The intersection of potential energy surfaces in polyatomic molecules

1975 ◽  
Vol 344 (1637) ◽  
pp. 147-156 ◽  
Keyword(s):  
Wave Function ◽  
Potential Energy ◽  
Electronic State ◽  
Configuration Space ◽  
Potential Energy Surfaces ◽  
Polyatomic Molecules ◽  
The State ◽  
State Changes ◽  
Energy Surfaces ◽  
Recent Claim

It is proved that if the wave function of a given electronic state changes sign when transported adiabatically round a loop in nuclear configuration space, then the state must become degenerate with another one at some point within the loop. I t is further shown that this condition is satisfied by certain unsymmetrical triatomic systems, thereby disposing of a recent claim that the non-crossing rule for diatomic molecules applies also to polyatomic molecules.

Spin-orbit coupling and the intersection of potential energy surfaces in polyatomic molecules

1976 ◽  
Vol 351 (1664) ◽  
pp. 141-150 ◽  
Keyword(s):  
Potential Energy ◽  
Configuration Space ◽  
Potential Energy Surfaces ◽  
Polyatomic Molecules ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Lower Symmetry ◽  
Symmetry Species ◽  
Energy Surfaces

Longuet-Higgins’ theorem, which shows that the existence of intersections between potential energy surfaces may be deduced from the behaviour of the wavefunction at points remote from the intersection, is generalized to cover cases where the Hamiltonian is complex. It is concluded that an intersection due to symmetry in one region of nuclear configuration space may imply that the same surfaces intersect over a region of higher dimen­sion and lower symmetry where their wavefunctions belong to the same symmetry species. It is shown that this behaviour occurs in d 1 octahedral complexes in the presence of spin-orbit coupling.

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.

scholarly journals Nonadiabatic dynamics in multidimensional complex potential energy surfaces

2020 ◽  
Vol 11 (36) ◽  
pp. 9827-9835 ◽  
Author(s):  
Fábris Kossoski ◽  
Mario Barbatti
Keyword(s):  
Wave Function ◽  
Potential Energy ◽  
Complex Potential ◽  
Potential Energy Surfaces ◽  
Nonadiabatic Dynamics ◽  
Continuous Development ◽  
Surface Hopping ◽  
Multidimensional Complex ◽  
Function Norm ◽  
Energy Surfaces

Despite the continuous development of methods for describing nonadiabatic dynamics, there is a lack of multidimensional approaches for processes where the wave function norm is not conserved. A new surface hopping variant closes this knowledge gap.

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