Efficient treatment of out-of-plane bend and improper torsion interactions in MM2, MM3, and MM4 molecular mechanics calculations

Simple and very efficient formulas are presented for four-body out-of-plane bend (used in MM2 and MM3 force fields) and improper torsion (used in the MM4 force field) internal coordinates and their first and second derivatives. The use of a small set of bend and stretch intermediates allows for order of magnitude decreases in calculation time for potential energies and their first and second derivatives, which are required in molecular mechanics calculations. The formulas are eminently suitable for use in molecular simulations of systems with complicated bond networks. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1804–1811, 1997     

Ab initio and molecular mechanics (MM2 and MM3) calculations of nonconjugated positively charged nitrogen-containing compounds

High-level ab initio calculations have been performed on N-methyl-N-methyleneammonium and related compounds to obtain accurate rotational barriers, structures, and vibrational frequencies. The 6-31G** basis set has been utilized at the Hartree-Fock level of theory for these calculations because little experimental data are available. The MM2(91) and MM3(94) force fields have been parameterized to include these nonconjugated charged nitrogen-containing compounds. Molecular mechanics geometries and vibrational frequencies compare well with the ab initio results. © 1995 John Wiley & Sons, Inc.     

Ab initio and molecular mechanics (MM2 and MM3) calculations of positively charged conjugated nitrogen-containing compounds

Ab initio calculations have been carried out on s-trans-N-vinylmethyleneammonium, pyridinium, and related compounds to obtain rotational barriers, structures, and vibrational frequencies. The restricted Hartree-Fock (RHF) level of theory with 6-31G** basis set was used for these calculations. In addition, the MM2(91) and MM3(94) force fields have been parameterized to calculate these positively charged nitrogen-containing compounds. A bond order term was incorporated in the force field to reproduce accurately the rotational barriers of s-trans-N-vinylmethyleneammonium and related compounds. Molecular mechanics geometries and vibrational frequencies compare well with those calculated by ab initio methods. © 1996 by John Wiley & Sons, Inc.     

Charge calculations in molecular mechanics. Part 8 Partial atomic charges from classical calculations

Summary The CHARGE2 programme, which involves the classical calculation of both the inductive and resonance contributions to the partial atomic charges in molecules is described, and the charges and electrostatic potentials obtained presented for some illustrative examples.In substituted methanes (CH₃X, CF₃X, CCl₃X) the effects of varying the electronegativity of the substituents and the - and -substituent contributions are clearly illustrated for a variety of substituent groups X.The problems involved in the inclusion of silicon into this scheme are detailed, together with the methods of overcoming them. The partial atomic charges ( and contributions) and electrostatic potentials for some silicon oxygen compounds are presented and discussed.The partial atomic charges from CHARGE2 for all the natural amino acids as their N-acetyl, N-methyl-amides are given and compared with those obtained from the AMBER and ECEPP/2 force fields. Considerable differences in these figures are observed, with the AMBER charges consistently much larger than those from the other two methods.The CHARGE2 partial atomic charges and electrostatic potentials for the four common nucleic acids, adenine, cytosine, guanine and thymine, are given and compared with those derived from other calculations. Again there is general similarity but also there are considerable differences, with those from the AMBER force field somewhat larger than the other methods.For previous parts in this series, see Refs. 1-7.     

Molecular mechanics calculations (MM2 and MM3) on enamines and aniline derivatives

The MM2 and MM3 force fields have been extended to cover this class of compounds. Structures, vibrational spectra, and other data for 13 compounds were examined and can be reproduced satisfactorily by MM3. Except for the spectra, the other data can be reproduced somewhat less well by MM2. © 1994 by John Wiley & Sons, Inc.     

Molecular mechanics calculations (MM3) on sulfones

The structures of several sulfones, including dimethyl sulfone, methyl ethyl sulfone, methyl vinyl sulfone, and diphenyl sulfone, have been fit with the MM3 force field to existing experimental data from electron diffraction and microwave spectroscopy. The vibrational spectra have also been fit for six of these compounds. The torsional parameters for the aliphatic sulfones were fit to ab initio 6-31G data. Heats of formation were also fit. © 1993 John Wiley & Sons, Inc.     

