Stationary points of the potential surface for the reaction F− + CH3Cl → FCH3 + Cl−: Results of large-scale coupled cluster calculations

Multireference Model Chemistries for Thermochemical Kinetics

By combining the generalized valence bond ansatz of correlated participating orbitals (CPO) with the complete-active-space prescription for selecting configurations and with the use of multireference second order perturbation theory (MRMP2) for including dynamical correlation, we define three levels of multireference (MR) theoretical model chemistries for electronic structure calculations of chemical reaction energies and barrier heights. The three levels differ in their choice of which orbitals are considered to be participating; the choices are called nominal (nom-CPO), moderate (mod-CPO), and extended (ext-CPO). Combining any of these three choices with a method for treatment of dynamical correlation energy and a one-electron basis set yields a theoretical model chemistry. Unlike the full-valence choice of active orbitals, the CPO choices lead to active spaces that contain the orbitals needed to include important static correlation effects on chemical reactions but do not increase with the size of the nonparticipating portion of the system, and hence they remain viable computational options even for many large and complex reacting systems. The accuracies of the new levels, combined with the MG3S basis set (a partially augmented, multiply polarized valence triple-ζ basis with appropriately tight d functions for 3p-block elements) and with the fully augmented correlation-consistent aug-cc-pVTZ basis set, are assessed against a previously presented database of barrier heights for diverse reaction types. We find that nom-CPO level captures the bulk of the static correlation energy, and MRMP2/nom-CPO calculations have an average error of only 1.4 kcal/mol in barrier heights, which may be compared to 5.0 kcal/mol for single-reference MP2 theory, 2.5 kcal/mol for CCSD, and 4.1 and 1.0 kcal/mol for the B3LYP and M06-2X density functionals, respectively. The accuracy of MRMP2/CPO for transition structure bond lengths and donor-acceptor distances is excellent, with a mean unsigned error of only 0.007 Å as compared to 0.018 Å for CCSD, 0.019 Å for M06-2X, and 0.039 Å for MP2 and B3LYP. We also introduce a new multireference diagnostic, called the M diagnostic, that allows one to measure the importance of static correlation in a given reagent or transition state.

Density Functional Calculations of E2 and SN2 Reactions: Effects of the Choice of Method, Algorithm, and Numerical Accuracy

Herein we provide a detailed account on how the potential energy surfaces of the E2 and SN2 reactions of X(-) + CH3CH2X (X = F, Cl) depend on various methodological and technical choices in density functional calculations. We cover a choice of density functionals (OLYP, various M06-types, and the new SSB-D), basis sets (up to quintuple- and quadruple-ζ for Gaussian- and Slater-type orbitals, respectively, plus polarization and diffuse functions), and other aspects of the computations (among others: nonrelativistic versus zeroth-order regular approximation relativistic; numerical integration accuracy; all-electron versus frozen core; self-consistent field (SCF) versus post-SCF). The program codes ADF and NWChem are used for calculations with Slater- and Gaussian-type basis sets, respectively. The fluoride systems (X = F) appear to not only depend extremely sensitively on the basis set size (especially the presence of diffuse functions) but also on other technical settings, especially in the case of hybrid meta-generalized gradient approximation functionals. This work complements a recent contribution (Y. Zhao, D. G. Truhlar, J. Chem. Theory Comput. 2010, 6, 1104) and provides recommendations for density functionals, basis sets, and technical settings.

Benchmark study on the smallest bimolecular nucleophilic substitution reaction: H⁻+CH₄-->CH₄+H⁻

We report here a benchmark study on the bimolecular nucleophilic substitution (S(N)2) reaction between hydride and methane, for which we have obtained reference energies at the coupled cluster toward full configuration-interaction limit (CC-cf/CBS). Several wavefunction (HF, MP2, coupled cluster) and density functional methods are compared for their reliability regarding these reference data.

Electronic structure theory study of the F(-) + CH(3)I → FCH(3) + I(-) potential energy surface

MP2 and DFT electronic structure theories, with the functionals OPBE, OLYP, HCTH407, BhandH, and B97-1 for the latter, were used to investigate stationary point properties on the F(-) + CH(3)I → FCH(3) + I(-) potential energy surface (PES). The aug-cc-pVDZ and aug-cc-pVTZ basis sets for C, H, and F, with Wadt and Hay's 3s3p valence basis and an effective core potential (ECP) for iodine, were employed for both MP2 and DFT. Single-point CCSD(T) calculations were also performed to obtain the complete basis set (CBS) limit for the stationary point energies. The CCSD(T)/CBS reaction exothermicity is only 5.0 kJ/mol different than the experimental value. MP2 and DFT do not predict the same stationary points on the PES. MP2 predicts the C(3v) F(-)-CH(3)I and FCH(3)-I(-) ion-dipole complexes and traditional [F-CH(3)-I](-) central barrier as stationary points, as well as a C(s) hydrogen-bonded F(-)-HCH(2)I complex and a [F-HCH(2)-I](-) transition state connecting this latter complex to the F(-)-CH(3)I complex. A CCSD(T)/CBS relaxed potential energy curve, calculated for the MP2 structures, shows that going from the F(-)-CH(3)I complex to the [F-CH(3)-I](-) TS is a barrierless process, indicating these two structures are not stationary points. This is also suggested by the DFT calculations. The structures and frequencies for CH(3)I and CH(3)Cl given by MP2 and DFT are in overall good agreement with experiment. The calculations reported here indicate that the DFT/B97-1 functional gives the overall best agreement with the CCSD(T) energies, with a largest difference of only 7.5 kJ/mol for the FCH(3)-I(-) complex.

