Electronic Structure Theory Study of the F−+ CH3I→ FCH3+ I

May 5, 2010 - B97-1 for the latter, were used to investigate stationary point properties on the F .... Geometries of stationary points for the F- + CH...
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J. Phys. Chem. A 2010, 114, 9635–9643

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Electronic Structure Theory Study of the F- + CH3I f FCH3 + I- Potential Energy Surface† Jiaxu Zhang and William L. Hase* Department of Chemistry and Biochemistry, Texas Tech UniVersity, Lubbock, Texas 79409-1061 ReceiVed: January 10, 2010; ReVised Manuscript ReceiVed: April 11, 2010

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- + CH3I f FCH3 + Ipotential 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 C3V F-sCH3I and FCH3sI- ion-dipole complexes and traditional [FsCH3sI]- central barrier as stationary points, as well as a Cs hydrogen-bonded F-sHCH2I complex and a [FsHCH2sI]- transition state connecting this latter complex to the F-sCH3I complex. A CCSD(T)/CBS relaxed potential energy curve, calculated for the MP2 structures, shows that going from the F-sCH3I complex to the [FsCH3sI]- 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 CH3I and CH3Cl 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 FCH3sIcomplex. I. Introduction Many gas-phase anion-molecule SN2 reactions of the type

X- + CH3Y f XCH3 + Y-

(1)

have potential energy surfaces (PESs) with a central barrier that separates the potential minima for the pre- and postreaction ion-dipole complexes X-sCH3Y and XCH3sY-.1-26 The family of SN2 reactions

F- + CH3Cl f FCH3 + Cl-

(2)

F- + CH3Br f FCH3 + Br-

(3)

F- + CH3I f FCH3 + I-

(4)

have been the subject of several investigations7,8,23,25,27-33 and are particularly interesting because of their large reaction exothermicities. It is known that for gas-phase reactions of the type in eq 1, the higher the reaction exothermicity, the lower the central barrier.23,34,35 An intriguing question is whether the reaction exothermicity can be sufficiently large that the PES no longer retains the central potential energy barrier.34,35 Recently, Wester and co-workers used crossed molecular beam ion imaging experiments to study the atomistic dynamics †

Part of the “Reinhard Schinke Festschrift”. * To whom correspondence should be [email protected].

addressed.

E-mail:

of the Cl- + CH3I f ClCH3 + I- and F- + CH3I f FCH3 + I- SN2 reactions.36,37 Using reactants with a well-defined relative kinetic energy, the experiments reveal how much of the total available energy is partitioned to product relative translation and, thus, also to the rotational and vibrational degrees of freedom of the molecular product. In addition, the experiments probe the products angular scattering. A direct chemical dynamics simulation, at the MP2(fc)/ECP/ aug-cc-pVDZ level of theory, was performed36 for the Cl- + CH3I f ClCH3 + I- SN2 reaction at an initial relative translational energy of 1.9 eV to compare with the experimental results.36,37 The simulations well reproduced the product energy partitioning and velocity scattering angle distributions observed in the experiments36,37 and identified two atomic-level reaction mechanisms. One is a direct reaction, leading to a high product relative translational energy, in which Cl- collides backside and displaces I- without forming either the pre- or postreaction complex. The other, identified as a “roundabout” mechanism, leads to a low product relative translational energy. For this mechanism, the Cl- ion transfers all (or nearly all) of its translational energy to the CH3-moiety upon initial impact, resulting in excitation of the C-I stretch and rotation of CH3 about the massive I-atom. The Cl- ion, sitting at rest, then displaces I- backside after the CH3-group undergoes a 2π or multiple 2π (much less likely) rotation about the I-atom. Detailed electronic structure theory studies, at the MP2 and DFT levels of theory, have been performed38 to investigate the Cl+ CH3I f ClCH3 + I- PES. These levels of theory give different representations of the PES, which may become important for simulations at low collision energies. Statistical theories such as Rice-Ramsperger-Kassel-Marcus (RRKM),39 phase space theory (PST),39 and transition state

10.1021/jp1002337  2010 American Chemical Society Published on Web 05/05/2010

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(TST)40 theory have been widely used to model kinetics of SN2 reactions. However, the results of some experimental studies of SN2 reactions are not adequately explained by these theories.2,4,5,9,20,31,41-43 Chemical dynamics simulations19,44-58 have proven very useful for interpreting the kinetics and dynamics of SN2 reactions and have brought into question fundamental assumptions of statistical theories regarding mode specific chemistry, intramolecular vibrational energy redistribution (IVR), the dynamics of central barrier crossing, and the efficiency of ion-molecule capture. Interpreting the dynamics and kinetics of SN2 reactions and comparing with experiments, by either statistical calculations or chemical dynamics simulations,59,60 requires accurate PESs. The energies for the reactions X- + CH3X f XCH3 + X- and X- + CH3Y f XCH3 + Y- (X, Y ) F, Cl, Br, I) have been calculated at the G2(+) level of theory.22-24 Density functional theory (DFT) and ab initio methods have been employed to providepropertiesforawiderangeofSN2reactions.15,17,18,26,31,32,61-66 A detailed evaluation of the accuracy of different DFT functionals for describing potential energy surface of various SN2 reactions has been made by Bickelhaupt and co-workers.17 The chemical dynamics simulations, based on accurate analytic and ab initio PESs, have been performed to study the Cl- + CH3Cl,14,21,49,51,67 Cl- + CH3Br,20,47 F- + CH3Cl,31,50 OH- + CH3F,52 and Cl- + CH3I36 reactions. In the work presented here, the DFT, MP2, and CCSD(T) theories, with different basis sets and DFT functionals, were employed to calculate stationary point properties for the F- + CH3I SN2 reaction. To determine the preferred method for a direct dynamics simulation, comparisons are made between the results of these calculations and with experimental and previously obtained theoretical results. II. Computational Methods MP268,69 and DFT,17,70-73 with the OPBE, OLYP, HCTH407, BhandH, and B97-1 functionals, were employed to investigate the ability of different electronic structure theory methods to determine accurate stationary point properties for the reactants, ion-dipole complexes, transition states, and products on the F- + CH3I f FCH3 + I- PES. Two basis sets, called ECP/d and ECP/t, were used for both the MP2 and DFT calculations. Two other basis sets, denoted as PP/d and PP/t, were used with only MP2 to test the sensitivity of the ab initio results to the iodine basis set. For ECP/d, Dunning and Woon’s aug-cc-pVDZ basis set74 is used for the C, H, and F atoms. For iodine, the Wadt and Hay effective core potential (ECP) was used for the core electrons and a 3s,3p basis set for the valence electrons,75 which was augmented by a d-polarization function with a 0.262 exponent, and s, p, and d diffuse functions with exponents of 0.034, 0.039, and 0.0873, respectively.76 For ECP/t, Dunning and Woon’s aug-cc-pVTZ basis set,74 without diffuse d and f functions,77 is used for the C, H, and F atoms. For iodine, the above basis was further augmented by a f-polarization function with a 0.52 exponent.77 For both ECP/d and ECP/t, the C, H, F, and I basis sets are similar in size and are, thus, considered compatible for the calculations reported here.76,77 For the basis sets PP/d and PP/t, the above double- (d) and triple- (t) ζ basis sets, aug-cc-pVDZ and aug-cc-pVTZ, were used for the C, H, and F atoms. However, the Peterson aug-cc-pVDZ and aug-cc-pVTZ basis sets, with a pseudopotential (PP),78 were used for iodine. Structures, frequencies, and energies were calculated at the MP2 level of theory with each of the above four basis sets and at the DFT level of theory with only the ECP/d and ECP/t basis

