dorsal/arxiv
View SchemaPath-integral virial estimator for reaction rate calculation based on the quantum instanton approximation
| Authors | Sandy Yang, Takeshi Yamamoto, William H. Miller |
|---|---|
| Categories | |
| ArXiv ID | physics/0511146 |
| URL | https://arxiv.org/abs/physics/0511146 |
| DOI | 10.1063/1.2171693 |
Abstract
The quantum instanton approximation is a type of quantum transition state theory that calculates the chemical reaction rate using the reactive flux correlation function and its low order derivatives at time zero. Here we present several path-integral estimators for the latter quantities, which characterize the initial decay profile of the flux correlation function. As with the internal energy or heat capacity calculation, different estimators yield different variances (and therefore different convergence properties) in a Monte Carlo calculation. Here we obtain a virial-type estimator by using a coordinate scaling procedure rather than integration by parts, which allows more computational benefits. We also consider two different methods for treating the flux operator, i.e., local-path and global-path approaches, in which the latter achieves a smaller variance at the cost of using second-order potential derivatives. Numerical tests are performed for a one-dimensional Eckart barrier and a model proton transfer reaction in a polar solvent, which illustrates the reduced variance of the virial estimator over the corresponding thermodynamic estimator.
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"abstract": "The quantum instanton approximation is a type of quantum transition state\ntheory that calculates the chemical reaction rate using the reactive flux\ncorrelation function and its low order derivatives at time zero. Here we\npresent several path-integral estimators for the latter quantities, which\ncharacterize the initial decay profile of the flux correlation function. As\nwith the internal energy or heat capacity calculation, different estimators\nyield different variances (and therefore different convergence properties) in a\nMonte Carlo calculation. Here we obtain a virial-type estimator by using a\ncoordinate scaling procedure rather than integration by parts, which allows\nmore computational benefits. We also consider two different methods for\ntreating the flux operator, i.e., local-path and global-path approaches, in\nwhich the latter achieves a smaller variance at the cost of using second-order\npotential derivatives. Numerical tests are performed for a one-dimensional\nEckart barrier and a model proton transfer reaction in a polar solvent, which\nillustrates the reduced variance of the virial estimator over the corresponding\nthermodynamic estimator.",
"arxiv_id": "physics/0511146",
"authors": [
"Sandy Yang",
"Takeshi Yamamoto",
"William H. Miller"
],
"categories": [
"physics.chem-ph"
],
"doi": "10.1063/1.2171693",
"title": "Path-integral virial estimator for reaction rate calculation based on the quantum instanton approximation",
"url": "https://arxiv.org/abs/physics/0511146"
},
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