The authors extend their recent method for the computation of vibrationally resolved optical spectra of large molecules, including both the Duschinsky rotation and the effect of finite temperature in the framework of the Franck-Condon (FC) approximation, to deal with the more general case of the Herzberg-Teller (HT) model, where also the linear dependence of the transition dipole moment on the nuclear coordinates is taken into account. This generalization allows us to investigate weak and vibronically allowed transitions by far extending the range of application of the method. The calculation of the spectra of sizable molecules is computationally demanding because of the huge number of final vibrational states that must be taken into account, and the inclusion of HT terms further increases the computational burden. The method presented here automatically selects the relevant vibronic contributions to the spectrum, independent of their frequency, and it is able to provide fully converged spectra with a modest computational requirement. The effectiveness of the method is illustrated by computing the HT absorption and fluorescence Q(x) spectra of free-base porphyrin both at T=0 K and at room temperature, performing for the first time an exact treatment of vibrations in harmonic approximation. Q(x) spectra are compared to experiments and FC/HT interferences are analyzed in detail.

Effective method for the computation of optical spectra of large molecules at finite temperature including the Duschinsky and Herzberg–Teller effect: The Qx band of porphyrin as a case study

The authors present a new method for the computation of vibrationally resolved optical spectra of large molecules, including the Duschinsky [Acta Physicochim. URSS 7, 551 (1937)] rotation of the normal modes. The method automatically selects the relevant vibronic contributions to the spectrum, independent of their frequency, and it is able to provide fully converged spectra with a quite modest computational time, both in vacuo and in condensed phase. Starting from the rigorous time-dependent expression they discuss indeed in which limits the spectrum of a molecule embedded in a solvent, described as a polarizable continuum, can be computed in a time-independent formalism, defining both nonequilibrium and equilibrium limits. In these cases the polarizable continuum model provides a suitable description of the solvent field. By computing the absorption spectra of anthracene in gas phase and of coumarin C153 in gas phase and cyclohexane, and the phosphorescence spectrum of the unsubstituted coumarin in ethanol they show that the method is fast and efficient.

Effective method to compute Franck-Condon integrals for optical spectra of large molecules in solution.

A general and effective time-independent approach to compute vibrationally resolved electronic spectra from first principles has been integrated into the Gaussian computational chemistry package. This computational tool offers a simple and easy-to-use way to compute theoretical spectra starting from geometry optimization and frequency calculations for each electronic state. It is shown that in such a way it is straightforward to combine calculation of Franck-Condon integrals with any electronic computational model. The given examples illustrate the calculation of absorption and emission spectra, all in the UV-vis region, of various systems from small molecules to large ones, in gas as well as in condensed phases. The computational models applied range from fully quantum mechanical descriptions to discrete/continuum quantum mechanical/molecular mechanical/polarizable continuum models.

Fully Integrated Approach to Compute Vibrationally Resolved Optical Spectra: From Small Molecules to Macrosystems

Effective method to compute Franck-Condon integrals for optical spectra of large molecules in solution (vol 126, pg 084509, 2007)

we show that a boson sampling device with a modied input state can be used to generate molecular vibronic spectra, including complicated eects such as Duschinsky rotations.

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Boson Sampling for Molecular Vibronic Spectra

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 A in the equilibrium C–C bond distance and no change in the C–H bond distance i...

T. E. Sharp

Papers

Franck—Condon Factors for Polyatomic Molecules