The symbol V denotes the potential energy operator for the inter hydrogen bond interactions in the excited vibrational state in the dimer. Thev symbol is the resonance interaction operator averaged with the respect to the proton vibration normal coordinates in the excited vibrational state in the dimer. 1 H is the average value of the proton displacement in the excited state of the proton vibration. On assuming a strong anharmonicity of the proton stretching vibrational motions in the dimer hydrogen bonds we obtain: in the first case by and in the second case by B and then integrate over the vibrational coordinates QA and Q B. This approach allows for the elimination of the vibrational coordinates in the procedure of the determination of the electronic functions in.
In the equation system the physical sense of the electro nic wave functions has changed since they are no longer depen dent p53 Signaling Pathway on the vibrational coordinates. Now we introduce new, symmetrized vibrational coordinates of the dimer, which belong to two diferent irreducible representations of the C i group. The H1p arameter value may be estimated from the potential energy surface parameters of the protonic motion in the single hydrogen bond, which in turn may be derived from spectroscopic data or from quantum chemical calculations. However, the main problem concerns the estimation of the matrix elements of the operators. Therefore, a precise solution of the matrix Schrodinger eq 29 does not seem feasible. On the other hand, to prove an efective mixing between the excited vibrational states via the vibronic mechanism a precise solution of eq 29 is not necessary.
The functions yield the non zero nondiagonal elements of the energy matrix. It means that an efective mixing involving the protonic vibrational states of diferent symmetry PARP Inhibitors may take place, since both functions are simultaneously diferent from zero. Therefore, the forbidden vibrational transition to the Ag state in the IR for the centrosymmetric hydrogen bond dimer can borrow its intensity from the allowed vibrational transition to the A u state. 6. DISCUSSION The presented model considers the vibronic coupling me chanism as well as the anharmonicity of the proton stretching vibrations in their first excited state as the main sources of the vibrational selection rule breaking in IR spectra of centrosym metric hydrogen bond dimers.
Formally, this mechanism is a kind of reverse of the familiar Herzberg_Teller mechanism, which was originally proposed for the interpretation of the UV_vis spectra of aromatic molecules. AMPK Signaling In this case, the dipole forbidden transition to the A g state of the proton vibra tions in the dimer is allowed due to the vibronic coupling involving the protonic and electronic motions in the system. As a result, the forbidden vibrational transition borrows the intensity from the symmetry allowed transition to the A u state. The fundamental equation describing the electronic movement in the dimer was obtained by averaging over the vibrational coordinates. Such an approach in its spirit is a kind of reverse of the separation of the vibrational and electronic move ments in molecules in terms of the Born_Oppenheimer approxi mation.
Changes in the electronic motions induced by the excited proton vibrations in the hydrogen bonds are small. However, even such small efects are important when the vibronic mechanism of IR transitions for hydrogen bond dimeric systems is discussed. 51,52 On analyzing the vibronic coupling mechanism in the cen trosymmetric dimers and the reason PLK for the dipole selection rule breaking in their IR spectra, one should jointly discuss the molecular geometry and the symmetry of the electronic charge distribution. The electronic contribution to the dynamics of the hydrogen bond atoms is responsible for the appearance of an efective asymmetry in the dimer geometry. This remark mainly concerns the proton positions in the dimers.
This seems to be the main source of the vibrational selection rule breaking in the IR spectra. The proton stretching vibrations VEGF are most strongly coupled with the movements of electrons occupying the nonbonding orbitals of the proton acceptor atoms in the hydrogen bonds. Also couplings of protons with electrons on the orbitals in molecular skeletons of the associating molecules should be considered. In the case of aliphatic carboxylic acid dimers in which only the hard core electrons exist the closest molecular environment of the hydrogen bonds should have a relatively small impact on to the vibronic coupling mechanism. It satisfies the Schr?odinger equation with new electronic func tions depending only on the electronic coordinates: The Hamiltonian is a purely electronic operator of the dimer. It relatestoitsaveragedgeometryinthe firstexcitedstateoftheproton vibrations in conditions of a strong anharmonicity of the motion. 5. 3. Spectral consequences of the model.