Full Iterative Solution of the Two-Dimensional Master Equation for Thermal Unimolecular Reactions

Jeffrey, Stephen; Gates, K. E.; Smith, Sean C.

doi:10.1021/jp953430y

Cited by 51 publications

(73 citation statements)

References 46 publications

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“…The code was allowed to run on in this instance to show that both routines produced the same rate coefficients. Jeffrey et al 21 noted that at elevated temperatures the Nesbet calculation is significantly less efficient. To test the efficiency of the RQI algorithm a calculation was performed at 1500 K and a bath concentration of 10 15 molecules cm y1 .…”

Section: Results and Conclusionmentioning

confidence: 99%

“…The basis of this transform is v the rigid rotor harmonic oscillator approximation. Jeffrey et al 21 discussed the difficulties with the straightforward application of this transform, especially in connection with detailed balance; but because our goal is to construct an approximate solution, and a starting point for more elaborate iterative techniques, the separation will be adopted here. For a spherical top it allows the total energy to be written as…”

Section: Diffusion Equation Approximationmentioning

confidence: 99%

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Application of inverse iteration to 2-dimensional master equations

et al. 1997

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Recent developments in unimolecular theory have placed great emphasis on the role played by angular momentum in determining the details of the dependence of the rate coefficient on pressure and temperature. The natural way to investigate these dependencies is through the master equation formulation, where the rate coefficient is recovered as the eigenvalue of the smallest magnitude of the spatial operator. Except for very simple cases, the master equation must be solved with numerical methods. For the 2‐dimensional master equation this leads to large sparse matrices and correspondingly lengthy computational times in order to determine the eigenvalue of the least magnitude. A reformulation of the problem in terms of a diffusion equation approximates the final matrix with a narrow banded matrix that can easily be factored using a variation of Gaussian elimination. The 2‐dimensional master equation can then be solved with inverse iteration, which rapidly converges to the desired eigenpair. This method can be up to 10 times faster than conventional iterative algorithms for finding the desired eigenpair. © 1997 John Wiley & Sons, Inc. J Comput Chem 18:1004–1010, 1997

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Section: Results and Conclusionmentioning

confidence: 99%

Section: Diffusion Equation Approximationmentioning

confidence: 99%

Application of inverse iteration to 2-dimensional master equations

et al. 1997

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“…The 2DME includes a kernel for collisional energy transfer transitions that depends on both variables. Although such treatments were first demonstrated decades ago [39][40][41][42][43] and exist in improved forms today, [39][40][41][42][43][44][45][46] they require input parameters that involve extensive additional calculations. 47 Instead of an explicit 2DME, most practical ME calculations utilize various methods for reducing the 2DME to one dimension.…”

Section: F I G U R Ementioning

confidence: 99%

Semiclassical transition state theory/master equation kinetics of HO + CO: Performance evaluation

Barker

Stanton

Nguyen

2020

Int J of Chemical Kinetics

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“…Using the same k(E,J) data resolution a similar full pressure dependent solution ͑incorporating effects of collisions͒ would involve the solution of a 14 000 ϫ14 000 matrix equation for each pressure. This sort of more sophisticated calculation 9,28 is unnecessary for our present purposes but worthy of future effort.…”

Section: A Solutionmentioning

confidence: 99%

Prediction of absolute rate coefficients and product branching ratios for the C(3P)+allene reaction system

Schranz

Smith

Mebel

et al. 2002

The Journal of Chemical Physics

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An ab initio/Rice-Ramsperger-Kassel-Marcus prediction of rate constant and product branching ratios for unimolecular decomposition of propen-2-ol and related H + CH 2 COHCH 2 reaction J. Chem. Phys. 129, 234301 (2008) Complex chemical reactions in the gas phase can be decomposed into a network of elementary ͑e.g., unimolecular and bimolecular͒ steps which may involve multiple reactant channels, multiple intermediates, and multiple products. The modeling of such reactions involves describing the molecular species and their transformation by reaction at a detailed level. Here we focus on a detailed modeling of the C( 3 P)ϩallene (C 3 H 4 ) reaction, for which molecular beam experiments and theoretical calculations have previously been performed. In our previous calculations, product branching ratios for a nonrotating isomerizing unimolecular system were predicted. We extend the previous calculations to predict absolute unimolecular rate coefficients and branching ratios using microcanonical variational transition state theory ͑-VTST͒ with full energy and angular momentum resolution. Our calculation of the initial capture rate is facilitated by systematic ab initio potential energy surface calculations that describe the interaction potential between carbon and allene as a function of the angle of attack. Furthermore, the chemical kinetic scheme is enhanced to explicitly treat the entrance channels in terms of a predicted overall input flux and also to allow for the possibility of redissociation via the entrance channels. Thus, the computation of total bimolecular reaction rates and partial capture rates is now possible.

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Full Iterative Solution of the Two-Dimensional Master Equation for Thermal Unimolecular Reactions

Cited by 51 publications

References 46 publications

Application of inverse iteration to 2-dimensional master equations

Application of inverse iteration to 2-dimensional master equations

Semiclassical transition state theory/master equation kinetics of HO + CO: Performance evaluation

Prediction of absolute rate coefficients and product branching ratios for the C(3P)+allene reaction system

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