PEFF: A program for the development of empirical force fields

PEFF is a new computer program designed to assist in the development of empirical force fields used in molecular mechanics calculations. Its main features are: constrained and unconstrained energy minimization available with four different techniques, rigid group refinement, crystal lattice summations, calculation of normal modes, thermodynamic functions and crystallographic temperature factors, vibrational corrections of calculated crystal structures, and a multidimensional driver to scan the energy hypersurface. Used in force field optimization mode, the program employs a least-squares method to fit the force field parameters to a set of experimental data.     

Analytical torisionL-tensor formulas for anharmonic force constant transformation

New analytical formulas for the torsionL-tensor are reported, which are used in molecular normal mode analysis calculations for the nonlinear transformation of the force constants from internal coordinates to normal coordinates. The proposed formalism exhibits a relative simplicity as compared to previous reported results. Sample calculations for methanol and hydrazine are presented.     

On the use of conformationally dependent geometry trends from ab initio dipeptide studies to refine potentials for the empirical force field CHARMM

Previous 4-21G ab initio geometry optimizations of various conformations of the model dipeptides (N-acetyl N'methyl amides) of glycine (GLY) and the alanine (ALA) have been used to help refine the empirical force constants and equilibrium geometry in the CHARMM force field for peptides. Conformationally dependent geometry trends from ab initio calculations and positions of energy minima on the ab initio energy surfaces have been used as guides in the parameter refinement, leading to modifications in the bond stretch, angle bending, and some torsional parameters. Preliminary results obtained with these refined empirical parameters are presented for the protein Crambin. Results for the cyclic (Ala-Pro-DPhe)₂ are compared with those from other calculations. It seems that the dihedral angle fit achieved by the new parameters is significantly improved compared with results from force fields whose derivation does not include ab initio geometry trends.     

Update of the anharmonic force field parameters of the ozone molecule

A new set of spectroscopic constants of the ¹⁶O₃ molecule (ω_i, x_ij, y_ijk, γ^DD, _i^X, β_ij^X,…), which determine vibrational dependence of band centres and rotational parameters, is derived from recent accurate analysis of high-resolution experimental ro-vibrational spectra through the theoretical approach based on second-order perturbation expansions in normal coordinates accounting for Darling–Dennison resonance interactions. These values are used to update empirical values of anharmonic coefficients (k_ijl, k_ijlm) of the potential function expansion in normal coordinates. Quadratic f_rr, f_r, f_rr′, f as well as cubic f_rst and quartic f_rstl force constants in internal (bond lengths, bond angle) coordinates are also derived. A detailed discussion is devoted to the accuracy of parameter determination for each of four steps of calculations. It is emphasised that the conventional method based on the inversion of formulae of the perturbation theory gives the largest uncertainties at the last step of calculations: the determination of the anharmonic force field in internal coordinates.     

Determination of force fields for formaldehyde,acetaldehyde and acetone by the CNDO/force method

CNDO/Force calculations have been done for formaldehyde, acetaldehyde and acetone, and the theoretical force fields evaluated. Experimental force fields are obtained from vibrational frequencies using the least-squares refinement method. The initial force fields considered are based on the bending and interaction force constants obtained from the CNDO/Force calculations and the stretching force constants transferred from chemically related molecules. Vibrational frequencies of H₂CO, D₂CO, HDCO, H₂¹³CO and D₂¹³CO for formaldehyde, CH₃CHO, CH₃CDO, CD₃CHO, CD₃CDO and CH₂DCHO for acetaldehyde, and CH₃COCH₃ CD₃COCH₃ and CD₃COCD₃ for acetone are employed in the force field refinements. The final force fields obtained are found to be reasonable with respect to the diagonal and interaction force constants.     

Calculation of optimum geometries and force fields by the CNDO/force method

CNDO/Force calculations have been performed on a series of molecules, H₂CO, F₂CO, CF₄, CHF₃, CH₂F₂ and CH₃F. The optimum geometries and force fields are reported. It is found that the method can successfully predict the geometries of polyatomic molecules. The bending force constants and interaction force constants are, in general, comparable with experimental values both with respect to sign and magnitude. The stretching force constants have higher values than the experimental force constants. However, the trend in stretching force constants of a series of molecules is comparable with that of the corresponding experimental values.     

Evaluations of AMBER force field parameters by MINA approach for copper-based nucleases

We describe the development of the AMBER force field parameters for 46 nucleases involving most kinds of copper nucleases with high DNA affinities and specificities by MINA approach that could evaluate accurate force constants for batch bonds/angles on the basis of energies of three adjacent lengths/angles geometries. The molecular mechanics (MM) and molecular dynamic simulations on adducts of the 21 representative copper-based nucleases with DNA are in excellent agreement with those of experimental results. Furthermore, to validate the evaluated parameters, the studied structures performed frequency analysis together with normal mode calculations in quantum mechanics and MM calculations. The force field parameters evaluated in this work provide an extension of AMBER force field, and the results of molecular dynamics simulations of adduct of copper nuclease and duplex DNA illustrate the potential utility of these parameters.     

