10531
J . Phys. Chem. 1991,95, 10531-10534 population, but not necessarily in the E mode since three other modes of different symmetry can also accept energy. The mechanistic information from these experiments is reasonably consistent with the available data from picosecond transient visible and resonance Raman experiments. The main observation of the early visible experiments was a fast rise time of 1-2 ps in c y ~ l o h e x a n edominated ~ ~ ~ ~ by Cr(CO)5.(solvent). We now can confirm that the fast reaction rate is possible because of efficient internal deposition of large amounts of energy in the CO stretching modes through a fast radiationless decay of the initially formed Cr(CO)5 excited state. Other visible absorption experiments at wavelengths to the red of the broad peak have measured a transient decay of about 20 ps in cyclohexane.I6 This transient could correspond to an absorbance of the naked Cr(CO)5 that we observe in the IR, since in our UV/vis experiments we found a 15 f 10 ps lifetime for this species. UV resonance Raman experiments detected the vibrationally excited symmetric stretching motion of CO with a lifetime similar to our value,I7 which is consistent with our observation of at least one quantum in the doubly degenerate E mode of the CO stretch. Also observed in the resonance Raman work was a similar long lifetime for M-CO stretching motions. That result suggests to us that the CO stretching modes at least partly decay internally into low-frequency modes. The long time for this process ensures that only rarely will sufficient excess energy be present to dissociate the weak metalsolvent bond once it is formed. Therefore, the large amounts of energy in the CO stretching modes can decay internally into (15) Joly, A. G.;Nelson, K. A. J . Phys. Chem. 1989, 93, 2876. (1 6) Lee, M.; Harris, C. B. J . Am. Chem. Soc. 1989, 11 I , 8963. (17) Yu,S.;Xu,X.;Lingle, R. Jr.; Hopkins, J. B. J. Am. Chem. Soc. 1990, 112, 3668.
M-CO motions without causing dissociation of the product, or externally by solvent collisions. Summary By using a 532-nm photolysis laser pulse to remove the solvent ligand from Cr(C0)5-C6H12,we observed a 15 f 10 ps IR transient at 1970 cm-’ within the spectral region expected for uncoordinated Cr(CO)5. Multiple decay paths to product were observed. Cr(CO)5-C6HIZ is formed quickly with one quantum of vibrational excitation in the CO stretching mode of E symmetry, which has a nominal lifetime of 100 ps. An efficient nonradiative energy relaxation into isolated CO stretching modes can account for the fast reaction of the uncoordinated species with the solvent since this energy is quickly removed from the RRKM energy pool. Finally, the Cr(CO), lifetime indicates that in our UV photolysis of Cr(C0)6 the >lOo-ps transient at 1970 cm-l is dominated by vibrationally excited Cr(C0)6rather than uncoordinated Cr(CO)+ These new results provide a mechanistic view of Cr(C0)6 and Cr(CO)5.C6H12 photolysis that is consistent with available transient visible and resonance Raman spectroscopic data. Additional descriptions of our data and its analysis, a more complete discussion of radiationless decay theory and RRKM theory, and comparisons with gas-phase and matrix data will be included in a full article. Acknowledgment. We thank the Strategic Defense Initiative Organizations through the Medical Free Electron Laser Program for their financial support. We also thank Xinming Zhu and Changzheng Wu for assistance in data collection and Liang Wang for his computer programming. R@try No. Cr(CO)5,26319-33-5; Cr(CO),, 13007-92-6; C6H12, 110-82-7.
Chemical Applications of Density Functional Theory: Comparison to Experiment, Hartree-Fock, and Perturbation Theory George Fitzgerald* and Jan Andzelm Cray Research, Inc., 655-E Lone Oak Dr., Eagan, Minnesota 55121-1560 (Received: July 22, 1991; In Final Form: October 21, 1991)
Density functional theory (DFT) offers an alternative method for the quantum mechanical computation of chemical properties. Although initial results have been very positive, the method still lacks the long history of calibration which exists for more conventional methods. This calibration is important for identifying particular strengths and weaknesses of each method. The present study attempts to establish such a calibration for DFT. Results are obtained for structures, vibrational frequencies, and heats of reaction. Results are generally comparable in accuracy to MP2 calculations. Certain properties are reproduced rather poorly by local density functional methods; the predicted values of some of these properties are improved by the use of nonlocal corrections, added perturbatively at the end of the local DFT calculation.
