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Benchmark {\em ab initio} energy profiles for the gas-phase S$_N$2 reactions Y$^-$ + CH$_3$X $\to$ CH$_3$Y + X$^-$ (X,Y = F,Cl,Br). Validation of hybrid DFT methods

The energetics of the gas-phase S$_N$2 reactions Y$^-$ + CH$_3$X $\longrightarrow$ CH$_3$Y + X$^-$ (where X,Y = F, Cl, Br), were studied using (variants on) the recent W1 and W2 {\em ab initio} computational thermochemistry methods. Our computed benchmark data (including cases for which experimental data are unavailable altogether) are used to assess the quality of a number of semiempirical compound thermochemistry schemes such as G2 theory, G3 theory, and CBS-QB3, as well as a variety of density functional theory methods. Upon applying some modifications to the level of theory used for the reference geometry (adding diffuse functions, replacing B3LYP by the very recently proposed mPW1K functional), the compound methods appear to perform well. Only the 'half-and-half' functionals BH&HLYP and mPWH&HPW91, and the empirical mPW1K functional, consistently find all required stationary points; the other functionals fail to find a transition state in the F/Br case. BH&HLYP and mPWH&HPW91 somewhat overcorrect for the tendency of B3LYP (and, to a lesser extent, mPW1PW91) to underestimate barrier heights. The Becke97 and Becke97-1 functionals perform similarly to B3LYP for the problem under study, while the HCTH and HCTH-120 functionals both appear to underestimate central barriers. HCTH underestimates complexation energies; this problem is resolved in HCTH-120. mPW1K appears to exhibit the best performance of the functionals considered, although its energetics are still inferior to the compound thermochemistry methods.