THEORETICAL-STUDY OF INTRAMOLECULAR VIBRATIONAL-RELAXATION OF ACETYLENIC CH VIBRATION FOR V = 1 AND 2 IN LARGE POLYATOMIC-MOLECULES (CX3)3YCCH, WHERE X = H OR D AND Y = C OR SI

Quantum calculations are reported for the intramolecular vibrational e nergy redistribution on and absorption spectra of the first two excite d states of the acetylenic CH stretch vibration in the polyatomic mole cules (CX3)3YCCH, where X=H or D and Y=C or Si. Using approximate pote ntial energy surfaces, comparison is made with the corresponding recen t experimental spectra. It is found that a model of intramolecular vib rational relaxation based on the assumption of sequential off-resonanc e transitions via third and fourth order vibrational couplings (as opp osed to direct high order couplings) is in agreement with experimental results on spectral linewidths. In a semiclassical limit this type of relaxation corresponds to a dynamic tunneling in phase space. It is s hown that the local density of resonances of third and fourth order, r ather than the total density of states, plays a central role for the r elaxation. It is found that in the Si molecule an accidental absence o f appropriate resonances results in a bottleneck in the initial stages of relaxation. As a result, an almost complete localization of the in itially prepared excitation occurs. It is shown that an increase of th e mass alone of the central atom from C to Si cannot explain the obser ved difference in the C and Si molecules. The spectral linewidths were calculated with the Golden Rule formula after prediagonalization of t he relevant vibrational states which are coupled in the molecule to th e CH vibration, directly or indirectly. For the spectral calculations, in addition to the direct diagonalization, a modified recursive resid ue generation method was used, allowing one to avoid diagonalization o f the transformed Lanczos Hamiltonian. With this method up to 30 000 c oupled states could be analyzed on a computer with relatively small me mory. The efficiency of C programming language for the problem is disc ussed.