Figure 1. Geometries of stationary points for the F- + CH3I f FCH3 + I- reaction optimized at the B97-1/ECP/t and MP2/ECP/t levels of theory. Geometries are given for the F-sHCH2I hydrogen-bonded complex, the [FsHCH2sI]- TS, and the FCH3sI- postreaction complex. The MP2/ECP/t geometries are given in parentheses.

sets. The frozen core (fc) orbital method was also used for the MP2 calculations to provide a comparison between all-electron and fc calculations. The stationary nature of the structures was confirmed by harmonic vibrational frequency calculations. The harmonic zero-point energy (ZPE) was obtained at all the above levels of theory. To ensure that the transition states connect designated minima, the intrinsic reaction coordinate (IRC)79 was calculated for both directions off the saddlepoint at both the MP2/ECP/d and DFT/ECP/d levels of theory. To obtain more reliable energies, high-level single-point energy calculations were performed at the CCSD(T) level of theory80 for the all-electron MP2/PP/d optimized geometries. MP2/PP/d, instead of MP2/ECP/d, optimized geometries were

F- + CH3I f FCH3 + I- Potential Energy Surface

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TABLE 1: Comparison of Deviations in Stationary Point Geometries, Frequencies, and Energies Calculated with Different Basis Sets and MP2a propertyb

ECP/d, ECP/d/fc

ECP/d, ECP/t

PP/d, PP/t

ECP/d, PP/d

ECP/t, PP/t

RC-H RC-Xc RC••Xd RF••He θf freq energy

0.001 (0.001-0.002) 0.001 (0-0.002) 0.001 (0.001-0.002) 0.003 (0.002-0.003) 0 (0-0.1) 3 (0-8) 0.5 (0-1.3)

0.014 (0.011-0.016) 0.037 (0.025-0.061) 0.037 (0.006-0.089) 0.033 (0.024-0.041) 1.1 (0.3-3.2) 28 (2-108) 3.0 (0.8-8.8)

0.014 (0.012-0.015) 0.033 (0.022-0.049) 0.034 (0.020-0.082) 0.005 (0.001-0.008) 0.6 (0.2-1.3) 22 (0-66) 2.0 (0-3.8)

0.0003 (0-0.001) 0.003 (0-0.006) 0.005 (0.001-0.009) 0.002 (0-0.004) 0.1 (0-0.4) 2 (0-12) 1.5 (0.4-2.9)

0.002 (0-0.003) 0.007 (0.003-0.018) 0.028 (0.004-0.076) 0.024 (0.003-0.044) 0.6 (0.1-1.8) 9 (0-64) 3.5 (1.7-7.1)

a Listed is the mean absolute deviation of the differences in the values for the property and the range of differences in parentheses, as given by the two basis sets. The analyses were made considering all 7 stationary points; i.e., CH3I, F-sCH3I, [FsCH3sI]-, FCH3sI-, CH3F, F-sHCH2I, and [FsHCH2sI]-. b Bond lengths are in Å, angles in degrees, and frequencies in cm-1. Energies are in kJ/mol and are at 0 K without ZPE. c RC-X represents the C-X bonds in CH3I, CH3F, and complexes. d RC••X represents the X-sC bonds in the complexes and XsC bonds in the TSs. e RF••H represents the F-sH bond in the F-sHCH2I complex and FsH bond in the [FsHCH2sI]- TS. f For the C3V stationary points, one H-C-X angle was included, but for the Cs stationary points both the H*-C-H and F-C-I angles are included (H* is the H-atom to which F- attaches).

used for consistency with the PP basis set used for the CCSD(T) calculations. The CCSD(T) calculations were performed with the fc orbital method and the correlation consistent Gaussian basis sets, denoted by aug-cc-pVXZ, where X is the cardinal number for the basis set (X ) D, T, and Q).74 These energies were extrapolated to the complete basis set (CBS) limit using the formula proposed by Peterson et al.81

TABLE 2: Reactant and Product (CH3X) Geometries for MP2 and Different DFT Functionalsa RC-H

OPBE

BhandH HCTH407

where n ) 2, 3, and 4, representing the PP/d, PP/t, and PP/q basis sets, respectively. The aug-cc-pVXZ basis was used for the C, H, and F atoms. The Peterson aug-cc-pVXZ basis, with a PP,78 was used for iodine. Following the terminology used above, for the MP2 and DFT calculations, these basis sets are identified as PP/x, where x ) d, t, and q. The NWChem system of programs82 was used to perform most of the above electronic structure calculations. GAMESS83 was used to calculate the IRCs. III. Results and Discussion A. Comparison of Basis Sets. The MP2 calculations were used to compare stationary point properties given by the ECP/ d, ECP/d/fc, PP/d, ECP/t, and PP/t basis sets. The MP2 calculations predict both C3V and Cs complexes and transition states (TS), and their structures, energies, and vibrational frequencies are given in Tables S1-S4 of the Supporting Information. The Cs and FCH3sI- stationary point geometries are shown in Figure 1. As discussed in the next section, the CCSD(T) and DFT results do not confirm the presece of the C3V F-sCH3I ion-dipole complex and [FsCH3sI]- SN2 TS on the PES. However, both the C3V and Cs structures may be used to compare the results of the different basis sets. Differences between stationary point geometries, vibrational frequencies, and energies are given in Table 1 for different pairs of basis set. Listed is the mean absolute deviation of the differences in the values of a property and the range of differences in the value. The geometries of CH3I and CH3F calculated with the ECP/d and ECP/t bases are compared with experiment in Table 2. Table 1 shows that the ECP/d and ECP/d/fc results are very similar. Bond lengths differ by at most 0.003 Å, and energy differences are only 1.3 kJ/mol or less. The ECP/d and ECP/ d/fc vibrational frequencies for the stationary points are listed in the Supporting Information, and their differences are very

