Nonadiabatic unimolecular reactions of polyatomic molecules

Desouter-Lecomte, Michèle; Dehareng, Dominique; Leyh‐Nihant, B.; Praet, Marie-Thérèse; Lorquet, Andrée; Lorquet, Jean-Claude

doi:10.1021/j100248a006

Cited by 107 publications

(63 citation statements)

References 4 publications

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“…We now introduce a pair of mass-weighted rectilinear coordinates Q x 1 and Q x 2 that correspond to the generalization of the concept of a first-order branching space, i.e., branching plane, [33][34][35][36] to a nondegenerate case. The pseudobranchingplane directions coincide in both adiabatic and diabatic pictures, as shown in Eqs.…”

Section: ͑3͒mentioning

confidence: 99%

Automatic generation of active coordinates for quantum dynamics calculations: Application to the dynamics of benzene photochemistry

Lasorne¹,

Sicilia²,

Bearpark³

et al. 2008

The Journal of Chemical Physics

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A new practical method to generate a subspace of active coordinates for quantum dynamics calculations is presented. These reduced coordinates are obtained as the normal modes of an analytical quadratic representation of the energy difference between excited and ground states within the complete active space self-consistent field method. At the Franck-Condon point, the largest negative eigenvalues of this Hessian correspond to the photoactive modes: those that reduce the energy difference and lead to the conical intersection; eigenvalues close to 0 correspond to bath modes, while modes with large positive eigenvalues are photoinactive vibrations, which increase the energy difference. The efficacy of quantum dynamics run in the subspace of the photoactive modes is illustrated with the photochemistry of benzene, where theoretical simulations are designed to assist optimal control experiments.

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Section: ͑3͒mentioning

confidence: 99%

Automatic generation of active coordinates for quantum dynamics calculations: Application to the dynamics of benzene photochemistry

Lasorne¹,

Sicilia²,

Bearpark³

et al. 2008

The Journal of Chemical Physics

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“…(But take note that the level crossing probability is zero when the initial velocities are zero or when the classical pathway goes across the ci. This is evident from Nikitin's expression for a ci level crossing probability [35,36], shown above in equation (46) . )…”

Section: A Lindblad-type Formalism For CImentioning

confidence: 94%

“…An analogous semi-classical formula for the passage across a ci was obtained by Nikitin [35]. Later developments were summarized in [36]. In a simplified form the expression of [35] for the asymptotic probability of transfer between the two diabatic states in a 2 -dimensional space (x, y) can be written as…”

Section: Descent Across a Conical Intersectionmentioning

confidence: 99%

A “square-root” method for the density matrix and its applications to Lindblad operators

Yahalom

Englman

2006

Physica A: Statistical Mechanics and its Applications

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The evolution of open systems, subject to both Hamiltonian and dissipative forces, is studied by writing the nm element of the time (t) dependent density matrix in the formThe so called "square root factors", the γ(t)'s, are non-square matrices and are averaged over A systems (α) of the ensemble. This square-root description is exact. Evolution equations are then postulated for the γ(t) factors, such as to reduce to the Lindblad-type evolution equations for the diagonal terms in the density matrix. For the off-diagonal terms they differ from the Lindblad-equations. The "square root factors" γ(t) are not unique and the equations for the γ(t)'s depend on the specific representation chosen. Two criteria can be suggested for fixing the choice of γ(t)'s one is simplicity of the resulting equations and the other has to do with the reduction of the difference between the γ(t) formalism and the Lindblad-equations. When the method is tested on cases which have been previously treated by other methods, our results agree with them. Examples chosen are (i) molecular systems, such that are either periodically driven 1 near level degeneracies, for which we calculate the decoherence occurring in multiple Landau-Zener transition, or else when undergoing descent around conical intersections in the potential surfaces, (ii) formal dissipative systems with Lindblad-type operators representing either a non-Markovian process or a two-state system coupled to bosons.Attractive features of the present factorization method are complete positivity, the no higher than linear increase of the implementation effort with the number of states involved and the introduction of randomness only at the start of the process.

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“…Moreover, the adequacy of the TSH method to describe nonadiabatic effects has been the subject of many investigations. [37][38][39] It has been shown to underestimate the relevant nonadiabatic transition probabilities when compared with exact quantum calculations. 40,41 In particular, Takayanagi et al 41 have studied the nonadiabatic (D + H 2 ) + reaction and concluded that the discrepancy between TSH and quantum results is due to the fact that nonadiabatic surface hopping takes place away from the crossing seam.…”

Section: Trajectory Surface Hopping Methodmentioning

confidence: 99%

Li + Li₂ Dissociation Reaction Using the Self-Consistent Potential and Trajectory Surface Hopping Methods

2002

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Self-consistent potential and trajectory surface hopping methods have been applied to study the Li + Li 2 dissociation reaction. Both methods fall into the classical trajectory methodology, with batches of 5000 trajectories being run over the translational energy range 25 e E tr e 100 kcal mol -1 keeping the internal state of Li 2 fixed at (V ) 0, j ) 10). The effect of vibrational excitation has also been studied by running additional sets of trajectories for E tr ) 25 kcal mol -1 with (V ) 10, j ) 10) and (V ) 20, j ) 10). All dissociative cross sections have been calculated using realistic double many-body expansion potential energy surfaces. The importance of nonadiabatic effects is investigated.

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Nonadiabatic unimolecular reactions of polyatomic molecules

Cited by 107 publications

References 4 publications

Automatic generation of active coordinates for quantum dynamics calculations: Application to the dynamics of benzene photochemistry

Automatic generation of active coordinates for quantum dynamics calculations: Application to the dynamics of benzene photochemistry

A “square-root” method for the density matrix and its applications to Lindblad operators

Li + Li₂ Dissociation Reaction Using the Self-Consistent Potential and Trajectory Surface Hopping Methods

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Nonadiabatic unimolecular reactions of polyatomic molecules

Cited by 107 publications

References 4 publications

Automatic generation of active coordinates for quantum dynamics calculations: Application to the dynamics of benzene photochemistry

Automatic generation of active coordinates for quantum dynamics calculations: Application to the dynamics of benzene photochemistry

A “square-root” method for the density matrix and its applications to Lindblad operators

Li + Li2 Dissociation Reaction Using the Self-Consistent Potential and Trajectory Surface Hopping Methods

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Li + Li₂ Dissociation Reaction Using the Self-Consistent Potential and Trajectory Surface Hopping Methods