On the release of strain in overcrowded substituted ethylenes

Minimum energy conformations of all possible Me, i-Pr, and t-Bu substituted ethylenes as well as some mixed methyl-t-butyl substituted ethylenes have been calculated using a consistent force field derived by least-squares fitting of a large set of observed conformational, vibrational, and thermochemical olefin properties. Large angle deformations and nonplanar double bond distortions were obtained for t-Bu containing systems. Nonbonded interactions appeared to decrease Me torsional frequencies of cis-dimethyl substituted ethylenes and to increase Me CH stretching frequencies of cis-di-t-Bu substituted ethylenes.     

The molecular structure of trans- and cis-bicyclo-[4.3.0]nonane in the gas phase,studied by electron diffraction and molecular mechanics

The structure and conformations of trans- and of cis-bicyclo[4.3.0]nonane have been studied in the gas phase. Molecular mechanics calculations applying the force field of Ermer and Lifson were used to obtain geometrical constraints, vibrational amplitudes and perpendicular vibrational corrections. The vibrational parameters were corrected for the large amplitude motion of the five-membered ring. The refinement for the trans-isomer confirms completely the predictions of the force field calculations. Although a stable solution could not be obtained for the cis-compound there is no contradiction between experiment and model calculations. The cyclohexane ring in both isomers is found to have a distorted chair conformation. In the cis-isomer it is flattened along the junction and more twisted in the other part. For the trans-compound the reverse is true.The following structural parameters r_g, r_α-structure) are put forward, (a) trans-compound: C₂-symmetry, _r(C-C)_av = 1.536 Å. Average bond angle and average torsion angle in the cyclohexane ring are 110.2° and 58.1°, respectively. The connection angle, defined as the angle between the planes bisecting C6-C1-C5-C9 and C2-C1-C5-C4, is 180°. (b) cis-compound: no symmetry, r(C-C)_av = 1.536 Å. Average bond and torsion angles in the cyclohexane ring are 112.2° and 52.3°, respectively. The connection angle is 124.8°.A comparison is made with structures of related compounds.     

Conformational analysis—CXVII : Methyl ethyl disulfide. Molecular mechanics and molecular orbital calculations

The conformation of methyl ethyl disulfide was investigated by molecular mechanics calculations using a recently developed force field for sulfur-containing alkanes. The results indicate that in the gas phase the molecule exists predominantly in two conformations, both with the CSSC dihedral angle gauche (84°), and the SSCC dihedral angle either gauche (72°) or trans (179°), and the methyl protons staggered. Ab initio molecular orbital calculations using an STO-3G basis set were employed to corroborate that these two conformations are of roughly equal stability, and that the next most stable conformation (by 0.6 kcal/mole) has the SSCC dihedral angle gauche (295°) with the terminal methyls proximal. In contrast to earlier CNDO/2 (spd) predictions, the SSCC cis conformer is the least stable, and no sizable attractive S?HC nonbonded interactions are discerned. Reasons for this are traced to a failure of the CNDO/2 method, which is especially serious when d orbitals are included in the basis set (spd) and the rigid rotor approximation is used. The present results are found to be consistent with recent electron diffraction, IR, Raman spectroscopic and X-ray diffraction data. The conformation of diethyl disulfide was also investigated by molecular mechanics calculations, and again gauche and trans SSCC arrangements are predicted to be preferred.     

The prediction of atomic kinetic energies from coordinates of surrounding atoms using kriging machine learning

A novel design of a next-generation force field considers not only the electronic inter-atomic energy but also intra-atomic energy. This strategy promises a faithful mapping between the force field and the quantum mechanics that underpins it. Quantum chemical topology provides an energy partitioning in which atoms have well-defined electronic kinetic energies, and we are interested in capturing how they respond to changes in the positions of surrounding atoms. A machine learning method called kriging successfully creates models from a training set of molecular configurations that can then be used to predict the atomic kinetic energies occurring in previously unseen molecular configurations. We present a proof-of-concept based on four molecules of increasing complexity (methanol, N-methylacetamide, glycine and triglycine). We test how well the atomic kinetic energies can be modelled with respect to training set size, molecule size and elemental composition. For all atoms tested, the mean atomic kinetic energy errors fall below 1.5 kJ mol^?1, and far below this in most cases. This represents errors all under 0.5 % and thus the kinetic energies are well modelled using the kriging method, even when using modest-to-small training set sizes.     

