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J. Phys. Chem. 1991,95, 10559-10560 the p/o conversion may propagate through hydrogen bond networks. Then, for example, if pwater is thermodynamically more stable in a condense phase or multilayers under adsorption field, as in H2(1.7 kcal/mol),l' and interacts more favorably with o-water in a vapor, the kinetic o/p conversion due to magnetic field might lead to the adsorption promotion through the cooperative process which would be much slower than the p/o conversion process. The mechanism above is only a possibility and thus very speculative, especially since we have no direct evidence on 0- and pwater, besides a book that describes spectroscopic observations of 0- and p-water in vapor.12 The magnetic effect on water
adsorption is, to be sure, unexpected from the current paradigms for bulk water, but the experiments, aside from the mechanism, indicate that water on solid surfaces can respond to magnetic field, suggesting that water under adsorption field from solids may be different from bulk water.
Acknowledgment. We thank Professor Kaneko for helpful discussions and encouragement and Mr. Uchiyama and Mr. Miyamoto for some experimental assistance. (12) Krassen, V. I. Magnetic Water System; Chimiya: Moscow, 1982; Chapter 3 (in Russian).
Importance of Attractive van der Waals Contribution in Empirical Energy Function Models for the Heat of Vaporization of Polar Liquidst Alexander D. MacKerell, Jr.,* and Martin Karplus* Department of Chemistry, Harvard University, Cambridge, Massachusetts 02138 (Received: October 16, 1991)
Monte Carlo simulations with an empirical energy function were performed on a series of polar liquids to determine the relative contributions of the Lennard-Jones and electrostatic nonbonded terms to the calculated mean interaction energies and heats of vaporization. Although the hnard-Jones term is destabilizing for water, it contributes 30% of the mean interaction energy for ethanol and 52% for N-methylacetamide. This demonstrates the importance of the magnitudes of the well depths, as well as the nonbonded radii, of the Lennard-Jones terms in empirical energy functions for polar fluids and for macromolecular systems like proteins.
Empirical energy functions of the molecular mechanics type are being used in the simulation of pure liquids and aqueous solutions of a wide range of systems from the noble gases to complex macromolecules.'J In most of the energy functions, the nonbonded interactions are described by a Coulombic term with partial atomic charges for the electrostatic contribution and a Lennard-Jones term to represent the van der Waals repulsion and dispersive attraction; more complex representations have been introduced in certain cases (e.g., a Buckingham potential' instead of the Lennard-Jones term and atomic multiples4 instead of monopoles for the charge distribution). To obtain an understanding of the relative importance of the two types of nonbonded interactions, we have performed Monte Carlo simulations of several polar liquids and determined the Coulombic and Lennard-Jones contributions to the heats of vaporization. The calculations show that even for molecules as polar as formamide and N-methylacetamide, the Lennard-Jones contribution is responsible for a significant fraction of the heat of vaporization. The nonbonded parameters are taken from an all hydrogen force field for proteins and nucleic acids that is being determined by fitting a wide range of experimental data and ab initio results (work in progress). The Lennard-Jones terms (see Table I) are very similar to those in force fields currently used for solution and macromolecular studies.5,6 The well depths, t, are on the order of those obtained with the Kirkwood-Slater formula and recent estimates of atomic polarizabilities' (e.& for a hydroxyl oxygen, t = 0.108 kcal/mol and for a carbonyl oxygen, t = 0.137 kcal/mol). Ab initio calculations of the interaction of polar groups with water were used for determining the charges. Some examples are given in Table 11; both the Coulombic and Lennard-Jones contributions to the empirical interaction energies are listed. The results of the Monte Carlo liquid simulations for a series of compounds are given in Table 111. The heats of vaporization Supported in part by grants from the National Science Foundation and the National Institutes of Health. f National Institutes of Health Postdoctoral Fellow.
