J. Phys. Chem. 1996, 100, 2689-2697
2689
Simulation of Liquid Amides Using a Polarizable Intermolecular Potential Function† Jiali Gao,* Joseph J. Pavelites, and Dariush Habibollazadeh Department of Chemistry, State UniVersity of New York at Buffalo, Buffalo, New York 14260 ReceiVed: August 2, 1995; In Final Form: January 9, 1996X
We have developed a polarizable intermolecular potential function (PIPF) for simulation of liquid amides. The PIPF potential includes a pairwise additive component, consisting of the familiar Lennard-Jones and Coulomb form, and a nonadditive polarization term. The empirical parameters were optimized through a series of statistical mechanical Monte Carlo simulations of liquid formamide, N-methylacetamide (NMA), N-methylformamide (NMF), and N,N-dimethylformamide (DMF). In deriving the empirical potential functions, bimolecular complexes of the amides dimers were studied by ab initio molecular orbital calculations using the 6-31G(d) basis set, and the results were compared with the PIPF predictions. The computed heats of vaporization and densities for the liquids using the final parameters are within 2% and 3% of experimental values, respectively. The polarization effects are found to be significant in all liquids, ranging from 6% for DMF to 14% for formamide of the total liquid energy. Electrostatic and polarization components dominate in primary and secondary amides, while the van der Waals contribution is greater than electrostatic terms for the tertiary amide DMF. In the present parameter optimization, polarization energies and induced dipole moments in the liquids are compared with results obtained from separate Monte Carlo simulations employing a combined quantum mechanical and molecular mechanical (QM/MM) approach. In the latter calculation, one amide monomer is treated quantum mechanically by the semiempirical AM1 theory, which is embedded in the liquid of the same amide represented by the empirical OPLS potential. In addition, structural features including hydrogen-bonding interactions and radial distribution functions are examined and found to be in good agreement with the previous computational results.
Introduction A great challenge in computer simulation of liquids and biopolymers is to incorporate the solvent polarization effect into the potential energy surface.1 The role of solvent polarization effects on molecules of biological importance is undoubtedly important, particularly for processes involving significant changes of the molecular environment, such as molecular recognition and protein-DNA interactions.2-6 This is emphasized by two recent studies of solvent effects on amide isomerization and the hydration of nucleotide bases from our laboratory. Employing a combined quantum mechanical and molecular mechanical (QM/MM) approach,1,7-9 we found that the molecular dipole moment of N,N-dimethylformamide (DMF) changes from the gas-phase value of 3.55 D to 3.62, 4.05, and 5.08 D in CCl4, CHCl3, and water, respectively, which is accompanied by polarization energies of -0.004, -0.32, and -3.47 kcal/mol in the three solvents.10a In addition, solvent polarization effects were determined to contribute 37-61% of solvation free energies of the five nucleotide bases in water.10b However, in the past, it is often difficult to decompose the observed binding energy into specific contributions, especially differentiating the “permanent” electrostatic and polarization terms. Consequently, there has been a lack of experimental and theoretical data that can be directly used for accurate parametrization of polarizable potential functions.1 Furthermore, the use of a polarizable potential in condensed-phase simulations typically requires a significant increase in computational time and computer memory over that employing pairwise effective potentials. As a result, the progress has been slow in developing polarizable intermolecular potential functions (PIPF) for molecular dynamics and Monte Carlo calculations. Perhaps the † This paper is dedicated to Professor Martin Karplus with great respect and deep appreciation on the occasion of his 65th birthday. X Abstract published in AdVance ACS Abstracts, February 1, 1996.
0022-3654/96/20100-2689$12.00/0
only exception is liquid water, for which a number of polarizable models have been reported in the literature.6 Within the framework of the combined QM/MM approach, we developed a polarization energy decomposition method in statistical mechanical Monte Carlo simulations.1,7 In this method, the solute molecule is treated quantum mechanically, which is embedded in the solvent environment represented by a classical, molecular mechanics force field.7-9 The wave function of the solute molecule in solution can, thus, be determined in Monte Carlo or molecular dynamics calculations. Consequently, the polarization energy and induced dipole moment of the solute molecule by the surrounding environment can be evaluated a priori in these simulations, providing valuable information necessary for calibration of the nonadditive potential functions.1,8 To this end, PIPF potentials have been developed for hydrocarbons and alcohols in our laboratory.11 Taking an approach pioneered by Jorgensen and co-workers in their development of the optimized potentials for liquid simulations (OPLS),12 the PIPF functions have been derived by fitting directly to experimental thermodynamic and structural data for the pure liquids. The polarization energies and induced dipoles are optimized to be consistent with the results obtained from combined QM/MM simulations.11 Although this approach requires iterative simulations of the pure liquids, and is extremely demanding of computer resources, the accuracy of the resulting potential functions is evident with an average error of only 1-3% in computed heats of vaporization and densities.11 This work is now extended to liquid amides. Amides represent an important class of organic compounds for use as organic solvents and, more importantly, as model systems for peptides. Consequently, there have been great efforts in the development of force fields for amides and peptides, and a number of well-tested models are available.12-18 All previous approaches have utilized pairwise, additive potential © 1996 American Chemical Society
2690 J. Phys. Chem., Vol. 100, No. 7, 1996
Gao et al.
TABLE 1: Standard Geometrical Parameters for Amidesa bond lengths, Å CdO C-H CO-N CH-N CO-C N-H a
bond angles, deg
1.229 1.090 1.335 1.449 1.522 0.960
OdC-N C(H)-CO-N C-N-CO H-N-CO N-C-H H-C-H
122.9 116.6 121.9 119.8 109.5 109.5
Epol ) -
References 12 and 19.
functions, although in many cases, the condensed-phase polarization effects are implicitly included in the effective parameters in an average sense.12 To our knowledge, the only simulation study of liquid amides employing a nonadditive polarizable potential was that of liquid N-methylacetamide by Caldwell and Kollman,5 although Ding et al. used a polarizable model to investigate the hydration of amines and amides.4 In view of the importance of the peptide bonds, along with our effort in developing a polarizable force field for simulation of proteins in aqueous solution, a systematic parametrization of the PIPF potential for liquid amides is warranted. In conjunction with previous works on liquid hydrocarbons and alcohols,11 PIPF potentials are now available for 11 amino acid residues (Ala, Asn, Gln, Gly, Ile, Phe, Pro, Ser, Thr, Tyr, and Val). In the following, we first describe the details of computational methods and parametrization. Then, results and discussion for liquid amides, including formamide (primary amide), N-methylacetamide (NMA) and N-methylformamide (NMF, secondary amides), and N,N-dimethylformamide (DMF, tertiary amide), will be presented. The paper is concluded with future perspectives. Computational Details Intermolecular Potential. An all-atom model is used in the present polarizable intermolecular potential functions (PIPF) for amides, with interaction sites located on each nucleus. Standard bond lengths and bond angles derived from X-ray structures are used in this study (Table 1).19 These geometrical parameters are kept fixed throughout the liquid simulation and calculation of hydrogen-bonded complexes; however, internal rotations of all dihedral angles are varied during the Monte Carlo sampling. Diffraction studies showed that the primary and secondary amides have a planar nitrogen bond geometry,20,21 whereas electron diffraction experiments revealed a pyramidal structure, about 15° off the amide plane.22 The total energy of the pure liquid system is given below, which consists of a pairwise term and a nonadditive polarization component:
Etot ) Epair + Epol
(1)
In eq 1, the pairwise potential is enumerated over pairs of monomers in the liquid (eq 2) N
Epair ) ∑Eab
(2)
a
