Full dimensional Franck-Condon factors for the acetylene $\tilde{\mathbf {A}}$Ã 1
 A
 u—$\mathbf {\tilde{X}}$X̃ $\mathbf {^1\Sigma _g^+}$Σg+1 transition. I. Method for calculating polyatomic linear—bent vibrational intensity factors and evaluation of calculated intensities for the gerade vibrational modes in acetylene

Park, G. Barratt

doi:10.1063/1.4896532

Cited by 9 publications

(11 citation statements)

References 66 publications

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“…Conversely, they are usually inadequate for flexible systems, due to the presence of strong anharmonic effects 11,12. This problem is worsened by the fact that couplings between modes are also usually large in cartesian coordinates, so that multidimensional anharmonic treatment are necessary 13–15. At variance, curvilinear internal coordinates often reduce those couplings, providing a better description of flexible systems.…”

Section: Introductionmentioning

confidence: 99%

“…In the past few years, the analysis of vibrational signatures in the electronic spectra of medium- to large-size molecular systems is being increasingly aided by quantum mechanical computations thanks to the development of effective and reliable electronic structure approaches (especially based on the density functional theory (DFT) , and its time-dependent (TD) extension , ), together with improved harmonic vibronic models. − Cartesian coordinates, that are currently employed in most cases as a reference set in the evaluation of vibronic effects, are effective and perfectly adequate for semirigid systems, with similar structures in the electronic states of interest. , Conversely, they are usually inadequate for flexible systems, due to the presence of strong anharmonic effects. , This problem is worsened by the fact that couplings between modes are also usually large in Cartesian coordinates, so that multidimensional anharmonic treatment is necessary. − At variance, curvilinear internal coordinates often reduce those couplings, providing a better description of flexible systems. , On those grounds, we have recently introduced general and effective harmonic vibronic models based on internal coordinates, , supporting any kind of molecular topology. Despite notable improvements, harmonic models in internal coordinates remain insufficient if progressions involving large-amplitude motions (LAMs) are predominant.…”

Section: Introductionmentioning

confidence: 99%

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Simulation of Vibronic Spectra of Flexible Systems: Hybrid DVR-Harmonic Approaches

Baiardi

Bloino

Barone

2017

J. Chem. Theory Comput.

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Our general framework for the simulation of vibrational signatures in electronic spectra has been extended to treat one large-amplitude motion (LAM) at the anharmonic level, coupled to the other small amplitude motions (SAM) treated as harmonic. The coupling between LAM and SAM is minimized thanks to the use of delocalized internal coordinates, which are built automatically from the molecular topology. General LAMs can be employed, ranging from intrinsic reaction coordinates to rigid or flexible paths based on the distinguished coordinate approach. The anharmonic model is based on a fully-numerical method based on the discrete variable representation (DVR) theory, supporting different types of boundary conditions. The inclusion of this model in a general-purpose electronic structure code makes available to the user a large panel of quantum chemistry models, for both isolated and condensed phases. The flexibility and reliability of the new framework are illustrated by some case studies, covering various types of LAMs, ranging from a small test case, the photoelectron spectrum of ammonia, to larger systems, such as phenylanthracene and cyclobutanone.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Simulation of Vibronic Spectra of Flexible Systems: Hybrid DVR-Harmonic Approaches

Baiardi

Bloino

Barone

2017

J. Chem. Theory Comput.

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“…This was a large part of the motivation for our recent full-dimensional FC calculation. 24,25 As a complement to previous work, we show that, when the X-state bending modes ν 4 ″ and ν 5 ″ are viewed in the basis of Cartesian doubly degenerate 2DHOs with in-plane (y) and outof-plane (x) bending quanta, there are additional, stricter, Franck−Condon propensities that require conservation of the number of in-plane versus out-of-plane cis-bend quanta. That is, there is a strong propensity for…”

