J. Phys. Chem. 1995,99, 10705-10707
10705
Properties of Hydrogen-Bonded Complexes Obtained from the B3LYP Functional with 6-31G(d,p) and 6=31+G(d,p)Basis Sets: Comparison with MP2/6-31+G(d,p) Results and Experimental Data Janet E. Del Bene* Department of Chemistry, Youngstown State University, Youngstown, Ohio 44555
Willis B. Person and Krystyna Szczepaniak Department of Chemistry, University of Florida, Gainesville, Florida 3261 I Received: February 17, 1995; In Final Form: May 3, 1 9 9 9
Density functional B3LYP/6-3 1G(d,p) calculations fail to yield reliable binding energies, intermolecular distances, and hydrogen-bonded X-H frequency shifts for eight selected hydrogen-bonded complexes for which experimental data are available. Properties of these complexes obtained with the B3LYP functional and the 6-31+G(d,p) basis are usually improved, and can be similar to MP2/6-31+G(d,p) values. In those cases where noticeable differences exist between B3LYP/6-3 l+G(d,p) and MP2/6-3 l+G(d,p) results, the MP2/6-31+G(d,p) values are in better agreement with experimental data.
It has been demonstrated that density functional theory (DFT) predicts molecular structures and harmonic vibrational frequencies of substantially higher accuracy than obtained via SCF calculations, and of similar accuracy to the predictions of MP2 calculations.’ Recent DFT studies have employed Becke’s nonlocal three-parameter exchange and correlation functional2 with the Lee-Yang-Parr correlation fun~tional.~ This hybrid functional, B3LYP, has been implemented in Gaussian 9uDFT,4 and B3LYP with the 6-31G(d) basis set has been recommended for use in future Given the success with isolated monomers, it is a logical next step to investigate how well DFT using the B3LYP functional and similar split-valence basis sets can describe hydrogen-bonded complexes. Some studies of small hydrogen-bonded complexes using DFT have appeared in the literature, and some successes have been n~ted.~-’OThe purpose of this letter is to present the results of a systematic DFT study of a set of eight selected hydrogen-bonded complexes for which experimental and previous ab initio theoretical data are available for comparison. There are three properties of hydrogen bonded complexes which are of major significance and which can be measured experimentally: the binding energy, the intermolecular X-Y distance in the X-H-Y hydrogen bond, and the shift of the X-H stretching frequency of the proton donor molecule. Previous studies in this have shown that intermolecular distances and vibrational frequency shifts are welldescribed at second-order many-body M@ller-Plesset perturbation theoryI3-l6 [MBPT(2) = MP21 with a split-valence plus polarization basis set which includes diffuse functions on nonhydrogen-atoms [6-31+G(d,p)].’7-20 MP2/6-31+G(d,p) structures and frequency shifts and experimental data will be used for comparison with B3LYP/6-3lG(d,p) and B3LYP/631+G(d,p) results. All monomers and complexes have been fully optimized at each level of theoretical treatment, and each structure was confirmed to be an equilibrium structure with no imaginary vibrational frequencies. Obtaining reliable binding energies for neutral hydrogen-bonded complexes requires that correlation effects be including using a basis set larger than 6-3 1+G(d,p).’ls2’ However, MW6-31+G(d,p) binding energies @
Abstract published in Advance ACS Abstracts, July 1, 1995.
for neutral complexes are reasonable, and these energies and experimental binding energies will be used for comparison with B3LYP/6-31G(d,p) and B3LYP/6-31+G(d,p) energies. All DFT calculations have been carried out using the Gaussian 92/ DFT suite of computer programs4 with the INT=FINEGRID option. The MP2/6-3 1+G(d,p) calculations were performed using the same program with the DIRECT and FC (frozen core) options. All calculations were performed on the Cray Y-MP8/ 864 computer at the Ohio Supercomputer Center. The computed B3LYP/6-31G(d,p), B3LYP/6-31+G(d,p), and MP2/6-3 l+G(d,p) binding energies, intermolecular distances, and X-H vibrational frequency shifts for eight hydrogen bonded complexes are reported in Table 1. These include complexes of HF and HC1 with HCN and CH3CN; (H20)2; (HF)2; (HCl)2; and ClH-OH2. Also reported are the available experimental data for these c ~ m p l e x e s . ~ ~For - ~ *ease of comparison, the experimental binding energies reported are “experimental electronic binding energies (A&)’’, derived from experimental binding enthalpies by back-correcting the experimental values, using unscaled MP2/6-31+G(d,p) frequencies to evaluate zeropoint and thermal vibrational contributions. The following observations can be made from the data of Table 1: 1. For complexes of HF with HCN and CH3CN, B3LYP/ 6-3 lG(d,p), and MW6-31+G(d,p) intermoleculardistances are similar, and in good agreement with the experimental distance for FH-NCH. B3LYP/6-3l+G(d,p) underestimates the intermolecular distance by 0.05 A. The binding energies computed by all three methods are similar, and are too large relative to experimental values. This is due primarily to the use of these split-valence basis sets, which tend to overestimate binding energies. MP2/6-31+G(d,p) F-H frequency shifts are in significantly better agreement with experimental values than B3LYP shifts. 2. For the complexes of HC1 with HCN and C H F N differences among computed binding energies are not significant. Intermolecular distances computed at MP2/6-31+G(d,p) and B3LYP/6-31+G(d,p) are in better agreement with experiment than B3LYP/6-31G(d,p) distances, which are too short.
