J . Phys. Chem. 1985, 89, 2192-2194
2192
energy at the equilibrium geometry; a small basis set (6-31G) perturbation c a l c ~ l a t i o nshows ~ ~ the electrostatic energy to be -0.0102 hartree, and the exchange-repulsion energy to be +0.0040 hartree., while polarization and charge transfer together contribute only -0.0010 hartree. Accordingly, the Buckingham-Fowler model,3 in which structures are predicted on the basis of electrostatic interactions as described using distributed multipoles, together with a hardsphere repulsive potential, should give a good account of the geometry. The structure predicted by this model is indeed the T-shaped structure found by Klemperer,] although a hydrogenbonded structure was also found at much higher energy. The intermolecular distances found by such a model have no predictive significance, being merely sums of hard-sphere radii, and in the absence of a suitable van der Waals radius for carbon we used (50) I. C. Hayes and A. J. Stone, Mol. Phys., 53, 83 (1984). (51) G.D. Zeiss and W. J. Meath, Mol. Phys., 33, 1155 (1977).
a value which gives the observed C-N distance when combined with the standard Pauling radius for nitrogen. For the electrostatic description we used the five-center DMA for COz given in Table X and the four-center DMA for N H 3 given in Table XI. In this paper we have attempted to show the very great wealth of information which can be obtained on the properties of molecules. Here we have concentrated on the ab initio calculation of those properties which affect the long-range interaction of molecules, several of which have not been calculated before, but are very important if that interaction is to be understood. These calculations have been performed at the S C F level with a good basis, and this is probably sufficient for the time being, especially when there is not much experimental information. Now that we have realized that these calculations are possible and meaningful, we aim to perform further investigations on the series of molecules mentioned in the opening paragraph of this paper. Registry No. C 0 2 , 124-38-9; NH,, 7664-41-7.
Theoretical Study of the Structure and Spectroscopic Characteristics of Protonated Carbon Dioxide Michael J. Frisch,* Henry F. Schaefer 111, Department of Chemistry, University of California, Berkeley, California 94720
and J. Stephen Binkley Theoretical Division 8341, Sandia National Laboratories, Livermore, California 94550 (Received: August 8, 1984)
Protonated carbon dioxide has been examined theoretically by using geometries optimized at the MP2/6-3 1G(d) level and energies computed at the MP4/6-3 11++G(d,p) level. It is concluded that the C, 0-protonated complex is the only observable form of C02H+when it is produced by association of H+ with C02and under most other conditions. The enthalpy of protonation of CO, is found to be 130.7 kcal mol-' at 298 K. Rotational constants are predicted to be 773.74, 10.79, and 10.65 GHz for C02H+and 43 1.18, 10.17, and 9.94 GHz for C02D+. Stretching vibrational frequencies are predicted to be 1292, 2330, and 3348 cm-I for C02H+ and 1270, 2316, and 2485 cm-I for C02D+. The 0-H (or 0-D)stretching mode is expected to produce the most intense fundamental transition in both the infrared and Raman spectra, and the 2330 (2316) cm-I C-O stretch is found to be the only other intense mode.
Introduction Protonated carbon dioxide, C02H+,is of interest in combustion chemistry and may be found in interstellar space. A recent ion cyclotron resonance experiment has observed what is tentatively proposed to be C02H+and further suggests that two forms of this complex are sufficiently stable to be observable.' Direct spectroscopic observation of this species has been hampered in part by the lack of reliable predictions of its vibrational frequencies and rotational constants. We have therefore examined the C02H+ singlet potential energy surface theoretically in order to determine (1) the stable structures (local minima on the potential energy surface) that exist for this system, (2) the energetics of the complex, including the heat of formation of C02H+,and the isomerization and activation energies for interconversion of the isomers (if more than one isomer exists), and (3) the vibrational and rotational frequencies of the stable structure(s). Methods The ground-state structure of carbon dioxide and the stationary points on the C 0 2 H +potential energy surface corresponding to (1) P. C. Burgers, A. A. Mommers, and J. L. Holmes,J. Am. Chem. Soc., 105, 5976 (1983).