Introduction During the past decade, density functional theory (DFT)14 has become a standard approach in the investigation of structural, electronic, and magnetic properties of bulk solids, surfaces, and interface^.^.^ (1) Hohenberg, P.; Kohn, W. Phys. Reo. 1964, 136, 864. ( 2 ) Kohn, W.; Sham, L. J. Phys. Rev. A 1965, 140, 1133. (3) Levy, M. Proc. Natl. Acad. Sci. U.S.A. 1979, 76,6062. (4) Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and Molecules; Oxford University Press: New York, 1989. ( 5 ) Jones, R. 0.;Gunnarsson, 0. Reu. Mod. Phys. 1990, 61, 689. ( 6 ) Wimmer, E.; Krakauer, H.; Freeman, A. J. Adu. Electron. Electron Phys. 1985.65, 357.
0022-3654/91/2095-10531$02.50/0
The application of the method to chemistry was delayed due to the lack of ability to optimize molecular structures and calculate accurate heats of reactions. Only recently, the gradient geometry optimization technique was introduced to the DFT method and the nonlocal DFT potentials allowed for an accurate prediction of energetics of chemical reactions.’,* However, in contrast to Hartree-Fock and the many-body methods, such as MP2: the DFT method lacks the extensive and _____
(7) Density Functional Methods in Chemistry; Labanowski, J., Andzelm, J., Eds.; Springer: New York, 1991. (8) Ziegler, T. Chem. Rev., in press. (9) Hehre, W. J.; Radom, L.; Schleyer, P.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986.
0 1991 American Chemical Society
Letters
10532 The Journal of Physical Chemistry, Vol. 95, No. 26, 1991 TABLE I: Optimized Ground-State Geometries (Bond Distances in A. Bond Andes in den) UMP2/ LSD/ UMP2/ LSD/ species 6-31G(d)' DZVP 6-31G(dp)' TZVPP expo HFCO CF 1.352 1.344 1.345 1.347 1.341 CH 1.094 1.113 1.094 1.109 1.100 1.184 1.183 1.191 1.183 CO 1.194 123.2 122.6 122.7 123.2 122.8 FCO 128.1 129.0 127.6 127.9 HCO 127.6 H2C0 CH 1.104 1.125 1.106 1.122 1.120 CO 1.220 1.212 1.210 1.206 1.210 HCO 122.2 121.8 122.2 121.9 121.0 CH,F CF 1.390 1.378 1.380 1.380 1.391 CH 1.092 1.107 1.091 1.104 1.095 HCF 109.1 109.4 109.2 109.3 108.0 HCH 109.8 109.6 109.7 109.7 109.5 1.099 1.09 1 1.102 1.090 CHI CH 1.090 109.5 109.5 109.5 109.5 109.5 HCH 1.327 1.334 1.327 1.329 FCO CF 1.340 1.170 1.177 1.169 1.181 1.184 CO 127.1 127.3 127.2 128.2 FCO 128.0 1.138 1.125 1.141 1.123 HCO CH 1.124 1.181 1.175 1.188 1.182 CO 1.191 123.8 123.5 125.0 123.1 HCO 123.4 ~
~~~
'UMP2 and experimental values are taken from ref
11.
systematicvalidation in studying problems of interest for chemists. For a method to be chemically useful, it is necessary to delineate both strengths and weaknesses. The present study constitutes one of our attempts to evaluate systematically the performance of DFT methods in chemistry.'~~~ The main focus here is the accuracy of the DFT method to study heats of isodesmic reactions involving atoms of prime importance for organic chemistry: C, 0, N, and F. The DFT method is judged by comparing the results with experimental, HartreeFock, and many-body calculations. Heats of reactions involving different types of bonds, hydrogenation reactions, proton affinities, and bond separation energies have been studied for selected, representative molecules. Comparison with available ab initio and experimental data9 and the HF results obtained by us establishes reasonable error bars for using the nonlocal spin density (NLSD) approach for studying chemical reactions.
