Journal ArticleDOI
Algorithm 448: number of multiply-restricted partitions
Terry Beyer,D. F. Swinehart +1 more
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Many combinatorial enumeration problems may be expressed in terms of the numbers <italic>P<subscrpt>c</subscRpt></italic>(“m”).Abstract:
Given a positiver integer m and an ordered k-tuple c = (c1, ··· , ck) of not necessarily distinct positive integers, then any ordered k-tuple s = (s1, ··· , sk) of nonnegative integers such that m = ∑ki-1sici is said to be a partition of m restricted to c. Let Pc(m) denote the number of distinct partitions of m restricted to c. The subroutine COUNT, when given a k-tuple c and an integer n, computes an array of the values of Pc(m) for m = 1 to n. Many combinatorial enumeration problems may be expressed in terms of the numbers Pc(m). We mention two below.read more
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Current status of transition-state theory
TL;DR: In this article, the authors present an overview of the current status of transition-state theory and its generalizations, including recent improvements in available methodology for calculations on complex systems, including the interface with electronic structure theory, progress in the theory and application of transitionstate theory to condensed-phase reactions, and insight into the relation of transition state theory to accurate quantum dynamics.
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Modeling the Kinetics of Bimolecular Reactions
Antonio Fernández-Ramos,James A. Miller,Stephen J. Klippenstein,Stephen J. Klippenstein,Donald G. Truhlar +4 more
TL;DR: This review is concerned with the theoretical and computational modeling of bimolecular reactions, especially with generally applicable methods for kinetics (i.e., overall rates as opposed to detailed dynamics), and includes a basic theoretical framework that can be used for gas-phase thermal reactions, gas- phase microcanonical and state-selected reactions, and condensed-phase chemical reactions.
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Multiple‐Well, multiple‐path unimolecular reaction systems. I. MultiWell computer program suite
TL;DR: In this article, the authors present a suite of computer programs that can be used to solve the internal energy master equation for complex unimolecular reactions systems, including the effects of collisional energy transfer.
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General Time Dependent Approach to Vibronic Spectroscopy Including Franck-Condon, Herzberg-Teller, and Duschinsky Effects.
TL;DR: An effective time-dependent approach to compute vibrationally resolved optical spectra from first principles is presented for the computation of one-photon electronic spectra induced by either electric or magnetic transition dipoles or by their mutual interaction, namely absorption, emission, and circular dichroism.
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Reactions and thermochemistry of small transition metal cluster ions
TL;DR: This review discusses the reactivities and thermodynamics of small-size-specific transition metal clusters and focuses on thermodynamic information, which has not been comprehensively discussed before.
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The Kinetics of the Recombination of Methyl Radicals and Iodine Atoms
TL;DR: In this article, the steric effect of pressure on the rate of free radical recombinations is investigated. But the authors focus on two main problems, namely, the magnitude of steric effects tending to reduce the rate below that calculated by the kinetic theory of collisions, and the effect of a small probability of such a process results in a reduced chance of the formation of the activated complex and thus not every collision of radical and atom is effective in producing an active molecule.
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Accurate and Facile Approximation for Vibrational Energy‐Level Sums
G. Z. Whitten,B. S. Rabinovitch +1 more
TL;DR: In this paper, exact sums of harmonic vibrational energy-level densities for 45 molecules were obtained at various energies with a digital computer, and an improved "corresponding vibrational states" type of approximation was described.
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Dissociation and Isomerization of Vibrationally Excited Species. II. Unimolecular Reaction Rate Theory and Its Application
TL;DR: In this article, the authors compared the results obtained from the quantum RRK theory in its classical limit with those obtained from experimentally when all of the reactant oscillators are assumed effective in intramolecular energy transfer.
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Algorithm 373: Number of doubly restricted partitions [A1]
TL;DR: This algorithm is a generalization of [1] which treats the case K = 1 as a set of partitions for all L, M such that N > L > M _> 0.