Kim Palmo

Potential energy functions: From consistent force fields to spectroscopically determined polarizable force fields

We review our methodology for producing physically accurate potential energy functions, particularly relevant in the context of Lifsons goal of including frequency agreement as one of the criteria of a self‐consistent force field. Our spectroscopically determined force field (SDFF) procedure guarantees such agreement by imposing it as an initial constraint on parameter optimization, and accomplishes this by an analytical transformation of ab initio “data” into the energy function format. After describing the elements of the SDFF protocol, we indicate its implementation to date and then discuss recent advances in our representation of the force field, in particular those required to produce an SDFF for the peptide group.

A new electrostatic model for molecular mechanics force fields

Abstract A new electrostatic model, designed for use in molecular mechanics force fields, is presented. In addition to atomic charges the model consists of atomic dipoles and is further enhanced by the possibility of explicitly accounting for polarizability in the form of induced charges and anisotropically induced atomic dipoles. The parameters of the model are determined in a consistent way from isolated molecules by fitting to ab initio electric potentials. The polarizability in different directions is probed by subjecting the molecules to various external electric fields. As an illustration of the model, parameters have been obtained for isolated water and formaldehyde molecules, and applied to a few hydrogen-bonded water dimers and water–formaldehyde complexes. The parameters transferred from the isolated molecules successfully reproduce the ab initio (MP2/6-31++G(d,p)) electric potentials, molecular dipole moments, and molecular polarizabilities of all the studied dimers and complexes. The performance of nonpolarizable models for these systems is also evaluated, and, for fixed hydrogen-bond distances, is found to be acceptable in most cases.

A polarizable electrostatic model of the N-methylacetamide dimer

Our previously developed polarizable electrostatic model is applied to isolated N‐methylacetamide (NMA) and to three hydrogen‐bonded configurations of the NMA dimer. Two versions of the model are studied. In the first one (POL1), polarizability along the valence bonds is described by induced bond charge increments, and polarizability perpendicular to the bonds is described by cylindrically isotropic induced atomic dipoles. In the other version (POL2), the induced bond charge increments are replaced by induced atomic dipoles along the bonds. The parameterization is done by fitting to ab initio MP2/6‐31++G(d,p) electric potentials. The polarizability parameters are determined by subjecting the NMA molecule to various external electric fields. POL1 turns out to be easier to optimize than POL2. Both models reproduce well the ab initio electric potentials, molecular dipole moments, and molecular polarizability tensors of the monomer and the dimers. Nonpolarizable models are also investigated. The results show that polarization is very important for reproducing the electric potentials of the studied dimers, indicating that this is also the case in hydrogen bonding between peptide groups in proteins.

Electrostatic Model for Infrared Intensities in a Spectroscopically Determined Molecular Mechanics Force Field

A new electrostatic model for the calculation of infrared intensities in molecular mechanics and molecular dynamics is presented. The model is based on atomic charges, atomic charge fluxes, and internal coordinate dipoles and their fluxes. The internal coordinate dipoles are used instead of atomic dipoles, thus simplifying the derivation of parameters. The model is designed to reproduce ab initio dipole derivatives, and the parameters can be obtained by (iterative) transformations from these, or by linear least squares fitting to them. A first application to linear alkanes has been made. For these molecules, the intensities can be predicted with an average accuracy of 30–40%. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 754–768, 1998

OPTIMIZATION OF PARAMETERS OF NONBONDED INTERACTIONS IN A SPECTROSCOPICALLY DETERMINED FORCE FIELD

Abstract A procedure is given by which parameters of nonbonded interactions in a molecular mechanics energy function can be optimized for maximum compatibility with ab initio force fields and structures. The method is based on a previously derived transformation of ab initio valence parameters to the molecular mechanics formalism. Explicit analytical expressions for the derivatives of the molecular mechanics force constants and reference geometry parameters with respect to the parameters of the nonbonded interactions are derived. The form of the goodness-of-fit function is discussed. A first application to a set of alanine dipeptides is described.

New out-of-plane angle and bond angle internal coordinates and related potential energy functions for molecular mechanics and dynamics simulations

With currently used definitions of out‐of‐plane angle and bond angle internal coordinates, Cartesian derivatives have singularities, at ±π/2 in the former case and π in the latter. If either of these occur during molecular mechanics or dynamics simulations, the forces are not well defined. To avoid such difficulties, we provide new out‐of‐plane and bond angle coordinates and associated potential energy functions that inherently avoid these singularities. The application of these coordinates is illustrated by ab initio calculations on ammonia, water, and carbon dioxide. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1067–1084, 1999

Spectroscopically Determined Force Field for Water Dimer: Physically Enhanced Treatment of Hydrogen Bonding in Molecular Mechanics Energy Functions