Computational Method DFT calculations reported in this paper have been obtained using the DGauss This is a density functional program utilizing Gaussian basis sets. The underlying theory, originated in the 1 9 7 0 ~ , ~has ~ -been ' ~ developed further by several research g r o ~ p s . ~ ~The - ~ *method employed in DGauss relies on the variational fitting of the density. The exchange-correlation potential is fit on a small adaptive set of grid points. The geometry optimization is carried out using analytic gradient~?~-~O whereas (10) Andzelm, J.; Wimmer, E., to be published. (11) Zhao, Y.; Francisco, J. S. Chem. Phys. Lett. 1990, 173, 551. (12) Sambe, H.; Felton, R. H. J . Chem. Phys. 1975, 862, 1122. (13) Dunlap, B. I.; Connolly, J. W. D.; Sabin, J. R. J . Chem. Phys. 1979, 71, 3396. (14) Salahub, D. R. In Ab Initio Methods in Quantum Methods in Quantum Chemistry; Lawley, K. P., Ed.; Wiley: New York, 1987; Vol. 11, p 447. ( I S ) Painter, G. S.; Averill, F. W. Phys. Rev. B 1983, 28, 5536. (16) Mintmire, J. W.; White, C. T. Phys. Reu. Lett. 1983, 50, 101. (17) Russo, N.; Andzelm, J.; Salahub, D. R. Chem.Phys. 1987,114,331. (18) Rosch, N.; Knappe, N.; Sandl, P.; Gorling, A.; Dunlap, B. I. In The Challenge of d and f Electrons: Theory and Computation; Salahub, D. R., Zerner, M. C., Eds.; ACS Symp. Ser. 1989,394, 180. (19) Dunlap, B. I. In Density Functional Methods in Chemistry; Labanowski, J., Andzelm, J., Eds.; Springer: New York, 1991; p 49. (20) Salahub, D. R.; Fournier, R.; Mlynarski, P.; Papai, I.; St-Amant, A.; Ushio, J. In ref 19, p 77. (21) Dixon, D. A.; Andzelm, J.; Fitzgerald, G.; Wimmer, E.; Jasien, P. In ref 19, p 33. (22) Mintmire, J. W. In ref 19, p 125. (23) Versluis, L.; Ziegler, T. J . Chem. Phys. 1988, 88, 322.
TABLE 11: Computed and Experimental Zero-Point Energies (kcal/mol) measd HF/ MP2/ LSD/ (harmonic) 6-31G*' 6-31G*" DZVPP co 3.1 (3.1) 3.5 3.0 3.1 CHI 27.1 (28.3) 30.0 29.2 27.3 H20 12.9 (13.5) 14.4 13.5 13.1 NH3 20.6 (21.5) 23.2 22.4 21.1 HCN 9.8 (10.0) 11.3 10.0 9.9 CHSOH 31.2 34.7 32.7 31.2 CHzO 16.1 (16.8) 18.3 17.0 16.1 N2 3.3 (3.4) 4.0 3.1 3.4 CHjNH2 39.2 43.2 41.3 39.0 CHSCH, 45.5 (47.5) 50.1 48.4 45.5 CHSCH2CHj 62.5 69.4b 63.0 CH(CHd3 79.5 88.3b 80.0 C(CHh4 96.4 107.1b 96.8 CHSCH2NH2 56.3 62.6b 56.5 CHSNHCHS 56.2 62.4b 56.2 CHJCHZOH 48.6 54.0b 48.7 CHSOCH3 48.7 54.1b 48.3 HFCO 12.7 13.4c 12.8 CHSF 24.0 25.4c 23.9 FCO 5.0 5.3' 5.2 HCO 7.8 8.4' 8.O 'Values taken from ref 9, table 6.41. bResults of HF/6-31G1 calculations have been multiplied by 0.9. CUMP2/6-31G*results from ref 11.