∠X-C-H

2.143 2.112 2.139 2.123 2.158 2.142 2.140 2.125 2.155 2.139 2.147 2.133 2.132

108.0 108.3 107.9 107.8 107.8 107.7 107.8 107.9 107.7 107.7 108.0 107.9 107.7

1.407 1.382 1.392 1.381 1.405 1.394 1.378 1.366 1.397 1.387 1.398 1.387 1.382

108.3 108.8 108.8 109.2 108.5 108.8 108.8 109.1 108.6 108.9 108.5 108.8 108.5

CH3I MP2

OLYP

E(n) ) ECBS + A exp[-(n - 1)] + B exp[-(n - 1)2] (5)

RC-X

B97-1 Exptb

1.094 1.079 1.097 1.090 1.096 1.089 1.093 1.084 1.093 1.085 1.095 1.086 1.084 CH3F

MP2 OPBE OLYP BhandH HCTH407 B97-1 Exptb

1.097 1.083 1.102 1.098 1.102 1.096 1.098 1.091 1.099 1.093 1.100 1.092 1.095

a Bond lengths are in angstroms (Å), and angles are in degrees. The upper values were calculated using the ECP/d basis set, and the lower values were calculated using the ECP/t basis set. b The experimental geometries of CH3I and CH3Cl are from ref 85.

small. The largest difference in magnitude is 8 cm-1 for the E CH3 deform and E C-H str of CH3I. The use of the fc model has only a small effect on the stationary point properties. As shown in Table 1, ECP and PP, with either the double-ζ (d) or triple-ζ (t) basis set, give similar stationary point properties. However, somewhat better agreement between ECP and PP is obtained with the d basis. The largest difference between the ECP and PP geometries is 0.076 Å for the CsI bond of the FCH3sI- complex. The largest frequency difference is 64 cm-1 for the A′ C-H str of the F-sHCH2I complex. The largest energy difference is 7.1 kJ/mol for the [FsCH3sI]- TS, and between ECP/t and PP/t. The ECP/d and PP/d basis sets give larger bond lengths and angles than do ECP/t and PP/t, with the latter giving geometries

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in better agreement with the experimental CH3I and CH3F geometries (see Tables S1 and S2, and Table 2). For ECP the C-H bond lengths calculated with the d and t basis sets are in better agreement than the lengths of the other three types of bonds. However, somewhat surprisingly, for PP the bond lengths calculated with the d and t basis sets are in the best agreement for the F · · H bond type. PP/d and PP/t give similar frequencies and energies with the largest difference of 66 cm-1 for the imaginary frequency of the [FsCH3sI]- TS and 3.8 kJ/mol for the FCH3 + I- products. ECP/d and ECP/t give somewhat larger differences, with largest differences of 108 cm-1 for the imaginary frequency of the [FsCH3sI]- TS and 8.8 kJ/mol for the [FsCH3sI]- TS energy. In choosing a basis set appropriate for a direct dynamics simulation, one must consider both the accuracy required and the expense of the calculations, since numerous electronic structure calculations are required for integrating the classical trajectories.19,44-53 For the F- + CH3I system the contracted Gaussian basis functions and primitive Gaussian basis functions are 95 and 147 in ECP/d, 105 and 212 in PP/d, 151 and 219 in ECP/t, and 216 and 392 in PP/t. The number of these basis functions is reduced for the fc model. For trajectories integrated by using the gradient,19,59 and not the Hessian,84 the relative compute time required to integrate trajectories with the ECP/ d/fc: ECP/d: PP/d: ECP/t: PP/t basis sets are ∼1: 1: 3: 4: 27. Thus, ECP/d is ∼3 times faster than PP/d, and ECP/t is ∼7 times faster than PP/t. After considering the relative accuracy of the different basis sets, and their computational efficiencies, ECP/d and ECP/t with the fc model are deemed most efficient for direct dynamics simulations. B. Stationary Points on the PES. As discussed above, MP2 theory predicts the existence of the traditional mechanism’s prereaction and postreaction ion-dipole complexes F-sCH3I and FCH3sI- and [FsCH3sI]-central barrier TS, as well as the hydrogen-bonded complex F-sHCH2I and a TS [FsHCH2sI]- connecting this complex to the F-sCH3I complex. However, this model for the PES is not supported by the CCSD(T) and DFT calculations. Single-point CCSD(T)/CBS frozen core calculations were performed at the MP2/PP/d geometries for F-sCH3I and [FsCH3sI]-, and along a MP2/PP/d potential energy curve connecting these two geometries. The geometries for the potential energy curve were determined by varying the FsC bond length from its value at the [FsCH3sI]- TS to its value at the F-sCH3I complex and optimizing the remaining internal coordinates. This procedure smoothly connected the MP2/PP/d geometries for the TS and complex. The resulting MP2/PP/d and CCSD(T) potential energy curves, at 0 K and without ZPE, are compared in Figure 2. Going from the complex to the TS is an uphill process at the MP2 level of theory. In contrast, CCSD(T) theory says that going from the F-sCH3I complex to the [FsCH3sI]- TS is a downhill process and, thus, the complex and TS are not stationary points on the actual PES. The CCSD(T)/CBS energies for the MP2 F-sCH3I and [FsCH3sI]- structures are -72.8 are -73.6 kJ/mol, respectively. DFT calculations were performed for five different functionalssOPBE,OLYP,HCTH407,BhandH,andB97-1susing the ECP/d and ECP/t basis sets, and they give a PES with stationary point features in agreement with those suggested by the CCSD(T) calculations. Of this set of calculations, with five different functionals and two basis sets, the C3V F-sCH3I complex and [FsCH3sI]- TS were only found as stationary points for the BhandH/ECP/t calculations. For the other DFT calculations, numerous attempts were made to locate the C3V

Zhang and Hase

Figure 2. MP2/PP/d and CCSD(T)/CBS potential energy curves connecting the MP2/PP/d C3V F-sCH3I complex and [FsCH3sI]- TS. Single-point CCSD(T)/CBS energies were calculated for the MP2/PP/d geometries, optimized versus the C-F bond length RC-F. The potential energy in kJ/mol is given versus RC-F at the TS minus the varying RC-F. The potential energy is the relative energy with respect to the F+ CH3I reactants, and is at 0 K and does not include zero-point energies.

