The Journal of
Physical Chemistry
0 Copyright 1994 by the American Chemical Society
VOLUME 98, NUMBER 4, JANUARY 27, 1994
LETTERS Structural Distortion of CH3I in an Ion-Dipole Precursor Complex Wei-Ping Hu and Donald G. Truhlar' Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 Received: October 20, 1993; In Final Form: December I O , 1993"
Extended basis set calculations including electron correlation are used to calculate the properties of I-.CH3I and I-CD3Iion-molecule complexes. The results show smaller geometrical distortions of the molecular entity upon complexation than were inferred from recent experiments.
1. Introduction Recent experiments in which ion-dipole-complex precursors to S Nreactions ~ are generated,lS2a ~ t i v a t e dand , ~ spectroscopically pr0bed~3~ in the gas phase provide a new type of quantitative information about structures partway between reactants and transition states. In particular, such studies provide detailed information about structural changes in the critical incipient phase of the motion of a reactive system along the reaction path. Since many of the most successful qualitative theories of chemical reactivity, such as frontier molecular orbital theory6 and electrostatic reactivity indexes,' are based on the properties or deformations of reactants in the presence of a weakly perturbing reactive partner, the opportunity to study the properties of such systems quantitatively is very promising in terms of fundamental theoretical kinetics. A stimulating experimental study of ion-dipole precursor complexes reported recently is the photoelectron spectroscopic characterization of I-CHJ and I-CD3I by Cyr et ~ 1 Their . ~ spectra were interpreted as being consistent with an experimental determination of the enthalpy of binding that yielded -9.0 f 0.2 kcal/mol.2 They observed a C-I stretching frequency progression accompanied by fundamentals in the C-H stretch and CH3 umbrella mode for both I-CH3I and I-CDsI. A Franck-Condon analysis indicated 0.06-0.07-and 0.01-0.025-A distortions of the C-I and C-H bond lengths, respectively, and a 1-2' distortion of the H-C-I bond angle. All the experimental distortions are Q
Abstract published in Advance ACS Abstracts, January 15, 1994.
0022-3654/94/2098- 1049$04.50/0
of indeterminate sign. In the present work we report correlated electronic structure calculations of these geometrical distortions.
2. Calculations We performed all-electron electronic structure calculations with two extended contracted Gaussian basis sets which will be abbreviated APDZ (augmented polarized double zeta) and APTZ (augmented polarized triple zeta). The APDZ basis consists of Dunning's augmented correlation consistent polarized valence double-zeta sets for H and C* and a comparable basis, called SVZP+, for I. The SV2P+ basis consists of Andzelm et ale's SV2P basis9augmented by onediffuse s function (exponent 0.034) and one diffuse p set (exponent 0.039). The APTZ basis consists of Dunning's augmented correlation consistent polarizedvalence triple-zeta basis for H and C,8 without the diffuse f function for C, and a comparable basis for I, in particular a basis obtained from the work of Stromberg et a1.10 To be consistent with the numbers of different types of contracted basis functions for C and H , we used a (5,24,12/5,2,14/3,13) contraction for the iodine basis. We then augmented the basis with diffuse s, p, and d functions and a polarization f function (with exponents 0.040,0.038,0.030, and 2.57, respectively). Since the iodine basis set is probably inferior to the C and H bases, we also decided to perform calculations with the same C and H bases but with the APTZ iodine basis uncontracted. We call this modified basis, uncontracted on I, the APTZ-UI basis set. All calculations with the basis sets mentioned above are nonrelativisitic. 0 1994 American Chemical Society