0022-3654/85/2089-2192$01.50/0
protonation at an oxygen (l),protonation at the carbon (3), and the intervening 1,2-hydrogen shift transition structure (2) were
L
2
3
optimized by use of second-order Merller-Plesset perturbation theory2 (MP2) and the polarized split-valence 6-3 1G(d) basis set3 Analytic energy derivatives4 and conjugate gradient optimization methods5 were used in the searches for the stationary points. The closed-shell singlet wave functions for the structures 2 and 3 were found to have instabilities with respect to relaxing the spin restrictions (allowing the wave function to have the unrestricted Mlaller-Plesset (UMP2) form).6 The lower energy unrestricted (2) C. Molller and M. S. Plesset, Phys. Reu., 46,618 (1934). (3) P. C. Hariharan and J. A. PoDle. Theor. Chim. Acta. 28.213 (1973). (4) J. A. Pople, R. Krishnan, and'H.'B. Schlegel, Int. J . Quantum Chem., Quantum Chem. Symp., No. 13, 325 (1979). ( 5 ) H. B. Schlegel, J. Compur. Chem., 8, 214 (1982). (6) R. Seeger and J. A. Pople, J . Chem. Phys., 66, 3045 (1977).
0 1985 American Chemical Society
Theoretical Study of Protonated Carbon Dioxide Hartree-Fock (UHF) wave functions are composed of orbitals having only C, symmetry and describe a biradial, with an a-spin electron localized on one oxygen and a P-spin electron localized on the other oxygen. The resulting complete S, = 0 U H F determinant maintains full C2, symmetry for structure 3 but is seriously contaminated by components of the lower lying triplet wave function. In view of this instability, the geometries of structures 2 and 3 were optimized by use of both restricted and unrestricted Mdler-Plesset theory (RMP2 and UMP2). Structural parameters determined at this level of theory are known to have small but systematic errors.' Consequently, the bond distances used for computing moments of inertia and rotational constants were empirically corrected by scaling each bond distance by the ratio of the experimental to the MP2/6-3 lG(d)-optimized distance for a known compound! Water and carbon dioxide were used to correct the 0-H and C-0 bond lengths, respectively. The force constants and resulting harmonic vibrational frequencies were determined by numerically differentiating the analytic first derivatives of the MP2 energy. These confirm that structures 1 and 3 are local minima on the MP2/6-31G(d) potential energy surface and that structure 2 is a saddle point. The vibrational frequencies were empirically corrected in the same manner as the bond lengths, by comparing experimental and MP2/6-31G(d) frequencies for water and carbon d i ~ x i d e . The ~ dipole derivatives and polarizability derivatives were computed analytically at the Hartree-Fock level by using the 6-31G(d) basis set. These were combined with the MP2/6-31G(d) normal modes to produce infrared and Raman intensities using the doubleharmonic approximation. lo The energetics of the association process were examined with fourth-order M d l e r - P l e ~ s e t ~(MP4) ~ theory using the larger 6-31 l++G(d,p) basis set12at each of the stationary point geometries determined at the MP2/6-31G(d) level of theory. The core electrons were not included in