complex and C3V TS, but they always lead to the hydrogenbonded Cs F-sHCH2I complex and Cs [FsHCH2sI]- TS. These calculations show that the F-sHCH2I complex directly passes to the postreaction complex FCH3sI-, after crossing the [FsHCH2sI]- saddle point, without first accessing a F-sCH3I complex. The potential energy curve and stationary points for the MP2/ECP/t and B97-1/ECP/d PESs are compared in Figure 3. As pointed out above, the BhandH/ECP/t calculations predict the existence of the F-sCH3I complex and [FsCH3sI]- TS C3V structures as stationary points on the PES, with almost identical energies of -73.525 and -73.521 kJ/mol, respectively. The respective F-sC and C-I bond lengths for the complex are 2.305 and 2.271 Å, and the respective FsC and CsI bond lengths for the TS are 2.252 and 2.302 Å. These structures are significantly different than the MP2/ECP/t structures in Table S1; that is, the respective MP2 bond lengths for the complex are 2.489 and 2.167 Å and for the TS are 2.064 and 2.381 Å. Single-point CCSD(T) frozen core calculations were performed for the BhandH/ECP/t C3V complex and TS. CCSD(T)/ PP/d gives an energy of -75.330 kJ/mol for the TS as compared to the higher energy of -75.082 kJ/mol for the complex. In going to the larger basis sets PP/t and PP/q the difference between the CCSD(T) energies for the TS and complex become smaller, and the interpolation of the PP/d, PP/t, and PP/q energies with eq 5 results in isoenergetic CBS energies of -73.016 kJ/mol for the TS and complex. The CCSD(T)/CBS calculations show that the PES is very flat in the vicinity of the BhandH/ECP/t F-sCH3I complex and [FsCH3sI]- TS. C. Properties of the Stationary Points. The DFT and CCSD(T) calculations indicate the F-sHCH2I hydrogen-bonded complex, [FsHCH2sI]- transition state, and FCH3sI- postreaction complex are the only stationary points on the PES, in addition to the reactants and products. In the following, properties of these stationary points as given by MP2 theory and the different DFT functionals, with the ECP/d and ECP/t basis sets, are compared. 1. Geometries. The calculated MP2 and DFT geometries of the reactant CH3I and product CH3F are listed in Table 2. The

F- + CH3I f FCH3 + I- Potential Energy Surface

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Figure 3. Potential energy curves and stationary points for the MP2/ECP/t and B97-1/ECP/d PESs. The experimental reaction exothermicity88 is in parentheses. The energy in kJ/mol is relative to the F- + CH3I reactants, is at 0 K, and does not include ZPEs.

Figure 4. Representations of the errors in the calculated CH3I and CH3F bond lengths, as compared to experiment.85 Plotted, for each level of theory, is the largest relative error for any one of the eight bond lengths.

geometries for the predicted complexes and transition state are given in Table S5 in the Supporting Information. Structures determined by B97-1/ECP/t and MP2/ECP/t are shown in Figure 1. The bond length difference between MP2 and the different DFT functionals mainly lies in CsI bond length of the FCH3sI- complex. The DFT functionals give larger values for this bond length. OPBE and B97-1 give the largest and smallest differences, respectively, with MP2. Overall, the geometries for CH3I and CH3F, obtained at the different levels of theory, are in good agreement with experiment.85 Bond angle differences are within 0.7°. The relative error in the bond length, |rcalc - rexp|/rexp, was determined for all the bonds, and the largest relative error was identified for each level of theory. The results are compared in Figure 4. The ECP/t basis set gives better agreement with experiment77 than ECP/d for all the theories except BhandH. HCTH407 and B97-1, with ECP/t, give the best agreement with experiment. 2. Vibrational Frequencies. The MP2 and DFT frequencies calculated with ECP/d and ECP/t basis for CH3I and CH3F, and the F-sHCH2I complex, [FsHCH2sI]- TS, and FCH3sIcomplex are compared in Table S6 of the Supporting Information. There are differences between the frequencies calculated by the five DFT functionals. BhandH gives the largest values for the frequencies, while OPBE and OLYP give the smallest. The largest difference between MP2 and a DFT functional

ranges from 66 cm-1 (A′ C-I str of [FsHCH2sI]-) BhandH and ECP/t to 391 cm-1 (A′ C-H str of F-sHCH2I) for OPBE and ECP/d. The calculated frequencies of the CH3I reactant and CH3F product at the different levels of theory were compared with experiment.86,87 In terms of the relative uncertainty |νcalc - νexp|/ νexp for each normal mode, most of the theories are in good agreement with experiment with a maximum deviation of 2-6%, except for MP2/ECP/t theory for which this deviation is 9%. B97-1/ECP/t theory gives the best agreement with the experimental frequencies for both CH3I and CH3F, with a maximum deviation of only 2%. The B97-1 frequencies for all the stationary point are listed in Table 3. 3. Energies. Energies for the F-sHCH2I hydrogen-bonded complex, [FsHCH2sI]- TS, FCH3sI- postreaction complex, and CH3F + I- reaction products, calculated with MP2, the DFT functionals, and the ECP/d and ECP/t basis sets, are presented in Table 4. These theories give substantial differences in the energies especially for FCH3sI- and CH3F + I-. High-level CCSD(T) calculations were performed to obtain more reliable energies and were chosen as a benchmark for the accuracy of the energies calculated at the MP2 and DFT levels of theory. The CCSD(T) calculations were performed with the PP/d, PP/t, and PP/q basis sets described in Section II and at the stationary point geometries optimized at the MP2/PP/d level of theory. The resulting energies are listed in Table 4. The fc orbital method was employed for these CCSD(T) calculations. Also listed are energies extrapolated to the CBS limit using eq 5. These PP basis sets appear to have converged the energies for F-sHCH2I and [FsHCH2sI]-. However, for FCH3sI- and the CH3F + I- products, there are considerable decreases in the energy as the size of the basis set is increased. The CCSD(T)/ CBS values for the F-sHCH2I potential energy minimum, the F-sHCH2I f [FsHCH2sI]- relative energy, the FCH3sIf CH3F + I- dissociation energy, and reaction exothermicity are -81.2, 11.3, 31.8, and -202.1 kJ/mol, respectively. The F- + CH3I f FCH3 + I- reaction is highly exothermic due to the strong binding between fluorine and carbon in the product molecule CH3F.8,23,29-33,37 As listed in Table 4, the experimental reaction exothermicity at 0 K, and without ZPE, is -197.1 kJ/mol88 and only 5.0 kJ/mol less negative than the CBS value. This good agreement illustrates the high accuracy of the CCSD(T)/CBS calculations. The B97-1 energies are in the best agreement with the CCSD(T)/CBS energies. Using the ECP/d basis set, the B97-1

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TABLE 3: B97-1 Harmonic Frequencies of Stationary Points for the F- + CH3I f CH3F + I- PESa mode

B97-1

E CH3 rock A1 CH3 deform E CH3 deform A1 C-H str E C-H str

A1 C-F str E CH3 rock A1 CH3 deform E CH3 deform A1 C-H str E C-H str

E I- bend A1 C-I str A1 F-C str E CH3 rock A1 CH3 deform E CH3 deform A1 C-H str E C-H str

A′ F- bend A′ F-C str A′′ CH3 torsion A′ C-I str A′′ CH3 rock A′ CH3 rock A′ CH3 deform A′′ CH3 deform A′ C-H str A′′ C-H str