0022-3654/95/2099-10705$09.00/0 0 1995 American Chemical Society
10706 J. Phys. Chem., Vol. 99, No. 27, 1995
Letters
TABLE 1: Binding Energies, hE (kcaVmol), Intermolecular Distances, R (A), and X-H Frequency Shifts, 6v (cm-l), for Hydrogen-Bonded Complexes complex FH-NCHb AE R 6V FH-NCCHjb AE R
62) C1H-NCHb AE R bv
CIH-NCCHjb AE R 6V
CIH-OH2 AE R BV
(HCl)? AE R &)(donor) &(acceptor) (HW2 AE R &(donor) &(acceptor) (H20)2 AE R Bv,' dllj' a
B3LYP/ B3LPYI 6-3 1G(d,p) 6-3 l+G(d,p)
MP2/ 6-3 l+G(d,p) experiment"
7.4 2.818 183
7.6 2.760 325
7.7 2.808 262
7.1' 2.805d (v) 245e
9.1 2.772 248
9.5 2.711 425
9.4 2.758 343
8.2f
5.3 3.334 153
4.6 3.361 140
5.3 3.376 113
5.59 3.402h (v) 79'
6.8 3.266 227
6.0 3.286 218
6.6 3.316 167
6.W 3.291h (v) 155k
9.0 3.094 386
6.8 3.149 275
6.9 3.185 177
3.215' (Ar) 207'
1.8 3.839 73 4
1.6 3.860 69 5
2.1 3.868 32 7
(Ar) 53' (Ar) 7"
9.4" 2.493
5.1 2.730 158 43
5.0 2.777 116 42
4.8" 2.79P (v) 934 (v) 32
7.7" 2.784
6.0 2.891 116 34
6.4 2.914 79 35
5.5' 2.9465 (Ar) 64" (Ar) 24
(v) 334'f
For ease of comparison, experimental binding enthalpies ( A S or
DO)have been "back-corrected" to give "experimental" electronic binding energies. Experimental vibrational data are shifts to lower frequencies from either vapor (v) or argon matrix (Ar) data. MP2/63 1+G(d,p) data are taken from ref 11. Reference 22. Reference 23. e Reference 24. f Reference 25. g Reference 26. Reference 27. Reference 28. Reference 29. Reference 30. [ Reference 3 1. " Reference 32. (HF)2 and (H20)2 have cyclic structures with very short F-F and 0-0 distances, respectively. The computed F-H and 0 - H frequency shifts should not he compared with the experimental frequency shifts for open structures. Reference 33. P Reference 34. 4 Reference 35. Reference 36. Reference 37. c h i is the difference between the and the hydrogen-bonded symmetric 0 - H stretch in the monomer (q) 0 - H stretching frequency in the dimer. 6v3 is the difference between the asymmetric 0-H stretch in the monomer ( ~ 3 ) and the nonhydrogen-bonded 0 - H stretching frequency of the proton donor molecule in the dimer. Reference 38.
'
Once again, the MP2/6-3 l+G(d,p) Cl-H frequency shifts are in better agreement with the experimental shifts than the DFT values. 3. For ClH-OH2, the B3LYP/6-31G(d,p) binding energy is significantly larger than B3LYP/6-3 1fG(d,p) and MP2/63 1+G(d,p) binding energies. The MP2/6-3 1+G(d,p) intermolecular distance is 0.03 A shorter than the experimental distance, while the B3LYP/6-31+G(d,p) and B3LYP/6-31G(d,p) distances are shorter by 0.07 and 0.12 A, respectively. The experimental C1-H frequency shift is significantly overestimated by 179 cm-' at B3LYP/6-31G(d,p), while B3LYP/6-31+G(d,p) overestimates this shift by 68 cm-I, and MP2/6-3 l+G(d,p) underestimates it by 30 cm-I. 4 . For (HC1)2, differences among the results obtained from the three calculations are not significant.
