Molecular mechanics. The MM3 force field for alkenes

The MM3 force field has been extended to include alkenes. Forty-five compounds were examined, and structures, conformational equilibria, heats of formation, and rotational barriers, were calculated. For a smaller representative group, the vibrational spectra and entropies were also calculated. In general, these quantities, except for the vibrational spectra, agree with available data to approximately within experimental error. The vibrational frequencies for a set of eight well-assigned structures were calculated to a root-mean-square error of 47 cm^?1.     

Ab initio parametrized MM3 force field for the metal-organic framework MOF-5

A new valence force field has been developed and validated for a particular class of coordination polymers known as nanoporous metal-organic frameworks (MOFs), introduced recently by the group of Yaghi. The experimental, structural, and spectroscopic data in combination with density functional theory calculations on several model systems were used to parametrize the bonded terms of the force field, which explicitly treats the metal-oxygen interactions as partially covalent as well as distinguishes different types of oxygens in the framework. Both the experimental crystal structure of MOF-5 and vibrational infrared spectrum are reproduced reasonably well. The proposed force field is believed to be useful in atomistic simulations of adsorption/diffusion of guest molecules inside the flexible pores of this important class of MOF materials.     

Directional hydrogen bonding in the MM3 force field: II

Extensive calculations on hydrogen bonded systems were carried out using the improved MM3 directional hydrogen bond potential. The resulting total function was reoptimized. Comparisons of the hydrogen bonding potential function from ab initio calculations (MP2/6-31G**); the original MM3(89); and the reoptimized MM3 force field MM3(96), for a variety of C, N, O, and Cl systems including the formamide dimer and formamide–water complex, are described herein. Hydrogen bonding is shown to be a far more complicated and ubiquitous phenomenon than is generally recognized. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1001–1016, 1998     

Derivation of class II force fields: V. Quantum force field for amides,peptides, and related compounds

As the field of biomolecular structure advances, there is an ever-growing need for accurate modeling of molecular energy surfaces to simulate and predict the properties of these important systems. To address this need, a second generation amide force field for use in simulations of small organics as well as proteins and peptides has been derived. The critical question of what accuracy can be expected from calculations in general, and with this class II force field in particular, is addressed for structural, dynamic, and energetic properties. The force field is derived from a recent methodology we have developed that involves the systematic use of quantum mechanical observables. Systematic ab initio calculations were carried out for numerous configurations of 17 amide and related compounds. Relative energies and first and second derivatives of the energy of 638 structures of these compounds resulted in 140,970 ab initio quantum mechanical observables. The class II peptide quantum mechanical force field (QMFF), containing 732 force constants and reference values, was parameterized against these observables. A major objective of this work is to help establish the role of anharmonicity and coupling in improving the accuracy of molecular force fields, as these terms have not yet become an agreed upon standard in the ever more extensive simulations being used to probe biomolecular properties. This has been addressed by deriving a class I harmonic diagonal force field (HDFF), which was fit to the same energy surface as the QMFF, thus providing an opportunity to quantify the effects of these coupling and anharmonic contributions. Both force field representations are assessed in terms of their ability to fit the observables. They have also been tested by calculating the properties of 11 stationary states of these amide molecules. Optimized structures, vibrational frequencies, and conformational energies obtained from the quantum calculations and from both the QMFF and the HDFF are compared. Several strained and derivatized compounds including urea, formylformamide, and butyrolactam are included in these tests to assess the range of applicability (transferability) of the force fields. It was found that the class II coupled anharmonic force field reproduced the structures, energies, and vibrational frequencies significantly more faithfully than the class I harmonic diagonal force field. An important measure, rms energy deviation, was found to be 1.06 kcal/mol with the class II force field, and 2.30 kcal/mol with the harmonic diagonal force field. These deviations represent the error in relative configurational energy differences for strained and distorted structures calculated with the force fields compared with quantum mechanics. This provides a measure of the accuracy that might be expected in applications where strain may be important such as calculating the energy of a system as it approaches a (rotational) barrier, in ligand binding to a protein, or effects of introducing substituents into a molecule that may induce strain. Similar results were found for structural properties. Protein dynamics is becoming of ever-increasing interest, and, to simulate dynamic properties accurately, the dynamic behavior of model compounds needs to be well accounted for. To this end, the ability of the class I and class II force fields to reproduce the vibrational frequencies obtained from the quantum energy surface was assessed. An rms deviation of 43 cm⁻¹ was achieved with the coupled anharmonic force field, as compared to 105 cm⁻¹ with the harmonic diagonal force field. Thus, the analysis presented here of the class II force field for the amide functional group demonstrates that the incorporation of anharmonicity and coupling terms in the force field significantly improves the accuracy and transferability with regard to the simulation of structural, energetic, and dynamic properties of amides. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 430–458, 1998     