Extensive all-atom Monte Carlo sampling and QM/MM corrections in the SAMPL4 hydration free energy challenge

We present our predictions for the SAMPL4 hydration free energy challenge. Extensive all-atom Monte Carlo simulations were employed to sample the compounds in explicit solvent. While the focus of our study was to demonstrate well-converged and reproducible free energies, we attempted to address the deficiencies in the general Amber force field force field with a simple QM/MM correction. We show that by using multiple independent simulations, including different starting configurations, and enhanced sampling with parallel tempering, we can obtain well converged hydration free energies. Additional analysis using dihedral angle distributions, torsion-root mean square deviation plots and thermodynamic cycles support this assertion. We obtain a mean absolute deviation of 1.7 kcal mol^?1 and a Kendall’s τ of 0.65 compared with experiment.     

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     

Molecular mechanics force-field parameterization procedures

A set of procedures and guidelines are presented for the estimation of bond length, bond angle, and torsional potential constants for molecular mechanics force fields. The force field constants are ultimately derived by “subtracting” nonbonded molecular mechanics energies from corresponding molecular orbital energies using a model compound containing the chemical structure to be parameterized. Case study examples of bond length, bond angle, and torsional rotation force field parameterizations are presented. A general discussion of molecular mechanics force field parameterization strategy is included for reference and completeness. Finally, a curve-fitting program to generate force field parameters from raw data is given in Appendix I.     

Infrared and Raman spectra and normal coordinate analysis of trans-1,2-dicyanocyclopropane and its deuterated isotopomers

Infrared and Raman spectra are presented for trans-1,2-dicyanocyclopropane and its 1,2-d₂- and 3,3-d₂-isotopomers. Most of the d₀ assignments agree with previous assignments of Strumpf and Dunker encompassing 26 of the 27 fundamentals. The 1,2-d₂ assignments are similar, but for the 3,3-d₂ species only 11 bands could be assigned. A complete ab initio quantum mechanical force field has been calculated for this molecule at the 6-31G* basis set level. This force-field was scaled and least-squares optimized using eight parameters for functionally related diagonal force constants and their geometric mean for off-diagonals. Both theoretical minimum energy and “experimentally corrected” geometries were used with no significant difference in results. An earlier calculation with a 4-31G basis set gave a similar frequency fit but different scaling factors. As an alternative approach, the scaled ab initio force field, was also used as a starting point for a more conventional refinement of 27 force constants which had a significant influence on the potential energy distribution. The remainder were fixed at the scaled ab initio values. This empirical force field resulted in a fit to 65 fundamentals of d₀, 1,2-d₂ and 3,3-d₂ to < 1% average error.     

Comparison of Secondary Structure Formation Using 10 Different Force Fields in Microsecond Molecular Dynamics Simulations

We have compared molecular dynamics (MD) simulations of a β-hairpin forming peptide derived from the protein Nrf2 with 10 biomolecular force fields using trajectories of at least 1 μs. The total simulation time was 37.2 μs. Previous studies have shown that different force fields, water models, simulation methods, and parameters can affect simulation outcomes. The MD simulations were done in explicit solvent with a 16-mer Nrf2 β-hairpin forming peptide using Amber ff99SB-ILDN, Amber ff99SB*-ILDN, Amber ff99SB, Amber ff99SB*, Amber ff03, Amber ff03*, GROMOS96 43a1p, GROMOS96 53a6, CHARMM27, and OPLS-AA/L force fields. The effects of charge-groups, terminal capping, and phosphorylation on the peptide folding were also examined. Despite using identical starting structures and simulation parameters, we observed clear differences among the various force fields and even between replicates using the same force field. Our simulations show that the uncapped peptide folds into a native-like β-hairpin structure at 310 K when Amber ff99SB-ILDN, Amber ff99SB*-ILDN, Amber ff99SB, Amber ff99SB*, Amber ff03, Amber ff03*, GROMOS96 43a1p, or GROMOS96 53a6 were used. The CHARMM27 simulations were able to form native hairpins in some of the elevated temperature simulations, while the OPLS-AA/L simulations did not yield native hairpin structures at any temperatures tested. Simulations that used charge-groups or peptide capping groups were not largely different from their uncapped counterparts with single atom charge-groups. On the other hand, phosphorylation of the threonine residue located at the β-turn significantly affected the hairpin formation. To our knowledge, this is the first study comparing such a large set of force fields with respect to β-hairpin folding. Such a comprehensive comparison will offer useful guidance to others conducting similar types of simulations.     

Accurate Backbone 13C and 15N Chemical Shift Tensors in Galectin-3 Determined by MAS NMR and QM/MM: Details of Structure and Environment Matter

Chemical shift tensors obtained from solid-state NMR spectroscopy are very sensitive reporters of structure and dynamics in proteins. While accurate ¹³C and ¹⁵N chemical shift tensors are accessible by magic angle spinning (MAS) NMR, their quantum mechanical calculations remain challenging, particularly for ¹⁵N atoms. Here we compare experimentally determined backbone ¹³C^α and ¹⁵N^H chemical shift tensors by MAS NMR with hybrid quantum mechanics/molecular mechanics/molecular dynamics (MD-QM/MM) calculations for the carbohydrate-binding domain of galectin-3. Excellent agreement between experimental and computed ¹⁵N^H chemical shift anisotropy values was obtained using the Amber ff15ipq force field when solvent dynamics was taken into account in the calculation. Our results establish important benchmark conditions for improving the accuracy of chemical shift calculations in proteins and may aid in the validation of protein structure models derived by MAS NMR.     

