Constraining the Mechanism and Kinetics of OH + NO 2 Using the Multiple-Well Master Equation Jieyuan Zhang † and Neil M. Donahue * 1 Geometry Calculation Results Table 1: Cartesian coordinates in ˚ A and vibrational frequencies in cm −1 calculated at B3LYP/6-31+G(d,p) level of theory by Gaussian 98 for HONO 2 isotopic scrambling transition state (TS3, from H( 18 O)NOO to HON( 18 O)O) Cartesian Coordinates ( ˚ A) At. x y z N -0.153299 -0.000080 -0.000008 O -1.344654 -0.000036 0.000003 O 0.651522 -1.033708 0.000001 O 0.651378 1.033785 0.000001 H 1.407124 0.000224 0.000010 Harmonic Vibrational Frequencies (cm −1 ) -1918.0010 614.0678 724.0505 840.2941 1063.4287 1097.9186 1348.3938 1683.1009 2332.6789 2 Master Equation Theory Building a multiple-well master equation within the matrix formalism requires extensive attention to detail and very large matrices. What follows is an outline of the essential details. 2.1 Master equation formalism The matrix form of the time-dependent population N(t) is: dN dt =[ω(P − I) −  K i ]N ≡ MN (1) in which M = ω(P − I) − ∑ K i , P is the normalized energy transfer matrix, I is the unit matrix, ω is the collision frequency, and K i is a matrix of unimolecular rate constants for the ith channel. The time-dependent solution of equation 1 is N(t)= U exp(Λt) U −1 N(0) (2) where N(0) is the initial population vector of N, U is the right eigenvector matrix of M and Λ is the diagonal matrix of eigenvalues of M. ∗ Carnegie Mellon University: nmd@andrew.cmu.edu † Carnegie Mellon University 1