A New Algorithm for Efficient Direct Dynamics Calculations of Large-Curvature Tunneling and Its Application to Radical Reactions with 9-15 Atoms Antonio Ferna ´ndez-Ramos Departmento de Quimica Fisica, Facultade de Quimica, UniVersidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain Donald G. Truhlar* Department of Chemistry and Supercomputing Institute, UniVersity of Minnesota, 207 Pleasant Street S. E., Minneapolis, Minnesota 55455-0431 Received June 15, 2005 Abstract: We present a new algorithm for carrying out large-curvature tunneling calculations that account for extreme corner-cutting tunneling in hydrogen atom, proton, and hydride transfer reactions. The algorithm is based on two-dimensional interpolation in a physically motived set of variables that span the space of tunneling paths and tunneling energies. With this new algorithm, we are able to carry out density functional theory direct dynamics calculations of the rate constants, including multidimensional tunneling, for a set of hydrogen atom transfer reactions involving 9-15 atoms and up to 7 nonhydrogenic atoms. The reactions considered involve the abstraction of a hydrogen atom from hydrocarbons by a trifluoromethyl radical, and in particular, we consider the reactions of CF 3 with CH 4 ,C 2 H 6 , and C 3 H 8 . We also calculate several kinetic isotope effects. The electronic structure is treated by the MPWB1K/6-31+G(d,p) method, which is validated by comparison to experimental results and to CBS-Q, MCG3, and G3SX(MP3) calculations for CF 3 + CH 4 . Harmonic vibrational frequencies along the reaction path are calculated in curvilinear coordinates with scaled frequencies, and anharmonicity is included in the lowest-frequency torsion. 1. Introduction Direct dynamics is “the calculation of rates or other dynami- cal observables directly from electronic structure information, without the intermediacy of fitting the electronic energies in the form of a potential energy function.” 1 Although most direct dynamics calculations are based on classical mechanics for the nuclear motion, 2-6 there has also been progress in including quantized vibrations and tunneling. 1,7-12 To make direct dynamics practical, one often uses inexpensive electronic structure methods, as in dynamics calculations based on semiempirical valence bond configu- ration interaction, 3 semiempirical molecular orbital theory, 1,2,8,9,12 or tight-binding molecular dynamics. 5 Using an affordable electronic structure method allows one to combine multidimensional tunneling calculations with varia- tional transition-state theory (VTST/MT) for relatively large systems. Therefore, one can calculate thermal rate constants at a low computational cost without building an analytical potential energy surface. For example, one can use semiem- pirical molecular orbital theory with specific-reaction pa- rameters (SRPs) fit to experimental or selected higher-level calculations. 1,9,12 This approach, although very successful in some cases, has the drawback that SRP surfaces do not form a model chemistry 13 and, hence, cannot be broadly validated. Another approach to lowering the cost is to use automatic and efficient fitting methods. 14 The third approach, which is * Corresponding author. Phone: (612) 624-7555. Fax: (612) 624- 9390. E-mail: editor@chem.umn.edu. 1063 J. Chem. Theory Comput. 2005, 1, 1063-1078 10.1021/ct050153i CCC: $30.25 © 2005 American Chemical Society Published on Web 08/25/2005