0022-3654/91/2095-10559$02.50/0
TABLE I: L"rd-Jones Parameters' atom type t , kcal / mol &in, A polar H 0.046 0.2245 aliphatic H 0.0078 1.468 nitrogen 0.20 1.85 carbonyl oxygen 0.12 1.70 1.77 hydroxyl oxygen 0.1521 carbonyl carbon 0.11 2.10 aliphatic carbon 0.1562 1.80 'Lennard-Jones energies were calculated with the formula ti,[(Rmin,i,/rj,)i2- 2(Rmin,i,/rij)6],where rij is the distance between the interacting atoms and the combining rules are tij - (eitj)'I2 and Rmin,ij= (Rmin,i + Rminj). and the average interaction energies with the Coulombic and Lennard-Jones contributions on a per molecule basis are given. The agreement between the calculated and experimental heats of vaporization is satisfactory. In the case of liquid water, where all atoms are involved in specific polar (hydrogen bonding) interactions, the Coulombic interaction is dominant and the Lennard-Jones term is repulsive. This is in accord with the results for isolated complexes (see Table 11), where the empirical Len~~
(1) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon: Oxford, 1987. (2) Brooks, C. L., III; Karplus, M.; Pettitt, B. M. Proteins: A Theoretical Perspective of Dynamics, Structure, and Thermodynamics; Adu. Chem. Phys.; Wiley: New York, 1988; Vol LXXI. (3) Burkert, U.; Allinger, N. L. Molecular Mechanics; American Chemical Society: Washington, D.C., 1982. (4) Stone, A. J.; Alderton, M. Mol. Phys. 1985, 56, 1047. (5) Weiner, S . J.; Kollman, P. A.; Nguyen, D. T.; Case, D. A. J. Comput. Chem. 1986, 2, 230. (6) Jorgensen, W. L.; TiradeRives, J. J . Am. Chem. Soc. 1988,110, 1647. (7) Miller, K. J. J . Am. Chem. SOC.1990, 112, 8533. ( 8 ) Jorgensen, W. L.;Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926. (9) Jorgensen, W. L. J . Phys. Chem. 1986, 90, 1276.
0 1991 American Chemical Society
10560 The Journal of Physical Chemistry, Vol. 95, No. 26. 1991
Letters
TABLE II: Minimum Interaction Energies (kcal/mol) and Geometries for Various Small Molecules with Water and Some Small Molecule Dimers scaled ab initio empirical"qb energy dist, A angle, deg energy (L-J)' dist, A angle, dea interaction water water dimer -6.55 2.02 124 -6.55 (1.50)' 1.81 153 methanol -5.71 (1.04) 1.84 MeOH 0 to HOH -5.73 2.05 MeOH 0-H to O H H -6.72 2.01 125.3 -6.64 (1.36) 1.80 158 -6.74 1.99 130.8 -6.58 (0.80) 1.82 129 dimer N-methylacetamide 1.98 145.5 -7.60 (0.93) 1.76 147 NMA C=O to HOH -7.61 -6.29 2.13 173.7 -6.30 (0.49) NMA N-H to OHH 1.93 171 2.08 dimer, parallel -1.75 -7.75 (-0.44) 1.84
" Charges were determined such that the calculated empirical interaction energies at the minimum distance for the interacting pairs are equivalent to the 6-31G* ab initio interaction energies scaled by 1.16. The 1.16 scaling of the 6-31G' energies is based on the ratio of the TIP3P empirical water dimer energy to the 6-31G* value. This introduces an effective polarization corresponding to the liquid and corrects for the attractive Lennard-Jones contribution that is not included in the Hartree-Fock calculations. bThe minimum empirical distances are chosen to be approximately 0.2 8, shorter than the ab initio values, in agreement with the TIP3P water dimer model8 and the requirement that pure liquid simulations yield the correct density.' 'For water, a slightly modified version of the TIP3P model8 was used (W. Reiher and M. Karplus, unpublished). dThe total empirical interaction energy is given with the Lennard-Jones contribution in parentheses. TABLE HI: Mean Jnteraction Energie (IE),Lennard-Jones (GJ), and Coulomb Contributions and Heats of Vaporization" compound IE L-J Coulomb AZ&ap,calo AHvap,sxpb 10.5 10.8 1.09 -11.30 water -10.21 9.2 8.9 -7.42 methanol -8.77 -1.35 10.1 10.2 -6.62 ethanol -9.52 -2.90 10.9 -6.18 11.2 2-propanol -10.58 -4.40 -9.81 14.1 14.7 -13.32 -3.51 formamide acetamide -13.83 -5.64 -8.19 14.4 NMA (100 "C) -12.35 -6.41 -5.94 13.1 14.2
dominate the structure,1° but also the well depths must be carefully determined to obtain correct thermodynamic properties for polar, as well as nonpolar, liquids. Since the interior of proteins contains peptide groups, which are often modeled by N-methylacetamide, and has hydrophobic regions that are presumed to be similar to liquid hydrocarbons or a l ~ o h o l s , ~careful ' ~ ' ~ parametrization of the attractive portion of the Lennard-Jones interaction is essential for reliable simulations.
