Anharmonic potential energy

The harmonic approximation is unrealistic in a dynamical description of the dissociation dynamics, because anharmonic potential energy terms will play an important role in the large amplitude motion associated with dissociation. An accurate potential energy surface must be used in order to obtain a realistic dynamical description of the dissociation process and, as in the quasi-classical approach for bimolecular collisions, a numerical solution of the classical equations of motion is required [2]. 

Fig. 19.5 MP2 anharmonic potential energy levels for v(NHN)+ and v(NDN)+, with solid lines for protonic and dashes ones for deuteronic motion. [17]...

Fig. 1.3. Upper Schematic view (dotted line) of cross-section of many-dimensional highly anharmonic potential energy surfaces for reactants plus solution (R) and (dotted line omitted) for products plus solution (P). TS occurs at the intersection. Lower Plot of free energy G for the above R and P systems vs. the reaction coordinate U.

The anharmonic free energy is evaluated for empty hydrate and cubic ice (ice Ic). The calculated free energy due to the anharmonic potential energy surface is given in Table 1. The anharmonic contribution to the free energy of empty... 

FIGURE 13.9. Harmonic and anharmonic potential energy functions. The harmonic function V u) is a simple parabola, but the anharmonic potential falls off at high displacements u. 

MAIN FEATURES OF IR SPECTRA RELATED TO THE ANHARMONIC POTENTIAL ENERGY SHAPE... 

The anharmonic potential energy is usually easier to represent in internal coordinates than in normal mode coordinates. However, what restricts the use of internal coordinates is the complicated expression for the vibrational/rotational kinetic energy in these coordinates (Pickett, 1972). It is difficult to write a general expression for the vibrational/rotational kinetic energy in internal coordinates and, instead, one usually considers Hamiltonians for specific molecules. For a bent triatomic molecule confined to rotate in a plane, the internal coordinate Hamiltonian is (Blais and Bunker, 1962) ... 

This indicates that the energy conservation holds for each individual mode. That is, energy exchange between different normal modes is impossible. Taking the anharmonic coupling into account, the anharmonic potential-energy function can be expressed as... 

Fundamentals of three isotopic species were derived from an anharmonic potential energy function, which was based on an ab initio calculation and on experimental information for the most common isotopic HOF species (for the fundamentals, see table above) [6]. Later calculations for HOF and DOF [15], using both SCF and Cl methods, were based upon the same potential energy function. 

The Ar-HF molecule serves as both a prototype for inert gas atoms clustering or solvating around a hydrogen-halide polar center and as a simple test-bed for refining and testing how we create anharmonic potential energy surfaces. Specifically, both the Ar-HF and the Ar-Ar potential energy surfaces are extremely well characterized and have been verified extensively... 

Venuti E, Halonen L, Delia VaUe RG (1999) High dimensional anharmonic potential energy surfaces The case of methane. J Chem Phys 110 7339... 

A perturbation theory treatment known as the method of contact transformations [162] provides a convenient approach in defining the anharmonic potential energy and transitional dipole moment [158-163]. Both mechanical and electrical anhaimonicities influence the intensities of overtone and combination bands. 

In reality, the harmonic oscillator is not a good model for molecular vibrations except at low-energy levels, and the system is better modeled by an anharmonic potential energy curve. Figure 3.4.1.1, described as a power series in (v + 1/2)... 

In conclusion, the work presented here has illustrated the effect of various potential energy surface properties on unimolecular dynamics. The calculations show that the energy distributions of the unimolecular products contain very little information about the intramolecular dynamics of the species undergoing unimolecular dissociation. It was also found that anharmonic potential energy surfaces may contain large fractions of quasiperiodic trajectories above the unimolecular threshold. 

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