General methodology in two dimensions for classical simulation of reactive and nonreactive events onab initio potential energy surfaces

Salazar, Michael R.; Bell, Richard L.

doi:10.1002/(sici)1096-987x(199810)19:13<1431::aid-jcc1>3.0.co;2-r

Cited by 9 publications

(12 citation statements)

References 13 publications

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“…28,30,31,[34][35][36][37] However, an essential component of the current interpolation is that it gives the correct trajectory for the specified initial condition. In future work it would be of interest to compare the computational efficiency of our interpolation scheme with the other proposed schemes, given the requirement they give the correct trajectory.…”

Section: Discussionmentioning

confidence: 99%

“…In addition, the possibility of using ab initio points, from previous integration steps of the current trajectory and those from previous trajectories in the ensemble, to interpolate a locally accurate PES for the immediate integration step, without additional ab initio calculations, should also be investigated. 66 The interpolation schemes proposed in earlier work 28,[34][35][36][37] should be considered, but as discussed above it is important for the interpolation scheme to give the correct trajectory for the specified initial condition.…”

Section: Discussionmentioning

confidence: 99%

“…[25][26][27] A number of different algorithms have been presented for developing analytic PESs by interpolating ab initio data points. [28][29][30][31][32][33][34][35][36][37] Ischtwan and Collins have proposed 28 and used extensively 29 a Shepherd interpolation scheme. In recent work 30 this method has been modified by using Bayesian analysis to define confidence regions for the interpolation.…”

Section: Introductionmentioning

confidence: 99%

“…Ho and Rabitz 31 proposed an interpolation procedure within the framework of a reproducing kernel Hilbert space, and this method has been used by Schatz and co-workers 32,33 in chemical dynamics simulations. Salazar and co-workers 34,35 have proposed a method similar to that of Collins and co-workers, [28][29][30] but different in the definition of the local fitting region and the interpolation. Eckert and Werner 36 have proposed a least-square interpolation scheme, related to the method of Collins and co-workers, but different in that it retains strict locality in a rectangular grid.…”

Section: Introductionmentioning

confidence: 99%

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Direct dynamics simulations using Hessian-based predictor-corrector integration algorithms

Lourderaj

Song²,

Windus³

et al. 2007

The Journal of Chemical Physics

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In previous research [ J. Chem. Phys.111, 3800 (1999)] a Hessian-based integration algorithm was derived for performing direct dynamics simulations. In the work presented here, improvements to this algorithm are described. The algorithm has a predictor step based on a local second-order Taylor expansion of the potential in Cartesian coordinates, within a trust radius, and a fifth-order correction to this predicted trajectory. The current algorithm determines the predicted trajectory in Cartesian coordinates, instead of the instantaneous normal mode coordinates used previously, to ensure angular momentumconservation. For the previous algorithm the corrected step was evaluated in rotated Cartesian coordinates. Since the local potential expanded in Cartesian coordinates is not invariant to rotation, the constants of motion are not necessarily conserved during the corrector step. An approximate correction to this shortcoming was made by projecting translation and rotation out of the rotated coordinates. For the current algorithm unrotated Cartesian coordinates are used for the corrected step to assure the constants of motion are conserved. An algorithm is proposed for updating the trust radius to enhance the accuracy and efficiency of the numerical integration. This modified Hessian-based integration algorithm, with its new components, has been implemented into the VENUS/NWChem software package and compared with the velocity-Verlet algorithm for the H2CO→H2+CO, O3+C3H6, and F−+CH3OOH chemical reactions. KeywordsInterpolation, Ab initio calculations, Trajectory models, Electronic structure, Angular momentum Disciplines Chemistry CommentsThe following article appeared in Journal of Chemical Physics 126 (2007) In previous research ͓J. Chem. Phys. 111, 3800 ͑1999͔͒ a Hessian-based integration algorithm was derived for performing direct dynamics simulations. In the work presented here, improvements to this algorithm are described. The algorithm has a predictor step based on a local second-order Taylor expansion of the potential in Cartesian coordinates, within a trust radius, and a fifth-order correction to this predicted trajectory. The current algorithm determines the predicted trajectory in Cartesian coordinates, instead of the instantaneous normal mode coordinates used previously, to ensure angular momentum conservation. For the previous algorithm the corrected step was evaluated in rotated Cartesian coordinates. Since the local potential expanded in Cartesian coordinates is not invariant to rotation, the constants of motion are not necessarily conserved during the corrector step. An approximate correction to this shortcoming was made by projecting translation and rotation out of the rotated coordinates. For the current algorithm unrotated Cartesian coordinates are used for the corrected step to assure the constants of motion are conserved. An algorithm is proposed for updating the trust radius to enhance the accuracy and efficiency of the numerical integration. This modified Hessian-based integration algorit...

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Direct dynamics simulations using Hessian-based predictor-corrector integration algorithms

Lourderaj

Song²,

Windus³

et al. 2007

The Journal of Chemical Physics

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“…To that end, we investigated interpolation from points of the mesh that constitute a simplex containing the point of interest, an approach already applied to some lower-dimensional systems. 27,28 Compared to Shepard interpolation, the downside of this approach is the necessity to generate a triangulation for the mesh, whose size grows very fast with the number of dimensions, 29 but the upside is the logarithmic scaling of the interpolation procedure with the number of mesh points as well as an extra order of accuracy for a given number of derivatives available at the mesh points. In comparison to the method of Ref.…”

Section: Introductionmentioning

confidence: 99%

A combined on-the-fly/interpolation procedure for evaluating energy values needed in molecular simulations

Karandashev

Vaníček

2019

The Journal of Chemical Physics

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We propose an algorithm for molecular dynamics or Monte Carlo simulations that uses an interpolation procedure to estimate potential energy values from energies and gradients evaluated previously at points of a simplicial mesh. We chose an interpolation procedure which is exact for harmonic systems and considered two possible mesh types: Delaunay triangulation and an alternative anisotropic triangulation designed to improve performance in anharmonic systems. The mesh is generated and updated on the fly during the simulation. The procedure is tested on two-dimensional quartic oscillators and on the path integral Monte Carlo evaluation of HCN/DCN equilibrium isotope effect.

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On using low-order Hermite interpolation in `direct dynamics' calculations of vibrational energies using the code `MULTIMODE'

Carter

Bowman

Braams

2001

Chemical Physics Letters

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General methodology in two dimensions for classical simulation of reactive and nonreactive events onab initio potential energy surfaces

Cited by 9 publications

References 13 publications

Direct dynamics simulations using Hessian-based predictor-corrector integration algorithms

Direct dynamics simulations using Hessian-based predictor-corrector integration algorithms

A combined on-the-fly/interpolation procedure for evaluating energy values needed in molecular simulations

On using low-order Hermite interpolation in `direct dynamics' calculations of vibrational energies using the code `MULTIMODE'

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