Energy landscapes of nucleophilic substitution reactions: A comparison of density functional theory and coupled cluster methods

We have carried out a detailed evaluation of the performance of all classes of density functional theory (DFT) for describing the potential energy surface (PES) of a wide range of nucleophilic substitution (SN2) reactions involving, amongst others, nucleophilic attack at carbon, nitrogen, silicon, and sulfur. In particular, we investigate the ability of the local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA as well as hybrid DFT to reproduce high-level coupled cluster (CCSD(T)) benchmarks that are close to the basis set limit. The most accurate GGA, meta-GGA, and hybrid functionals yield mean absolute deviations of about 2 kcal/mol relative to the coupled cluster data, for reactant complexation, central barriers, overall barriers as well as reaction energies. For the three nonlocal DFT classes, the best functionals are found to be OPBE (GGA), OLAP3 (meta-GGA), and mPBE0KCIS (hybrid DFT). The popular B3LYP functional is not bad but performs significantly worse than the best GGA functionals. Furthermore, we have compared the geometries from several density functionals with the reference CCSD(T) data. The same GGA functionals that perform best for the energies (OPBE, OLYP), also perform best for the geometries with average absolute deviations in bond lengths of 0.06 A and 0.6 degrees, even better than the best meta-GGA and hybrid functionals. In view of the reduced computational effort of GGAs with respect to meta-GGAs and hybrid functionals, let alone coupled cluster, we recommend the use of accurate GGAs such as OPBE or OLYP for the study of SN2 reactions.

The molecular potential energy surface and vibrational energy levels of methyl fluoride. Part II

New analytical bending and stretching, ground electronic state, potential energy surfaces for CH(3)F are reported. The surfaces are expressed in bond-length, bond-angle internal coordinates. The four-dimensional stretching surface is an accurate, least squares fit to over 2000 symmetrically unique ab initio points calculated at the CCSD(T) level. Similarly, the five-dimensional bending surface is a fit to over 1200 symmetrically unique ab initio points. This is an important first stage towards a full nine-dimensional potential energy surface for the prototype CH(3)F molecule. Using these surfaces, highly excited stretching and (separately) bending vibrational energy levels of CH(3)F are calculated variationally using a finite basis representation method. The method uses the exact vibrational kinetic energy operator derived for XY(3)Z systems by Manson and Law (preceding paper, Part I, Phys. Chem. Chem. Phys., 2006, 8, DOI: 10.1039/b603106d). We use the full C(3v) symmetry and the computer codes are designed to use an arbitrary potential energy function. Ultimately, these results will be used to design a compact basis for fully coupled stretch-bend calculations of the vibrational energy levels of the CH(3)F system.

Model Identity SN2 Reactions CH3X + X- (X = F, Cl, CN, OH, SH, NH2, PH2): Marcus Theory Analyzed

The structures of seven gas phase identity S(N)2 reactions of the form CH(3)X + X(-) have been characterized with seven distinct theoretical methods: RHF, B3LYP, BLYP, BP86, MP2, CCSD, and CCSD(T), in conjunction with basis sets of double and triple zeta quality. Additionally, the energetics of said reactions have been definitively computed using focal point analyses utilizing extrapolation to the one-particle limit for the Hartree-Fock and MP2 energies using basis sets of up to aug-cc-pV5Z quality, inclusion of higher order correlation effects [CCSD and CCSD(T)] with basis sets of aug-cc-pVTZ quality, and additional auxiliary terms for core correlation and scalar relativistic effects. Final net activation barriers for the reactions are E(b)(F,F)= -0.8, E(b)(Cl,Cl)= 1.6, E(b)(CN,CN)= 28.7, E(b)(OH,OH)= 14.3, E(b)(SH,SH)= 13.8, E(b)(NH2,NH2)= 28.6, and E(b)(PH2,PH2)= 25.7 kcal mol(-1). General trends in the energetics, specifically the performance of the density functionals, and the component energies of the focal point analyses are discussed. The utility of classic Marcus theory as a technique for barrier predictions has been carefully analyzed. The standard Marcus theory results show disparities of up to 9 kcal mol(-1) with respect to explicitly computed results. However, when alternative approaches to Marcus theory, independent of the well-depths, are considered, excellent performance is achieved, with the largest deviations being under 3 kcal mol(-1).

