Quantum theory of inelastic collisions of a diatomic molecule in a 2Π electronic state with an uncorrugated surface: Λ‐doublet, spin‐orbit, and polarization effects in NO (X 2Π)–Ag (111) scattering

1984 ◽  
Vol 80 (7) ◽  
pp. 3485-3493 ◽  
Author(s):  
Millard H. Alexander
Keyword(s):  
Quantum Theory ◽  
Electronic State ◽  
Diatomic Molecule ◽  
Inelastic Collisions ◽  
Spin Orbit ◽  
Polarization Effects

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.

Quantum state control on the chemical reactivity of a transition metal vanadium cation in carbon dioxide activation

2019 ◽  
Vol 21 (13) ◽  
pp. 6868-6877 ◽  
Author(s):  
Yih Chung Chang ◽  
Yuntao Xu ◽  
Cheuk-Yiu Ng
Keyword(s):  
Carbon Dioxide ◽  
Transition Metal ◽  
Electronic State ◽  
Quantum State ◽  
Electron Spin ◽  
Chemical Reactivity ◽  
Ion Source ◽  
Atomic Transition ◽  
Spin Orbit ◽  
State Control

By utilizing a newly developed spin-orbit electronic state selected ion source for atomic transition metal vanadium cation (V+), the chemical reactivity of V+ with CO2 has been examined in detail, indicating that the titled reaction is dominantly governed by electron spin conservation, and thus the chemical reactivity can be controlled by quantum electronic state selections.

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