A′′ CH3 torsion A′ F-C str

516 534 887 899 1256 1284 1429 1468 3072 3071 3191 3177 CH3F 1038 1059 1173 1195 1446 1481 1457 1491 3029 3019 3127 3103 FCH3sI76 72 68 66 950 973 1136 1155 1408 1442 1448 1482 3063 3048 3173 3145 F-sHCH2I 77 78 297 282 312 317 436 466 909 930 920 937 1298, 1411 1329, 1446 1461 1499 2246, 3072 2268, 3070 3142 3136 [FsHCH2sI]- TS 142 136 179

mode

exptb A′ C-I str

CH3I A1 C-I str

TABLE 3: Continued

539 A′ CH3 rock 901 A′′ CH3 rock 1276 A′ CH3 deform 1465 A′′ CH3 deform 3080 A′ C-H str 3188 A′′ C-H str 1078 1204 1496 1515 3075 3147

reaction coordinate

B97-1 172 352 383 682 709 861 877 1125, 1166, 1398 1441 3074, 3080, 3239 3226 148i 138i

exptb

1388 1430 3214 3204

a Frequencies are in units of cm-1. Upper values were calculated using the ECP/d basis set and the lower values were calculated using the ECP/t basis set. b The experimental frequencies of CH3I and CH3F are from refs 86 and 87, respectively.

values for the F-sHCH2I potential energy minimum, the F-sHCH2I f [FsHCH2sI]- relative energy, the FCH3sIf CH3F + I- dissociation energy, and reaction exothermicity are -84.5, 10.0, 31.0, and -195.4 kJ/mol, which are in overall good agreement with the CCSD(T)/CBS values of -81.2, 11.3, 31.8, and -202.1 kJ/mol discussed above. The role of ZPE on the stationary point energies was investigated for the CCSD(T)/CBS calculations. As shown in Table 4, the ZPE effect is small for the F-sHCH2I complex and [FsHCH2sI]- TS. But for the FCH3sI- complex and reaction products, the ZPE effect is large increasing their respective energies by 8.4 and 7.3 kJ/mol. This results from the higher vibrational frequencies for the product CH3F as compared to the reactant CH3I. Although the I-sCH3F complexation energy has not been measured, the CCSD(T)/CBS value of 30.7 kJ/mol for 0 K (see Table 4) is consistent with complexation energies of other XsCH3Y complexes.10 Complexation energies of X-sCH3Y complexes depend primarily on the identity of X- and a much smaller extent on the identity of CH3Y,23 although there appears to be a small decrease in the complexation energy in going from CH3I to CH3F.10,23 The experimental ∆Hcomp(298) for I-sCH3I is 38.9 kJ/mol,10 which corresponds to ∆Ecomp(298) of 36.4 kJ/ mol. The CCSD(T)/CBS ∆Ecomp(0) of 30.7 kJ/mol for I-sCH3F is consistent with the experimental ∆Ecomp(298) for I-sCH3I. (The effect of thermal energy in going from 0 to 298 K is small and decreases ∆Ecomp by less than 1 kJ/mol.) D. Comparisons with Previous Calculations. In previous work,23 the F- + CH3I f CH3F + I- PES has been investigated using G2(+) electronic structure theory. With this theoretical model, geometries and frequencies are calculated using the MP2(fc)/6-31+G(d) and HF/6-31+G(d) theories, respectively. Then single-point energies, calculated using MP2 with larger basis sets, are combined with MP4 and QCISD(T) single-point energies and an empirical correction, for the number of valence pairs energies, to obtain energies which approximate those for the 6-311+G(3df,2p) basis set and high-level corrections for electron correlation. ZPE is included, so that the G2(+) energies represent those at 0 K. The previous G2(+) calculations for the F- + CH3I reaction located structures for the C3V traditional SN2 pre- and postreaction complex F-sCH3I and FCH3sI- and [FsCH3sI]- TS,

F- + CH3I f FCH3 + I- Potential Energy Surface

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TABLE 4: Electronic Structure Theory Energies for F- + CH3I f CH3F + I- Stationary Points.a,b stationary points theory MP2 OPBE OLYP BhandH HCTH407 B97-1 CCSD(T) /PP/dc CCSD(T)/PP/t CCSD(T)/PP/q CCSD(T)/CBS

-

F sHCH2I

[FsHCH2sI] TS

FCH3sI-

CH3F + I-

-79.1 -79.9 -75.7 -71.1 -72.8 -67.8 -87.9 -84.5 -80.8 -76.1 -84.5 -81.2 -82.0 -80.8 -80.8 -81.2 (-81.2)d

-66.1 -64.9 -64.0 -59.4 -71.5 -61.1 -74.5 -70.7 -74.5 -69.5 -74.5 -70.7 -70.7 -69.0 -69.5 -69.9 (-69.9)

-208.8 -210.5 -207.5 -200.0 -202.5 -194.6 -259.4 -255.2 -213.8 -205.9 -226.4 -220.5 -222.2 -222.6 -229.3 -233.9 (-225.5)

-172.4 -175.3 -187.4 -180.7 -180.3 -173.6 -230.1 -226.8 -184.9 -177.8 -195.4 -190.8 -187.4 -190.0 -197.1 -202.1 (-194.8) -197.1e

expt

-

a Energies are in kJ/mol with respect to the F- + CH3I reactants, and are at 0 K and do not include ZPE . b For the MP2 and DFT energies the upper values were calculated using the ECP/d basis set and the lower values were calculated using the ECP/t basis set. c The fc orbital method was used for the CCSD(T) calculations. For the PP/x basis sets, x ) d, t, and q, the aug-cc-pVXZ (X ) D, T, and Q) basis sets were used for the C, H, and F atoms and the aug-cc-pVXZ basis, with a PP, was used for iodine. d Values in () include ZPE, with ZPE calculated at the MP2/PP/d level of theory (see the text). e The reaction exothermicity at 0 K without ZPE calculated from standard molar enthalpies of formation in ref 88 and harmonic frequency data in refs 86 and 87.