TABLE III: Calculated and Experimental Proton Affinities (kcal/mol) 6-31G**/6-31G1 DZVPP molecule HF' MP2' MP4' LSD BP expt'ib 124 125 121 124 122 N2 121 HF 127 130 131 119 122 116 161 163 152 160 156 C2H2 165 172 172 164 170 168 C2H4 177 180 179 169 172 179 H20 180 220 220 208 213 213 NH3 220 CHSOH 196 196 195 182 187 CH3NH2 230 230 230 218 223 222 aValues taken from ref 9, table 6.77. bExperimentai data corrected for zero-point energy and temperature effects.
the force matrix is calculated from two-point differences of the gradients. Calculations were carried out using local spin density (LSD) 0ptimized~~3~~ Gaussian orbital basis sets. For most calculations the standard DGauss basis sets have been used. The DZVP set is comparable in size to the 6-31G* Popleg set; the DZVPP corresponds to a 6-31G** set; the TZVPP set is composed of a triple-{ basis set for second-row atoms, comparable to 6-31 lG* with a double-{ basis set for hydrogen. In some cases a better representation of the core orbitals has been accomplished by using DZVPZ basis set.31,32 The geometries and the vibrational frequencies have been computed using the local DFT Hamilt~nian.~~ Nonlocal (NLSD) (24) Andzelm, J.; Wimmer, E.; Salahub, D. R. In The Challenge of d and f Electrons; Theory and Computation; Salahub, D. R., Zerner, M. C., Eds.; ACS Symp. Ser. 1989, 394, 22. (25) Fournier, R.; Andzelm, J.; Salahub, D. R. J . Chem. Phys. 1989,90,
6371. (26) Dunlap, B. I.; Rosch, N. Chim. Phys-Chim. Biol. 1989, 86, 671. (27) St-Amant, A.; Salahub, D. R. Chem. Phys. Lett. 1990, 169, 387. (28) Averill, F. W.; Painter, G. S. Phys. Reu. B 1985, 32, 2141. (29) Andzelm, J. In Density Functional Methods in Chemistry; Labanowslu, J., Andzelm, J., Eds.; Springer: New York, 1991; p 155. (30) Dunlap, B. I.; Andzelm, J.; Mintmire, J. W. Phys. Reu. A 1990, 42, 6354. (31) Gcdbout, N.; Andzelm, J.; Wimmer, E.; Salahub, D. R. Can. J . Chem., submitted. (32) Andzelm, J.; Radzio, E.; Salahub, D. R. J . Comput. Chem. 1985, 6, 520, 533.
The Journal of Physical Chemistry, VO~. 95, No. 26, 1991 10533
Letters
TABLE I V Calculated and Experimental Heats of Reaction ( k c d m o l ) . Experimental Numbers Corrected for Zero-Point Energies 6-31G'*/6-31GC DZVP DZVPP reaction HF MP2 MP4" LSDb BP LSD BP (A) HCN 3H2 -P CH4 NH3 -79 -7 1 -70 -99 -78 -102 -81 -54 -8 7 (B) CO + 3H2 CH4 + H20 -59 -58 -64 -93 -70 -26 -64 -39 -71 -33 -28 -47 (C) N2 + 3H2 2NH3 (D) CO + 2CH4 + 2 H 2 0 3CH30H 30 27 33 -14 10 -9 14 5 -32 -7 -29 -5 (E) HCN 2CH4 + 2NH3 3CH3NH2 4 4 6 -14 -1 -1 1 0 1 2 (F) CHiO CH4 + H20 -* 2CH3OH
+
+ +
+
-- -
expt' -76 -63 -37 27 4 1
"The results are taken from tables 6.65 and 6.67 of ref 9. bTotalLSD(BP) energies in au are as follows: HCN = -92.629419 (-93.436933); H2 = -1.136856 (-1.176359); CH4 = -40.111039 (-40.522365); NH3 = -56.087284 (-56.568593); CO = -112.443039 (-113.333252); HZ0 -75.881 560 (-76.442428); N2 = 108.661 727 (-109.545710); CH3OH = -114.816957 (-115.749 148); CH3NH2 = -95.025 546 (-95.876824); CH2O -1 13.618 898 (-1 14.531 776). energies were computed at the optimized geometries using the exchange and correlation functionals of Becke and Perdew (BP), r e ~ p e c t i v e l y . ~ NLSD ~ - ~ ~ energies are added perturbatively, to the converged LSD results; in the case of geometry optimizations, NLSD results are only computed at the final geometry.
