The parametrization and testing of the OPLS all-atom force field for organic molecules and peptides are described. Parameters for both torsional and nonbonded energetics have been derived, while the bond stretching and angle bending parameters have been adopted mostly from the AMBER all-atom force field. The torsional parameters were determined by fitting to rotational energy profiles obtained from ab initio molecular orbital calculations at the RHF/6-31G*//RHF/6-31G* level for more than 50 organic molecules and ions. The quality of the fits was high with average errors for conformational energies of less than 0.2 kcal/mol. The force-field results for molecular structures are also demonstrated to closely match the ab initio predictions. The nonbonded parameters were developed in conjunction with Monte Carlo statistical mechanics simulations by computing thermodynamic and structural properties for 34 pure organic liquids including alkanes, alkenes, alcohols, ethers, acetals, thiols, sulfides, disulfides, aldehydes, ketones, and amides. Average errors in comparison with experimental data are 2% for heats of vaporization and densities. The Monte Carlo simulations included sampling all internal and intermolecular degrees of freedom. It is found that such non-polar and monofunctional systems do not show significant condensed-phase effects on internal energies in going from the gas phase to the pure liquids.

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An overview is provided on the development and status of potential energy functions that are used in atomic-level statistical mechanics and molecular dynamics simulations of water and of organic and biomolecular systems. Some topics that are considered are the form of force fields, their parameterization and performance, simulations of organic liquids, computation of free energies of hydration, universal extension for organic molecules, and choice of atomic charges. The discussion of water models covers some history, performance issues, and special topics such as nuclear quantum effects.T he last 30 years have witnessed remarkable progress in condensed-phase theory. Before that time, atomic-level computer simulations of fluids were largely restricted to atomic and diatomic systems. The first simulation of liquid water was not reported until 1969 and was a Monte Carlo (MC) effort (1), which was followed by the molecular dynamics (MD) studies of Rahman and Stillinger (2, 3) in the early 1970s. The state-of-the-art simulations of water in 1974 were performed for 216 molecules for Ͻ10 ps (3). Even by 1990, there had been almost no MD simulations for a protein in aqueous solution covering 100 ps (4), whereas today MD simulations for a protein with Ϸ10,000 water molecules for many nanoseconds or mixed quantum and molecular mechanics (QM͞ MM) simulations for an enzymatic reaction are not problematic. Of course, performing longer simulations for larger systems does not guarantee the production of useful results. Key underlying issues for accuracy are adequate configurational sampling and the quality of the description of the intramolecular and intermolecular energetics. Progress on the former issue has been aided greatly by massive increases in computing power, although the substantial technical developments in the latter area are the focus of this overview. The topic also has received attention in comprehensive, recent reviews for the treatment of water (5) and biomolecular systems (6-10) that go far beyond the present page limitations. So, the presentation here will be more condensed with a focus on force-field development, water, and aqueous solutions and with some emphasis on our personal experiences and viewpoint. Force FieldsA force field consists of classical potential energy expressions and the associated adjustable parameters. The large majority of condensed-phase simulations have invoked pairwise additivity such that the total potential energy for a collection of molecules and͞or ions (components) with coordinates X ជ is given by the sum of the intermolecular interaction energies between all components plus the sum of the intramolecular energies of the components (Eq. 1).The intramolecular potential energy is typically represented by harmonic terms for bond stretching and angle bending, a Fourier series for each torsional angle, and Coulomb and Lennard-Jones interactions between atoms separated by three or more bonds (Eqs. 2-5). The latter ''nonbonded'' interactions also are evaluated between intermolecular at...

The development and validation of new peptide dihedral parameters are reported for the OPLS-AA force field. High accuracy quantum chemical methods were used to scan φ, ψ, χ1, and χ2 potential energy surfaces for blocked dipeptides. New Fourier coefficients for the dihedral angle terms of the OPLS-AA force field were fit to these surfaces, utilizing a Boltzmann-weighted error function and systematically examining the effects of weighting temperature. To prevent overfitting to the available data, a minimal number of new residue-specific and peptide-specific torsion terms were developed. Extensive experimental solution-phase and quantum chemical gas-phase benchmarks were used to assess the quality of the new parameters, named OPLS-AA/M, demonstrating significant improvement over previous OPLS-AA force fields. A Boltzmann weighting temperature of 2000 K was determined to be optimal for fitting the new Fourier coefficients for dihedral angle parameters. Conclusions are drawn from the results for best practices for developing new torsion parameters for protein force fields.