as was done by the MP2 calculations reported here (see above). This is not unexpected, since G2(+) optimizes structures using MP2(fc)/6-31+G(d) theory and the only difference with the current MP2 calculations are the different and larger basis sets used for the latter (see Table S1). But G2(+) neither located the F-sHCH2I hydrogen-bonded complex or the [FsHCH2sI]TS. In general, the G2(+) structures for the C3V stationary points are in good agreement with the MP2 values reported here, with the principal difference in CsI bond length of the FCH3sIcomplex. For the 5 basis sets considered here, the difference ranges from 0.140 to 0.216 Å. The G2(+) value for the F-sCH3I f [FsCH3sI]- potential energy barrier is 0.8 kJ/mol in comparison to the MP2 values of 2.1 to 9.2 kJ/mol found here (Table S1). The G2(+) complexation energy for the FCH3sI- complex is 30.7 kJ/mol, the same as the CCSD(T)/CBS value in Table 4. Also of interest is the G2(+) complexation energy of 69.6 kJ/mol for the F-sCH3I complex, which is in quite good agreement with the CCSD(T)/CBS and ZPE value of 72.0 kJ/mol, calculated for the MP2/PP/d geometries. Finally, the G2(+) F- + CH3I f CH3F + I- reaction exothermicity is -177.5 kJ/mol. As shown in Table 4, the CCSD(T)/CBS and experimental values are -194.8 and -188.7 kJ/mol, respectively. Botschwina et al.89 studied the Cl-sHCCl3 hydrogen-bonded complex with CCSD(T) theory and a modified aug-cc-pVQZ basis set. Using extrapolation schemes they suggest a 0 K classical complexation energy of 74.5 kJ/mol, which is 74.9 kJ/mol if ZPE is included. The CCSD(T)/CBS 0 K complexation energy is 81.2 kJ/mol for the F-sHCH2Cl hydrogen-bonded complex studied here. This difference in complexation energies is consistent with previous calculations showing that F- forms a stronger complex than does Cl-.23 IV. Summary In the work presented here, properties of stationary points on the F- + CH3I f FCH3 + I- PES were investigated by various electronic structure methods including MP2 and CCS-

D(T) and the DFT functionals OPBE, OLYP, HCTH407, BhandH, and B97-1. The ECP/t and ECP/d basis sets74,75 were used for the MP2 and DFT calculations. The PP/d and PP/t basis sets78 were used for the MP2 and CCSD(T) calculations. The PP/q basis set was included with the CCSD(T) calculations to estimate the complete basis set (CBS) limit. The calculations show that the stationary point properties, including structures, frequencies, and energies, are similar for the above basis sets. For the highest level of theory reported here, CCSD(T)/CBS, the F- + CH3I f FCH3 + I- reaction exothermicity is -202.1 kJ/mol. Since this reaction is the most exothermic among the nonidentity SN2 nucleophilic substitution reactions,23 it is of considerable interest to determine if it retains a central barrier.23,34,35 MP2 theory, with each basis set, identified the C3V F-sCH3I ion-dipole complex, [FsCH3sI]- central barrier structure, and FCH3sI- ion-dipole complex as stationary points on the PES, as well as the Cs F-sHCH2I hydrogen-bonded prereaction complex and [FsHCH2sI]- TS connecting this complex with the F-sCH3I complex. However, the presence of the F-sCH3I and [FsCH3sI]- structures as stationary points on the PES was not confirmed by CCSD(T)/CBS calculations. Single-point CCSD(T)/CBS energies for the MP2/PP/d potential energy curve connecting the F-sCH3I complex and the [FsCH3sI]- TS show that the energy continually decreases in going from the complex to the TS, as compared to the increase for the MP2/PP/d curve. The absence of the C3V F-sCH3I and [FsCH3sI]- structures as stationary points is also suggested by the DFT calculations. Thus, the proposed IRC reaction path79 for product formation is F- + CH3I f F-sHCH2I f [FsHCH2sI]- f FCH3sI- f FCH3 + I- as shown in Figure 3. (The structure of the F-sH2CHI TS connecting two F-sHCH2I complexes was not identified in the work presented here). In general, the calculated reactant CH3I and product CH3F structures are in good agreement with experiment85 for all the theoretical methods, with the ECP/t basis set providing better agreement with experiment than ECP/d. Overall, the CH3I and

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CH3F vibrational frequencies, obtained for the different levels of theory and basis sets, agree well with experiment86,87 with maximum differences ranging from 2-6%, except for MP2/ ECP/t which has a maximum difference of 9%. The B97-1/ ECP/t vibrational frequencies are in the best agreement with experiment. The different electronic structure theories and basis sets give quite different energies for the stationary points, with the differences most pronounced for the FCH3sI- postreaction complex and the CH3F + I- products (see Table 4). CCSD(T)/ CBS calculations were performed to determine approximate “benchmark” values for the stationary point energies, and the CCSD(T)/CBS reaction exothermicity is within 5.0 kJ/mol of the experimental value.88 Although the FCH3sI- f CH3F + I- dissociation energy has not been measured experimentally, the CCSD(T) value is consistent with values for other X-sCH3Y dissociations10 and the same as the G2(+) value.23 The B97-1/ECP/d energies are in the best agreement with the CCSD(T)/CBS energies, with a largest difference of 7.5 kJ/ mol for the FCH3sI- complex. Finally, an important feature of the F- + CH3I reaction is the relatively flat PES for structures in the vicinity of the F-sHCH2I hydrogen-bonded complex. The CCSD(T)/CBS energy for this complex is -81.2 kJ/mol. The energy of the [FsHCH2sI]- TS is -69.9 kJ/mol and only 11.3 kJ/mol higher than that of the complex. Moving from this TS to the FCH3sIpostreaction complex are structures for the C3V F-sCH3I ion-dipole complex and [FsCH3sI]- TS (see Figure 3), which appear to not be stationary points on the actual PES. The CCSD(T) energies for these two respective structures, as given by MP2/PP/d, are -72.8 and -73.6 kJ/mol and are only slightly lower than that for the [FsHCH2sI]- TS. Thus, the reactantside region of the PES is relatively flat, which may have important implications for the reaction dynamics.37 Acknowledgment. This material is based upon work supported by the National Science Foundation under Grant Nos. CHE-0615321 and CHE-0957521, and the Robert A. Welch Foundation under Grant No. D-0005. Support was also provided by the High-Performance Computing Center (HPCC) at Texas Tech University, directed by Philip W. Smith. The authors wish to acknowledge important conversations with the Roland Wester research group, at the University of Freiburg, Germany, concerning dynamics of the F- + CH3I and Cl- + CH3I SN2 nucelophilic substitution reactions. Supporting Information Available: Stationary point geometries, frequencies and energies calculated by MP2 and DFT with different basis sets. This information is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Angel, L. A.; Ervin, K. M. J. Phys. Chem. A 2004, 108, 9827. (2) DeTuri, V. F.; Hintz, P. A.; Ervin, K. M. J. Phys. Chem. A 1997, 101, 5969. (3) Angel, L. A.; Ervin, K. M. J. Am. Chem. Soc. 2003, 125, 1014. (4) Graul, S. T.; Bowers, M. T. J. Am. Chem. Soc. 1994, 116, 3875. (5) Graul, S. T.; Bowers, M. T. J. Am. Chem. Soc. 1991, 113, 9696. (6) Gronert, S. Chem. ReV. 2001, 101, 329. (7) Olmstead, W. N.; Brauman, J. I. J. Am. Chem. Soc. 1977, 99, 4219. (8) DePuy, C. H.; Gronert, S.; Mullin, A.; Bierbaum, V. M. J. Am. Chem. Soc. 1990, 112, 8650. (9) Viggiano, A. A.; Morris, R. A.; Paschkewitz, J. S.; Paulson, J. F. J. Am. Chem. Soc. 1992, 114, 10477. (10) Li, C.; Ross, P.; Szulejko, J. E.; McMahon, T. B. J. Am. Chem. Soc. 1996, 118, 9360. (11) Bickelhaupt, F. M.; Buisman, G. J. H.; de Koning, L. J.; Nibbering, N. M. M.; Baerends, E. J. J. Am. Chem. Soc. 1995, 117, 9889.