The structure of trimethoxymethane in the gas phase,an electron diffraction,ab initio and molecular mechanics study

The structure of trimethoxymethane in the gas phase was studied by electron diffraction, ab initio molecular orbital calculations and molecular mechanics. The molecule was found to exist almost exclusively as an asymmetric all-staggered TGG conformer. The electron diffraction structural parameters (r_g distances, r_α angles) as obtained from geometrically consistent r_α-refinements are: r(C-O) central 1.382(6) Å, r(C-O) terminal 1.418(6) Å, r(C-H) 1.112(1) Å, ∠(O-C-O) in the gauche—gauche chain 115.0(1.0)°, in the gauche-anti chains 109.2(0.6)° ∠(C-O-C) 114.3(0.6)°, ∠(O-C-H)_Me 109.9(0.3)°, methyl torsion 68(6)°. The structure is adequately reproduced by molecular mechanics calculations applying Allinger's force field. The structures of methoxymethanes can be explained in terms of the anomeric effect. This is confirmed by ab initio calculations.     

Conformational study of the structure of free 12-thiacrown-4 and some of its cation metal complexes

Conformational search of 12-thiacrown-4, 12t4, was performed using the CONFLEX method and the MMFF94S force field whereby 156 conformations were predicted. Optimized geometries of the 156 predicted conformations were calculated at the HF, B3LYP, CAM-B3LYP, M06, M06L, M062x and M06HF levels using the 6-311G** basis set. The correlation energy was recovered at the MP2 level using the same 6-311G** basis set. Optimized geometries at the MP2/6-311G** level and G3MP2 energies were calculated for some of the low energy conformations. The D ₄ conformation was predicted to be the ground state conformation at all levels of theory considered in this work. Comparison between the dihedral angles of the predicted conformations indicated that for the stability of 12t4, a SCCS dihedral angle of 180° requirement is more important than a gauche CSCC dihedral angle requirement. Conformational search was performed also for the 12t4?CAg⁺, Bi³⁺, Cd²⁺, Cu⁺ and Sb³⁺ cation metal complexes using the CONFLEX method and the CAChe-augmented MM3 and MMFF94S force fields. Conformations with relative energies less than 10?kcal/mol at the MP2/6-31+G*//HF/6-31+G* level, with double zeta quality basis set on the metal cations, were considered for computations at the same levels as those used for free 12t4, using also the 6-311G** basis set. The cc-pVTZ-pp basis set was used for the metal cations. The predicted ground state conformations of the 12t4?CAg⁺, Bi³⁺, Cd²⁺, Cu⁺ and Sb³⁺ cation metal complexes are the C ₄, C ₄, C ₄, C _2v and C ₄ conformations, respectively. This is in agreement with the experimental X-ray data for the 12t4?CAg⁺ and Cd²⁺ cation metal complexes, but experimentally by X-ray, the 12t4?CBi³⁺ and Cu⁺ cation metal complexes have C _s and C ₄ structures, respectively.     

Prediction of hydration free energies for the SAMPL4 data set with the AMOEBA polarizable force field

Hydration free energy calculations are often used to validate molecular simulation methodologies and molecular mechanics force fields. We use the free-energy perturbation method together with the AMOEBA polarizable force field and the Poltype parametrization protocol to predict the hydration free energies of 52 molecules as part of the SAMPL4 blind challenge. For comparison, similar calculations are performed using the non-polarizable General Amber force field. Against our expectations, the latter force field gives the better results compared to experiment. One possible explanation is the sensitivity of the AMOEBA results to the conformation used for parametrization.     

Origin of intrinsic 3(10)-helix versus strand stability in homopolypeptides and its implications for the accuracy of the Amber force field