Transition state dynamics and a QM/MM model for the Cl– + C2H5Cl SN2 reaction

A MP2/6-31G* direct dynamics simulation is used to study the dynamics of the central barrier [Cl-C2H5-Cl]– for the Cl– + C2H5 SN2 reaction. The majority of the trajectories move off the central barrier to form the Cl––C2H5Cl complex and appear to undergo efficient IVR as assumed by RRKM theory. However, some of the trajectories move directly to products without forming the complex, a non-RRKM result. A hydrogen atom link-atom QM/MM model is described for studying the dynamics of [X-CH2R-Y]– central barriers with the -R substituent. The model is used to calculate vibrational frequencies for the [Cl-C2H5-Cl]– central barrier.Key words: SN2 reaction dynamics, RRKM theory, QM/MM model, central barrier dynamics, direct dynamics classical trajectories.

The anharmonic potential energy surface of methyl fluoride

A large experimental spectroscopic data set sensitive to the cubic anharmonic potential energy surface (PES) of methyl fluoride has been compiled from the literature for six symmetric and asymmetric top isotopomers of methyl fluoride: 12CH3F, 13CH3FF, 12CD3F, 13CD3F, 12CHD2F and 12CH2DF. This empirical data set has been used to critically assess the best available literature ab initio cubic force field and various 'improved' theoretical force fields. A perturbation-resonance approach to the calculation of the observables from the force constants has been utilized and existing PESs were found to reproduce the data poorly. The careful treatment required for the correct theoretical reproduction of empirical spectroscopic constants arising from highly correlated least-squares fits to the original data is discussed. A new fit to the data has been performed (optimising 19 of the 38 cubic force constants) resulting in a much improved PES. The latter has been used to predict currently unknown spectroscopic constants for the least well-characterised isotopomer 12CH2DF. The prospects for a future empirical determination of the complete cubic force field of methyl fluoride are discussed and new data most likely to yield new information on the PES identified.

Dynamics of the gas-phase reactions of chloride ion with fluoromethane: high excess translational activation energy for an endothermic S(N)2 reaction

Guided ion beam tandem mass spectrometry techniques are used to examine the competing product channels in the reaction of Cl(-) with CH(3)F in the center-of-mass collision energy range 0.05-27 eV. Four anionic reaction products are detected: F(-), CH(2)Cl(-), FCl(-), and CHCl(-). The endothermic S(N)2 reaction Cl(-) + CH(3)F --> CH(3)Cl + F(-) has an energy threshold of E(0) = 181 +/- 14 kJ/mol, exhibiting a 52 +/- 16 kJ/mol effective barrier in excess of the reaction endothermicity. The potential energy of the S(N)2 transition state is well below the energy of the products. Dynamical impedances to the activation of the S(N)2 reaction are discussed, including angular momentum constraints, orientational effects, and the inefficiency of translational energy in promoting the reaction. The fluorine abstraction reaction to form CH(3) + FCl(-) exhibits a 146 +/- 33 kJ/mol effective barrier above the reaction endothermicity. Direct proton transfer to form HCl is highly inefficient, but HF elimination is observed above 268 +/- 95 kJ/mol. Potential energy surfaces for the reactions are calculated using the CCSD(T)/aug-cc-pVDZ and HF/6-31+G(d) methods and used to interpret the dynamics.

Fourier Transform Infrared Spectra of CH(2)DF: The nu(5) and nu(6) Bands

Results of a high-resolution infrared study of the spectroscopy of monodeuterated methyl fluoride, CH(2)DF, are reported for the first time. Spectra ranging from 500 to 3300 cm(-1) have been obtained and cover all the fundamental bands at resolutions down to 0.005 cm(-1). The two lowest energy fundamentals, the nu(5) and nu(6) bands, have been analyzed in detail. Since the molecule has C(s) symmetry, in principle both these bands are AB hybrids, since they belong to the irreducible representation A'. However, it was found that both are almost pure A-type bands. A total of 597 A-type lines of the nu(5) band and 619 A-type lines of the nu(6) band have been assigned. Vibrational and rotational spectroscopic constants have been determined by least-squares fitting to the data. An improved band center for nu(7) is also reported. Copyright 2001 Academic Press.

The General Harmonic Force Field of Methyl Chloride

The complete general harmonic force field of methyl chloride has been recalculated using the most recent literature frequency, Coriolis zeta, and centrifugal distortion data for (12)CH(3)(35)Cl, (13)CH(3)(35)Cl, (12)CD(3)(35)Cl, (12)CHD(2)(35)Cl, (12)CH(2)D(35)Cl, (12)CH(3)(37)Cl, (12)CD(3)(37)Cl, (12)CHD(2)(37)Cl, (12)CH(2)D(37)Cl, and (13)CH(3)(37)Cl. The anharmonic corrections applied to the observed frequency data are considered to be more realistic than those used hitherto. There is excellent agreement between the fitted force constants and literature high-quality ab initio force fields. The results of the least-squares refinement of the full-harmonic force field is compared with least-squares refinement of only the scale factors for an SCF calculated force field since the latter approach may be useful for larger molecules where more sophisticated calculations are impractical. The results of a refinement of only the scale factors for an MP4 calculated force field are also reported. Copyright 2001 Academic Press.