Our ab initio transformed spectroscopically determined force field (SDFF) methodology emphasizes, in addition to accurate structure and energy performance, comparable prediction of vibrational properties in order to improve reproduction of interaction forces. It is now applied to the determination of a molecular mechanics (MM) force field for the water monomer and dimer as an initial step in developing a more physically based treatment of the hydrogen bonding that not only underlies condensed-phase water but also must be important in molecular-level protein-water interactions. Essential electrical components of the SDFF for monomer water are found to be the following: an off-plane charge distribution, this distribution consisting of four off-atom charge sites in traditional lone pair (LP) but also in inverted lone pair (ILP) positions; allowance for a diffuse size to these off-atom sites; and the incorporation of charge fluxes (i.e., the change in charge with change in internal coordinate). Parametrization of such an LP/ILP model together with the SDFF analytically transformed valence force field results in essentially exact agreement with ab initio (in this case MP2/6-31++G(d,p)) structure, electrical, and vibrational properties. Although we demonstrate that the properties of this monomer electrical model together with its van der Waals and polarization interactions are transferable to the dimer, this is not sufficient in reproducing comparable dimer properties, most notably the huge increase in infrared intensity of a donor OH stretch mode. This deficiency, which can be eliminated by a large dipole-derivative-determined change in the effective charge flux of the donor hydrogen-bonded OH bond, is not accounted for by the charge flux change in this bond due to the induction effects of the acceptor electric field alone, and can only be fully removed by an added bond flux associated with the extent of overlap of the wave functions of the two molecules. We show that this overlap charge flux (OCF) emulates an actual O-H...LP-O intermolecular dipole flux, reflecting the unitary nature of the hydrogen-bonded system in the context of MM-separable molecules. The effectiveness of incorporating the OCF noncanonical character demonstrates that a distinctively QM-unique property can be substantively represented in MM energy functions.

A new formalism for molecular dynamics in internal coordinates

Abstract Internal coordinate molecular dynamics (ICMD) has been used in the past in simulations for large molecules as an alternative way of increasing step size with a reduced operational dimension that is not achievable by MD in Cartesian coordinates. A new ICMD formalism for flexible molecular systems is presented, which is based on the spectroscopic B -matrix rather than the A -matrix of previous methods. The proposed formalism does not require an inversion of a large matrix as in the recursive formulations based on robot dynamics, and takes advantage of the sparsity of the B -matrix, ensuring computational efficiency for flexible molecules. Each molecule’s external rotations about an arbitrary atom center, which may differ from its center of mass, are parameterized by the SU (2) Euler representation, giving singularity free parameterization. Although the formalism is based on the use of nonredundant generalized (internal and external) coordinates, an MD simulation in linearly dependent coordinates can be done by finding a transformation to a new set of independent coordinates. Based on the clear separability in the generalized coordinates between fast varying degrees of freedom and slowly varying ones, a multiple time step algorithm is introduced that avoids the previous nontrivial interaction distance classification. Also presented is a recursive method for computing nonzero A -matrix elements that is much easier to apply to a general molecular structure than the previous method.

Chain elastic modulus of polyethylene: A spectroscopically determined force field (SDFF) study

Our SDFF for linear saturated hydrocarbon chains has been used to calculate the chain modulus of isolated and crystalline chains of n-alkanes of varying lengths. This has been done for static deformations and for the dynamic deformation in the longitudinal acoustic mode (LAM). Extrapolation to infinite chain length gives a common value of the room-temperature crystal modulus of 303 GPa (also obtained in an infinite chain calculation). Experimental Raman LAM measurements, corrected for chain-end interactions, give a modulus of 305 GPa, in excellent agreement. Problems with the experimental values obtained by inelastic neutron scattering and x-ray diffraction are discussed.

Conversion of ab-initio force fields and structures to molecular mechanics energy functions

Abstract The rapid development of computers in recent years has brought increasingly complex compounds into the range of high level ab-initio calculations. Such calculations produce valuable results which in many cases would be difficult or even impossible to obtain, with comparable accuracy, in any other way (Fogarasi & Pulay, Annu. Rev. Phys. Chem. 35, 191, 1984). Thus, it is highly desirable to be able to utilize these results in the construction of potential energy functions used in molecular mechanics (MM), molecular dynamics and Monte-Carlo calculations. For instance, the significance of quadratic cross terms in MM energy functions is still insufficiently explored (Lii & Allinger, J. Am. Chem. Soc. 111, 8566, 1989). In order to make possible the complete utilization of ab-initio results in MM calculations, we have developed a method by which scaled ab-initio (or empirical) force fields and structures can be directly converted to MM potential energy parameters, without sacrificing any of the original accuracy with regard to vibrational frequencies or structure. Here we briefly outline the conversion procedure, a more complete analysis being published separately.