Vibrational energy levels computer program

The optimized geometries and resulting energies for the reactants, entrance complex, transition state, exit complex, and products were predicted. Harmonic vibrational frequencies predicted at the same level (up to cc-pVQZ and cc-pVQZ-PP basis sets) were used for the characterization of stationary points and zero-point vibrational energies (ZPVE). The CFOUR program of Stanton, Gauss, Harding, Szalay, and coworkers was used for the coupled-cluster computations [24]. Most DZ results are not shown in text, but they are available in Supplementary Material. 

Many programs for computing energy levels use normal coordinates [9-14]. An important disadvantage of the Watson normal coordinate KEO is its complexity. The vibrational KEO is simple, only if one discards all the jrn cross terms. If the 7Z7Z cross terms are retained, the KEO is complicated because n depends on all the coordinates. If the mass of the molecule is large the K nn terms are, in general, small. 

To make quantitative statements about the product internal distribution a computer program is utilized to simulate the observed excitation spectrum [10]. As input for the calculations we estimate the relative vibrational and rotational populations. Each line is weighted by the population of the initial (v, J ) level, by the Franck-Condon factor and the rotational line strength of the pump transition. At each frequency, the program convolutes the lines with the laser bandwidth and power to produce a simulated spectrum such spectra are compared visually with the observed spectra and new estimates are made for the (v ,J") populations. Iteration of this process leads to the "best fit" as shown in the lower part of Fig. 3. For this calculated spectrum all vibrational states v" = 0...35 are equally populated as is shown in the insertion. The rotation, on the other hand, is described by a Boltzmann distribution with a "temperature" of 1200 K. With such low rotational energy no band heads are formed for v" < 5 in the Av = 0 sequence and for nearly all v" in the Av = +1 sequence (near 5550 A). 

The numerical representations for the wave functions and energies so obtained can then be used in further computation, such as that of transition probabilities. The approach of Davidson is particularly necessary when it is not sufficient to approximate the potential function by a standard Morse function. Such an eventuality arises, for example, if one desires a careful investigation of the size of errors in vibrational and rotational levels induced by the Bom-Oppenheimer approximation itself. For such an investigation it is necessary to take an accurate numericed representation of an a priori potential function and compute the vibrational and rotational energies for comparison with experiment. However, if such a program is to be meaningful, the accuracy of the a priori potential function must be of an order greater than the size of the deficiencies due to the Bom-Oppen-heimer approximation. 

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