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.     

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.     

Electrostatic interactions in molecular mechanics (MM2) calculations via PEOE partial charges I. Haloalkanes

The PEOE (partial equalization of orbital electronegativity) procedure has been modified slightly and reparametrized for haloalkanes to calculate partial atomic charges suitable for evaluation of dipole moments and electrostatic energies in conjunction with molecular mechanics (MM2) calculations. Dipole moments of 66 haloalkanes are calculated with an average absolute deviation of 0.14 D from experimental values. The conformational energies of 40 compounds have been calculated and the agreement with experimental data is generally good and compares well with calculations by the IDME (induced dipole moment and energy) method. In addition, carbon and proton charges correlate well with C-1s core binding energies and ¹H-NMR (nuclear magnetic resonance) shifts for halomethanes. The most striking benefit of treating electrostatics through a set of partial charges compared to the standard MM2 bond dipole approach is demonstrated by calculations on 1,4-disubstituted cyclohexanes, for which standard MM2 fails to predict the most stable conformation.     

Approaches to charge calculations in molecular mechanics

Alternative methods of estimating atomic charges in haloalkanes are presented, derived from quantum mechanical and classical treatments. A scheme based on a breakdown of the transmission of charge by polar atoms into one-bond, two-bond, and three-bond additive contributions is given, in which the one-bond effect is proportional to the difference in the electronegativities of the bonded atoms, and the two- and three-bond effects functions of the atomic electronegativity and polarizability. Suitable developments of the basic scheme, including an iterative self-consistent process, give calculated dipole moments for a variety of haloalkanes in good agreement with the observed values. The atomic charges obtained by this scheme are compared with other estimates of these charges. They are similar to those derived from a simple LCAO –MO scheme but differ from those obtained by population analysis of more refined quantum mechanical calculations.     

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 (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.     

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     

Ab initio and molecular mechanics calculations on imine derivatives: A study of the rotational barriers and the development of MM2 parameters

The application of molecular mechanics methods for the study of structures has become a standard approach to conformational analysis. The MM2 force field has been extended to include imines. In general, a diverse group of aliphatic and aromatic imine structures can now be treated. The rotational energy profiles and barriers to N-substituted imines about the C_sp2? C_sp2 single bonds adjacent to C?N functional group were calculated via ab initio MO theory. Information obtained from the quantum mechanical calculations at the 3-21G, 6-31G*, and MP4/6-31G* //6-31G* levels was used both to study the phenomena involved and to parameterize MM2. The syn-anti isomerization was also studied, and the mechanistic pathways have been evaluated. In cases where the comparison with experimental data can be made, the agreements are good.     

MoBioTools: A toolkit to setup quantum mechanics/molecular mechanics calculations

We present a toolkit that allows for the preparation of QM/MM input files from a conformational ensemble of molecular geometries. The package is currently compatible with trajectory and topology files in Amber, CHARMM, GROMACS and NAMD formats, and has the possibility to generate QM/MM input files for Gaussian (09 and 16), Orca (≥4.0), NWChem and (Open)Molcas. The toolkit can be used in command line, so that no programming experience is required, although it presents some features that can also be employed as a python application programming interface. We apply the toolkit in four situations in which different electronic-structure properties of organic molecules in the presence of a solvent or a complex biological environment are computed: the reduction potential of the nucleobases in acetonitrile, an energy decomposition analysis of tyrosine interacting with water, the absorption spectrum of an azobenzene derivative integrated into a voltage-gated ion channel, and the absorption and emission spectra of the luciferine/luciferase complex. These examples show that the toolkit can be employed in a manifold of situations for both the electronic ground state and electronically excited states. It also allows for the automatic correction of the active space in the case of CASSCF calculations on an ensemble of geometries, as it is shown for the azobenzene derivative photoswitch case.     

Application of molecular mechanics method to structural calculations of π-complexes of transition metals

A. N. Nesmeyanov Institute of Heteroorganic Compounds. Translated from zhurnal Strukturnoi Khimii, Vol. 28, No. 4, pp. 3–13, July–August, 1987.     

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.     

Comparative quantum mechanics/molecular mechanics (QM/MM) and density functional theory calculations on the oxo-iron species of taurine/alpha-ketoglutarate dioxygenase

We present here the first quantum mechanical/molecular mechanics (QM/MM) studies of taurine/alpha-ketoglutarate dioxygenase (TauD) enzymes. Our studies are focused on the chemical properties of the oxo-iron species and the effect of the protein environment on its structural and electronic behavior. Although the active site region of TauD is very polar with many key hydrogen bonding interactions and salt bridges, the actual effect of the protein environment on the ordering and relative energies of the possible spin state structures is found to be quite small. Optimized geometries are very close to ones observed with density functional theory models that did not take the protein environment into consideration. The calculations show that protonation of the histidine ligands of iron is essential to reproduce the correct electronic representations of the enzyme. Hydroxylation studies of taurine by the oxo-iron active species predict that it is a very efficient catalyst that reacts with substrates via low reaction barriers.     

Approaches to charge calculations in molecular mechanics. 2 Resonance effects in conjugated systems

A previously published scheme of estimating atomic charges in haloalkanes is extended to include olefines, alcohols amines, acids, ethers, and amides. In the conjugated systems the effects of mesomeric transfer of charge are explicitly included. Generally good agreement with the observed dipole moments of these compounds and their substituted derivatives is found. The atomic charges so obtained are compared with those of other semiempirical and quantum-mechanical calculations for the amide group. The charges so obtained fall within the range of values obtained by these other schemes, supporting the general validity of this approach.     

Molecular mechanics (MM2) calculations on peptides and on the protein Crambin using the CYBER 205

The MM2 potential functions for amides and peptides have been further extended by examining the experimental crystal structures for cyclo-(-Ala-Ala-Gly-Gly-Ala-Gly-), I, and cyclo-(-Ala-Ala-Gly-Ala-Gly-Gly-), II. The force field obtained was then applied to a study of the structure of the hydrophobic protein Crambin, for which a high resolution crystal structure is available. The energy minimization was carried out using a version of MM2 adapted to the CYBER 205.     

A computationally efficient alternative to the Buckingham potential for molecular mechanics calculations

This paper describes a (6-8) variant of the Lennard-Jones (6-12) potential,for computing the energy of non-bonded interactions in molecular mechanicscalculations, which combines the overall precision of the Buckingham (6-exp)potential with the computational efficiency of the standard Lennard-Jones(6-12) potential. There is also a note on the radius of convergence of thefull matrix Newton–Raphson optimization procedure.     

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