Intramolecular dynamics. I. Curvilinear normal modes, local modes, molecular anharmonic Hamiltonian, and application to benzene

Abstract

The Hamiltonian based on curvilinear normal modes and local modes (CNLM) is discussed using Wilson's exact vibrational Hamiltonian as basis, the CNLM representation diagonalizing only the normal mode block of FG matrix in curvilinear internal coordinates. Using CNLM the kinetic and potential energy operators for benzene are given, including cubic and quartic anharmonicity in the potential energy and cubic and quartic terms in the kinetic energy expansion in curvilinear coordinates. Using symmetrized coordinates and cubic and higher force constants the number and identity of the independent symmetry allowed (A ,g ) such force constants are obtained. The relation to conventional anharmonic force constants is then given and the allowed contributions of the latter are obtained. The results are applied to CH overtone spectra and intramolecular vibrational dynamics in Part III of this series.

Quantum mechanical study of intramolecular vibrational energy redistribution in the second CH stretch overtone state in benzene

“…[21][22][23][24][25] Several quantum mechanical studies of the CH(vϭ3) state in benzene have been carried out. 11,[14][15][16][17][18][19][20]26,27 The theoretically calculated absorption spectra and dynamical IVR characteristics ͑initial state survival probabilities͒ were in reasonable accord with the experimental measurements. A major difficulty inherent to the quantum mechanical approach is connected with the large vibrational level densities involved.…”

“…28͒ is based on the full vibrational rotationless Hamiltonian H, expressed in curvilinear internal coordinates x i . 4,29 Our derivation is close in spirit to that of Zhang and Marcus, 16,17 except for the employment of complex symmetrized basis functions ͉i͘. As a result of a series of transformations, H is reduced to the form:…”

“…As described in more detail in Ref. 28, interaction terms HЈ of various orders contain contributions of two types ͑which are of comparable magnitude͒: ͑i͒ kinetic part, which can be calculated exactly using relevant terms in the Taylor series expansions of the analytical expressions for G i j (x) matrix elements ͑Zhang and Marcus 16,17 have done this for the in-plane modes; we have included the out-of-plane modes as well͒; ͑ii͒ potential part-determined by force constants, which can be taken from ab initio calculations ͑Refs. 31 and 33͒.…”

“…͑i͒ For a DDV i (iϭ6, 8,9,10,16,17,18,19), pairs of complex conjugated coordinates q ia , q ib as well as raising and lowering operators are employed: 8,29,32…”

“…[2][3][4][5][6][7][8] The second overtone state CH(vϭ3) in benzene has been the object of numerous studies, both experimentally and theoretically. [9][10][11][12][13][14][15][16][17][18][19][20] From their gas phase photoacoustic spectrum of the CH(vϭ3) state, Reddy, Heller, and Berry 10 inferred a homogeneous intramolecular vibrational redistribution ͑IVR͒ bandwidth of ϳ23 cm Ϫ1 and pronounced nonstatistical ͑nonergodic͒ redistribution character. Later Page, Shen, and Lee, 12 using state selective multilevel saturation spectroscopy of rotationally jet-cooled molecules (T rot ϳ5 K) observed a central peak of 10 cm Ϫ1 width.…”