the evaluation of the correlation energy in these calculations. The 6-311++G(d,p) basis is of triple-c quality and includes both diffuse and polarization functions on all atoms. Zero-point vibrational corrections and temperature corrections were applied to the MP4 energies using the empirically corrected MP2/6-3 1G(d) frequencies to produce enthalpies of activation and reaction at 298 K.13 All calculations were performed using the GAUSSIAN 82 system of programs on a Cray 1 s computer.14 Results and Discussion The optimized and the empirically corrected geometries are listed in Table I, along with the previously published MP2/63 1G(d) structure of f~rmaldehydel~ and experimental geometries.l6?l7 Total energies at the HF/6-31G(d), MP2/6-31G(d), HF/6-31 l++G(d,p), MP2/6-31 l++G(d,p), MP3/6-31 l++G(d,p), and MP4/6-31 l++G(d,p) levels of theory at the optimized structures are given in Table 11. The experimental,18 computed, (7) D. J. DeFrees, B. A. Levi, S. K. Pollack, W. J. Hehre, J. S. Binkley, and J. A. Pople, J . Am. Chem. Soc., 102, 2513 (1980). (8) k.H. Nobes and L. Radom, Chem. Phys., 60,l (1981). (9) M. E. Colvin, G. P. Raine, H. F. Schaefer 111, and M.Dupuis, J. Chem. Phys., 79, 1551 (1983). (10) M. J. Frisch, J. S. Binkley, Y. Yamaguchi, J. Gaw, and H. F. Schaefer 111, to be submitted for publication. (1 1) R. Krishnan, M. J. Frisch, and J. A. Pople, J . Chem. Phys., 72, 4244 (1980). (12) M. J. Frisch, J. A. Pople, and J. S. Binkley, J. Chem. Phys., 80,3265 (1984). (1 3) "Statistical Thermodynamics", D. A. McQuarrie, Ed., Harper and Row, New York, 1973. (14) J. S. Binkley, M.J. Frisch, D. J. DeFrees, K. Raghavachari, R. A. Whiteside, H. B. Schlegel, and J. A. Pople, "Gaussian-82", Carnegie-Mellon Chemistry Publishing Unit, Pittsburgh, PA, 1984. (15) L. B. Harding, H.B. Schlegel, R. Krishnan, and J. A. Pople, J . Phys. Chem., 84, 3394 (1980). (16) "Infrared and Raman Spectra", G. Herzberg, Ed., Van Nostrand Reinhold, New York, 1945. (17) J. H. Callomon, E. Hirota, K. Kuchitsu, W. J. Lafferty, A. G. Maki, and C. S. Potein "Numerical Data and Function Relationships in Science and Technology", vol. 7, K. H. Hellwege, Ed., Springer-Verlag, West Berlin, 1976.
The Journal of Physical Chemistry, Vol. 89, No. 11, 1985 2193 TABLE I: MP2/6-31G(d), Experimental, Structural Parameters" point structure group parameter H20 Cb R(O-H) LH-0-H CO2 D.h R(C-0) H2CO Cb R(C-0) R(C-H) LH-C-0 OI=C=02-H+ (1) C, R(C-01) R(C-02) R(O2-H) CO1-C-02 LC-02-H OI-C(H)-Oz+ (2) C, R(C-01) (RMP2) R(C-02) R(02-H) LO,-C-02 LH-02-C C, R(C-01) OI-C(H)-02+ (2) (UMP2) R(C-02) R(O2-H) LO,-C-02 LH-02-C Cb R(C-0) 0-CH-0' (3) (RMP2) R(C-H) LO-C-H 0-CH-0' (3) C2, R(C-0) (UMP2) R(C-H) LO-C-H
and Empirically Corrected ~~~
MP2 0.9686 104.00 1.1787 1.2210 1.1043 122.19 1.1465 1.2341 0.9979 173.64 119.34 1.2158 1.2060 1.6397 177.28 48.43 1.1933 1.2235 1.7208 164.85 88.78 1.2145 1.2181 90.45 1.2718 1.1049 118.17
MP2 exptlb corrected 0.9584 104.45 1.1615 1.203 1.101 121.75 1.1298 1.2161 0.9874 173.64 119.34
'Distances are in angstroms, and angles in degrees. Where necessary, the method (RMPZ or UMP2) is indicated in parentheses. Experimental values are taken from ref 16 and 17.