Alcohols,ethers, carbohydrates,and related compounds. I. The MM4 force field for simple compounds

Simple alcohols and ethers have been studied with the MM4 force field. The structures of 13 molecules have been well fit using the MM4 force field. Moments of inertia have been fit with rms percentage errors as indicated: 18 moments for ethers, 0.28%; 21 moments for alcohols, 0.22%. Rotational barriers and conformational equilibria have also been examined, and the experimental and ab initio results are reproduced substantially better with MM4 than they were with MM3. Much of the improvement comes from the use of additional interaction terms in the force constant matrix, of which the torsion-bend and torsion-torsion are particularly important. Induced dipoles are included in the calculation, and dipole moments are reasonably well fit. It has been possible for the first time to fit conformational energetic data for both open chain and cyclic alcohols (e.g., propanol and cyclohexanol) with the same parameter set. For vibrational spectra, over a total of 82 frequencies, the rms error is 27 cm(-1), as opposed to 38 cm(-1) with MM3. Both the alpha and beta bond shortening resulting from the presence of the electronegative oxygen atom in the molecule are well reproduced. The electronegativity of the oxygen is sufficient that one must also include not only the alpha and beta electronegativity effects on bond lengths, but also on angle distortions, if structures are to be well reproduced. The heats of formation of 32 alcohols and ethers were fit overall to within experimental error (weighted standard deviation error 0.26 kcal/mol).     

An empirical MM2 augmented force field for the cycloimmonium ylides

An original procedure approach taking into account the implementation of parameters determined, using calculations based on density functional theory, for the amidocyano-pyridinium methylide in the MM2 augmented harmonic potential function has been proposed. A good agreement between theoretical force field calculation and X-ray diffraction data has been observed. Thus an empirical force field for cycloimmonium ylides has been established. It provides good quality geometries for cycloimmonium ylide molecules by energy minimization. In this study we proposed a new MM2 augmented atom-type for the ylidic carbon atom. To our knowledge no attempt has been done in this way for such organic systems. Thus, we have shown that parameterization established by the DFT method is able to reproduce or to predict with good accuracy the structures of the cycloimmonium ylide compounds. This study also includes a full conformational analysis.     

A force field for allenes and for nonlinear acetylenes within the MM2 approximation

Geometries and heats of formation for allenes may now be calculated with an extended version of MM2. The torsional barriers about bonds in an acetylenic unit are much more complicated than originally thought, if the unit is nonlinear. Ab initio calculations have been used to show just what these torsional barriers are, and the MM2 force field has been adapted to this information.     

Improving the Q2MM method for transition state force field modeling

The Quantum‐to‐molecular mechanics method (Q2MM) for converting quantum mechanical transition states (TSs) to molecular mechanical minima has been modified to allow a fit to the “natural” reaction mode eigenvalue. The resulting force field gives an improved representation of the energy curvature at the TS, but can potentially give false responses to steric interactions. Ways to address this problem while staying close to the “natural” TS force field are discussed. © 2014 Wiley Periodicals, Inc.     

Ab initio calculations and molecular mechanics (MM3) force field development for ammonium and protonated aliphatic amines

The geometries and vibrational frequencies of 11 training molecules containing the ammonium ion moiety were calculated at the MP2/6-31+G* level of theory. Various torsional energy profiles were also calculated using this basis set. From those ab initio calculations, a molecular mechanics (MM3) force field was developed using our Parameter Analysis and Refinement Toolkit System (PARTS). Using this set of parameters, the MM3 force field was found to well reproduce the molecular geometries and vibrational spectra for the all training molecules. CPU time was reduced from days to seconds. The availability of this new force field dramatically increases the feasibility of the computer-assisted drug design involving ammonium and protonated amino groups. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18 : 1371–1391, 1997     

