Reaction path Hamiltonian for polyatomic molecules

Miller, William H.; Handy, Nicholas C.; Adams, John E.

doi:10.1063/1.438959

Cited by 1,430 publications

(970 citation statements)

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“…Here, F ) 3N -6 is the number of vibrational degrees of freedom of a nonrotating N-atom system, and the Fth degree of freedom is defined to be the reaction coordinate s. For zero total angular momentum, the RPH is Here, ω k (s) is the frequency of mode k, and B k,l is the coupling, defined as where L k (s) (k ) 1, ..., F -1) and L F (s) denote the kth normal mode vector and the normalized gradient vector, respectively, at s. The squared frequencies ω k (s) 2 and the normal mode vectors L k (s) (k ) 1, ..., F -1) are the eigenvalues and eigenvectors, respectively, of the Hessian matrix at s from which infinitesimal translations and rotations and the gradient vector L F (s) have been projected. Note that B k,l (s) (k,l ) 1, ..., F -1) are the coupling elements between normal modes Q k and Q l , and B k,F (s) (k ) 1, ..., F -1) are the coupling elements between the normal mode Q k and the reaction coordinate s. As described in ref 23, the coupling elements in the denominator of the first term of eq 1 describe the effects of reaction path curvature, where the curvature is defined as…”

Section: Methodsmentioning

confidence: 99%

“…30 The MEPs were analyzed within the framework of the RPH developed by Miller, Handy, and Adams. 23 This RPH is expressed in terms of the reaction coordinate s and its conjugate momentum p s , as well as the coordinates and momenta {Q k , P k } (k ) 1, ..., F -1) of the orthogonal vibrational modes. Here, F ) 3N -6 is the number of vibrational degrees of freedom of a nonrotating N-atom system, and the Fth degree of freedom is defined to be the reaction coordinate s. For zero total angular momentum, the RPH is Here, ω k (s) is the frequency of mode k, and B k,l is the coupling, defined as where L k (s) (k ) 1, ..., F -1) and L F (s) denote the kth normal mode vector and the normalized gradient vector, respectively, at s. The squared frequencies ω k (s) 2 and the normal mode vectors L k (s) (k ) 1, ..., F -1) are the eigenvalues and eigenvectors, respectively, of the Hessian matrix at s from which infinitesimal translations and rotations and the gradient vector L F (s) have been projected.…”

Section: Methodsmentioning

confidence: 99%

“…23 This RPH characterizes the reaction in terms of motion along the MEP and vibrational motion orthogonal to this path, where the MEP is defined as the steepest-descent path in mass-weighted coordinates from the saddle point down toward reactants and toward products. The RPH depends on the potential energy, frequencies, and couplings along the MEP.…”

Section: Introductionmentioning

confidence: 99%

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Reaction Path Hamiltonian Analysis of Dynamical Solvent Effects for a Claisen Rearrangement and a Diels−Alder Reaction

Kobrak

et al. 2000

J. Phys. Chem. A

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The solvent effects for a Claisen rearrangement and a Diels-Alder reaction are investigated. Electronic structure methods are used to generate the frequencies, couplings, and curvatures along the minimum energy paths for these reactions in the gas phase and in the presence of two water molecules. The geometries and charge distributions along the minimum energy paths are analyzed to determine the structural and electrostatic roles of the water molecules. Reactive flux molecular dynamics methods based on a reaction path Hamiltonian are used to calculate the dynamical transmission coefficients, which account for recrossings of the transition state. The transmission coefficients for the Claisen rearrangement are nearly unity both in the gas phase and in the presence of two water molecules. The transmission coefficients for the Diels-Alder reaction are 0.95 and 0.89 in the gas phase and in the presence of two water molecules, respectively. These differences in the transmission coefficients are explained in terms of the locations and magnitudes of the curvature peaks along the reaction path, as well as the shape of the potential energy along the reaction coordinate near the transition state. Analysis of the dynamical trajectories provides insight into the dynamical role of the water molecules and elucidates possible reaction mechanisms.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Reaction Path Hamiltonian Analysis of Dynamical Solvent Effects for a Claisen Rearrangement and a Diels−Alder Reaction

Kobrak

et al. 2000

J. Phys. Chem. A

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“…One treats these DOF at a high level of theory, while treating more approximately the remaining DOF and the coupling of them to the reaction surface coordinates. Miller et al 22 developed the original reaction path Hamiltonian using a curvilinear minimum energy path. For hydrogen transfer reactions, however, the curvature of this path is substantial, and this curvature leads to large kinetic couplings.…”

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 an adiabatic description, one can think of the reaction as involving the passage from a local minimum of the total potential energy of the reactants through a transition state that corresponds to a saddle point of the potential energy and then down to another local minimum corresponding to the final products. The reaction is thus described classically by a reaction path, corresponding to a one-dimensional approximately decoupled manifold [209]. An approximate Hamiltonian for the system, often sufficient for studying the given reaction, can be obtained by expanding the full Hamiltonian about the reaction path and retaining quadratic terms (the small oscillation approximation).…”

Section: A Survey Of Literaturementioning

confidence: 99%

Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

2000

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The goal of the present account is to review our efforts to obtain and apply a "collective" Hamiltonian for a few, approximately decoupled, adiabatic degrees of freedom, starting from a Hamiltonian system with more or many more degrees of freedom. The approach is based on an analysis of the classical limit of quantum-mechanical problems. Initially, we study the classical problem within the framework of Hamiltonian dynamics and derive a fully self-consistent theory of large amplitude collective motion with small velocities. We derive a measure for the quality of decoupling of the collective degree of freedom. We show for several simple examples, where the classical limit is obvious, that when decoupling is good, a quantization of the collective Hamiltonian leads to accurate descriptions of the low energy properties of the systems studied. In nuclear physics problems we construct the classical Hamiltonian by means of time-dependent mean-field theory, and we transcribe our formalism to this case. We report studies of a model for monopole vibrations, of 28 Si with a realistic interaction, several qualitative models of heavier nuclei, and preliminary results for a more realistic approach to heavy nuclei. Other * Email: Giu.Dodang@th.u-psud.fr † Email: aklein@walet.physics.upenn.edu ‡ Email: Niels.Walet@umist.ac.uk 1 topics included are a nuclear Born-Oppenheimer approximation for an ab initio quantum theory and a theory of the transfer of energy between collective and non-collective degrees of freedom when the decoupling is not exact. The explicit account is based on the work of the authors, but a thorough survey of other work is included. PACS number(s): 21.60.-n, 21.60.Jz, 21.60.Ev

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Reaction path Hamiltonian for polyatomic molecules

Cited by 1,430 publications

References 29 publications

Reaction Path Hamiltonian Analysis of Dynamical Solvent Effects for a Claisen Rearrangement and a Diels−Alder Reaction

Reaction Path Hamiltonian Analysis of Dynamical Solvent Effects for a Claisen Rearrangement and a Diels−Alder Reaction

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

Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

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