A variational approach for calculating Franck-Condon factors including mode-mode anharmonic coupling

Luis, Josep M.; Christiansen, Ove

doi:10.1063/1.2360944

Cited by 41 publications

(45 citation statements)

References 40 publications

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“…Anharmonic corrections can be included perturbatively [4][5][6][7] or variationally. [8][9][10][11] In smaller systems, it is feasible to apply anharmonic corrections to both eigenstates and eigenvalues, which affects both positions and intensities of vibronic transitions. 5,10,12 In larger systems, however, this is computationally challenging and the anharmonic corrections are almost exclusively included only through the frequencies, without affecting the Franck-Condon factors.…”

Section: Introductionmentioning

confidence: 99%

Single-Hessian thawed Gaussian approximation

Begušić

Cordova

Vaníček

2019

The Journal of Chemical Physics

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To alleviate the computational cost associated with on-the-fly ab initio semiclassical calculations of molecular spectra, we propose the single-Hessian thawed Gaussian approximation, in which the Hessian of the potential energy at all points along an anharmonic classical trajectory is approximated by a constant matrix. The spectra obtained with this approximation are compared with the exact quantum spectra of a one-dimensional Morse potential and with the experimental spectra of ammonia and quinquethiophene. In all cases, the single-Hessian version performs almost as well as the much more expensive on-the-fly ab initio thawed Gaussian approximation and significantly better than the global harmonic schemes. Remarkably, unlike the thawed Gaussian approximation, the proposed method conserves energy exactly, despite the time dependence of the corresponding effective Hamiltonian, and, in addition, can be mapped to a higher-dimensional time-independent classical Hamiltonian system.We also provide a detailed comparison with several related approximations used for accelerating prefactor calculations in semiclassical simulations.

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Section: Introductionmentioning

confidence: 99%

Single-Hessian thawed Gaussian approximation

Begušić

Cordova

Vaníček

2019

The Journal of Chemical Physics

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“…It is possible to incorporate the anharmonic effect in our approach, if the wavefunctions of anharmonic oscillators are expressed as linear combinations of those of HOs. [56, 57] In this way, the FCIs of anharmonic oscillators can be obtained from linear combinations of the FCIs of HOs.…”

Section: Resultsmentioning

confidence: 99%

An analytical approach for computing Franck‐Condon integrals of harmonic oscillators with arbitrary dimensions

Chang¹,

Huang²,

Chen³

et al. 2012

J Comput Chem

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We have developed an analytical approach for computing Franck-Condon integrals (FCIs) of harmonic oscillators (HOs) with arbitrary dimensions in which the mode-mixing Duschinsky effect is taken into account. A general formula of FCIs of HOs was obtained and was applied to study the photoelectron spectroscopy of vinyl alcohol and ovalene (C(32)H(14)). The equilibrium geometries, harmonic vibrational frequencies and normal modes of vinyl alcohol, ovalene, and their cations were computed at the B3LYP/aug-cc-pVTZ or the B3LYP/6-31G(d) level, from which Franck-Condon factors were calculated and photoelectron spectra were simulated. The adiabatic ionization energies of vinyl alcohol were also computed by extrapolating the CCSD(T) energies to the complete basis set limit with aug-cc-pVXZ (X = D, T, Q, 5). The simulated photoelectron spectra of both vinyl alcohol and ovalene are in agreement with the experiments. The computed adiabatic ionization energies of syn- and anti-vinyl alcohol are in consistent with the experiment within 0.008 eV and 0.014 eV, respectively. We show, for the first time, that the analytical approach of computing FCIs is also efficient and promising for the studies of vibronic spectra of macrosystems.

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“…Once the Duschinsky rotation 106 has been accounted for, two possible routes for the calculation of FC overlap integrals appear feasible: firstly the rotation of the wave functions onto each other and, secondly, the rotation of the Hamiltonian as proposed by Luis and Kirtman. [103][104][105] We focus on the former approach. The FC integral between two electronic states (quantities of the excited state are indicated by a prime, while those belonging to the reference state appear without the prime) essentially can be reduced to a summation over multi-dimensional overlap integrals of the distributed Gaussian basis functions χ μi , i.e.…”

Section: Vibronic Transitionsmentioning

confidence: 99%

“…However, in practice applications are limited either to the harmonic approximation or to the treatment of molecules with three or four atoms only. [99][100][101][102][103][104][105] The reason for this arises from the increasing number of basis functions and the Duschinsky rotation, which essentially leads to an exponential scaling of the computational cost for the 99 have focussed primarily on the harmonic approximation. Once the Duschinsky rotation 106 has been accounted for, two possible routes for the calculation of FC overlap integrals appear feasible: firstly the rotation of the wave functions onto each other and, secondly, the rotation of the Hamiltonian as proposed by Luis and Kirtman.…”

Section: Vibronic Transitionsmentioning

confidence: 99%

Selected Aspects Concerning the Efficient Calculation of Vibrational Spectra beyond the Harmonic Approximation

Oschetzki¹,

Neff²,

Meier³

et al. 2012

Croat. Chem. Acta

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Abstract. This feature article discusses some selected aspects in the field of vibrational structure calculations based on vibrational self-consistent field, VSCF, and vibrational configuration interaction, VCI, theory. As the quality of such calculations depends strongly on the accuracy of the underlying multidimensional potential energy surface, PES, some techniques will be discussed to establish high-quality PESs in a fully automated manner. As an alternative to VCI theory multiconfiguration self-consistent field, VMCSCF, theory and in particular specific aspects concerning the integral evaluation relevant to both approaches will also be presented. Further aspects concern the efficient calculation of infrared intensities and Franck-Condon factors in vibronic transitions.(doi: 10.5562/cca2149)

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A variational approach for calculating Franck-Condon factors including mode-mode anharmonic coupling

Cited by 41 publications

References 40 publications

Single-Hessian thawed Gaussian approximation

Single-Hessian thawed Gaussian approximation

An analytical approach for computing Franck‐Condon integrals of harmonic oscillators with arbitrary dimensions

Selected Aspects Concerning the Efficient Calculation of Vibrational Spectra beyond the Harmonic Approximation

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