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

Abstract

A full-dimensional Franck-Condon calculation has been applied to theà 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 theà 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.

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

“…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…”

“…As shown in ref 25, it is also straightforward to transform to the basis of local bending modes relevant to the acetylene ⇌ vinylidene isomerization. Indeed, the quest to find A-state levels that grant access to local bending levels along the acetylene−vinylidene isomerization path was a major motivating factor for the work described here.…”

“…Note that the overlaps from the in-plane 6 2 vibrational level and the out-ofplane 4 2 vibrational level are identical in magnitude but have a phase relationship that gives rise to qualitatively different bending dynamics and spectral intensity patterns. 25 From the correlation table connecting D ∞h to C 2h , we find that, in emission to l = 0 levels of the X̃state, the vibrational selection rules are a g → σ g…”

Communication: Observation of local-bender eigenstates in acetylene

“…In order to sidestep the limited spectroscopic access provided by the Franck-Condon active vibrational levels, we have reinvestigated the à ← X spectrum of acetylene with a focus on the non-totally symmetric vibrational modes. [14][15][16][17][18][19][20] This work has enabled us to perform a detailed calculation of the Franck-Condon factors 21,22 and to develop a model that successfully describes the Franck-Condon fluorescence propensities from the non-totally symmetric modes of the S 1 state. 23 The model takes into account anharmonic interactions and correctly reproduces the observed emission patterns from B 1 and B 2 polyads.…”

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

“…We will discuss this problem in detail in Sec. II D, and consequences for the full-dimensional Franck-Condon propensities will be discussed in Paper II 72 of this series. Weber and Hohlneicher 47 have calculated multi-dimensional Franck-Condon factors for the acetyleneÃ-X transition, but their calculation constrains the molecule to planarity, so they have not considered a number of the symmetry properties and propensity rules that we investigate here in our full-dimensional treatment.…”