1050 The Journal of Physical Chemistry, Vol, 98, No. 4, 1994
TABLE 1: Basis Set Sizes. ~
H
APDZ
(5~2~) WPl (6s3p2d) [4s3p2d] (6~3p2d) [4s3pZd]
C ( 1Os5p2d)
~~
I (14sl lp7d)
[4s3p2d] [7s6p3d] APTZ (lls6p3dlf) (16s12p7dlf) [5s4p3dlfl [8s7pSdlfl APTZ-UI (1 l~6p3dlf) (16~12~7dlf) [5s4p3dlfl [16s12p7dlfl ECP (5~2~) (10s5p2d) (4s4p2d)b [ 4s3p2dI [4s4p2dIb WPl (...)denotesthe primitive basis, and [..,I denotes thecontractedbasis. The d sets consist of six functions in APDZ and APTZ sets and consist of five functions in the APTZ-UI and ECP sets. All f sets consist of seven functions. This basis is used with an effective core potential on I. Considering that basis set superposition error7aJ1(BSSE) is often severe in calculations of association energies, especially when the basis set does not saturate the space of thecore electrons, and that relativistic effects might not be negligible for iodine, we also carried out a set of calculations in which we used Wadt and Hay's relativistic effective core potentialI2 (ECP) for iodine to represent the core electrons. For these calculations we used an uncontracted iodine basis set consisting of Wadt and Hay's 3s3p valence basis augmented with a d polarization function and diffuse s, p, and d functions (with exponents 0.262, 0.034, 0.039, and 0.0873, respectively). We combined this new basis and the effective core potential for iodine with the APDZ basis set for C and H. We call this new basis the ECP basis set. The basis set sizes are summarized in Table 1. All bases were used to optimize the geometries of CH31and I-.CH3I including electron correlation at the level of MrallerPlesset second-order perturbation theory (MP2I3). In addition, we calculated vibrational frequencies at the MP2/APDZ level. We also used the APDZ basis to optimize the geometry with electron correlation included by quadratic configuration interaction including single and double substitutions with the triples included pert~rbativelyl~ [QCISD(T)/APDZ]. The calculations were carried out with GAUSSIAN 92 programlson theCray Y-MP C916/8256 computer at Minnesota Supercomputer Center. 3. Results The calculated geometries are compared to experiment in Table 2. The optimized geometries of CH31 and I-CHJ are of C3, symmetry as expected. (The geometries are independent of isotopic substitution because of the Born-Oppenheimer approximation.) The I-C-I bond angle in the complex is 180'. The experimental values for CH31are from microwave data.I6J7The experimental values for the changes upon complexation are averages of the values inferred from the I-.CH31 and I-.CD31 spectra by Cyr et al.5 The distance from the iodide ion to the carbon atom in the complex was calculated to be 3.396 A at the MP2/APDZ level, 3.388 A at the QCISD(T)/APDZ level, 3.484 A at the MP2/ ECP level, 3.377 8,at the MP2/APTZ level, and 3.396 A at the MPZ/APTZ-UI level, with either the MP2/ECP value or the last mentioned value presumed to be most accurate. Table 3 gives calculated and experimental vibrational frequencies. The experimental frequencies are harmonic values from Dickson et al.I8 Table 4 gives results for dipole moments,l9320 the absolute energies, and the electron affinity21 of I. Since neutral I has an odd number of electrons, the MP2 results for I are based on unrestricted MP2 theory, which is still abbreviated MP2. Since unrestricted MP2 theory does not yield spin eigenfunctions, neutral I was also calculated with spin-projected MP2 theory, abbreviated PMP2.25 This lowered the energy 0.7 kcal/mol for all four basis sets.