Results and Discussion Geometries. Optimized geometries have previously been reported for a number of organic and inorganic The structures reported in Table I include several open-shell species, and comparisons are done with ab initio UMPZ calculations. The geometrical parameters obtained using DZVP and TZVPP basis sets and the default set of computational parameters in DGauss'O (integral threshold, precision of numerical integration, grid threshold, gradient threshold) shows that the LSD geometry is converged to within 0.01 A and less than lo. Apparently, larger deviations with basis set size can be found in the UMP2 results. The LSD and UMPZ geometry results agree exceptionally well for the TZVPP level of calculations in the case of angles and bond distances involving heavy atoms. The bonds involving hydrogen are consistently too long in comparison to both experiment and UMPZ results. This fact seems to be a common drawback of all LSD calculation^^^^ regardless of the level of the basis set or computational parameters used. Comparison with the experimental data shows that the marimum errors in bond distances of LSD method are less than 0.02 A for DZVP model and less than 0.01 A for TZVPP approach. The bond angles are within 2O of experimental data. Zero-Point Energies. The zero-point energies (ZPE) provide a convenient way of combining a great deal of vibrational data into a single number. Table I1 summarizes the ZPE for a range of compounds including some open-shell species. The LSD method appears to provide ZPE in close agreement with experiment. That finding may be of practical importance since the DFT method is computationally less expensive than H F (N3 and N4, respectively). However, one must interpret this finding cautiously, bearing in mind the comparison is between computed harmonic and experimental anharmonic frequencies. One of the most attractive features of the HartreeFock frequencies is the consistency with which they overestimate experimental results by 10%; HartreeFock results are typically scaled to yield highly reliable values. Although LSD yields harmonic results which are generally closer to experiment, it remains to be seen whether this will continue to hold true for other systems, whether scaling factors can be developed, and whether improved energy functionals will adversely affect this result. For the present, we note that, overall, the harmonic LSD results offer a reliable way to predict experimental frequencies. Proton Affiities. The computed proton affinities are presented in Table 111. The DFT results appear very reliable, reproducing (33) Vosko, S. H.;Wilk, L.; Nusair, M. Can. J . Phys. 1980, 58, 1200. (34) Becke, A. D. Phys. Rev. A 1988, 38, 3098. (35) Becke, A. D. In The Challenge of d and f Electrons: Theory and Computation; Salahub, D. R.,Zerner, M. C., Eds.; ACS Symp. Ser. 1989, 394, 165. (36) Perdew, J. P.Phys. Reu. B 1986, 33, 8822. (37) Delley, B. J . Chem. Phys. 1990, 92, 508.
-
TABLE V DFT Computed Heats of Reaction for HCN ZNH3 3CH3NH,
basis
comparable basis
DZVP DZVPZ/DZVP DZVP2IDZVP DZVPP DZVP4 DZVPP DMol DND DMol DNP
6-31G' 6-31G* 6-31G' 6-31G** 6-31GS*++ 6-311GS* 6-31G* 6-31G"
grid medium medium fine medium
fine fine
LSD -32 -33 -33 -29 -28 -24 -27 -29
+ ZCH, + LSD+BP -7 -8 -8
-5 -3 0
'DZVP2 basis set is used for C and N and DZVP is us4 for H.