Chlorosilanes: Development and application of MM2 force field parameters

The geometries, relative conformational energies, and dipole moments of mono and polychlorosilanes have been calculated using ab initio molecular orbital (MO) theory. Calculations at the HF/3–21G(*) level, with the exception of dipole moments, give reasonable agreement with experimental data. A new MM2 force field for chlorosilanes, which includes terms for bond length shortening and bond angle compression due to the attachment of electronegative Cl atoms, has been developed on the basis of experimental and ab initio results. The new force field is generally successful in predicting structural parameters, but is unable to reproduce the dipole moments of several model systems. While dipole moment predictions are not the authors' main interest, this failure defines a shortcoming in the MM2 method. The new parameters have been applied to problems in the prediction of stereochemistries of cyclic systems, and compared with experimental results where data are available.     

Development of a molecular mechanics (MM2) force field for α-chlorosilanes

Molecular mechanics (MM2) parameters for silanes which have a Si-C-Cl fragment have been developed based on available experimental data and ab initio molecular orbital (MO) calculations. Molecular properties, mainly rotational barriers and geometries, of α-chlorosilanes have been studied using our new MM2 parameter set. Changes in the Si-C bond lengths and several bond angles of α-chlorosilanes due to the additional attachment of polar atom(s) have been investigated utilizing ab initio calculations. An electronegativity correction to both bond lengths and angles helps MM2 to reproduce results from ab initio calculations. The new force field has been applied to the conformational analysis of l-(chloromethyl)-1,2-dimethylsilacyclopentane, a model used in our studies of rearrangements of α-halosilanes.     

Dual-topology/dual-coordinate free-energy simulation using QM/MM force field

We have developed a dual-topology/dual-coordinate free-energy simulation method for use with a QM/MM force field. By combining two parallel processes into one alchemical process, we are able to compute the double free-energy difference (delta deltaF) within a single simulation, which eliminates half of the expensive quantum-mechanical simulation in general. The method has been tested in computing the solvation free-energy differences of several molecular pairs and shows close agreement with experimental results.     

Development of an internal searching algorithm for parameterization of the MM2/MM3 force fields

Application of Allinger's MM2/MM3 force fields to molecules of real interest is frequently hindered by the lack of parameters for various heterocyclic systems and for poly-functionalized molecules. A common approach to this problem is to manually choose missing parameters “by analogy” with those that are part of the force field's internal parameter set. Naturally, this is generally attempted only by those possessing extensive experience with force fields. In order to use the MM2/MM3 force fields to study herbicides, an algorithm has been developed to automate this process for the non MM2 specialist. Using a set of “relative cost” criteria for atom type replacement, the algorithm searches the force field parameter set and selects the most appropriate parameters for a given molecule whose MM2 output file contains “missing parameter” errors. The program selects parameter error messages from a standard MM2 output file, finds analogous parameters, asks the user to verify their appropriateness and creates a standard MM2 parameter deck for the molecule of interest.     

Ab initio force field for simulations of proteins and nucleic acids

We present a new self-consistent set of ab initio analytical pair potential to predict specific nonbonded interactions of protein with nucleic acid, of protein with protein, and of nucleic acid with nucleic acid. The purpose of this study is to represent the interaction between biological molecules with an accuracy equivalent to the ab initio molecular orbital calculations, which are used as reference data to obtain the pair potentials. Atoms in nucleic acids and proteins are classified according to their chemical environments. An “effective charge,” a modification of a charge obtained from the Mulliken population analysis, is introduced and used to represent the electrostatic energy. More than 30,000 SCF interaction energies have been calculated to provide the reference data for the fitting procedure that we have adopted in the parameterization of the potentials. The standard deviation is 1.61 kcal/mol for interaction energies spanning the range from about ?220 kcal/mol to +20 kcal/mol. Molecular dynamics simulations, using the above new set of force field, have been performed successfully for the systems where adequate treatments of specific interactions are required: The stability of α-helix of C-peptide and the interaction of spermine with oligonucleotide are examined as preliminary examples.     