The accurate calculation of protein/nucleic acid–ligand interactions or condensed phase properties by force field-based methods require a precise description of the energetics of intermolecular interactions. Despite the progress made in force fields, small molecule parameterization remains an open problem due to the magnitude of the chemical space; the most critical issue is the estimation of a balanced set of atomic charges with the ability to reproduce experimental properties. The LigParGen web server provides an intuitive interface for generating OPLS-AA/1.14*CM1A(-LBCC) force field parameters for organic ligands, in the formats of commonly used molecular dynamics and Monte Carlo simulation packages. This server has high value for researchers interested in studying any phenomena based on intermolecular interactions with ligands via molecular mechanics simulations. It is free and open to all at jorgensenresearch.com/ligpargen, and has no login requirements.

The OPLS all‐atom (AA) force field for organic and biomolecular systems has been expanded to include carbohydrates. Starting with reported nonbonded parameters of alcohols, ethers, and diols, torsional parameters were fit to reproduce results from ab initio calculations on the hexopyranoses, α,β‐d‐glucopyranose, α,β‐d‐mannopyranose, α,β‐d‐galactopyranose, methyl α,β‐d‐glucopyranoside, and methyl α,β‐d‐mannopyranoside. In all, geometry optimizations were carried out for 144 conformers at the restricted Hartree–Fock (RHF)/6–31G* level. For the conformers with a relative energy within 3 kcal/mol of the global minima, the effects of electron correlation and basis‐set extension were considered by performing single‐point calculations with density functional theory at the B3LYP/6–311+G** level. The torsional parameters for the OPLS‐AA force field were parameterized to reproduce the energies and structures of these 44 conformers. The resultant force field reproduces the ab initio calculated energies with an average unsigned error of 0.41 kcal/mol. The α/β ratios as well as the relative energies between the isomeric hexopyranoses are in good accord with the ab initio results. The predictive abilities of the force field were also tested against RHF/6–31G* results for d‐allopyranose with excellent success; a surprising discovery is that the lowest energy conformer of d‐allopyranose is a β anomer. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1955–1970, 1997

Testing of the commonly used hybrid density functional B3LYP with the 6-31G(d), 6-31G(d,p), and 6-31+G(d,p) basis sets has been carried out for 622 neutral, closed-shell organic compounds containing the elements C, H, N, and O. The focus is comparison of computed and experimental heats of formation and isomerization energies. In addition, the effect of an empirical dispersion correction term has been evaluated and found to improve agreement with the experimental data. For the 622 compounds, the mean absolute errors (MAE) in the heats of formation are 3.1, 2.6, 2.7, and 2.4 kcal/mol for B3LYP/6-31G(d), B3LYP/6-31G(d,p), B3LYP/6-31+G(d,p), and B3LYP/6-31+G(d,p) with the dispersion correction. A diverse set of 34 isomerizations highlights specific issues of general interest, such as performance on differences in steric effects, conjugation, and bonding. The corresponding MAEs for the isomerizations are 2.7, 2.4, 2.2, and 1.9 kcal/mol. Improvement is obtained for isomerizations of amines and alcohols when both polarization and diffuse functions are used, but the overstabilization of linear alkanes compared to branched isomers can be relieved only with the dispersion correction. Besides the insights on DFT methods, the study also aimed to quantify the gains in accuracy that can be achieved by replacing energetics from NDO-based semiempirical methods with DFT results. Since the MAEs obtained with the PDDG/PM3 method for the 622 heats of formation and 34 isomerizations are 2.8 and 2.3 kcal/mol, negligible advantage in accuracy for the B3LYP-based methods emerged in the absence of the dispersion corrections.

An overview is provided of the capabilities for the current versions of the BOSS and MCPRO programs for molecular modeling of organic and biomolecular systems. Recent applications are noted, particularly for QM/MM studies of organic and enzymatic reactions and for protein-ligand binding.