A new method for deriving force fields for molecular simulations has been developed. It is based on the derivation and parameterization of analytic representations of the ab initio potential energy surfaces. The general method is presented here and used to derive a quantum mechanical force field (QMFF) for alkanes. It is based on sampling the energy surfaces of 16 representative alkane species. For hydrocarbons, this force field contains 66 force constants and reference values. These were fit to 128,376 quantum mechanical energies and energy derivatives describing the energy surface. The detailed form of the analytic force field expression and the values of all resulting parameters are given. A series of computations is then performed to test the ability of this force field to reproduce the features of the ab initio energy surface in terms of energies as well as the first and second derivatives of the energies with respect to molecular deformations. The fit is shown to be good, with rms energy deviations of less than 7% for all molecules. Also, although only two atom types are employed, the force field accounts for the properties of both highly strained species, such as cyclopropane and methylcyclopropanes, as well as unstrained systems. The information contained in the quantum energy surface indicates that it is significantly anharmonic and that important intramolecular coupling interactions exist between internals. The representation of the nature of these interactions, not present in diagonal, quadratic force fields (Class I force fields), is shown to be important in accounting accurately for molecular energy surfaces. The Class I1 force field derived from the quantum energy surface is characterized by accounting for these important intramolecular forces. The importance of each 'Author to whom all correspondence should be addressed. tl'resent address: Dept. of Chemistry, Ben Gurion Univ. of the Negev, Beersheva 84105, Israel. Journal of Computational DERIVATION OF CLASS II FORCE FIELDSof the interaction terms of the potential energy function has also been assessed. Bond anharmonicity, angle anharmonicity, and bond/angle, bond/ torsion, and angle/angle/ torsion cross-term interactions result in the most significant overall improvement in distorted structure energies and energy derivatives. The implications of each energy term for the development of advanced force fields is discussed. Finally, it is shown that the techniques introduced here for exploring the quantum energy surface can be used to determine the extent of transferability and range of validity of the force field. The latter is of crucial importance in meeting the objective of deriving a force field for use in molecular mechanics and dynamics calculations of a wide range of molecules often containing functional groups in novel environments.

We present a technique for addressing the problem of deriving potential energy functions for the simulation of organic, polymeric, and biopolymeric systems, as well as for modeling vibrational spectroscopic properties. This method is designed to address three major objectives: deriving and comparing optimal functional forms for describing the energies of molecular deformations and interactions, developing a technique to rapidly and objectively determine reasonable force constants for intermolecular and intramolecular interactions, and determining the transferability of these potential forms and constants. The first two of these objectives are addressed in this paper, while the latter problem will be treated elsewhere. The technique uses ab initio molecular energy surfaces, which are described by the energy and its first and second derivatives with respect to coordinates. As an example, application to a small model compound (i.e., the formate anion) is given. A variety of analytical forms for the potential are tested against the data, to find which forms are best. The importance of anharmonicity and cross terms in accounting for structure and energy, as well as for dynamics, is demonstrated and a more accurate representation of the out-of-plane deformation for a trigonal center is derived from the energy surfaces. Section 1. Introduction Theoretical techniques are currently being applied to problems such as ligand binding to receptors, simulation of the structure and conformational fluctuations of flexible molecules, and the design of drugs. These techniques include molecular mechanics and dynamics simulations, Monte Carlo simulations, and vibrational normal-mode analysis (1). Such techniques ultimately will offer the possibility of understanding the complex behavior of organic molecules, polymers, biomolecules, and biomolecular complexes in terms of fundamental intermolecular and intramolecular physical forces, thus allowing an understanding of the molecular behavior of these systems at a level that is inaccessible to experimental techniques alone. However, the results of these simulations depend critically on the set of potential energy functions (i.e., force field) used. Although a great deal ofeffort has gone into the derivation offorce fields now in use (2-21), there remain many more organic and biomolecular functional groups for which adequate parameters have yet to be derived. Moreover, even the functional form required to describe molecular energy surfaces is still a subject of research (1).The derivation of the force constants and the appropriate functional forms to be used in describing the energy surfaces for biomolecular systems have been addressed previously (6,7,(9)(10)(11)(12). These studies relied for the most part on the fit of experimental properties and followed the Lifson consistentforce-field approach (3). In the crystal studies, ab initio calculations were used to obtain information about patterns of charge distribution (11), while the values of the partial charges were determined fr...

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Visual pigments are a class of proteins found in the membranes of photoreceptor cells (for reviews, see refs. 1 and 2). Their chromophoric unit is 11-cis-retinal covalently bound in the form of a Schiff base to the c-amino group of a lysine. The absorption of a photon by a visual pigment initiates a sequence of biochemical events that eventually lead to the generation of a neural signal by a photoreceptor cell. The identity of the primary photochemical event has been a subject of considerable interest and controversy. It was originally suggested that the primary event was an isomerization of the chromophore from its 1 1-cis to an all-trans conformation (3, 4). The strongest evidence favoring this mechanism was the observation (based on spectral data at low temperature) that an artificial pigment containing a 9-cis chromophore had the same photoproduct as rhodopsin itself. It was quite reasonably concluded that the most plausible common photoproduct formed from the two cis isomers is a trans isomer. A number of picosecond absorption studies of the primary event have raised widespread doubts as to the validity of the original model. It was found (5) that the primary event is complete in less than a few picoseconds at room temperature, and it was argued that this is too short a time for isomerization to occur [although other picosecond studies have reached the opposite conclusion (6)]. More recent evidence has come from the observation that at low temperature the rate of the process is significantly inhibited by deuterium replacement of the exchangeable protons on the pigment (7). Since only one proton on the chromophore is exchangeable, it is unlikely that this would have a measurable effect on the rate of isomerization. The picosecond measurements have generated numerous models (7-11) whose major feature is a photochemical proton transfer followed by a thermal cis-trans isomerization that occurs at a later stage. However, the original evidence upon which the suggestion of a cis-trans isomerization was originally based has never been discredited and, thus, it appears necessary to find a molecular model that is consistent with the entire body of available evidence. The purpose of this paper is to present such a model.There are, in fact, a fairly large number of observations that can be used in the construction and evaluation of alternative models. For example, we have shown, by using simple thermodynamic arguments, that a significant fraction of the photon's energy is "stored" in the primary photoproduct (12). Clearly a mechanism for energy storage must be an important component of any model that is proposed. Another energetic constraint may be derived from psychophysical and electrophysiological measurements of the level of thermal noise in photoreceptor cells. We show below that these observations may be interpreted directly in molecular terms and that they require an unusually high thermal activation energy for the primary event that appears to be inconsistent with many of the models that have been proposed.The ...

Various models of visual-pigment spectra are critically discussed in terms of the spectral properties of protonated Schiff bases and the common structural features of most proteins. The opsin apoprotein is capable of regulating visual pigment wavelengths in ways that are difficult or impossible to reproduce in model systems. Theories based on solvent effects of the spectra of protonated Schiff bases may be misleading. Careful parameterization using known polyene spectra allows accurate calculation of the spectral properties of protonated Schiff bases. It is shown that an isolated protonated Schiff base of retinal should absorb near 600 nm and that blue-shifted spectra seen in solution arise from associated counterions or solvent molecules. We conclude that the most plausible specific model of chromophore-protein interactions is one in which the protonated Schiff base is closely associated with its counterion and where additional negatively charged or polar groups are positioned by the protein in the vicinity of the ring half of the chromophore. Pigment absorption maxima, bandwidths, and the A2-A1 pigment absorption differences arise naturally from these simple models of pigment spectra.