Acknowledgment. We thank W. L. Jorgensen for permission to use his Monte Carlo program (MCBOSS), Dr. Jiali Gao for "Calculations were performed on 128 molecules with an NPT (1 helpful discussions and aid with the MCBOSS program, and Dr. atm, 25 OC, unless noted) ensemble by use of the MCBOSS p r ~ g r a m . ' ~ . ' ~ Annick Dejaegere for helpful discussions. The ab initio calcu1M configurations were used for equilibration followed by 2M config lations were performed with GAUSSIAN 82 and 86 at Cray Research urations for thermodynamic averaging. See ref 15. and on a TITAN computer on loan from the Stardent Corp. We thank Dr. Eric Wimmer for making possible the calculations at nard-Jones contribution is generally small and unfavorable because Cray Research. the orientations optimize the charge interactions. Upon adding aliphatic groups, as in the series H20, methanol, ethanol, and 2-propanol, the contribution of the Lennard-Jones term increases. (10) Weeks,J. D.; Chandler, D.; Andersen, H. C. J. Chem. Phys. 1971, It is equal to 15% of the interaction energy for methanol and 42% 54, 5237. for 2-propanol. This trend is even more striking for the amides. (11) Kauzmann, W. Adu. Protein Chem. 1959, 14, 1. For fommide, the Lennard-Jones component is significant (27%), (12) Privalov, P. L.; Gill, S. J. Adu. Protein Chem. 1988, 39, 191. (13) Jorgensen, W. L.; Madura, J. D.; Swenson, C. J. J. Am. Chem. SOC. although the Coulombic term dominates. Upon adding the methyl 1984, 106, 6638. group in acetamide, the Lennard-Jones contribution increases (14) Jorgensen, W. L.; Swenson, C. J. J. Am. Chem. SOC.1985,107,569. (41%), and it is slightly larger than the electrostatic term in (15) Water: Dorsey, N. E. Properties of Ordinary Water Substances; N-methylacetamide (52%). For sulfur-containing compounds, Rheinhold: New York, 1940. Alcohols: Wilhoit, R. C.; Zwolinski, B. J. J. such as methanethiol (results not shown), the Lennard-Jones term Phys. Chem., Ref Data, Suppl. 1973, 2. Formamide: Somsen, G.;Coop, J. R e d . Trau. Chim. Pays-Bas 1965,84,985. NMA: Lemire, R. H.; Sears, provides 90% of the heat of vaporization. P. G.Top. Current Chem. 1978, 74, 45. See also: Cox, J. D.; Pilcher, R. The present analysis shows the importance of the attractive Thermochemistry of Organic and Organometallic Compounds; Academic: Lennard-Jones term in the interaction energy of empirical energy London, 1970. Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Organic Soluents, 4th ed.; Wiley: New York, 1986. calculations. Thus, not only the van der Waals radii, which