Molecular mechanics (MM4) calculations on carbonyl compounds part I: aldehydes

Aliphatic aldehydes have been studied with the aid of the MM4 force field. The structures, moments of inertia, vibrational spectra, conformational energies, barriers to internal rotation, and dipole moments have been examined for six compounds (nine conformations). MM4 parameters have been developed to fit the indicated quantities to the wide variety of experimental data. Ab initio (MP2) and density functional theory (B3LYP) calculations have been used to augment and/or replace experimental data, as appropriate. Because more, and to some extent, better, data have become available since MM3 was developed, it was anticipated that the overall accuracy of the information calculated with MM4 would be better than with MM3. The best single measure of the overall accuracy of a force field is the accuracy to which the moments of inertia of a set of compounds (from microwave spectroscopy) can be reproduced. For all of the 20 moments (seven conformations) experimentally known for the aldehyde compounds, the MM4 rms error is 0.30%, while with MM3, the most accurate force field presently available, the rms error over the same set is 1.01%. The calculation of the vibrational spectra was also improved overall. For the four aldehydes that were fully analyzed (over a total of 78 frequencies), the rms errors with MM4 and MM3 are 18 and 38 cm^?1, respectively. These improvements came from several sources, but the major ones were separate parameters involving the carbonyl carbon for formaldehyde, the alkyl aldehydes and the ketones, and new crossterms featured in the MM4 force field that are not present in the MM3 version. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1396–1425, 2001     

Molecular mechanics (MM2) calculations and cone angles of phosphine ligands

Molecular mechanics (MM2) calculations were performed on 54 conformations of 18 phosphines (PH₃; PH_3−nR_n, where n = 1,…3, and R = Me and Et, n = 1 or 2 and R =ⁱPr, and n = 1 and R =^tBu, PMe₂Et, PMeEt₂, and PPhMe₂, and PPh₂R where R = Me, Et, ⁱPr, ^tBu and Ph). The results are compared to those previously obtained from MINDO/3 and MNDO calculations, and to experimental data. Single conformer cone angles and weighted average cone angles were calculated from MM2 optimized geometries employing Tolman's general definition, and they are compared to Tolman's values, MINDO/3 results, and T.L. Brown's E_R values. Of the cone angle definitions used, the weighted average values are suggested as the best single representation of phosphine ligand sizes. The steric parameters (cone angle and E_R values) alone, and in conjunction with electronic parameters, are correlated with experimental data.     

Molecular mechanics calculations (MM3) on bicycloalkyl hydrocarbons

A series of bicycloalkyl hydrocarbons were studied using molecular mechanics methods (MM3), and the results were compared with the experimental data available. Five compounds were studied: bicyclopropyl, bicyclobutyl, bicyclopentyl, bicyclohexyl and 2,3-dimethylbutane. In general, the MM3 results are in good agreement with experimental values. Predicted structures and conformations are given for the bicyclopentyl previously uninvestigated experimentally.     

Ab initio and molecular mechanics (MM3) calculations of protonated-neutral diamine hydrogen bonds

Ab initio calculations of cation-neutral diamine complexes have been carried out at the MP2/6-311+G** level. The geometry and energetics of the charge-reinforced hydrogen bond are analyzed with respect to the alkyl substitution of both the protonated and neutral nitrogen atoms, and these results have been used to improve the quality of the MM3(2000) force field. In addition, specialized hydrogen bond parameters optimized for MM3(2000) are presented. These parameters allow very accurate gas-phase modeling of the charge-neutral diamine environment. Molecular mechanics calculations can model effectively protonated amine-neutral amine hydrogen bonds in the gas phase and solution (continuum dielectric) through a combination of charge-dipole interactions and explicit hydrogen-bonding terms.     

Molecular mechanics (MM3) calculations on conjugated hydrocarbons

The MM3 molecular mechanics program has been extended to conjugated systems. A VESCF method is applied to the pi-system to calculate bond orders, from which various stretching and torsional parameters are obtained. The procedure gives somewhat better results than the analogous MM2 calculations. It has been applied to a study of 81 compounds of aromatic and other conjugated hydrocarbons, as well as 45 alkenes and unconjugated polyenes. The structures calculated are generally in good agreement with experiment, and the heats of formation of these compounds can be calculated with a rms value of 0.62 kcal/mol, which may be compared with the average experimental error of 0.61 kcal/mol. In addition, vibrational frequencies for five representative conjugated model structures are calculated, with an rms value of 46 cm^?1, and from these, other properties such as entropy can be calculated.     

Molecular mechanics (MM3) calculations on azoxy compounds

The MM3 force field has been extended to include azoxy compounds and also the related amine oxides, both aliphatic and aromatic. The structures of nine molecules were all well fit. The heats of formation for the aliphatic compounds were also well fit, and the vibrational spectra of eight compounds were also fit to the accuracy expected for such calculations. Because many of the experimental data needed to derive the force field were either lacking or were inadequate, ab initio calculations on structures, optimized at the MP2/6-31G* level, were used as needed. © 1994 by John Wiley & Sons, Inc.     