5. For (HF)2 and (H20)2, B3LYP/6-31G(d,p) fails to reproduce the known experimental open structures which have C,symmetry. The computed B3LYP/6-3 lG(d,p) structures are cyclic with very short.0-0 and F-F distances and large binding energies. Because these structures are incorrect, the computed properties of these dimers should not be compared with experimental data. 6. For ( H F ) 2 and (H20)2, B3LYP/6-31+G(d,p) and MP2/63 1+G(d,p) binding energies are similar and again greater than the experimental energies. The MP2/6-3 l+G(d,p) intermolecular distances are in better agreement with experiment than the B3LYP/6-31+G(d,p) distances, which are too short. In addition, MP2/6-31+G(d,p) F-H and 0-H stretching frequency shifts for proton donor HF and H20 molecules are in better agreement with experiment than B3LYP/6-3 1+G(d,p) shifts. Latajka and Bouteiller9 and Kim and Jordan'O have investigated (HF)2 and (H20)2, respectively, using the B3LYP functional and the conrelated MP2 level of theory with much larger augmented basis sets. A conclusion of both studies is that the B3LYP functional with these large basis sets provides a description of (HFh and of (H20)2 similar to MP2, in agreement with the present results. The data obtained in this work show that B3LYP/6-31G(d,p) calculations fail to yield reliable binding energies, intermolecular distances, and vibrational frequency shifts. Therefore, B3LYP/ 6-31G(d,p) should not be used for studies of hydrogen-bonded complexes. Properties of hydrogen bonded complexes obtained from DFT calculations with the B3LYP functional and the 6-3 1+G(d,p) basis set are usually improved and may be similar to those obtained from MP2/6-3 1+G(d,p) calculations. However, in those cases where noticeable differences exist between computed B3LYP/6-3 1+G(d,p) and MP2/6-3 1+G(d,p) results, the MP2/6-3 l+G(d,p) values are in better agreement with experimental data. This suggests that improvements in functionals are still needed so that DFT can better describe longrange interactions and provide reliable predictions of the properties of hydrogen-bonded complexes. Acknowledgment. This work was supported by a grant of supercomputer time from the Ohio Supercomputer Center. References and Notes (1) (a) Ziegler, T. Chem. Rev. 1991, 91, 651. (b) Densify Functional Methods in Chemistry; Labanowski, J. K., Andzelm, J., Eds.; SpringerVerlag: New York, 1991. (c) Johnson, B. G.; Gill, P. M. W.; Pople, J. A. J. Chem. Phys. 1993, 98, 5612. (d) Handy, N. C.; Murray, C. W.; Amos, R. D. J. Phys. Chem. 1993, 97, 4392. (e) Oliphant, N.; Bartlett, R. J. J. Chem. Phys. 1994, 100, 6550. (0Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.: Frisch, M. J. J. Phys. Chem. 1994, 98, 11623. (g) Rauhut, G.: Pulay, P. J . Am. Chem. SOC. 1995,117,4167. (h) Rauhut, G.; Pulay. P. J. J. Phys. Chem. 1995, 99, 3093. (2) Becke, A. D. J. Chem. Phys. 1993, 98, 1372, 5648. (3) Lee, C.: Yang, W.: Parr, R. G. Phys. Rev. B 1988, 41, 785. (4) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.: Johnson, B. G.; Wong, M. W.; Foresman, J. B.; Robb, M. A,; Head-Gordon, M.; 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 92". Rev. G.3; Gaussian, Inc.: Pittsburgh, PA, 1993. (5) k m , F.; St-Amant, A.; Papai, I: Salahub, D. R. J. Am. Chem. Soc. 1992, 114, 4391. (6) Mijoule, C.; Latajka, Z.; Boris, D. Chem. Phys. Lett. 1993, 208, 364. (7) Barone, V.; Adamo, C. Chem. Phys. Lett. 1994, 224, 432. (8) Barone, V.; Orlandini, L.: Adamo, C. Chem. Phys. Lett. 1994, 231, 295. (9) Latajka, Z . ; Bouteiller, Y. J. Chem. Phys. 1994, 101, 9793. (10) Kim,K.; Jordan, K. D. J. Phys. Chem. 1994, 98, 10089. (1 1) Del Bene, J. E. In?. J. Quantum Chem. Quantum Chem. Symp. 1992, 26, 557. (12) Del Bene, J. E.: Mettee, H. D. J. Phys. Chem. 1993. 97, 9650 (13) Pople, J. A.; Binkley, J. S.: Seeger. R. In?. J . Quantum Chem., Quantum Chem. Symp. 1976, 10, 1. (14) Krishnan, R.: Pople, J. A. Int. J. Quantum Chem. 1978, 14, 91.
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