Phase-space derivation of propensity rules for energy transfer processes between Born–Oppenheimer surfaces

Empirical Determination of the Harmonic Force Constants in Benzene. 4. The Fermi Resonances

In this article, we present a continuation of our work on the refinement of the harmonic force constants Fi,k in benzene (in symmetrized Whiffen's coordinates) and on a growing number of higher order (anharmonic) force constants, Fi,j,k and Fi,j,k,l, that are of importance for the benzene isotopomer invariant potential energy surface. The refined set of harmonic and anharmonic force constants improves the agreement between the experimental levels and those calculated theoretically. The emphasis of the present work is on the analysis of the two notable Fermi resonances in benzene (nu8 +nnu1 <=> (n +1)nu1 + nu6, where n = 0, 1, ... m, and nu20 <=> nu8 + nu19 <=> nu1 + nu6 + nu19). For this purpose, we have further extended our fully dimensional, fully symmetrized, and nonperturbative vibrational procedure to the vibrational structure of the benzene isotopic species with D6h symmetry.

Simulation of photoelectron spectra with anharmonicity fully included: Application to the X̃A22←X̃A11 band of furan

Using a new unconventional procedure for calculating Franck-Condon factors with anharmonicity fully included the X 2A2<--X 1A1 band in the photoelectron spectrum of furan (and deuterated furan) was simulated at the second-order perturbation theory level. All 21 vibrational modes were considered but, in the end, only 4 are required to accurately reproduce the spectrum. Except for our own recent work on ethylene such calculations have been previously limited to tri- or tetraatomic molecules. Most of the effect of anharmonicity is accounted for in first order, although second-order corrections to the vibrational frequencies are important. Based on these simulations we were able to improve upon and extend previous assignments as well as suggest further measurements.

A phase-space approach to the T1⇝S0 radiationless decay in benzene: The effect of deuteration

The influence of full deuteration on the T1 right arrow-wavy S0 intersystem crossing in benzene is studied by a phase space approach. A full treatment of all the vibrational modes in the molecule leads to a ratio of the rate between the two isotopomers which is very close to the experimental value. Several aspects of the results are compared to previous estimates, and the effects of anharmonicity on the rates and accepting modes are examined. This first successful application of the method to a real physical system encourages the possibility of establishing a routine procedure for simple calculations of transition rates even for relatively large molecules.

Calculation of Franck–Condon factors including anharmonicity: Simulation of the C2H4+X̃B3u2←C2H4X̃Ag1 band in the photoelectron spectrum of ethylene

Our new simple method for calculating accurate Franck-Condon factors including nondiagonal (i.e., mode-mode) anharmonic coupling is used to simulate the C2H4+X2B3u<--C2H4X1A(g) band in the photoelectron spectrum. An improved vibrational basis set truncation algorithm, which permits very efficient computations, is employed. Because the torsional mode is highly anharmonic it is separated from the other modes and treated exactly. All other modes are treated through the second-order perturbation theory. The perturbation-theory corrections are significant and lead to a good agreement with experiment, although the separability assumption for torsion causes the C2D4 results to be not as good as those for C2H4. A variational formulation to overcome this circumstance, and deal with large anharmonicities in general, is suggested.

A different approach for calculating Franck–Condon factors including anharmonicity

An efficient new procedure for calculating Franck-Condon factors, based on the direct solution of an appropriate set of simultaneous equations, is presented. Both Duschinsky rotations and anharmonicity are included, the latter by means of second-order perturbation theory. The critical truncation of basis set is accomplished by a build-up procedure that simultaneously removes negligible vibrational states. A successful test is carried out on ClO2 for which there are experimental data and other theoretical calculations.