Franck—Condon Factors for Polyatomic Molecules

Abstract

General expressions are derived for calculating Franck—Condon factors for most transitions of polyatomic molecules (excluding transitions between linear and bent configurations) in the harmonic oscillator approximation. The derivation employs the method of generating functions and also linear transformation of normal mode coordinates between initial and final states. Input data required in the general case are geometries, frequencies, and vibrational force fields for the initial and final states. Explicit algebraic expressions are presented for the transition between linear, symmetric, triatomic initial and final states. The results are used to show that fragmentation cannot result from direct vertical ionization to the ground electronic states of CS2+ and CO2+ or to the excited 2IIu state of CO2+. An attempt was made to fit the experimental photoionization data for C2H2 and C2D2. This resulted in an estimated increase of 0.05 Å in the equilibrium C–C bond distance and no change in the C–H bond distance in C2H2+ as compared to C2H2.

Geometries of the Halocarbene anions HCF− and CF2−: ab initio calculation and Franck–Condon analysis

“…The definitions of B and L are consistent with Ref. [28]. After several substitutions, the relation to relate Q to Q 0 is obtained as: …”

“…Having then computed J and K, the FCFs are easily produced using the algebraic expressions below. Following Sharp et al [28], the arrays A through E are defined in terms of the Duschinsky rotations arrays, J and K, and the harmonic frequencies. A diagonal matrix G has the harmonic frequencies as diagonal elements.…”

“…We chose the multidimensional generating function method described by Sharp and Rosenstock [28] for the integrals. First, the Duschinsky effect, or mode mixing of the initial and final electronic states, is expressed as:…”

“…Different methods [27][28][29][30][31][32][33] have been proposed to calculate multidimensional FC integrals. We chose the multidimensional generating function method described by Sharp and Rosenstock [28] for the integrals.…”

Quantum Dynamics of Radiationless Electronic Transitions Including Normal Modes Displacements and Duschinsky Rotations: A Second-Order Cumulant Approach

“…[29][30][31] Dimensionless coordinates are defined, as usual, in terms of standard normal coordinates (Q) as…”