Current all-atom force fields often fail to recognize the native structure of a protein as the lowest free energy minimum. One possible cause could be the mathematical form of the potential based on the assumption that the conformation of a residue is independent of its neighbors. Here, using quantum mechanical (QM) methods (MP2/6-31g**//HF/6-31g** and MP2/cc-pVDZ//cc-pVDZ//HF/cc-pVDZ), the intrinsic correctness of the gas phase terms (without solvation) of the Amber ff03 and ff99 potentials are examined by testing their ability to reproduce the relative 3(10)-helix versus extended structure stabilities in the gas phase for 1-7-residue alanine, valine, leucine, and isoleucine homopolypeptides. The 3(10)-helix versus extended state stability strongly depends on chain length and less on the amino acid identity. The helical conformation becomes lower in energy than the extended conformation for all tested peptides longer than two residues, and its stability increases with the increase of chain length. The ff03 potential better describes the 3(10)-helix versus extended state energy than ff99 and also reproduces the curvature of the relative helix-extended state energies. Therefore, the mathematical form of the Amber potential is sufficient to describe the local effect of 3(10)-helix versus extended structure stabilization in the gas phase. However, the energy curves are shifted and the backbone geometries differ compared with the QM results. This may cause significant geometric discrepancies between native and predicted structures. Therefore, extant molecular mechanics force fields, such as Amber, need refinement of their parameters to correctly describe helix-extended state energetics and geometry of major conformations.     

Development of glycyl radical parameters for the OPLS-AA/L force field

On the basis of quantum chemical calculations C(alpha)-glycyl radical parameters have been developed for the OPLS-AA/L force field. The molecular mechanics hypersurface was fitted to the calculated quantum chemical surface by minimizing their molecular mechanics parameter dependent sum-of-squares deviations. To do this, a computer program in which the molecular mechanics energy derivatives with respect to the parameters were calculated analytically was developed, implementing the general method of Lifson and Warshel (J Chem Phys 1968, 49, 5116) for force field parameter optimization. This program, in principle, can determine the optimal parameter set in one calculation if enough representative value points on the quantum chemical potential energy surface are available and there is no linear dependency between the parameters. Some of the parameters in quantum calculations, including several new torsion types around a bond as well as angle parameters at a new central atom type, are not completely separable. Consequently, some restrictions and/or presumptions were necessary during parameter optimization. The relative OPLS-AA energies reproduced those calculated quantum chemically almost perfectly.     

A Molecular Mechanics Model for Flavins

Flavin containing molecules form a group of important cofactors that assist a wide range of enzymatic reactions. Flavins use the redox-active isoalloxazine system, which is capable of one- and two-electron transfer reactions and can exist in several protonation states. In this work, molecular mechanics force field parameters compatible with the CHARMM36 all-atom additive force field were derived for biologically important flavins, including riboflavin, flavin mononucleotide, and flavin adenine dinucleotide. The model was developed for important protonation and redox states of the isoalloxazine group. The partial charges were derived using the CHARMM force field parametrization strategy, where quantum mechanics water–solute interactions are used to target optimization. In addition to monohydrate energies and geometries, electrostatic potential around the compound was used to provide additional restraints during the charge optimization. Taking into account the importance of flavin-containing molecules special attention was given to the quality of bonded terms. All bonded terms, including stiff terms and torsion angle parameters, were parametrized using exhaustive potential energy surface scans. In particular, the model reproduces well the butterfly motion of isoalloxazine in the oxidized and reduced forms as predicted by quantum mechanics in gas phase. The model quality is illustrated by simulations of four flavoproteins. Overall, the presented molecular mechanics model will be of utility to model flavin cofactors in different redox states. © 2019 Wiley Periodicals, Inc.     

Additive CHARMM force field for naturally occurring modified ribonucleotides

More than 100 naturally occurring modified nucleotides have been found in RNA molecules, in particular in tRNAs. We have determined molecular mechanics force field parameters compatible with the CHARMM36 all‐atom additive force field for all these modifications using the CHARMM force field parametrization strategy. Emphasis was placed on fine tuning of the partial atomic charges and torsion angle parameters. Quantum mechanics calculations on model compounds provided the initial set of target data, and extensive molecular dynamics simulations of nucleotides and oligonucleotides in aqueous solutions were used for further refinement against experimental data. The presented parameters will allow for computational studies of a wide range of RNAs containing modified nucleotides, including the ribosome and transfer RNAs. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Mathematical Relationships Between Bond-Bending Force Fields

Molecular mechanics softwares adopt various set of force field functions. In some cases, reliable data from one set of force field parameters cannot be used in a software that adopts another set of force field. Using mathematical approach, exact relationships between parameters from three bond-bending force fields, namely the (i) harmonic cosine angle, (ii) polynomial series, and (iii) Fourier series, are herein developed. Parameters from these three potential functions are further related to the approximate form, the harmonic angle function, which is valid for small change in chemical bond angle.     

Derivation of class II force fields. I. Methodology and quantum force field for the alkyl functional group and alkane molecules

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 II force field derived from the quantum energy surface is characterized by accounting for these important intramolecular forces. The importance of each 4.2 to 18.2%. This fourfold increase in the second derivative error dramatically demonstrates the importance of bond anharmonicity in the ab initio potential energy surface. The Class II force field derived from the quantum energy surface is characterized by accounting for these important intramolecular forces. The importance of each of 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. © 1994 by John Wiley & Sons, Inc.