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     

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).     

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 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. 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.     

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.     

A comparison of conformational energies calculated by molecular mechanics (MM2(85), Sybyl 5.1, Sybyl 5.21, and ChemX) and semiempirical (AM1 and PM3) methods

Conformational energies of different conformers have been calculated for a series of molecules using various molecular mechanics and semiempirical methods. The quality of the force fields has also been tested by calculating barriers to rotation about carbon-carbon bonds. The molecular mechanics force fields used are MM2(85), Sybyl 5.1, Sybyl 5.21, and ChemX, ver. Jan 89. The semiempirical methods used are AM1 and PM3. Molecules with different functional groups, for which good experimental data exist, have been selected. The semiempirical methods generally calculate barriers to rotation which are lower than the experimentally determined. The conformational energies for hydrocarbons are reasonably well reproduced by all tested methods although MM2(85) gives the quantitatively best agreement with experiments. For compounds containing oxygen, nitrogen and halogens MM2(85) gives results which are in best agreement with the experimentally determined values.     

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.     

- and β-cyclodextrin complexes with n-alkyl carboxylic acids and n-alkyl p-hydroxy benzoates. A molecular mechanics study of 1:1 and 1:2 associations

Molecular mechanics (MM) methods were employed to evaluate stabilization upon formation of inclusion compounds between two different guest molecules and - and β-cyclodextrins (CDs) for two different stoichiometries 1:1 and 1:2. The two guest molecules studied were n-alkyl carboxylic acids and n-alkyl p-hydroxy benzoates with variety of chain lengths. The computed stability for the inclusion compounds between -CDs and n-alkyl carboxylic acids reproduced experimental data reported in the literature. The transition between 1:1/1:2 complexes occurred at an alkyl chain length of n_C=9. It was previously demonstrated by diffusion coefficients measures that a stable 1:2 stoichiometry inclusion compound could be formed between n-alkyl p-hydroxy benzoates and -CD for the chain length n_C>4. The computed results reproduced the experimental ones. The combination between OPLS and GB/SA resulted in better agreements with experiments than those obtained with MM2 and MM3.     

The MM3 force field for amides,polypeptides and proteins

The potential functions for simple amides, several peptides and a small protein have been worked out for the MM3 force field. Structures and energies were fit as previously with MM2, but additionally, we fit the vibrational spectra of the simple amides (average rms error over four compounds, 34 cm^?1), and examined more carefully electrostatic interactions, including charge-charge and charge-dipole interactions. The parameters were obtained and tested by examining four simple amides, five electrostatic model complexes, two dipeptides, six crystalline cyclic peptides, and the protein Crambin. The average root-mean-square deviation from the X-ray structures for the six cyclic peptide crystals was only 0.10 Å for the nonhydrogen atomic positions, and 0.011 Å, 1.0°, and 4.9° for bond lengths, bond angles, and torsional angles, respectively. The parameter set was then further tested by minimizing the high resolution crystal structure of the hydrophobic protein Crambin. The resultant root-mean-square deviations for the non-hydrogen atomic data, in the presence of the crystal lattice, are 0.22 Å, 0.023 Å, 2.0°, and 6.4° for coordinates, bond lengths, bond angles, and torsional angles, respectively.     

Comparative performance of MM3(92) and two TINKER MM3 versions for the modeling of carbohydrates

The 1992 version of MM3 was largely used for modeling mono-, di-, and trisaccharides. In later versions of MM3 improvements were made in some parameters that may be important for carbohydrates. This corrected MM3 force field is part of the Tinker package, freely available (as its 4.1 version), and included in the Chem 3D Ultra 8.0 package (as the 3.7 version). The latter version lacks the corrections to the standard bond lengths produced by electronegativity and anomeric effects, whereas the Tinker 4.1 version only lacks the latter correction. The present work compares the performance of the three MM3 versions (and in some cases, DFT and/or HF/ab initio procedures) on several carbohydrate model problems as the chair and rotamer equilibria in 2-hydroxy- and 2-methoxytetrahydropyran, hydrogen bonding in cis-2,3-dihydroxytetrahydropyran, and the potential energy surfaces around the glycosidic bonds of two sulfated disaccharides and two trisaccharides. Tinker MM3 can be used accurately to estimate carbohydrate energies and geometries, and-with the help of some programming-to pursue studies on the potential energy surfaces of di- and trisaccharides. In most cases results obtained using the three MM3 versions are similar, although large energy differences are obtained when comparing a rotameric distribution around a O-C-O-H dihedral, which is almost forced to the exo-anomeric position by the Tinker versions. In other systems smaller energy differences are found, but they can nevertheless lead to a different global minimum when comparing conformers of similar energy. MM3(92) establishes better the differences between the bond lengths in both anomers, as an expected expression of the anomeric correction.     

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.     

