Gradient extremals

Hoffman, David K.; Nord, R. S.; Ruedenberg, Klaus

doi:10.1007/bf00527704

Cited by 148 publications

(132 citation statements)

References 3 publications

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“…Quite recently several alternatives have been proposed. One method, the gradient extremal method [214,215], is tantamount to the LHA with the neglect of curvature corrections. A second proposal [216] is to use a suitably chosen straight line path of descent from the saddle point to each of the minima.…”

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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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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“…Thus, chemical reaction rates [10][11][12][13][14][15] are sensitive to energy barriers calculated for transition structures, and thermodynamic properties 16,17 depend on the accuracy of the calculated harmonic and anharmonic frequencies. 18 This demand is motivating work on ab initio methods capable of yielding the desired accuracy 4,5,[19][20][21] and the search for new methodological approaches. [22][23][24][25][26][27] Interest also continues in methods for deducing accurate potential energy functions directly from observed vibrational spectra.…”

Section: Introductionmentioning

confidence: 99%

Accurate ab initio potential energy curve of F2. III. The vibration rotation spectrum

Bytautas

Matsunaga

Nagata

et al. 2007

The Journal of Chemical Physics

134

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An analytical expression is found for the accurate ab initiopotential energy curve of the fluorine molecule that has been determined in the preceding two papers. With it, the vibrational and rotational energy levels of F2 are calculated using the discrete variable representation. The comparison of this theoretical spectrum with the experimental spectrum, which had been measured earlier using high-resolution electronic spectroscopy, yields a mean absolute deviation of about 5cm−1 over the 22 levels. The dissociation energy with respect to the lowest vibrational energy is calculated within 30cm−1 of the experimental value of 12953±8cm−1. The reported agreement of the theoretical spectrum and dissociation energy with experiment is contingent upon the inclusion of the effects of core-generated electron correlation,spin-orbit coupling, and scalar relativity. The Dunham analysis [Phys. Rev.41, 721 (1932)] of the spectrum is found to be very accurate. New values are given for the spectroscopic constants. KeywordsAb initio calculations, Dissociation energies, Polynomials, Dissociation, Electron correlation calculations Disciplines Chemistry CommentsThe following article appeared in Journal of Chemical Physics 127 (2007) An analytical expression is found for the accurate ab initio potential energy curve of the fluorine molecule that has been determined in the preceding two papers. With it, the vibrational and rotational energy levels of F 2 are calculated using the discrete variable representation. The comparison of this theoretical spectrum with the experimental spectrum, which had been measured earlier using high-resolution electronic spectroscopy, yields a mean absolute deviation of about 5 cm −1 over the 22 levels. The dissociation energy with respect to the lowest vibrational energy is calculated within 30 cm −1 of the experimental value of 12 953± 8 cm −1 . The reported agreement of the theoretical spectrum and dissociation energy with experiment is contingent upon the inclusion of the effects of core-generated electron correlation, spin-orbit coupling, and scalar relativity. The Dunham analysis ͓Phys. Rev. 41, 721 ͑1932͔͒ of the spectrum is found to be very accurate. New values are given for the spectroscopic constants.

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“…[2][3][4][5][6][7][8][9][10][11][12][13][14] Since the TS is a stationary point with a single negative Hessian eigenvalue this implies that the energy has to be maximized for one direction and minimized for all other directions. In a high-dimensional space, the direction, in which the energy has to be maximized, is difficult to determine.…”

Section: Search For a Ts Utilizing Newton Trajectoriesmentioning

confidence: 99%

“…In the latter case, the 1D search curve is implicitly in use; it has a loose connection to the gradient extremal of Ruedenberg and co-workers. [12] Other 1D search curves used in the past are NTs [13] or the gradient extremals [12,14].…”

Section: Search For a Ts Utilizing Newton Trajectoriesmentioning

confidence: 99%

Finding the Transition State of Quasi-Barrierless Reactions by a Growing String Method for Newton Trajectories: Application to the Dissociation of Methylenecyclopropene and Cyclopropane

2007

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A method for finding a transition state (TS) between a reactant minimum and a quasi-flat, high dissociation plateau on the potential energy surface is described. The method is based on the search of a growing string (GS) along reaction pathways defined by different Newton trajectories (NT). Searches with the GS-NT method always make it possible to identify the TS region because monotonically increasing NTs cross at the TS or, if not monotonically increasing, possess turning points that are located in the TS region.The GS-NT method is applied to quasi-barrierless and truly barrierless chemical reactions. Examples are the dissociation of methylenecyclopropene to acetylene and vinylidene, for which a small barrier far out in the exit channel is found, and the cycloaddition of singlet methylene and ethene, which is barrierless for a broad reaction channel with C s -symmetry reminding of a mountain cirque formed by a glacier.

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Gradient extremals

Cited by 148 publications

References 3 publications

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

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

Accurate ab initio potential energy curve of F2. III. The vibration rotation spectrum

Finding the Transition State of Quasi-Barrierless Reactions by a Growing String Method for Newton Trajectories: Application to the Dissociation of Methylenecyclopropene and Cyclopropane

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