Letters The complexation energies are also summarized in Table 4. In this table, AE is the electronic energy change upon complexation, and the internal energy change at 0 K is
AU, = AE
+ A(ZPE)
(1) where ZPE is the harmonic zero-point energy. The enthalpy change at temperature T is
AH, = AU,,
+ AE( T ) - R T
(2)
where A,!?( T )is the thermal vibrational-rotational-translational excitation energy change, R is the gas constant, and T is temperature. Table 4 gives two sets of theoretical results for thecomplexation energies and enthalpies. The first set is based on the directly calculated AE, and the second set is based on AE values with a counterpoise c ~ r r e c t i o n I ~(CC) ~ ~ ~ to - ~ account ~ for basis set superposition error. Table 4 also lists experimental values for AVOand AHT. The first value given for AVOis from ref 5 and corresponds to the shift of the I-sCH3I photoelectron spectra from that of I-. This shift equals AVOunder the assumption5 that the energy of interaction of neutral I with CH3I is negligible at the I-.CH3I geometry. The second value of AVOis discussed in the next paragraph. The experimental enthalpy change in Table 4 from ref 2 is interpreted as avalue at the center of the experimental temperature range, namely 488 K. We also decided to test the assumption mentioned in the previous paragraph that was used to interpret the experiment of ref 5. An energy balance analysis based on the Franck-Condon principle shows that (3) where A(hu) is the shift (+8.8 kcal/mol) of the I-CH3I photoelectron spectrum from the I- one, and K.CH,Iis the interaction energy of I with CH31 at the I-CH3I geometry. We calculated VI.CH~I at the MP2 level with all the basis sets used in this work, and the results are summarized in Table 5. (Results calculated with the MP2 and PMP2 methods agree to the precision shown in the table.) Using the average value of the counterpoisecorrected calculated interaction energy of neutral I with CH31 at the I-CH3I equilibrium geometry, we calculated a corrected "experimental" value of AVO,and this is given in Table 4, last column, footnoted as h. We also searched with the APDZ and ECP basis sets for other local minima of the potential energy that might correspond to other binding geometries of the complex. We found another minimum with both basis sets for a complex with C3, symmetry in which the I- approaches the I end of CH31 with a collinear I-I-C bond angle. The calculated binding energies AE with the counterpoise corrections are-2.3 and-4.3 kcal/mol for the APDZ and ECP basis sets, respectively, for this second minimum. These binding energies are significantly smaller than for the I-.CH31 global minimum with 180' I-C-I bond angle, so only the latter geometry is considered further in this paper. No other minimumenergy geometry of the ion-dipole complex was found. 4. Discussion
We first look at the calculated dipole moment of CH31because this dipole moment is largely responsible for the stability of the ion-dipole complex. Table 4 shows that the dipole moments calculated from the MP2 density are in good agreement with the experimental values.19~20Table 4 also shows the dipole moments calculated from the S C F density, which are about 25% high. We concluded that the inclusion of electron correlation has a significant effect on the single-particle density of CH31. For this reason we present only results for correlated calculations (Le., MP2 and QCISD(T) calculations) for all other quantities in this paper.
Letters TABLE 2
The Journal of Physical Chemistry, Vol. 98, No. 4, 1994 1051 Geometries of CHd in Isolation and in I - C H p
C-H bond length, A H-C-I bond angle, deg C-I bond length, A H-C-H bond angle, deg
MP2/APDZ 1.095b -0.003c 108.05 -0.06 2.150 +0.034 110.86 +0.05
QCISD(T)/APDZ 1.098 -0.003 107.92 -0.16 2.165 +0.040 110.98 +0.15
MP2/ECP 1.096 -0.003 107.78 -0.15 2.146 +0.033 111.11 +0.14
MP2/APTZ 1.082 -0.003 108.16 +0.26 2.109 +0.026 110.75 -0.25
MP2IAPTZ-UI 1.082 -0.003 108.28 +0.33 2.110 +0.026 110.64 -0.32
exP 1.100, 1.092b *(0.018 0.005)c 107.9, 106.7 f(1.5 0.5) 2.139,2.139 f(0.066 0.005) 111.0,112.1 d
* *
a Both C3,. Upper value: CH3I. Experimental value from ref 16 followed by value from ref 17. Lower value: change upon complexation with I-. Experimental value from ref 5. Not available.