Searching for conformers of nine- to twelve-ring hydrocarbons on the MM2 and MM3 energy surfaces: Stochastic search for interconversion pathways

The stochastic search method was employed to find as many conformers on the MM2 and MM3 energy surfaces as possible for cyclic saturated hydrocarbons with ring sizes from 9 through 12. The number found was 8 MM2 (8 MM3) for 9 rings, 18 MM2 (16 MM3) for 10 rings, 40 MM2 (29 MM3) for 11 rings, and 111 MM2 (90 MM3) for 12 rings. A measure of similarity between pairs of conformers of a compound, called conformational distance, is described. It was used to correlate similar MM2 and MM3 conformers. It was discovered that some conformers on each energy surface are not close to minima on the other surface in rings larger than 9. On refinement with the other optimizer, they changed considerably—going downhill to other previously found minima on the other energy surface or (in a few cases) going to minima which had not been found by direct searches. Conformational distance was also employed as an indication of which pairs of MM2 (or MM3) conformers are likely to interconvert rapidly. A new stochastic procedure of using small kicks was used to search for the most likely interconversion processes among the conformers. There is fairly good agreement between the most facile pathways located by it and unusually short conformational distances. Several additional 12-ring conformers (not found with previous methods) were located through application of this small kick procedure.     

Molecular mechanics studies (MM4) of sulfides and mercaptans

The MM4 force field has been extended to the title class of compounds. The vibrational spectra, structures, conformational equilibria, and heats of formation have been studied for 47 conformers of 29 compounds. In general, the properties may be calculated with accuracy that is competitive with that for hydrocarbons. The structures are better fit than previously because of the inclusion of a torsion–bend interaction term, which has its origin in the lone pair (Bohlmann) effect. Available experimental data do not suffice to yield detailed torsional potentials, or geometries as a function of torsion angle, and these quantities were determined by ab initio calculations at the MP2/6-31G* level. The rms error in the calculated frequencies of seven representative structures (with a total of 64 experimental and 96 ab initio frequencies) is 25 cm⁻¹. The heats of formation for 23 compounds have a weighted rms error of 0.36 kcal/mol. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1827–1847, 1997     

α- and β-cyclodextrin complexes with n-alkyl carboxylic acids and n-alkyl p-hydroxy benzoates. A molecular mechanics study of 1:1 and 1:2 associations

Molecular mechanics (MM) methods were employed to evaluate stabilization upon formation of inclusion compounds between two different guest molecules and α- and β-cyclodextrins (CDs) for two different stoichiometries 1:1 and 1:2. The two guest molecules studied were n-alkyl carboxylic acids and n-alkyl p-hydroxy benzoates with variety of chain lengths. The computed stability for the inclusion compounds between α-CDs and n-alkyl carboxylic acids reproduced experimental data reported in the literature. The transition between 1:1/1:2 complexes occurred at an alkyl chain length of n_C=9. It was previously demonstrated by diffusion coefficients measures that a stable 1:2 stoichiometry inclusion compound could be formed between n-alkyl p-hydroxy benzoates and α-CD for the chain length n_C>4. The computed results reproduced the experimental ones. The combination between OPLS and GB/SA resulted in better agreements with experiments than those obtained with MM2 and MM3.     

Calculating distribution coefficients based on multi-scale free energy simulations: an evaluation of MM and QM/MM explicit solvent simulations of water-cyclohexane transfer in the SAMPL5 challenge

One of the central aspects of biomolecular recognition is the hydrophobic effect, which is experimentally evaluated by measuring the distribution coefficients of compounds between polar and apolar phases. We use our predictions of the distribution coefficients between water and cyclohexane from the SAMPL5 challenge to estimate the hydrophobicity of different explicit solvent simulation techniques. Based on molecular dynamics trajectories with the CHARMM General Force Field, we compare pure molecular mechanics (MM) with quantum-mechanical (QM) calculations based on QM/MM schemes that treat the solvent at the MM level. We perform QM/MM with both density functional theory (BLYP) and semi-empirical methods (OM1, OM2, OM3, PM3). The calculations also serve to test the sensitivity of partition coefficients to solute polarizability as well as the interplay of the quantum-mechanical region with the fixed-charge molecular mechanics environment. Our results indicate that QM/MM with both BLYP and OM2 outperforms pure MM. However, this observation is limited to a subset of cases where convergence of the free energy can be achieved.     

Thienyl carboxylate ligands bound to and bridging MM quadruple bonds, M = Mo or W: models for polythiophenes incorporating MM quadruple bonds

A series of compounds of the form [M(2)L(4)] and [[((t)()BuCO(2))(3)M(2)](2)(mu-L')] have been made where M = Mo or W, L = a thienyl, bithienyl, or terthienyl carboxylate, and L' = a corresponding thienyl dicarboxylate. The electronic absorption spectra are reported and the electronic structures discussed. Intense metal-to-ligand charge transfer bands traverse the visible and near-IR regions of the electronic absorption spectrum. The compounds show reversible metal-based oxidations and quasireversible ligand-based reductions. The molecular structure of Mo(2)(O(2)C-2-Th)(4).2THF is reported, on the basis of a single crystal X-ray diffraction study. These compounds provide insight into the expected properties of related dimetalated polythiophenes incorporating MM quadruple bonds.     

Molecular mechanics (MM3) parameterization of hydroxylamine and methyl derivatives

Based on results of electron diffraction, gas phase infrared spectroscopy (IR), and MP2/6-31 + G* ab initio calculations, a set of molecular mechanics (MM3) parameters was developed for molecules containing the N(sp³)—O(sp³) moiety. Using this set of parameters, MM3 is able to reproduce structures (bond lengths and bond angles) and vibrational spectra satisfactorily. © 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.