Franck-Condon factors for multidimensional harmonic oscillators

Malmqvist, Per‐Åke; Forsberg, Niclas

doi:10.1016/s0301-0104(97)00347-9

Cited by 68 publications

(56 citation statements)

References 15 publications

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“…The matrix elements describing the transition moment function are expressed in terms of FranckCondon factors, that is, overlaps between two sets of harmonic oscillator functions representing the force fields of the participating states. 35 The vibronic transition moment is computed as…”

Section: Methods and Computational Detailsmentioning

confidence: 99%

Theoretical characterization of the lowest-energy absorption band of pyrrole

Roos

Malmqvist

Molina

et al. 2002

The Journal of Chemical Physics

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122

145

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The lowest-energy band of the electronic spectrum of pyrrole has been studied with vibrational resolution by using multiconfigurational second-order perturbation theory ͑CASPT2͒ and its multistate extension ͑MS-CASPT2͒ in conjunction with large atomic natural orbital-type basis sets including Rydberg functions. The obtained results provide a consistent picture of the recorded spectrum in the energy region 5.5-6.5 eV and confirm that the bulk of the intensity of the band arises from a * intravalence transition, in contradiction to recent theoretical claims. Computed band origins for the 3s,3p Rydberg electronic transitions are in agreement with the available experimental data, although new assignments are suggested. As illustrated in the paper, the proper treatment of the valence-Rydberg mixing is particularly challenging for ab initio methodologies and can be seen as the main source of deviation among the recent theoretical results as regards the position of the low-lying valence excited states of pyrrole.

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Section: Methods and Computational Detailsmentioning

confidence: 99%

Theoretical characterization of the lowest-energy absorption band of pyrrole

Roos

Malmqvist

Molina

et al. 2002

The Journal of Chemical Physics

Self Cite

122

145

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“…Observe that all matrices and vectors associated to the electronic excitation of a molecule are real matrices and real vectors, and this fact will be used to simplify all the expressions reported below. The two sets of QHOs are related by the Duschinsky relation and this relation can be expressed in terms of a modification of the ladder operators [21] as given bŷ…”

Section: B Vibronic Transitionsmentioning

confidence: 99%

“…In this work, we present a connection between boson sampling and the calculation of molecular vibronic (vibrational and electronic) spectra related to molecular processes such as absorption, emission, photoelectron and resonance Raman (see Table I) [19][20][21][22][23][24] . The proposed simulation scheme provides a second, chemically-relevant reason to realize boson sampling machines.…”

Section: Introductionmentioning

confidence: 99%

Boson sampling for molecular vibronic spectra

et al. 2015

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Quantum computers are expected to be more efficient in performing certain computations than any classical machine. Unfortunately, the technological challenges associated with building a fullscale quantum computer have not yet allowed the experimental verification of such an expectation. Recently, boson sampling has emerged as a problem that is suspected to be intractable on any classical computer, but efficiently implementable with a linear quantum optical setup. Therefore, boson sampling may offer an experimentally realizable challenge to the Extended Church-Turing thesis and this remarkable possibility motivated much of the interest around boson sampling, at least in relation to complexity-theoretic questions. In this work, we show that the successful development of a boson sampling apparatus would not only answer such inquiries, but also yield a practical tool for difficult molecular computations. Specifically, we show that a boson sampling device with a modified input state can be used to generate molecular vibronic spectra, including complicated effects such as Duschinsky rotations.

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“…In general, matrix elements of any polynomial in one or many coordinates over displaced harmonic oscillators with different force constants can be evaluated in terms of overlaps. A program for this kind of analysis, using a new method for evaluating the Franck-Condon factors 28 was used to evaluate the vibronic transition moment matrix elements.…”

Section: ͑1͒mentioning

confidence: 99%

A theoretical study of the 1B2u and 1B1u vibronic bands in benzene

Bernhardsson

Forsberg

Malmqvist

et al. 2000

The Journal of Chemical Physics

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The two lowest bands, 1 B 2u and 1 B 1u , of the electronic spectrum of the benzene molecule have been studied theoretically using a new method to compute vibronic excitation energies and intensities. The complete active space ͑CAS͒ self-contained field ͑SCF͒ method ͑with six active -orbitals͒ was used to compute harmonic force field for the ground state and the 1 B 2u and 1 B 1u electronic states. A linear approximation has been used for the transition dipole as a function of the nuclear displacement coordinates. Derivatives of the transition dipole were computed using a variant of the CASSCF state interaction method. Multiconfigurational second-order perturbation theory ͑CASPT2͒ was used to obtain absolute excitation energies ͑12 active -orbitals͒. The results show that the approach works well. Vibrational progressions are well described in both bands and intensities, and energies are in agreement with experiment, in particular when CASPT2 derived geometries are used. One interesting result is that computed vertical energies fall about 0.1 eV on the high energy side of the band maximum.

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Franck-Condon factors for multidimensional harmonic oscillators

Cited by 68 publications

References 15 publications

Theoretical characterization of the lowest-energy absorption band of pyrrole

Theoretical characterization of the lowest-energy absorption band of pyrrole

Boson sampling for molecular vibronic spectra

A theoretical study of the 1B2u and 1B1u vibronic bands in benzene

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