TABLE 3: Harmonic Vibrational Frequencies (cm-1) mode X=H X=D system (symmetry) MP2/APDZ exp' MP2/APDZ exp" 3111 1293 559 3234 1461 896 3143 1235 492 66 3280 1434 870 64
3060 1288 533 3229 1504 906
2224 979 522 2401 1059 665 2245 923 466 66 2435 1041 643 51
2210 975 502 2400 1083 676
The association energies in Table 4 calculated without the counterpoise calculation correction differ from experiment275 by 3-4 kcal/mol. Although the differences are large, association energies are notoriously hard to calculate, and the BSSE tends to cause them to be too negative. The calculated results with counterpoise correction greatly improve the agreement with experiment. Also, from Table 5 we learn that the interaction energy V,.CH,I is not negligible, and we used eq 3 and the average value from Table 5 to assign a new value for the experimental AVO,which is included in the last column of Table 4. This new value, -7.9 kcal/mol, of AVO agrees even better with our counterpoise-corrected calculations, which are in the range -7.5 to -8.3 kcal/mol, with the best basis set yielding -7.7 kcal/mol. The calculated enthalpy changes are still different from the experimental value in ref 2 by 1.0-1.8 kcal/mol, but we suspect that this older experimental value is not very accurate. We expected that the overestimate of the binding energy in the original calculations arose primarily from BSSE associated with the incompleteness of the basis set for iodine core electrons, and so we replaced the iodine core by an ECP. Table 4 shows that this reduced the BSSE on the binding energy AE by a factor of about 3. Similarly uncontracting the iodine basis improves the representation of the core and decreases the counterpoise correction by 17%. Another check of the energies is provided by the electron affinity. Table 4 shows good agreement of this quantity with experiment.21 The electron affinity calculation involves the neutral I atom, which is an open-shell system. For open-shell systems it is sometimes better to use the spin-projected PMP2 method than to use straight MP2; this lowers the electron affinities by 0.7 kcal/mol for all four basis sets, resulting in improved agreement with experiment. The PMP2 electron affinity with the largest basis, APTZ-UI, is 70.8 kcal/mol, only 0.3 kcal/mol different from experiment. The vibrational frequencies were calculated only with the smaller basis set, but Table 3 shows that they are remarkably (and reassuringly) accurate, with an average unsigned deviation from the experimental values of only 22 cm-1 for CH31 and 12
cm-1 for CD31. Frequency changes upon complexation range from -67 cm-1 for v3 to +46 cm-' for u4, and the frequencies of the two loose transitional modes are predicted to be 64-66 cm-1, but there are no experimental data to compare with these predictions. We next turn to Table 2, which is the main point of comparison with the new experiments. Our results agree qualitatively with experiment5 in that the largest structural change upon complexation is the C-I bond length, but Table 2 shows that all the calculated geometrical distortions, with all basis sets and both levels of treating electron correlation, are considerably smaller than inferred5 from experiment. We would expect the calculated values of these distortions to be more accurate than the absolute geometries and not to suffer greatly from BSSE. This is confirmed by the similar magnitudes of the geometrical distortions calculated with all electrons and with the iodine ECP. The fact that the calculated distortion of the C-H bond distance and the angles are lower than the experimental values is perhaps not too surprising (even though the discrepancies between experiment and the calculations with our largest basis set are factors of 6 and 4l/2, respectively) because the C-H fundamental is weak and the umbrella mode is not actually