and empirically corrected vibrational frequencies are found in Table 111, along with predicted relative intensities. Previous theoretical studies19 on other systems have indicated that protonation occurs preferentially at lone-pair sites, and in accord with this observation, structure 1 is found to be the lowest energy structure on the COzH+ potential energy surface at all levels of theory. The U H F wave function for the C-protonated structure 2 is badly contaminated by triplet components and has an (S2) value of 1.028. ( S 2 )evaluated from the first-order Mraller-Plesset wave function is 1.017 and indicates that the effects of spin contamination can be expected to remain in the correlated energies. The energies computed by use of restricted MdlerPlesset theory are lower than the unrestricted ones, in spite of the lower unrestricted Hartree-Fock energy. The RMP2 and UMP2 optimized geometries for the C-protonated form differ dramatically. The UMP2 structure has the form illustrated in structure 3, with approximately equal bond angles, while the RMP2 structure takes the form of a nearly linear C02 molecule with a proton adjacent to the carbon. This difference reflects the fact that within the restriction of a closed-shell wave function there is insufficient flexibility to properly describe the biradial produced by making the COz nonlinear. An accurate description of the geometry of this structure requires a multiconfiguration reference wave functionzO*zland will be the subject of a future study. Comparison of the MP2/6-3 1G(d) and experimental geometries for HzO, CO2,and HzCO shows the 0.01-0.02 A overestimation of bond lengths found previously at this level of t h e ~ r y .The ~ MP2/6-31G(d) bond angles in water and formaldehyde are accurate to better than 1% and hence do not need correction for the purpose of predicting rotational constants. T h e rotational constants at the empirically corrected geometry are 773.74, 10.79, and 10.65 GHz for COzH+ and 43 1.18, 10.17, and 9.94 GHz for COzD+. (18) Shimanouchi, Nufl.Stand. Ref Datu Ser. (US., Natl. Bur. Stand.), NSRDS-NBS 39 (1972). (19) J. E.Del Bene, M. J. Frisch, K. Raghavachari, and J. A. Pople, J . Phys. Chem., 86, 1529 (1982). (20) L. Engelbrecht and B. Liu, J . Chem. Phys., 78, 3097 (1983). (21) D. Feller, E. R. Davidson, and W. T. Borden, J. Am. Chem. Sm.,105, 3347 (1983).
2194
Frisch et al.
The Journal of Physical Chemistry, Vol. 89, No. 1 1 , 1985
TABLE I t Total Energies (in nu) from the 6-31C(d) and 6311++C(d,p) Basis Sets, at MP2/6-3lG(d)-Optimized Geometries 6-31G(d) 6-31 I++G(d,p) structure" HF MP2 HF MP2 MP3 MP4 -188.18368 -188.23275 -187.62841 -188.11836 -187.68323 -188.20628 co2 -188.402 13 -188.44797 -188.324 18 -187.89660 -188.41925 OCOH' (1) -187.837 58 -188.281 73 -188.23545 -188.31654 -188.18985 -187.69809 OC(H)O+ (2) R -187.63976 -187.755 17 -188.213 15 -188.22323 -188.25975 -187.69820 -188.121 44 U -188.231 87 -188.31721 -187.69062 -188.281 97 -187.63281 -188.190 14 OCHO' (3) R -188.249 17 -188.27484 -187.80655 -188.22997 -187.75463 -188.14286 U
"R or U indicates restricted or unrestricted wave functions. TABLE 111: Vibrational Frequencies in cm-' structure H20
D20
C02
mode 0-Hstr 0-H str H-0-H bend 0-Dstr 0-D str D-0-D bend C-Ostr C-0 str
0-c-0
bend OCOH 0 - H s t r C-0 str C-0 str bend torsion bend OCOD 0 - D s t r C-0 str C-0 str bend torsion bend
" Experimental
MP2 re1 intens MP2/ sYm 6-31G(d) exPt1' corrected IR b n a n B2 AI AI
3918 3776 1735
3757 3656 1595
B2 AI AI
2870 2722 1270
2788 267 1 1178
=* n"
2"
2455 1337 642
2349 1388 667
A' A' A' A/ A" A' A' A' A' A' A" A'
3475 2435 1245 1033 573 525 2545 242 1 1223 835 565 480
3348 2330 1292
2485 2316 1270
1.0 0.8 0.0 0.5 0.1 0.1 1.0 0.5 0.1 0.2 0.1 0.1
1.0 0.4 0.2 0.1 0.0 0.0 1.0 0.2 0.3 0.0 0.0 0.0
values taken from ref 17.
