CHARMM (Chemistry at HARvard Macromolecular Mechanics) is a highly flexible computer program which uses empirical energy functions to model macromolecular systems. The program can read or model build structures, energy minimize them by first- or second-derivative techniques, perform a normal mode or molecular dynamics simulation, and analyze the structural, equilibrium, and dynamic properties determined in these calculations. The operations that CHARMM can perform are described, and some implementation details are given. A set of parameters for the empirical energy function and a sample run are included.

CHARMM: A program for macromolecular energy, minimization, and dynamics calculations

A general all-atom force field for atomistic simulation of common organic molecules, inorganic small molecules, and polymers was developed using state-of-the-art ab initio and empirical parametrization techniques. The valence parameters and atomic partial charges were derived by fitting to ab initio data, and the van der Waals (vdW) parameters were derived by conducting MD simulations of molecular liquids and fitting the simulated cohesive energies and equilibrium densities to experimental data. The combined parametrization procedure significantly improves the quality of a general force field. Validation studies based on large number of isolated molecules, molecular liquids and molecular crystals, representing 28 molecular classes, show that the present force field enables accurate and simultaneous prediction of structural, conformational, vibrational, and thermophysical properties for a broad range of molecules in isolation and in condensed phases. Detailed results of the parametrization and validation f...

COMPASS: An ab Initio Force-Field Optimized for Condensed-Phase ApplicationsOverview with Details on Alkane and Benzene Compounds

An improved method for computing potential-derived charges is described which is based upon the CHELP program available from QCPE.1 This approach (CHELPG) is shown to be considerably less dependent upon molecular orientation than the original CHELP program. In the second part of this work, the CHELPG point selection algorithm was used to analyze the changes in the potential-derived charges in formamide during rotation about the CN bond. In order to achieve a level of rotational invariance less than 10% of the magnitude of the electronic effects studied, an equally-spaced array of points 0.3 A apart was required. Points found to be greater than 2.8 A from any nucleus were eliminated, along with all points contained within the defined VDW distances from each of the atoms. The results are compared to those obtained by using CHELP. Even when large numbers of points (ca. 3000) were sampled using the CHELP selection routine, the results did not indicate a satisfactory level of rotatational invariance. On the basis of these results, the original CHELP program was found to be inadequate for analyzing internal rotations.

Determining atom-centered monopoles from molecular electrostatic potentials. The need for high sampling density in formamide conformational analysis

A geometrical analysis has been performed on π–π stacking in metal complexes with aromatic nitrogen-containing ligands based on a Cambridge Structural Database search and on X-ray data of examples in the recent literature. It is evident that a face-to-face π–π alignment where most of the ring-plane area overlaps is a rare phenomenon. The usual π interaction is an offset or slipped stacking, i.e. the rings are parallel displaced. The ring normal and the vector between the ring centroids form an angle of about 20° up to centroid–centroid distances of 3.8 A. Such a parallel-displaced structure also has a contribution from π–σ attraction, the more so with increasing offset. Only a limited number of structures with a near to perfect facial alignment exists. The term π–π stacking is occasionally used even when there is no substantial overlap of the π-ring planes. There is a number of metal–ligand complexes where only the edges of the rings interact in what would be better described a C–H⋯π attraction.

A critical account on π–π stacking in metal complexes with aromatic nitrogen-containing ligands

We present an all atom potential energy function for the simulation of proteins and nucleic acids. This work is an extension of the CH united atom function recently presented by S.J. Weiner et al. J. Amer. Chem. Soc., 106, 765 (1984). The parameters of our function are based on calculations on ethane, propane, n−butane, dimethyl ether, methyl ethyl ether, tetrahydrofuran, imidazole, indole, deoxyadenosine, base paired dinucleoside phosphates, adenine, guanine, uracil, cytosine, thymine, insulin, and myoglobin. We have also used these parameters to carry out the first general vibrational analysis of all five nucleic acid bases with a molecular mechanics potential approach.

An all atom force field for simulations of proteins and nucleic acids.

The previously described least‐squares derivation of nonbonded potential parameters from crystalline aromatic hydrocarbons was extended to include nonaromatic hydrocarbons. Further evidence was obtained that no specially large energy effects are present in the aromatic crystal structures with their π‐electron systems. A better separation of the nonbonded energy into C···C, C···H, and H···H components was obtained when the observational equations for the aromatic and nonaromatic structures were combined. The potentials obtained from the combined observational equations gave better fits to the nonaromatics than to the aromatics. Evidence is presented favoring an H–C–H angle of less than 106° in crystalline n‐pentane and n‐hexane. The parallel packing of molecular chains in the n‐hexane crystal and the nonparallel packing in the n‐pentane crystal were reproduced by a steepest descent minimization of the lattice energy using the observed lattice constants.

