The excitation of the A g vibrations in the dimer generates the lower frequency transition branch of the N_H band when the A u vibrations are responsible for the higher frequency band branch. According to the formalism of the strong coupling theory, the N_H band shape of a dimer depends on the following system parameter determines the splitting of the component bands of the dimeric spectrum corresponding to the excitation of the proton vibrational motions of diferent symmetries, A and A. In its simplest, original version, the strong coupling model predicts reduc tion of the distortion parameter value for the deuterium bond systems according to the relation. For the C O and C 1 resonance interaction parameters the theory predicts the isotopic efect expressed by the 1.
0 to 2 fold reduction of the parameter values for D bonded dimeric systems. Figure 10 shows the results of model calculations, which quantita tively reconstitute the residual band contour shapes from the spectra of PAM crystals, isotopically diluted by deuterium. The theoretical spectrum was treated MLN8237 as a superposition of the plus and minus component bands taken with their appropriate statistical band contour shapes from the spectra of the PAM crystals, isotopically diluted by hydrogen, is presented in Figure 11. When the corresponding calculated spectra and the experimental spectra are compared, it can be noticed that a satisfactorily good reconstitution of the two analyzed band shapes has been achieved. The results also remain in agreement with the linear dichroic efects measured in the crystalline spectra.
The b H parameter describes the change in the equilibrium geometry for the low energy hydrogen bond stretching vibrations, accompanying the excitation of the high frequency mTOR Inhibitors proton stretching N_H. The C O and C 1 parameters are responsible for the exciton interactions between the hydrogen bonds in a dimer. They denote the subsequent expansion coefcients in the series on developing the resonance interaction integral C with respect to the normal coordinates of the N 3 3 3 O low frequency stretching vibra tions of the hydrogen bond. This is in accordance with the formula where Q 1 represents the totally symmetric normal coordinate for the low frequency hydrogen bridge stretching vibrations in the dimer. This parameter system is closely related to the intensity distribution vibrations in the dimeric band.
The b H and C 1 parameters are directly related to the dimeric component bandwidth. The CO The Journal of Physical Chemistry A contour shapes are reconstituted, Ion Channel the so called dimeric minus sub band,correspondingtothein phaseprotonvibrations,reproducethe lower frequency branches of the band. The higher energy branches ofthe bandsarereproducedbytheso called plus dimericsub band related to the out of phase proton vibrations. The calculation results have suggested that the two dimeric component sub bands, minus and plus, contributed to the results with their comparable statistical weights, represented by the appropriate F and F parameter values. However, it was found that the minus band, theoretically forbidden by the symmetry rules for dipole vibrational transitions, appeared in the IR spectra of a centrosymmetric dimer.
The explanation of this efect is given in the next section of this article. 5. 1. Single Hydrogen Bond. In this section we will analyze the problem of the activation of the symmetry forbidden transi tion in IR, which is responsible for the generation of the lower frequency Protease N_H band branch in the crystalline spectra of PAM. For this purpose let us assume a simplified model of a single N_H 3 3 3 O hydrogen bond, in which the proton stretching vibration couples with electronic motions. The vibronic Hamil tonian of the system is as follows: for the n electronic function. The expansion takes into the account a linear term dependence of the electronic wave function of nth electronic state upon the normal coordinate of the proton stretching vibration.
In the limits of the adiabatic approximation the electronic function is as HSP follows: where the symbols q and p denote the coordinates and the momenta of electrons, whereas the Q and P symbols represent the normal coordinate of the proton stretching vibration and the momentum conjugated with it. T N, T el, and U subsequently denote the kinetic energy operator of the proton vibration, the energy operator of the electrons, and the potential energy operator for a single hydrogen bond. The total vibronic wave function of the model hydrogen bond satisfies the Schr?odinger equation: The electronic operators Ah and Bh in are considered as a sum of contributions introduced subsequently by the individual hydrogen bonds themselves as well as by their molecular surroundings. The operators introduced above have a strictly defined physical meaning: H0A and H0B are the Hamiltonians of the individual hydrogen bonds in the dimer, when each operator is averaged with respect to the vibrational coordinates.