Combined application of pair potentials and the MM2 force field for the modeling of ionophores

Complexes of alkali and alkaline earth cations with organic compounds are modeled by describing ionligand interaction energies with pair potentials and intraligand as well as interligand energies with the MM2 potential. New pair potentials for the interaction of Li⁺, Na⁺, K⁺, Mg²⁺, and Ca²⁺ ions are derived on the basis of 30,000 ab initio interaction energy values with 70 selected model ligand molecules. Various problems of the combination of these two basically different potentials are discussed. An application for the K⁺ complex of 18-crown-6 is presented. For more flexible ligands the introduction of three-body correction terms of the pair potentials seems necessary.     

A new force field (ECEPP-05) for peptides, proteins, and organic molecules

Parametrization and testing of a new all-atom force field for organic molecules and peptides with fixed bond lengths and bond angles are described. The van der Waals parameters for both the organic molecules and the peptides were taken from J. Phys. Chem. B 2003, 107, 7143 and J. Phys. Chem. B 2004, 108, 12181. First, the values of the 1-4 nonbonded and electrostatic scale factors appropriate to the new force field were determined by computing the conformational energies of six model molecules, namely, ethanol, ethylamine, propanol, propylamine, 1,2-ethanediol, and 1,3-propanediol with different values of these factors. The partial atomic charges of these molecules were obtained by fitting to the electrostatic potentials calculated with the HF/6-31G quantum-mechanical method. Two different charge models (single- and multiple-conformation-derived) were also considered. We demonstrated that the charge model has a stronger effect on the conformational energies than the 1-4 scaling. The choice of a charge model affected the conformational energies of even the smallest molecules considered, whereas the effect of the 1-4 electrostatic or nonbonded scaling was apparent only for 1,3-propanediol. The best agreement with high-level ab initio data was obtained with the multiple-conformation-derived charges and with no scaling of the 1-4 nonbonded or electrostatic interactions (scale factors of 1.0). Next, the torsional parameters of a large number of neutral and charged organic molecules, assumed to be models of the side chains of the 20 naturally occurring amino acids, were computed by fitting to rotational energy profiles obtained from ab initio MP2/6-31G calculations. The quality of the fits was high with average errors for torsional profiles of less than 0.2 kcal/mol. To derive the torsional parameters for the peptide backbone, the partial atomic charges of the 20 neutral and charged amino acids were obtained by fitting to the electrostatic potentials of terminally blocked amino acids using the HF/6-31G quantum-mechanical method. Then, the phi-psi energy maps of Ac-Ala-NMe and Ac-Gly-NMe were computed using MP2/6-31G//HF/6-31G quantum-mechanical methods. The phi-psi energy map of Ac-Ala-NMe was used for refinement of the nonbonded parameters for the backbone nitrogen and hydrogen bonded to it. Subsequently, the main-chain torsional parameters were obtained by fitting the molecular mechanics energies to the phi-psi energy maps of Ac-Ala-NMe and Ac-Gly-NMe. The transferability of the entire force field was demonstrated by reproducing the main energy minima of terminally blocked Ala3 from the literature. The performance of the force field was also evaluated by simulating crystal structures of small peptides. By comparison of simulated and experimental data, examination of the torsional-angle and atom-positional root-mean-square deviations of the energy-minimized crystal structures from the corresponding X-ray model structures demonstrated high accuracy of the force field.     

Understanding the dielectric properties of liquid amides from a polarizable force field

The role played by electronic polarization in the dielectric properties of liquid N-methyl acetamide (NMA) is examined using molecular dynamics simulations with a polarizable force field based on classical Drude oscillators. The model presented is the first force field shown to reproduce the anomalously large dielectric constant of liquid NMA. Details of the molecular polarizability are found to be important. For instance, all elements of the polarizability tensor, rather then just the trace, impact on the condensed phase properties. Two factors related to electronic polarizability are found to contribute to this large dielectric constant. First is the significant enhancement of the mean amide molecular dipole magnitude, which is 50% larger in the liquid than in the gas phase. Second is the consequent strong hydrogen bonding between molecular neighbors that enhances the orientational alignment of the molecular dipoles. Polarizable models of amide compounds that have two (acetamide) and zero (N,N-dimethyl acetamide) polar hydrogen-bond donor atoms are also investigated. Experimentally, the neat liquid dielectric constants at 373 K are 100 for NMA, 66 for acetamide and 26 for N,N-dimethyl acetamide. The polarizable models replicate this trend, predicting a dielectric constant of 92+/-5 for NMA, 66+/-3 for acetamide and 23+/-1 for N,N-dimethyl acetamide.