# [TMJ] Calculating RRKM Rate Constants from Vibrational Frequencies

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New THE MATHEMATICA JOURNAL article:

## Calculating RRKM Rate Constants from Vibrational Frequencies and Their Dynamic Interpretation

by ADAM C. MANSELL, DAVID J. KAHLE, DARRIN J. BELLERT

ABSTRACT: Rice–Rampsberger–Kassel–Marcus (RRKM) theory calculates an energy-dependent microcanonical unimolecular rate constant for a chemical reaction from a sum and density of vibrational quantum states. This article demonstrates how to program the Beyer–Swinehart direct count of the sum and density of states for harmonic oscillators, as well as the Stein–Rabinovitch extension for anharmonic oscillators. Microcanonical rate constants are calculated for the decomposition of vinyl cyanide ( $C_3 H_3 N$) into $HCN$, $HNC$ and $HCCH$ as an example.