Multidimensional Franck–Condon integrals and Duschinsky mixing effects

Kupka, Hans; Cribb, Peter H.

doi:10.1063/1.451216

Cited by 139 publications

(71 citation statements)

References 19 publications

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“…The multidimensional Franck-Condon overlap integrals are evaluated using standard generating function techniques. [36][37][38][39][40] Note that D͑N 1 , ... ,N N int͒ Յ 1, where…”

Section: ͑4͒mentioning

confidence: 99%

The simulated photoelectron spectrum of 1-propynide

Papas

Schuurman

Yarkony

2009

The Journal of Chemical Physics

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The negative ion photoelectron spectrum of 1-propynide is computed by employing the multimode vibronic coupling approach. A three-state quasidiabatic Hamiltonian, H(d), is reported, which accurately represents the ab initio determined equilibrium geometries and harmonic frequencies of the ground X (2)A(1) state as well as the low-lying Jahn-Teller distorted components of the A (2)E excited state. It also reproduces both the minimum energy crossing point (MECP) on the symmetry-required (2)E(x)-(2)E(y) conical intersection seam and the MECP on the same symmetry (2)A(1)-(2)E(x) conical intersection seam. H(d) includes all terms through second order in internal coordinates for both the diagonal and off-diagonal blocks. It is centered at the (2)E(x)-(2)E(y) MECP and is determined using ab initio gradients and derivative couplings near both the (2)E(x)-(2)E(y) MECP and the X (2)A(1) equilibrium geometry. This construction is enabled by a recently reported normal equation based algorithm. The C(3v) symmetry of the system is used to significantly reduce the computational cost of the ab initio treatment. This H(d) is then expressed in a vibronic basis that is chosen for its ability to reduce the dimension of the vibronic expansion. The vibronic Hamiltonian matrix is diagonalized to obtain a negative ion photoelectron spectrum for 1-propynide-h(3). The determined spectrum compares favorably with previous spectroscopic results. In particular, the lines attributable to the (2)E state are found to be much weaker than those corresponding to the (2)A(1) state of 1-propynyl. This diminution of the (2)E state is attributable principally to the (2)E(x)-(2)A(1) conical intersection rather than an intrinsically small electronic transition moment for the production of the (2)E state.

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“…The multidimensional Franck-Condon overlap integrals are evaluated using standard generating function techniques. [36][37][38][39][40] Note that D͑N 1 , ... ,N N int͒ Յ 1, where…”

Section: ͑4͒mentioning

confidence: 99%

The simulated photoelectron spectrum of 1-propynide

Papas

Schuurman

Yarkony

2009

The Journal of Chemical Physics

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“…[32][33][34][35][36][37] This algorithm is an extension of the one previously reported by our group for a = 0, which could handle vibronic expansions comprised of >10 9 terms. In general, the Franck-Condon overlap integrals, s a,m , are only difficult to determine when the w and w represent different normal coordinate systems with different origins and orientations.…”

Section: Appendix B: Analytic Expressions For the Overlap Factorsmentioning

confidence: 99%

“…(7)] are evaluated using recursion relations derived from standard generating function techniques. [32][33][34][35][36][37] We have previously discussed 38 the evaluation of s a,n for a = 0. In Appendix B, we provide a derivation of the analytic expressions for the recursion relations and discuss their implementation for the hot band case a j = 1, a k = 0, k =j, required here.…”

Section: Determination Of the Spectral Amplitudesmentioning

confidence: 99%

On the simulation of photoelectron spectra complicated by conical intersections: Higher-order effects and hot bands in the photoelectron spectrum of triazolide (CH)2N3−

Dillon

Yarkony

Schuurman

2011

The Journal of Chemical Physics

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We report simulated photoelectron spectra for 1,2,3-triazolide (CH) 2 N 3 − , which reveal the vibronic energy levels of the neutral radical 1,2,3-triazolyl, (CH) 2 N 3 . The spectral simulation using a quasidiabatic Hamiltonian H d comprised of polynomials through 4th order (thereby extending conventional quadratic expansions), is compared to both the experimental spectrum and a standard Franck-Condon (adiabatic) simulation. The quartic H d is far superior to the quadratic H d , reproducing the main features of the experimental spectrum and allowing for their subsequent assignment. The contributions from excited anion states successfully reproduce the observed vibronic transitions to the red of the assigned band origin of the neutral species. The algorithmic extensions required for the determination of these hot band contributions to the total spectrum are discussed. Convergence of the spectral envelope with respect to the vibronic basis, including both the principal and hot bands, required more than 10 9 terms.

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“…3 26 ). See also Roche (1990) and Kupka and Cribb (1986). A common feature of most spectral intensity calculations is the use of ad hoc model potentials that include one or two degrees of freedom.…”

Section: Polyatomic Moleculesmentioning

confidence: 99%