Potential energy surfaces polyatomic molecules

The theory coimecting transport coefficients with the intemiolecular potential is much more complicated for polyatomic molecules because the internal states of the molecules must be accounted for. Both quantum mechanical and semi-classical theories have been developed. McCourt and his coworkers [113. 114] have brought these theories to computational fruition and transport properties now constitute a valuable test of proposed potential energy surfaces that... 

Schinke R and Huber J R 1993 Photodissociation dynamics of polyatomic molecules. The relationship between potential energy surfaces and the breaking of molecular bonds J. Rhys. Chem. 97 3463... 

There are forces other than bond stretching forces acting within a typical polyatomic molecule. They include bending forces and interatomic repulsions. Each force adds a dimension to the space. Although the concept of a surface in a many-dimensional space is rather abstract, its application is simple. Each dimension has a potential energy equation that can be solved easily and rapidly by computer. The sum of potential energies from all sources within the molecule is the potential energy of the molecule relative to some arbitrary reference point. A... 

We envision a potential energy surface with minima near the equilibrium positions of the atoms comprising the molecule. The MM model is intended to mimic the many-dimensional potential energy surface of real polyatomic molecules. (MM is little used for very small molecules like diatomies.) Once the potential energy surface iias been established for an MM model by specifying the force constants for all forces operative within the molecule, the calculation can proceed. 

If we require similar information regarding the ground state potential energy surface in a polyatomic molecule the electronic emission specttum may again provide valuable information SVLF spectroscopy is a particularly powerful technique for providing it. 

Murrel JM (1977) The Potential Energy Surfaces of Polyatomic Molecules. 32 93-146... 

Another polyatomic molecule provided an opportunity to study the effect of the Gouy phase discussed in Section III [62]. Figure 12 depicts a slice of the potential energy surfaces of vinyl chloride, where the vertical arrows correspond to 532 nm photons. The two pathways for dissociation correspond to CO3 versus 3ce>i, whereas those for ionization correspond to m3 + 2coi versus 5ce>i (i.e., I = 2, m = 1, n = 3). Figure 13 shows the phase lag for ionization... 

Before we do this, though, we point out that for a simple diatomic molecule, assuming ideal conditions, one can in principle calculate the rate of the uni-molecular process. This is so because the lower excited states of the ion are (relatively) few and well separated. If the potential curves are then given, the value of the rate can be provided. For a polyatomic molecule, two great complications immediately arise (1) the number of lower excited states increases tremendously and (2) multidimensional potential energy surfaces make trajectory calculations intractable. 

Molecular dynamic studies used in the interpretation of experiments, such as collision processes, require reliable potential energy surfaces (PES) of polyatomic molecules. Ab initio calculations are often not able to provide such PES, at least not for the whole range of nuclear configurations. On the other hand, these surfaces can be constructed to sufficiently good accuracy with semi-empirical models built from carefully chosen diatomic quantities. The electric dipole polarizability tensor is one of the crucial parameters for the construction of such potential energy curves (PEC) or surfaces [23-25]. The dependence of static dipole properties on the internuclear distance in diatomic molecules can be predicted from semi-empirical models [25,26]. However, the results of ab initio calculations for selected values of the internuclear distance are still needed in order to test and justify the reliability of the models. Actually, this work was initiated by F. Pirani, who pointed out the need for ab initio curves of the static dipole polarizability of diatomic molecules for a wide range of internuclear distances. 

The Section on Molecular Rotation and Vibration provides an introduction to how vibrational and rotational energy levels and wavefunctions are expressed for diatomic, linear polyatomic, and non-linear polyatomic molecules whose electronic energies are described by a single potential energy surface. Rotations of "rigid" molecules and harmonic vibrations of uncoupled normal modes constitute the starting point of such treatments. 

Dependent Band Model for Lanthanide Compounds and Conditions for Interconfiguration Fluctuations J. N Murrell The Potential Energy Surfaces of Polyatomic Molecules J-A-Duffy Optical Electron ativity and Nephelauxetic Effect in Oxide Systems Application to Conducting, Semi-Conducting and Insulating Metal Oxides... 

For polyatomic molecules with 3 N-6 internal degrees of freedom it has been generally agreed (JJ, J7)thatit would be possible to satisfy two conditions of the type established above and therefore that potential energy surfaces could cross even if they had the same symmetry. For example, a linear triatomic has two internal degrees of freedom and hence surfaces of the same symmetry could be expected to cross at a point. This supposition was called into question byNaqvi (38) who based his conclusion on an extension of the diatomic proof (which was based upon perturbation theory) given by himself and Byers-Brown (34). However, proof... 

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