Bidimensional tunneling splitting in the Ã 1B2 and X̃ 1A1 states of tropolone

Paz, Juan J.; Moreno, Miquel; Lluch, José M.

doi:10.1063/1.469647

Cited by 58 publications

(16 citation statements)

References 45 publications

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“…As the sudden straight line paths are expected to be the most probable reaction mechanism yielding the highest rates, the LCG3 tunneling probability has been used for this estimate. However, if more precise information, such as mode-specific splittings, are desired, other approaches to obtain tunneling-splittings have to be applied. ,− …”

Section: Methodsmentioning

confidence: 99%

Toward Elimination of Discrepancies between Theory and Experiment: Double Proton Transfer in Dimers of Carboxylic Acids

Loerting

Liedl

1998

J. Am. Chem. Soc.

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We present for the first time a fully ab initio dual-level reaction path dynamics calculation of the synchronous proton exchange in carboxylic acid dimers that is consistent with a wide variety of experimental findings, such as reaction rates k, tunneling splittings ∆ 0 , apparent activation energy curves E a (T), crossover temperatures T c and kinetic isotope effects. For the dimer of formic acid, we find k ) 2.5 × 10 9 s -1 (300 K), with an associated ground-state splitting ∆ 0 ) 0.09 cm -1 . Similar to experiments with crystals of benzoic acid dimers, we obtain T c ) 100 K as the border between the high-and low-temperature regions of the rate constant. More than half of the hydrogenic motion occurs by quantum tunneling. The total hydrogenic motion of about 0.7 Å coincides perfectly with neutron scattering results. In contrast to all previous studies, the experimental activation energy curves can be reproduced reasonably by inclusion of tunneling from the vibrational ground state for three different isotopic species. Remaining small discrepancies from experiments with benzoic acid dimers in the coherent limit (k ≈ 10 10 s -1 (300 K), ∆ 0 ) 0.32 cm -1 ) are explained mainly by vibrational excitation of normal modes coupled to the reaction path and the higher reaction barrier in the formic acid dimer, i.e., a difference of 1.0 kcal/mol at the B3LYP/6-31+G(d) level of theory. Closer inspection of the normal modes involved reveals that the excitation of the interdimer stretch and the OH stretch could enhance the rates and enlarge the splittings considerably by shortening the O-O distance. The reaction path with a total of 103 Hessian calculations has been obtained at the B3LYP/6-31+G(d) level of theory and corrected to a G2* reaction barrier and MP2/6-31G(d,p) frequencies at the stationary points stemming from a recent excellent benchmark study by Kim [Kim, Y.

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Section: Methodsmentioning

confidence: 99%

Toward Elimination of Discrepancies between Theory and Experiment: Double Proton Transfer in Dimers of Carboxylic Acids

Loerting

Liedl

1998

J. Am. Chem. Soc.

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“…The computationally demanding aspect of constructing a reaction surface, as opposed to the path, is the calculation of the Hessian along the two versus one DOF. The additional computational work is often needed as Lluch and co-workers have demonstrated the importance of the multidimensional nature of proton-transfer reactions using bidimensional models of proton transfer in tropolone 6 and malonaldehyde. 24 In this work, we develop a reduced dimensional model of tunneling splittings in FAD that includes 8 A 1g and B 3g normal modes of the D 2h transition state structure.…”

Section: Introductionmentioning

confidence: 99%

Symmetric Double Proton Tunneling in Formic Acid Dimer: A Diabatic Basis Approach

2007

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A model of double proton tunneling in formic acid dimer is developed using a reaction surface Hamiltonian. The surface includes the symmetric OH stretch plus the in-plane stretch and bend interdimer vibrations. The surface Hamiltonian is coupled to a bath of five A 1g and B 3g normal modes obtained at the D 2h transition state structure. Eigenstates are calculated using Davidson and block-Davidson iterative methods. Strong mode specific effects are found in the tunneling splittings for the reaction surface, where splittings are enhanced upon excitation of the interdimer bend motion. The results are interpreted within the framework of a diabatic representation of reaction surface modes. The splitting patterns observed for the reaction surface eigenstates are only slightly modified upon coupling to the bath states. Splitting patterns for the bath states are also determined. It is found that predicting these splittings is greatly complicated by subtle mixings with the inter-dimer bend states.

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“…In this section we show how the action-based LD can be used to reveal the phase space structures of a 2 DoF Hamiltonian system. In particular, we consider a 2 DoF Hamiltonian model that has been used to study proton transfer and isomerization reactions in chemistry [31]. The Hamiltonian function is given as the sum of kinetic plus potential energies of the form:…”

Section: A Two Dof Hamiltonian Modelmentioning

confidence: 99%

Lagrangian Descriptors and the Action Integral of Classical Mechanics

García-Garrido,

Wiggins

2022

Preprint

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In this paper we bring together the method of Lagrangian descriptors and the principle of least action, or more precisely, of stationary action, in both deterministic and stochastic settings. In particular, we show how the action can be used as a Lagrangian descriptor. This provides a direct connection between Lagrangian descriptors and Hamiltonian mechanics, and we illustrate this connection with benchmark examples.

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Bidimensional tunneling splitting in the Ã 1B2 and X̃ 1A1 states of tropolone

Cited by 58 publications

References 45 publications

Toward Elimination of Discrepancies between Theory and Experiment: Double Proton Transfer in Dimers of Carboxylic Acids

Toward Elimination of Discrepancies between Theory and Experiment: Double Proton Transfer in Dimers of Carboxylic Acids

Symmetric Double Proton Tunneling in Formic Acid Dimer: A Diabatic Basis Approach

Lagrangian Descriptors and the Action Integral of Classical Mechanics

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