Zhang and Hase (12) Wladkowski, B. D.; Brauman, J. I. J. Phys. Chem. 1993, 97, 13158. (13) Moylan, C. R.; Brauman, J. I. In AdVances in Classical Trajectory Methods; Hase, W. L., Ed.; JAI press: New York, 1994; Vol 2, p 95. (14) Tucker, S. C.; Truhlar, D. G. J. Am. Chem. Soc. 1990, 112, 3338. (15) Tucker, S. C.; Truhlar, D. G. J. Phys. Chem. 1989, 93, 8183. (16) Chandrasekhar, J.; Smith, S. F.; Jorgensen, W. L. J. Am. Chem. Soc. 1985, 107, 154. (17) Swart, M.; Sola`, M.; Bickelhaupt, F. M. J. Comput. Chem. 2007, 28, 1551. (18) Bento, A. P.; Sola`, M.; Bickelhaupt, F. M. J. Comput. Chem. 2005, 26, 1497. (19) Hase, W. L. Science 1994, 266, 998. (20) Wang, H.; Zhu, L.; Hase, W. L. J. Phys. Chem. 1994, 98, 1608. (21) Vande Linde, S. R.; Hase, W. L. J. Phys. Chem. 1990, 94, 2778. (22) Glukhovtsev, M. N.; Pross, A.; Radom, L. J. Am. Chem. Soc. 1995, 117, 2024. (23) Glukhovtsev, M. N.; Pross, A.; Radom, L. J. Am. Chem. Soc. 1996, 118, 6273. (24) Glukhovtsev, M. N.; Pross, A.; Bernhard Schlegel, H.; Bach, R. D.; Radom, L. J. Am. Chem. Soc. 1996, 118, 11258. (25) Shaik, S.; Ioffe, A.; Reddy, A. C.; Pross, A. J. Am. Chem. Soc. 1994, 116, 262. (26) Parthiban, S.; de Oliveira, G.; Martin, J. M. L. J. Phys. Chem. A 2001, 105, 895. (27) Lieder, C. A.; Brauman, J. I. J. Am. Chem. Soc. 1974, 96, 4029. (28) Brauman, J. I.; Olmstead, W. N.; Lieder, C. A. J. Am. Chem. Soc. 1974, 96, 4030. (29) Su, T.; Morris, R. A.; Viggiano, A. A.; Paulson, J. F. J. Phys. Chem. 1990, 94, 8426. (30) O’Hair, R. A. J.; Davico, G. E.; Hacaloglu, J.; Dang, T. T.; DePuy, C. H.; Bierbaum, V. J. Am. Chem. Soc. 1994, 116, 3609. (31) Wang, H.; Hase, W. L. J. Am. Chem. Soc. 1997, 119, 3093. (32) Botschwina, P.; Horn, M.; Seeger, S.; Oswald, R. Ber. BunsenGes. Phys. Chem. 1997, 101, 387. (33) Su, T.; Wang, H.; Hase, W. L. J. Phys. Chem. A 1998, 102, 9819. (34) Shaik, S. S.; Schlegel, H. B.; Wolfe, S. Theoretical Aspects of Physical Organic Chemistry, The SN2 Mechanism; Wiley: New York, 1992. (35) Wolfe, S. Can. J. Chem. 1984, 62, 1465. (36) Mikosch, J.; Trippel, S.; Eichhorn, C.; Otto, R.; Lourderaj, U.; Zhang, J.-X.; Hase, W. L.; Weidemu¨ller, M.; Wester, R. Science 2008, 319, 183. (37) Mikosch, J. Ph.D. Dissertation, Dynamics of Anion-Molecule Reactions at Low Energy; Physikalisches Institut, Universita¨t Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany, 2007. (38) Zhang, J.-X.; Lourderaj, U.; Addepalli, S. V.; de Jong, W. A.; Hase, W. L. J. Phys. Chem. A 2009, 113, 1976. (39) Baer, T.; Hase, W. L. In Unimolecular Reaction Dynamics Theory and Experiments; Oxford: New York, 1996. (40) Glasstone, S.; Laidler, K. J.; Eyring, H. In The Theory of Rate Processes; McGraw-Hill: New York, 1941. (41) Craig, S. L.; Brauman, J. I. J. Phys. Chem. A 1997, 101, 4745. (42) Chabinyc, M. L.; Craig, S. L.; Regan, C. K.; Brauman, J. I. Science 1998, 279, 1882. (43) Wang, H.; Hase, W. L. J. Am. Chem. Soc. 1995, 117, 9347. (44) Vande Linde, S. R.; Hase, W. L. J. Am. Chem. Soc. 1989, 111, 2349. (45) Hase, W. L.; Cho, Y. J. J. Chem. Phys. 1993, 98, 8626. (46) Wang, H.; Peslherbe, G. H.; Hase, W. L. J. Am. Chem. Soc. 1994, 116, 9644. (47) Peslherbe, G. H.; Wang, H.; Hase, W. L. J. Am. Chem. Soc. 1996, 118, 2257. (48) Mann, D. J.; Hase, W. L. J. Phys. Chem. A 1998, 102, 6208. (49) Li, G.; Hase, W. L. J. Am. Chem. Soc. 1999, 121, 7124. (50) Su, T.; Wang, H.; Hase, W. L. J. Phys. Chem. A 1998, 102, 9819. (51) Sun, L.; Hase, W. L.; Song, K. J. Am. Chem. Soc. 2001, 123, 5753. (52) Sun, L.; Song, K.; Hase, W. L. science 2002, 296, 875. (53) Wang, Y.; Hase, W. L.; Wang, H. J. Chem. Phys. 2003, 118, 2688. (54) Schmatz, S.; Botschwina, P.; Hauschildt, J.; Schinke, R. J. Chem. Phys. 2002, 117, 9710. (55) Hennig, C.; Oswald, R. B.; Schmatz, S. J. Phys. Chem. A 2006, 110, 3071. (56) Schmatz, S.; Hennig, C. Chem. Phys. Lett. 2007, 446, 250. (57) Schmatz, S.; Hennig, C. J. Chem. Phys. 2009, 131, 224303. (58) Basilevsky, M. V.; Ryaboy, V. M. Chem. Phys. Lett. 1986, 129, 71. (59) Bolton, K.; Hase, W. L.; Peslherbe, G. H. Multidimensional Molecular Dynamics Methods; Thompson, D. L. Ed.; World Scientific Publishing, Inc.: London, 1998; pp 143-189. (60) Lo´pez, J. G.; Vayner, G.; Lourderaj, U.; Addepalli, S. V.; Kato, S.; deJong, W. A.; Windus, T. L.; Hase, W. L. J. Am. Chem. Soc. 2007, 129, 9976. (61) Deng, L.; Branchadell, V.; Ziegler, T. J. Am. Chem. Soc. 1994, 116, 10645.