but is not sufficient for the accurate prediction of absolute intensities.I0 Consequently, only relative intensities are provided in Table 111. The 0-H stretching mode is found to produce the strongest transition in both the infrared and Raman spectra, with the antisvmmetric C-O stretching mode also having considerable intensity: The major effect of deuteration is to reduce the infrared intensities of the antisymmetric C-O stretching mode and of the bending modes. The MP4/6-3 1l++G(d,p) association energy for formation of structure 1 is -135.1 kcal mol-'. The RMP4/6-31 l++G(d,p) and UMP4/6-31 l++G(d,p) energies of the C-protonated structure are much higher than that of the 0-protonated structure and yield association energies of -29.3 and -26.4 kcal mol-', respectively. The transition structure 2 is lower in energy than separated H+ and COz and presents a classical barrier of 0.4 kcal mol-' (RMP4 at the RMP2-optimized geometry) or 9.5 kcal mol-' (UMP4 at the UMPZoptimized geometry) to the 1,2-hydrogen shift. The energies of 2 and 3 are expected to be lowered relative to both 1 and separated H+ C 0 2 by the use of an improved reference wave function. However, since the 1,2-hydrogen shift transition structure lies below the separated species even at the present level of theory, it is clear that formation of COzH+ by association will produce only the highly thermodynamically favored 0-protonated form. The small rearrangement barrier suggests that while the C-protonated form is a local minimum, if it is produced under conditions which provide it with even a modest amount of internal energy, it will rearrange rapidly and leave only the 0-protonated form to be observed. Using the empirically corrected frequencies to determine vibrational populations and energies and treating translations and rotations classically, we found the enthalpy of the protonation reaction to be -130.7 kcal mol-' at 298 K, in fair agreement with the experimental value of -126.8 kcal mol-'.23
+
The uncorrected values differ by about 20 GHz in the larger constants and 0.3 GHz in the smaller ones. Similarly, the harmonic MP2/6-3 1G(d) vibrational frequencies for water and C 0 2 overestimate the observed fundamentals by about 7%. It is known that most of this error arises from vibrational anharmonicity rather than inaccuracies in the MP2/6-3 1G(d) force and this is illustrated by the closer agreement of the predicted and observed values for D 2 0 than for HzO. Consequently, separate corrections were used for the 0-H and 0-D stretching modes in C02H+and C02D+. The bending and torsional modes of COzH' are both more anharmonic than the stretching modes and less easily related to experimentally observed model compounds, and consequently, no attempt has been made to correct these frequencies. Also, since both the R M P and U M P descriptions of C-protonated C 0 2 H + are less than satisfactory and produce very different structural parameters, no prediction of the vibrational frequencies and rotational constants of this species will be made. The level of theory used here reproduces qualitative trends in vibrational intensities
Conclusion This study suggests that only the 0-protonated form of protonated carbon dioxide is likely to be observable. The rotational constants of both protonated and deuterated carbon dioxide have been predicted, as have the vibrational frequencies. The 0-H stretching mode and the antisymmetric C-0 stretching mode should produce the most intense vibrational transitions.
(22) M. J. Frisch, J. S. Binkley, and H.F. Schaefer 111, accepted for publication in J . Chem. Phys.
(23) "Gas Phase Ion Chemistry", Aue and Bowers, Eds.,Academic Press, New York, 1979.
Acknowledgment. This work was supported at Sandia National Laboratories by the U S . Department of Energy and at the University of California by the Miller Institute for Basic Research. Registry No. C 0 2 H t , 50924-41-9; C 0 2 D t , 95120-72-2.
