An efficient microcanonical sampling method

Séverin, Éric; Freasier, B.C.; Hamer, N.D.; Jolly, D.L.; Nordholm, Sture

doi:10.1016/0009-2614(78)80363-7

Cited by 92 publications

(38 citation statements)

References 6 publications

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“…Thus, if the approximation is made that B(q) =C(q) (i.e., a prolate top), one has from Eq. (51) that B*(q,~) =B(q), leading directly to (57) and…”

Section: Xsin-2[e*-v(q)-b*(q;)j(j+1)]1i2mentioning

confidence: 99%

Angular-momentum resolution in transitional-mode state counting for loose transition states

Smith

1992

The Journal of Chemical Physics

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Microscopic rate coefficients in reactions with flexible transition states: Analysis of the transitional-mode sum of states J. Chem. Phys. 95, 3404 (1991) The classical evaluation of the angular-momentum-resolved sum of states for the loosely hindered rotational degrees of freedom, i.e., the transitional modes, in loose transition states occurring in unimolecular dissociation, radical-radical recombination, ion-molecule, and other collision-complex-forming bimolecular reactions is considered. Exact analytic expressions are derived for the momentum-space volume available to the transitional modes at a given configuration q with energy E and total angular momentum vector J. The results are completely general with respect to the type of fragment rotors involved and their relative orientation within the loose transition state, and constitute a dramatically simplified technique for J-resolved classical state counting. The utility of the expressions lies in the fact that they obviate the necessity of numerical integration over the system's momentum space, thus reducing substantially the computational effort involved in the exact evaluation of the transitional-mode sum of states. The present results verify expressions which were postulated to apply to arbitrary configurations in our earlier work.

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“…Thus, if the approximation is made that B(q) =C(q) (i.e., a prolate top), one has from Eq. (51) that B*(q,~) =B(q), leading directly to (57) and…”

Section: Xsin-2[e*-v(q)-b*(q;)j(j+1)]1i2mentioning

confidence: 99%

Angular-momentum resolution in transitional-mode state counting for loose transition states

Smith

1992

The Journal of Chemical Physics

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“…Microcanonical sampling enables one to efficiently sample the initial states of the target molecule of equal energy to obtain the trajectory initial conditions necessary to perform the MD/QCT calculations. 13 For the DSMC simulations, the reaction probability of a chemical reaction as a function of translational energy, E tr , and molecular internal energy, E int , is used. The reaction cross section, r , is obtained by evaluating whether a O + HCl collision ends in a chemical reaction by…”

Section: A Md/qct Reaction Probabilitymentioning

confidence: 99%

Chemical reaction modeling for hypervelocity collisions between O and HCl

2007

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The sensitivity of a rarefied-to-transitional flow to the fidelity of the chemical reaction model is investigated for a new molecular dynamics/quasiclassical trajectory (MD/QCT)-derived model and compared with the widely used total collision energy (TCE) model of Bird. For hypervelocity collisions that occur in the space environment, it is not clear, a priori, that the TCE model will provide reasonable results for the required high energy range and, particularly, if strong favoring of the reaction among different forms of reactant energy occurs. In fact, in previous work, the TCE model, using available Arrhenius parameters, has been found, for these flow conditions, to give unphysical probabilities. A chemical reaction model, suitable for use in the direct simulation Monte Carlo (DSMC) method, is developed to simulate the hypervelocity collisions of O(P3)+HCl(Σ+1)→OH(Π2)+Cl(P2), an example of an important reaction in high-altitude atmospheric-jet interactions. The model utilizes the MD/QCT method with a new benchmark triplet A″ surface. Since the modeling of chemical reactions in DSMC simulations requires the use of a reaction probability, the adequacy of the overall collision cross section, usually modeled by the variable hard sphere (VHS) model, is also considered. To obtain an accurate collision cross section, the approach of Tokumasu and Matsumoto was used in the MD/QCT method with the aforementioned potential energy surface. Energy transfer between the target HCl translational and internal energy modes was investigated and it was found that the variation of the inelastic cross section has a negligible effect on the transport cross section. Therefore, a MD/QCT VHS equivalent collision cross section was obtained and along with the MD/QCT reaction cross sections were utilized in the full DSMC calculation of the flow field. It was found that for a low enthalpy reaction, in hypervelocity collisions, the TCE model with accurate Arrhenius rates appears to agree well with the rigorous MD/QCT calculations which shows that the reaction does not exhibit strong favoring.

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“…For the case of spectral densities, the Beyer-Swinehart 36 and Stein-Rabinovitch 5 algorithms provide exact, very fast solutions for separable Hamiltonians, and monte carlo integration in phase space [24][25][26][27][28][29][30][31] provides an efficient and classically exact solution for nonseparable Hamiltonians. It is desirable and, given the difficulty of a full quantum trace, necessary to take advantage of the accuracy of such approximate methods in formulating an improved solution to the quantum problem.…”

Section: The Spectral Densitymentioning

confidence: 99%

“…͑2͒ for multidimensional nonseparable Hamiltonians by Monte Carlo integration is a feasible objective for moderately sized molecules. The integration is made substantially easier by analytic evaluation of the momentumspace integrals 24 and has been applied and extended by a number of authors. [25][26][27][28][29][30][31] For separable Hamiltonians, the evaluation of the trace is dramatically simplified, since the multidimensional integral reduces to a series of convolutions of one-dimensional densities, which are themselves trivially evaluated.…”

Section: Introductionmentioning

confidence: 99%

On the calculation of absolute spectral densities

Smith

Jeffrey

1996

The Journal of Chemical Physics

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On the relation of protein dynamics and exciton relaxation in pigment-protein complexes: An estimation of the spectral density and a theory for the calculation of optical spectra J. Chem. Phys. 116, 9997 (2002) A new method of calculating the absolute spectral density of a Hamiltonian operator is derived and discussed. The spectral density is expressed as the solution of an integral equation in which the kernel is a renormalized one-sided energy correlation function of the full microcanonical density operator and a microcanonical density operator for a reference Hamiltonian. The integral operator associated with this equation transforms a known spectral density function for the reference Hamiltonian into the spectral density of the full Hamiltonian. The integral equation, by virtue of its formulation in energy space, is inherently one-dimensional and offers no storage difficulties, and the elements of its kernel may be computed by applying the Lanczos algorithm to randomly selected eigenfunctions of the reference Hamiltonian. This spectral density correlation method offers a number of advantages over variational methods. In particular, it has the potential for overcoming the hitherto largely insurmountable problem of tracing over a multidimensional Hilbert space in order to compute the spectral density of a nonseparable molecular Hamiltonian.

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An efficient microcanonical sampling method

Cited by 92 publications

References 6 publications

Angular-momentum resolution in transitional-mode state counting for loose transition states

Angular-momentum resolution in transitional-mode state counting for loose transition states

Chemical reaction modeling for hypervelocity collisions between O and HCl

On the calculation of absolute spectral densities

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