1996
DOI: 10.1021/jp953430y
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Full Iterative Solution of the Two-Dimensional Master Equation for Thermal Unimolecular Reactions

Abstract: The application of the Nesbet algorithm to the full iterative solution of the two-dimensional master equation for thermal unimolecular reactions is presented. This leads to an efficient algorithm for computing thermal rate coefficients in the falloff regime for reactions such as simple fission dissociations, radical-radical recombinations, and ion-molecule reactions wherein microcanonical dissociation rate coefficients are sensitive to both the vibrational energy and the angular momentum of the excited species. Show more

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Cited by 51 publications
(73 citation statements)
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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%
See 1 more Smart Citation
“…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%
“…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%
“…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%