experimental results to within 1-7 kcal/mol. This is a significant improvement over the HF results which are off by 1-12 kcal/mol. MP2 and MP4 results do not improve the proton affinities significantly. Heats of Reactions. Various heats of reactions are reported in Table IV. In all cases, the LDF results have a significant error, -30 kcal/mol. Use of the BP nonlocal correction improves this considerably, most errors being in the 5-10 kcal/mol range. One of these reactions, E, was therefore studied in some detail to try to understand the source of the error. The error in reaction E is noteworthy, since in this case, the reaction is predicted to be exothermic rather than endothermic. Table V summarizes these results. Note that in addition to the Gaussian basis calculations, two LDF calculations were performed with numerical basis sets using the DMol program.37 The DND numerical basis is comparable in size to 6-31G*, while DNP is comparable to 6-31G**. In all cases, the LDF results are -25 to -33 kcal/mol, far too low. Inclusion of the BP correction improves these numbers by about 25 kcal/mol. It is only by using a very large basis (comparable to 6-31 1G*) that reasonable agreement with experiment is obtained; the predicted A,!? is in error by only 4 kcal/mol. Apparently the NLSD (BP) Hamiltonian is not yet accurate enough to provide accurate results for heats of reactions involving different types of bonds.'JO In general, however, the LSD BP results appear to give fairly reliable answers. Table VI compares the heats of isodesmic reactions for HF, DIT, and experiment. On average, the LSD and NLSD energies appear to show similar errors. In general, the DZVP and DZVPP basis sets yield very similar agreement with experiment. Note, however, that for the reaction involving (CH3),N, the NLSD + ZPE result are sensitive to basis set; the predicted reaction energies are in error by 5.9 and 2.5 kcal/mol with the DZVP and DZVPP basis sets, respectively. The maximum observed error for both H F and DFT occurs for the reaction involving C(CH3),; errors of 7.1 and 5.2 kcal/mol, respectively are observed. On the basis of the work of Fan and Ziegler,38we estimate the effect of including the nonlocal correction in a self-consistent manner to be less than 1 kcal/mol. Note that the theoretical values given in parentheses include zero-point corrections, while the experimental data in parentheses include zero-point energies and temperature effects. We estimate that the error introduced by not correcting
+
(38) Fan, L.;Ziegler, T. J . Chem. Phys. 1991, 6057.
10534 The Journal of Physical Chemistry, Vol. 95, No. 26, 1991
Letters
TABLE VI: Hwb of Isodesmic R w c t i m (kd/mol). ZPE-Corrected Resuth is Pareftthesea reaction H Fa LSDb 0.8 (1.6) 2.7 CH3CH2CH3 + CH4 2CH3CH3 3.0 1.9 (3.9) 7.2 CH(CH3)3 2CH4 3CH3CH3 7.5 2.7 (6.0) 11.8 C(CH3)4 3CH4 4CHjCHj 14.8 CH3CHZNH2 CH4 -.+ CHjCH3 + CH3NH2 2.7 (3.4) 4.1 4.9 2.2 (3.0) 4.5 CH3NHCH3 NH3 -.+ 2CH3NH2 4.2 (CH3)3N+ 2NH3 3CH3NH2 6.9 10.4 CH3CH20H + CHI CH3CHj + CH3OH 4.2 (5.0) 5.6 6.5 CH3OCH3 + HzO 2CHjOH 2.9 (3.8) 5.6 5.1
NLSDbvC 1.2 (1.9) 1.3 (2.0) 2.8 (4.8) 3.0 (4.9) 3.7 (7.3) 4.6 (7.9) 3.1 (3.9) 3.2 (3.9) 2.8 (3.8) 2.8 (3.5) 2.8 (5.2) 6.8 (8.6) 4.4 (5.1) 4.7 (5.4) 3.3 (4.2) 3.1 (4.1)
-
+
+
-+
+ +
-
exptd (2.6)
(7.5) (13.1) 2.9 (3.6) 3.8 (4.4) 9.5 (11.1) 5.0 (5.7) 4.4 (5.4)
"6-31GS//6-31G* calculations from ref 9. bFirst row in each pair is DZVP results. Second row is DZVPP results. 'ZPE correction computed from LSD frequencies. Experimental results are enthalpies of reaction, corrected for zero-point energies and temperature effects. Uncorrected heats are given in parentheses. Data taken from ref 9.