resolved; thus, the experimentalists refer to these values as upper bounds and rough estimates. But the theoretical/experimental discrepancy of a factor of 11/2-21/2 for the C-I stretch is quite surprising since a clear progression was resolved for this mode. The analysis of the experiments included the Duschinsky effect26 but assumed harmonic vibrations, the same force constants in the neutral and anionic molecules, and the validity of the Franck-Condon approximation. It seems unlikely that principal (Le., intramode) anharmonicity can account for the discrepancy, but perhaps m o d e mode coupling, the change in force constants upon excitation, or the geometry dependence of the electronic transition moment needs to be considered. The small changes in the calculated bond angles indicate that very little change in carbon hybridization has occurred in the ion-dipole complex. The small changes in the C-I bond length, which is the reaction coordinate, indicate that the precursor complex has not proceeded very far in the direction of products. The calculations in Table 2 provide checks on both the basis set size, APDZ vs APTZ and APTZ-UI, and the level of electron correlation, MP2 vs QCISD(T). The QCISD(T) calculation, since it includes triple excitations, also provides a check on the adequacy of basing the electron correlation calculations on a single reference configuration. Comparing each of the more complete calculations to the MP2/APDZ calculations shows that the geometrical distortions are well converged in all of these respects. Tadjeddine27 performed calculations on CH31with and without spin-orbit coupling. Their calculations predict that spin-orbit coupling increases the C-I bond length by 0.005 A. It is not clear how this increase would be affected by the presence of I- in the complex, but presumably most of the spin-orbit effect would cancel when one considers the effect of complexation on bond length in the molecule. One possible explanation-in the theory-for the qualitative
1052 The Journal of Physical Chemistry, Vol. 98, No. 4, 1994
TABLE 4
Letters
Dipole Moments, Energies, Energy and Enthalpy Changes upon Complexation, and Electron Affinity of I
P (CHsI), D E(CHsI), hartreesc E(1-), hartrees E(I-.CHJ), hartrees E(I), hartrees EA! kcal/mol
AE, kcal/mol AVO,kcal/mol A H z g 8 , kcal/mol M 4 8 8 , kcal/mol
AE, kcal/mol AVO,kcal/mol A H 2 9 8 , kcal/mol Aff488, kcal/mol
MP2/APDZ 1.77 (2.15)' -6952.4883 -6912.7963 -13865.3037 -6912.6808 72.5
QCISD(T)/APDZ (2.17) -6952.5240 -6912.8058 -13865.3494 -6912.6940 70.1
-12.0 -11.9 -1 1.8 -11.6 -8.0 -7.9 -7.8 -7.6
MP2/ECP 1.69 (2.02) -51.0521 -1 1.3690 -62.4366 -11.2521 73.4
MP2/APTZ 1.62 (2.04) -6955.9377 4916.1949 -13872.153 1 -6916.0818 71.0
MPZ/APTZ-UI 1.65 (2.07) -6957.6470 -6917.9078 -1 3875.5741 -691 7.7939 71.5
Interaction Energies without Counterpoise Correction -12.3 -9.7 -12.8 [-9.61 [-12.71 [-12.2Y [-9.51 [-12.61 [-12.11 [-11.91 [-9.31 [-12.41
-12.1 [-12.01 [-11.91 [-11.71
Interaction Energies Including Counterpoise Correction -7.6 -8.4 [-7.51 [-8.31 [-8.21 [-7.41 [-7.21 [-8.01
-7.8 [-7.71 [-7.61 [-7.41
exP 1.64, 1.62b
70.5e
-8.8 f 0.5,#-7.9 f 1.1* -9.0 f 0.2'
-8.8 f 0.5, -7.9 f 1.1 -9.0 f 0.2
4 S C F values in parentheses. Value from ref 19 followed by value from ref 20. 1 hartree = 627.51 kcal/mol. EA E(1) - E(I-). Reference 21. /Values in brackets were obtained by calculating AE at the level indicated in the column heading and calculating A(ZPE) and the translationalrotational-vibrational contributions to AE(T) at the MP2/APDZ level. 8 Reference 5. From eq 3 and the last column of Table 5. Reference 2.
'
*
TABLE 5
Interaction Energy
V, kcal/mol F C , O kcal/mol
MPZIAPDZ
MP2lECP
MP21APTZ
MPZ/APTZ-UI
average
-1.5 1.6
-1 .o 0.1
-1.9 1.4
-2.1 0.5
0.9 f 0.6b
Interaction energy including counterpoise calculation correction. Root-mean-square deviation from average.