Molecular mechanics (MM3) calculations on alkyl radicals

The MM3 force field has been extended to cover alkyl radicals. Structures, conformational energies, vibrational spectra, and heats of formation have been well fit, mostly to ab initio data. © 1994 by John Wiley & Sons, Inc.     

Molecular mechanics (MM3) calculations on lithium amide compounds

The MM3 force field has been extended to deal with the lithium amide molecules that are widely used as efficient catalysts for stereoselective asymmetric synthesis. The MM3 force field parameters have been determined on the basis of the ab initio MP2/6-31G* and/or DFT (B3LYP/6-31G*, B3-PW91/6-31G*) geometry optimization calculations. To evaluate the electronic interactions specific to the lithium amides derived from the diamine molecules properly, the Lewis bonding potential term for the interaction between the lithium atom and the nonbonded adjacent electronegative atom such as nitrogen was introduced into the MM3 force field. The bond dipoles were evaluated correctly from the electronic charges on the atoms calculated by fitting to the electrostatic potential at points selected. The MM3 results on the molecular structures, conformational energies, and vibrational spectra show good agreement with those from the quantum mechanical calculations.     

Application of parallel processing techniques to improving the efficiency of MM2 molecular mechanics calculations

The application of parallel processing techniques to molecular mechanics calculations is evaluated. Using the standard molecular mechanics package, MM2, four different parallel versions of the program are implemented in a four-processor computing environment. A set of 529 test structures is used to compare the efficiency of the parallel versions of MM2 to a standard serial version of the program. Statistics describing execution times and program execution cycles are gathered and analyzed. The effects of parallel processing overhead and computer system load are explored, and the practical utility of parallel processing in molecular mechanics is estimated. The results of these parallelization experiments indicate that for geometry optimizations requiring significant amounts of computing time an improvement in program execution speed approaching 50% is realizable. © 1993 John Wiley & Sons, Inc.     

Intensities of infrared bands in molecular mechanics (MM3)

The MM3 molecular mechanics program calculates a fair representation of vibrational frequencies for molecules. To make this information more useful, a qualitative intensity calculation has been added, as is described herein. Because each bond in the molecule is assigned a dipole moment, and the vibrational amplitudes are known from the frequency calculation, the change in dipole moment corresponding to each normal mode is readily calculated. In some cases a charge flux has to be added empirically for bond stretchings. This relatively simple calculation has been applied to a number of different functional groups, and gives band intensities adequate for dividing the bands into very strong, strong, medium, weak, or very weak (forbidden) categories. © 1992 by John Wiley & Sons, Inc.     

Isotope effects in molecular mechanics (MM2). Calculations deuterium compounds

Parameters have been derived so as to enable the inclusion of deuterium in the MM2 molecular mechanics force field. Several compounds were studied and the results are compared with experiment. The results are never qualitatively wrong, but the accuracy ranges from excellent to only fair. They are quite good for hydrocarbons, but less so for ketones.     

Coupled semiempirical quantum mechanics and molecular mechanics (QM/MM) calculations on the aqueous solvation free energies of ionized molecules

The aqueous solvation free energies of ionized molecules were computed using a coupled quantum mechanical and molecular mechanical (QM/MM) model based on the AM1, MNDO, and PM3 semiempirical molecular orbital methods for the solute molecule and the TIP3P molecular mechanics model for liquid water. The present work is an extension of our model for neutral solutes where we assumed that the total free energy is the sum of components derived from the electrostatic/polarization terms in the Hamiltonian plus an empirical “nonpolar” term. The electrostatic/polarization contributions to the solvation free energies were computed using molecular dynamics (MD) simulation and thermodynamic integration techniques, while the nonpolar contributions were taken from the literature. The contribution to the electrostatic/polarization component of the free energy due to nonbonded interactions outside the cutoff radii used in the MD simulations was approximated by a Born solvation term. The experimental free energies were reproduced satisfactorily using variational parameters from the vdW terms as in the original model, in addition to a parameter from the one-electron integral terms. The new one-electron parameter was required to account for the short-range effects of overlapping atomic charge densities. The radial distribution functions obtained from the MD simulations showed the expected H-bonded structures between the ionized solute molecule and solvent molecules. We also obtained satisfactory results by neglecting both the empirical nonpolar term and the electronic polarization of the solute, i.e., by implementing a nonpolarization model. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1028–1038, 1999