Section: Franck−condon Propensity Rules In Thementioning

confidence: 88%

Simplified Cartesian Basis Model for Intrapolyad Emission Intensities in the Bent-to-Linear Electronic Transition of Acetylene

et al. 2015

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The acetylene emission spectrum from the trans-bent electronically excited Ã state to the linear ground electronic X̃ state has attracted considerable attention because it grants Franck–Condon access to local bending vibrational levels of the X̃ state with large-amplitude motion along the acetylene ⇌ vinylidene isomerization coordinate. For emission from the ground vibrational level of the Ã state, there is a simplifying set of Franck–Condon propensity rules that gives rise to only one zero-order bright state per conserved vibrational polyad of the X̃ state. Unfortunately, when the upper level involves excitation in the highly admixed ungerade bending modes, ν4′ and ν6′, the simplifying Franck–Condon propensity rule breaks down--as long as the usual polar basis (with v and l quantum numbers) is used to describe the degenerate bending vibrations of the X̃ state--and the intrapolyad intensities result from complicated interference patterns between many zero-order bright states. In this article, we show that, when the degenerate bending levels are instead treated in the Cartesian two-dimensional harmonic oscillator basis (with vx and vy quantum numbers), the propensity for only one zero-order bright state (in the Cartesian basis) is restored, and the intrapolyad intensities are simple to model, as long as corrections are made for anharmonic interactions. As a result of trans ⇌ cis isomerization in the Ã state, intrapolyad emission patterns from overtones of ν4′ and ν6′ evolve as quanta of trans bend (ν3′) are added, so the emission intensities are not only relevant to the ground-state acetylene ⇌ vinylidene isomerization, they are also a direct reporter of isomerization in the electronically excited state.

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“…This affects the structure of the coordinate transformation and the symmetry properties of the wavefunctions that participate in the integral, but the consequences have been neglected by previous investigators. Furthermore, because of the generality of the method developed in Paper I 57 for polyatomic linear-bent transitions-provided that the FC integral does not accumulate near the linear geometry-we predict that analogous consequences should appear in the Franck-Condon propensities of other linear-bent systems. In general, application of the aaxis Eckart constraint for the linear molecule (restoring the χ Euler angle) will remove one of the degrees of freedom from the bending vibrations of the linear molecule, and this degree of freedom will not contribute to the Franck-Condon integral away from linear geometry.…”

Section: Discussionmentioning

confidence: 99%

Full dimensional Franck-Condon factors for the acetylene $\tilde{\mathbf {A}}$Ã 1 A u—$\mathbf {\tilde{X}}$X̃ $\mathbf {^1\Sigma _g^+}$Σg+1 transition. II. Vibrational overlap factors for levels involving excitation in ungerade modes

Park

Baraban

Field

2014

The Journal of Chemical Physics

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A full-dimensional Franck-Condon calculation has been applied to theÃ 1 A u -X 1 + g transition in acetylene in the harmonic normal mode basis. Details of the calculation are discussed in Part I of this series. To our knowledge, this is the first full-dimensional Franck-Condon calculation on a tetra-atomic molecule undergoing a linear-to-bent geometry change. In the current work, the vibrational intensity factors for levels involving excitation in ungerade vibrational modes are evaluated. Because the Franck-Condon integral accumulates away from the linear geometry, we have been able to treat the out-of-plane component of trans bend (ν 4 ) in the linearX state in the rotational part of the problem, restoring the χ Euler angle and the a-axis Eckart conditions. A consequence of the Eckart conditions is that the out-of-plane component of ν 4 does not participate in the vibrational overlap integral. This affects the structure of the coordinate transformation and the symmetry of the vibrational wavefunctions used in the overlap integral, and results in propensity rules involving the bending modes of theX state that were not previously understood. We explain the origin of some of the unexpected propensities observed in IR-UV laser-induced fluorescence spectra, and we calculate emission intensities from bending levels of theÃ state into bending levels of theX state, using normal bending mode and local bending mode basis sets. Our calculations also reveal Franck-Condon propensities for the Cartesian components of the cis bend (ν 5 ), and we predict that the bestÃ-state vibrational levels for populatingX-state levels with large amplitude bending motion localized in a single C-H bond (the acetylene↔vinylidene isomerization coordinate) involve a high degree of excitation in ν 6 (cis-bend). Mode ν 4 (torsion) populates levels with large amplitude counter-rotational motion of the two hydrogen atoms.

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Cited by 9 publications

References 66 publications

Simulation of Vibronic Spectra of Flexible Systems: Hybrid DVR-Harmonic Approaches

Simulation of Vibronic Spectra of Flexible Systems: Hybrid DVR-Harmonic Approaches

Simplified Cartesian Basis Model for Intrapolyad Emission Intensities in the Bent-to-Linear Electronic Transition of Acetylene

Full dimensional Franck-Condon factors for the acetylene $\tilde{\mathbf {A}}$Ã 1 A u—$\mathbf {\tilde{X}}$X̃ $\mathbf {^1\Sigma _g^+}$Σg+1 transition. II. Vibrational overlap factors for levels involving excitation in ungerade modes

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