difference of theory and experiment for the shift in C-I bond length is inadequate accounting for configuration interaction effects responsible for dispersion forces, which are more significant relative to electrostatic and induction forces for heavy atoms than for light ones. Further experimental work would also be valuable before we place too much confidence in chemical interpretations of the distortions. Acknowledgment. The authors are grateful to Mark Johnson for a preprint of ref 5 and to Doreen Leopold for helpful discussions. This work was supported in part by the National Science Foundation. References and Notes (1) (a) Riveros, J. N.; Breda, A. C.; Blair, L. K. J . Am. Chem. SOC.1973, 95,4066. (b) Dougherty,R. C.;Dalton, J.; Roberts, J. D. 0rg.Mass.Spectrom. 1974, 8, 77. (c) Dougherty, R. C.; Roberts, J. D. Ibid. 1974, 8, 85. (d) Dougherty, R. C. Ibid. 1974,8, 85. (e) Olmstead, W. N.; Brauman, J. I. J. Am. Chem. SOC.1977,99, 4219. (0 Sen Sharma, D. K.; Kebarle, P. Ibid. 1982,104,19. (g) Dcdd, J. A.; Brauman, J. I. J . Phys. Chem. 1986,90,3559. (2) Dougherty, R. C.; Dalton, J.; Roberts, J. D. Org. Mass. Spectrom. 1974, 8, 8 1. (3) (a) Graul, S. T.; Bowers, M. T. J. Am. Chem. SOC.1991,113,9696. (b) Cyr, D. M.; Posey, C. A.; Bishea, G. A.; Han, C.-C.; Johnson, M. A. Ibid. 1991. 113. 9697. IC) Wilbur. J. L.: Brauman. J. I. Ibid. 1991. 113. 9699. (4) Cyr, D. M'.;'Bishea, G. A,; Scarton, hi. G.; Johnson, hi. A. j . Am. Chem. SOC.1992, 97, 5911. (5) Cyr, D. M.; Scarton, M. G.; Johnson, M. A. J . Chem. Phys. 1993, 99, 4869. (6) (a) Fukui, K. In Molecular Orbitals in Chemistry, Physics, and Biology;Lilwdin, P. O., Pullman, B., Eds.; Academic: New York, 1964; p 513. (b) Klopman, G. J . Am. Chem. SOC.1968, 90, 223. (7) (a) Morokuma, K.; Kitaura, K. In Chemical Applications of Atomic and Molecular Electrostatic Potentials; Politzer, P., Truhlar, D. G., Eds.; Plenum: NewYork, 1981;p215. (b) Kollman,P.A.Ibid.,p243. (c)Tomasi, J. Ibid., p 295.
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1984, 5, 146. (10) Strdmberg, A.; Gropen, 0.;Wahlgren, U.J . Comput. Chem. 1983, 4, 181. (11) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 17, 553. (12) Wadt, W. R.; Hay, P. J. J. Chem. Phys. 1985,82, 284. (13) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab initio Molecular Orbital Theory; Wiley: New York, 1986. (14) Pople, J. A.; Head-Gordon, M. J . Chem. Phys. 1987, 87, 5968. (15) Gaussian 92, Revision D.2: Frisch, M. J.; Trucks, G. W.; HeadGordon, M.; Gill, P. M.; Wong, M. W.; Foresman, J. B.;Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A., Gaussian, Inc., Pittsburgh, PA, 1992. (16) Gordy, W.; Simmons, J. W.; Smith, A. G. Phys. Rev.1948,74,243. (17) Chang, T . 4 . Ph.D. Thesis, University of Michigan, 1954, as quoted in: King, W. T.; Mills, I. M.; Crawford, B., Jr. J . Chem. Phys. 1957,27,455. (18) Dickson,A. D.; Mills, I. M.;Crawford, B., Jr. J . Chem. Phys. 1957, 27, 445. (19) McClellan, A. L. Tables of Experimental Dipole Moments; W. H. Freeman: San Francisco, CA, 1963. (20) Nelson, R. D., Jr.; Lide, D. R., Jr.; Maryott, A. A. Selected Values of Electric Dipole Moments for Molecule in the Gas Phase; National Bureau of Standards: Washington, DC, 1967. (21) 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. 11, 2. (22) Meunier, A.; Levy, B.; Berthier, G. Theor. Chim. Acta 1973,29,49. (23) Kolos, W. Theor. Chim. Acta 1979, 51, 219. (24) Schwenke, D. W.; Truhlar, D. G. J . Chem. Phys. 1985, 82, 2418, 1987, 86, 3760 (E). (251 Schlenel, H. B. J . Chem. Phvs. 1986. 84, 4530. (26) (a) Duschinsky, F. ActaPhysicochim. CJRSS1937,1,551. (b) Small, G . J. J . Chem. Phys. 1971, 54, 3300. (27) Tadjeddine, M.; Flament, J. P.;Teichteil, C. Chenz. Phys. 1987,118, 45.
