; E. F. Lowry in 1924 failed to analyse the structureless doublets of carbon monoxide, although his apparatus was similar to that used by Imes. It does not seem possible that the fine-structure would reveal itself if a lower pressure of the gas were used (E. F. Lowry worked at one atmosphere pressure). The molecule of CO, like those of the hydrogen halides, has a permanent electric moment, and its bands must be similar in kind. Apart from HF, HCI, HBr, HI and CO, NO is the only other diatomic molecule with a permanent electric moment, and its choice as the subject of this research was natural. It is more definitely homopolar than the hydrogen halides, although the distinction is almost certainly one of degree; there was the interest of establishing the self-evident proposition that there is no fundamental difference in the bands of No and the bands HCI. There was also the advantage of knowledge of the electronic band spectrum of the molecule acquired by Guillery, Jenkins, Barton and Mulliken, and summarised by Mulliken. The thoroughness of this work makes NO one of the best-known of molecules to the spectroscopist. It has been mentioned in the introduction to Part I that throughout this series of papers there will be maintained the deal of correlation between infra-red and electronic band spectra. Accordingly, it became our aim to compare the constants of the molecule in the normal state as derived from electronic band spectra and as obtained from the direct measurements of the infra-red. The unexcited electronic state of the molecule measurements of the infra-red. The unexcited electronic state of the molecule is, of course, the only one with which infra-red observations are concerned.

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