Nonbonded Potential Parameters Derived from Crystalline Hydrocarbons

Electrostatic potentials and Mulliken net atomic charges were calculated from STO-3G, 6-31G, and 6-31G** SCF-MO wavefunctions for hydrogen fluoride, water, ammonia, methane, acetylene, ethylene, carbon dioxide, formaldehyde, methanol, formamide, formic acid, acetonitrile, diborane, and carbonate ion. In each case optimized net atomic charges (potential-derived charges) were also obtained by fitting the electrostatic potentials calculated directly from the wavefunctions in a shell enveloping the molecules outside of their van der Waals surfaces. The electrostatic potentials calculated from the potential-derived charge distributions were then compared with the defined quantum mechanical electrostatic potentials and with the electrostatic potentials of the Mulliken charge distributions.

Representation of the molecular electrostatic potential by a net atomic charge model

Nonbonded (exp−6) potential parameters for C···C, C···H, and H···H interactions were derived from the crystal structures and properties of aromatic hydrocarbons. The exponent of the C···C repulsion term was taken from a calculation based on the interplanar spacing and compressibility of graphite. The exponent of the H···H repulsion was taken from a quantum‐mechanical calculation of the repulsion between two hydrogen molecules. The coefficients of the attractive and repulsive terms were fitted by weighted least squares to 77 observational equations involving the geometrical crystal structures, elastic constants, and sublimation energies of nine aromatic hydrocarbons. It was found necessary to externally estimate the H···H repulsion coefficient to obtain an appropriate partition between the C···C, C···H, and H···H energy terms. The geometrical mean combining law was applied for the attractive and repulsive coefficients.The resulting nonbonded potential parameters, when used to minimize the lattice energy by a steepest descent procedure, were found to reproduce the crystal structures of benzene, napthalene, and anthracene to within about 0.05 A in the carbon‐atom positions and within about 1% in the lattice constants. No assumption of anisotropic forces based on π‐electron polarizabilities was necessary to reproduce herringbone‐type packing. The position of the minimum in the best C···H nonbonded potential was less than expected, while the minimum in the H···H potential was larger than expected. The minima positions were found to be sensitive to the H···H repulsion coefficient. The correlation coefficients between the potential parameters found by this method were found to be large.

Nonbonded Potential Parameters Derived from Crystalline Aromatic Hydrocarbons

Calculation of the crystal structures of hydrocarbons by molecular packing analysis

Ab initio wave functions using the 6‐31G** basis set were calculated for a set of 24 organic molecules which included saturated and unsaturated hydrocarbons, fluoro compounds, hydroxyl and ether compounds, carboxylic acids, esters, amines, carbonyl compounds, amides, and N‐methyl amides. The electric potential on a grid within a van der Waals shell around each molecule was calculated directly from the wavefunctions. The electric potential values were modeled by placing multipoles up to quadrupoles at atomic sites. The electric potential was well fitted by a model which included atomic monopoles, dipoles, and quadrupoles. Also, the electric potential was modeled by placing dipoles at bond centers. This bond dipole was either allowed to point in any direction, or was restricted to the bond direction. In general the values shown for the monopoles and the values and directions for the bond dipoles were as expected from considerations of electronegativity and reactivity. For the general bond dipole model in a number of cases the direction of the bond dipole was not parallel to the bond direction. It is suggested that this is an artifact caused by the effects of lone pair electrons or electron delocalization on the model. The restricted bond dipole model fitted the electric potential about as well as the atomic monopole model. Atomic monopole values (net atomic charges) and bond dipole values for various atoms, functional groups, and bonds are discussed. Since bond‐dipole interaction energy has better long‐range convergence than monopole interaction energy, bond dipoles are a useful alternative to atomic monopoles.

Donald E. Williams

Papers

Nonbonded Potential Parameters Derived from Crystalline Hydrocarbons

Representation of the molecular electrostatic potential by a net atomic charge model

Nonbonded Potential Parameters Derived from Crystalline Aromatic Hydrocarbons

Calculation of the crystal structures of hydrocarbons by molecular packing analysis

Representation of the molecular electrostatic potential by atomic multipole and bond dipole models