TABLE VII: Calculated Heats of Reactions (kcal/mol) Reactim Involving Own-Shell Species' method A 28.7 MP4' MP4 AZPEb.' 29.0 31.2 LSDJDZVP NLSD/DZVP 26.8 31.8 LSDJTZVPP NLSD/TZVPP 28.2 NLSDITZVPP + AZPEd 28.1
+
-
for Isodesmic B 13.0 13.6 12.7 11.3 13.4 12.0 12.5
AE level
-
'A: HFCO + CH4 H2CO + CH3F. B: HFCO + HCO H2CO + FCO. MP4SDTQ/6-3 1lG(d,p)//UMP2/6-3 1 lG(d,p) from ref 9. AZPE from experimental data (see ref 9). AZPE calculated on LSDJDZVP level.
the theoretical data to 300 K is less than 2 kcal/moL9 Finally, Table VI1 lists the isodesmic heats for reactions involving HFCO. These reactions involve open-shell species and so represent an additional test of the theory. For both reactions, the nonlocal D R results are within about 1 kcal/mol of the MP4. Isomeric Energy Difference. The ability to compute correctly energy differences for isomers is one important ability for an electronic structure method. The molecules in Table VI11 provide an especially difficult test of this, as the two isomers have different electronic states. Table VI11 summarizes the energy differences for CH3X+CA,) and CH2XH+('A') for X = 0 and S. Energies have been computed up to the MP4SDTQ level of theory. Not counting zerepoint energies, the results converge to 86 kcal/mol for X = 0 and to 25 kcal/mol for X = S. The LSD BP results are quite good for the sulfur isomers, 28 kcal/mol, comparable with MP2 and MP3. However, the results for oxygen are poor, 7 5 kcal/mol. The hE for the oxygen isomers is observed to change considerably as a function of the level of theory. For example, for the 6-31G//4-31G basis set calculations, the hE varies from 43 to 83 to 74 kcal/mol for HF, MP2, and MP3 calculations, respectively. This indicates the importance of electron correlation in this system. It is likely that further corrections to the LSD energy will be necessary to obtain reliable answers for this system. By contrast, the hE for the sulfur isomers are far less sensitive to the level of theory, and the LSD + BSP results are quite close to the MP4 answer.
+
TABLE WI: Energy Difference between CH$+(3AI) and CH*XH+('A')
HF/6-31G//4-31G HF/6-31G**//4-3 1G MP2/6-31G//4-3 1G MP2/6-31GS*//4-31G MP3/6-3 1G//4-3 1G MP3/6-31G**//6-3 1G MP3/6-31G**//MP2/6-3 1G MP2/6-3 lG*//MP2/6-3 1G* MP4SDQ/6-3 IG**//MP2/6-31G*
x=o
42.6" 61.1" 82.8' 102.8' 73.9' 92.4' 93.9' 89.8 84.6 MP4SDTQ/6-31G**//MP2/6-3lG* 86.1 LSD/DZVP 75.5 72.9 LSD+BP/DZVP LSDJDZVPP 76.5 LSD+BP/DZVPP 72.6 LSD/TZVP 79.5 LSD BP/TZVP 75.2
x-s -16.6 7.3 5.6 28.8 4.4 28.3 27.6 22.2 22.0 24.6 29.0 27.1 29.0 28.0
+
'Results taken from Table 6.84 of ref 9.
Conclwions In the present paper we carried out comparisons for the geometries, vibrational frequencies, and energetia of reactions using DFT, HF, many-body correlated, and experimental results. Overall, the D I T results compare well with correlated ab initio results. In some cases,notably the calculation of proton affities, the NLSD approach (using perturbative NLSD corrections) provides more reliable results than MP2-MP4 correlated methods. For reactions involving different types of bonds, the LSD approach is unreliable. While the NLSD method corrects most of the error in LSD, significant errors still remain. These can be reduced substantially by using a more extended DFT wave function. Certainly, there is a need for exploring more accurate NLSD Hamiltonians as well. In many of the caw studied, NLSD (BP) corrections appear to be essential to provide quantitative agreement with correlated ab initio and experimental results. Acknowledgment. We thank all colleagues at Cray Research who created a stimulating environment to carry out this work. A generous allocation of computer time from Cray Research, Inc., is gratefully acknowledged.