F- + CH3I f FCH3 + I- Potential Energy Surface (62) Gonzales, J. M.; Cox, R. S., III.; Brown, S. T.; Allen, W. D.; Schaefer, H. F., III. J. Phys. Chem. A 2001, 105, 11327. (63) Gonzales, J. M.; Allen, W. D.; Schaefer, H. F., III. J. Phys. Chem. A 2005, 109, 10613. (64) Wladkowski, B. D.; Allen, W. D.; Brauman, J. I. J. Phys. Chem. 1994, 98, 13532. (65) Botschwina, P. Theor. Chem. Acc. 1998, 99, 425. (66) Borisov, Y. A.; Arcia, E. E.; Mielke, S. L.; Garrett, B. C.; Dunning, T. H., Jr. J. Phys. Chem. A 2001, 105, 7724. (67) Cho, Y. J.; Vande Linde, S. R.; Zhu, L.; Hase, W. L. J. Chem. Phys. 1992, 96, 8275. (68) Hehre, W. J.; Radom, L.; Schleyer, P. V. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986. (69) Adams, G. F.; Bent, G. D.; Bartlett, R. J.; Purvis, G. D. In Potential Energy Surfaces and Dynamics Calculations; Truhlar, D. G., Ed.; Plenum: New York, 1981; p 133. (70) Koch, W.; Holthausen, M. C. A Chemist’s Guide to Density Functional Theory; Wiley-VCH: Weinheim, Germany, 2000. (71) Parr, R. G.; Yang, W. Density Functional Theory of Atoms and Molecules; Oxford University Press: New York, 1989. (72) Dreizler, R.; Gross, E. Density Functional Theory; Plenum Press: New York, 1995. (73) Perdew, J. P.; Ruzsinszky, A.; Tao, J. M.; Staroverov, V. N.; Scuseria, G. E.; Csonka, G. I. J. Chem. Phys. 2005, 123, 062201. (74) (a) Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007. (b) Woon, D. E.; Dunning, T. H., Jr. J. Chem. Phys. 1993, 98, 1358. (75) Wadt, W. R.; Hay, P. J. J. Chem. Phys. 1985, 82, 284. (76) Hu, W.-P.; Truhlar, D. G. J. Phys. Chem. 1994, 98, 1049. (77) Hu, W.-P.; Truhlar, D. G. J. Am. Chem. Soc. 1995, 117, 10726. (78) Peterson, K. A.; Shepler, B. C.; Figgen, D.; Stoll, H. J. Phys. Chem. A 2006, 110, 13877. (79) Fukui, K. Acc. Chem. Res. 1981, 14, 363. (80) Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M. Chem. Phys. Lett. 1989, 157, 479.

J. Phys. Chem. A, Vol. 114, No. 36, 2010 9643 (81) Peterson, K. A.; Woon, D. E.; Dunning Jr, T. H. J. Chem. Phys. 1994, 100, 7410. (82) (a) Bylaska, E. J.; de Jong, W. A.; Govind, N.; Kowalski, K.; Straatsma, T. P.; Valiev, M.; Wang, D.; Apra, E.; Windus, T. L.; Hammond, J.; Nichols, P.; Hirata, S.; Hackler, M. T.; Zhao, Y.; Fan, P.-D.; Harrison, R. J.; Dupuis, M.; Smith, D. M. A.; Nieplocha, J.; Tipparaju, V.; Krishnan, M.; Wu, Q.; Van Voorhis, T.; Auer, A. A.; Nooijen, M.; Brown, E.; Cisneros, G.; Fann, G. I.; Fruchtl, H.; Garza, J.; Hirao, K.; Kendall, R.; Nichols, J. A.; Tsemekhman, K.; Wolinski, K.; Anchell, J.; Bernholdt, D.; Borowski, P.; Clark, T.; Clerc, D.; Dachsel, H.; Deegan, M.; Dyall, K.; Elwood, D.; Glendening, E.; Gutowski, M.; Hess, A.; Jaffe, J.; Johnson, B.; Ju, J.; Kobayashi, R.; Kutteh, R.; Lin, Z.; Littlefield, R.; Long, X.; Meng, B.; Nakajima, T.; Niu, S.; Pollack, L.; Rosing, M.; Sandrone, G.; Stave, M.; Taylor, H.; Thomas, G.; van Lenthe, J.; Wong, A.; Zhang, Z., NWChem, A Computational Chemistry Package for Parallel Computers, Version 5.1; Pacific Northwest National Laboratory, Richland, Washington 99352-0999, USA, 2007. (b) Kendall, R. A.; Apra, E.; Bernholdt, D. E.; Bylaska, E. J.; Dupuis, M.; Fann, G. I.; Harrison, R. J.; Ju, J.; Nichols, J. A.; Nieplocha, J.; Straatsma, T. P.; Windus, T. L.; Wong, A. T. Comput. Phys. Commun. 2000, 128, 260–283. (83) Gordon, M. S.; Schmidt, M. W. Theory Appl. Comput. Chem.: First Forty Years 2005, 1167. (84) Lourderaj, U.; Song, K.; Windus, T. L.; Zhuang, Y.; Hase, W. L. J. Chem. Phys. 2007, 126, 044105. (85) Lide, D. R. In CRC Handbook of Chemistry and Physics, 86th ed.; CRC Press: Boca Raton, 2005. (86) Duncan, J. L.; Allan, A.; Mckean, D. C. Mol. Phys. 1970, 18, 289. (87) Law, M. M.; Duncan, J. L.; Mills, I. M. J. Mol. Struct. 1992, 260, 323. (88) Chase, M. W., Jr.; Davies, C. A.; Downey, J. R., Jr.; Frurip, D. J.; McDonald, R. A.; Syverud, A. N. J. Phys. Chem. Ref. Data 1985, 14 (Suppl. 1) ., (89) Botschwina, P.; Oswald, R.; Dyczmons, V. Int. J. Mass Spectrom. 2007, 267, 308.

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