Theoretical study of the force field and vibrational assignments of acetamide and deuterated analogues

The complete harmonic force constants of acetamide have been evaluated by ab initio calculations at the Hartree-Fock level with the 4–31G(d) basis set. The force field was scaled to compensate for the systematic overestimations of the Hartree-Fock-level force constants by empirical factors using the matrix isolation IR spectra of CH₃CONH₂ and CD₃CONH₂. A normal coordinate treatment has been carried out with the scaled force field to analyze the vibrational spectra of CH₃CONH₂. A normal coordinate treatment has been carried out with the scaled force field to analyze the vibrational spectra of CH₃COND₂, cis-CH₃CONHD and trans-CH₃CONHD. The effect of cis/trans isomerism of CH₃CONHD on the fundamental bands was well reproduced by the calculations. The fundamental vibrations were also predicted for CD₃COND₂, cis-CD₃CONHD and trans-CD₃CONHD.     

Semiempirical calculation of harmonic force constants: CNDO/2 and MINDO/2 study of C2H6, C2H4 and C2H2

The complete quadratic force fields of ethane, ethylene and acetylene have been calculated from CNDO/2 and MINDO/2 wavefunctions by the force method. Agreement with experiment is satisfactory for both methods. In the CNDO method the stretching force constants must be scaled empirically to obtain realistic values. It is particularly significant that stretching-deformation and deformation-deformation coupling force constants are correctly reproduced by the CNDO method and with the exception of the rocking-rocking couplings, also by the MINDO method. It is concluded that such calculations may usefully contribute to the determination of force fields.     

Calculation of macromolecular force constants

Force constant refinement may be carried under a system of constraints imposed on well characterized modes as the refinement proceeds. Resulting stability permits the accurate calculation of many independent macromolecular force constants. A useful formalism for this technique is developed. Prediction of initially poorly characterized modes can emerge from this stability. A brief discussion of currently used refinement schemes has been included. We show that the standard least-squares procedure is a special case of our present more general method, the former being useful when the molecule is not too large.     

Use of semiempirical molecular orbital calculations for the evaluation of force fields

Various methods, employing molecular orbital calculations of varying approximations, for evaluation of force fields of polyatomic molecules have been reviewed. Applications ofcndo/force method for the force field calculations are specially dealt with in detail because of its ease of operation and being economically more viable in terms of computer time. The calculated C=O stretching force constants for a series of organic molecules are shown to have linear relationship with substituent constants.     

Effect of hydrogen bonding and cooperativity on stretching force constants of formamide

Stretching force constants for formamide and its seven associated species involving two to four molecules hydrogen-bonded through linear and cyclic configurations and 10 structures containing formamide hydrogen-bonded with one to five water molecules are reported. Since ab initio calculations are rather inconvenient to perform on such big clusters and are time-consuming, CNINDO MO calculations were carried out using the gradient method. The results demonstrate, on the one hand, the feasibility of semiempirical calculations for the evaluation of trends in force constants for big clusters where generally ab initio calculations become much involved and, on the other hand, explain the effect of hydrogen bonding and cooperativity on force constants and vibrational spectra of biologically important systems composed of formamide in the condensed phase and its aqueous solutions. The C?O and N? H stretching force constants are found to reduce significantly on hydrogen bonding. The reduction in force constant is further enhanced when two cyclic dimers become associated through a linear hydrogen bond. The results indicate justification for the stabilization of the formamide structure with two cyclic dimers hydrogen-bonded together. The reduction in the force constants on hydrogen bonding also reflect the cooperativity contribution. The C?O and C? N stretching force constants for the structures corresponding to formamide in liquid and aqueous solution phases are in agreement with the experimental vibrational frequencies reported.     

Normal coordinate ab initio force relaxation

A procedure for optimization of molecular geometries is presented, combining ab initio calculations with vibrational molecular data from spectroscopy or empirical force fields. Theoretical cartesian forces are transformed to vibrational normal coordinate forces from which geometry increments are calculated. Test results indicate that the method saves considerable effort compared to other optimization schemes.     

Harmonic force fields from molecular energy calculations : Tests of a method using indo and MINDO/2 semiempirical molecular energies

A numerically stable method for simultaneous calculation of force constants and coupling constants from energy data has been designed and tested. It has been used to obtain harmonic force fields for a set of small molecules from INDO and MINDO/2 calculations.     

Accurate prediction of absolute acidity constants in water with a polarizable force field: substituted phenols, methanol, and imidazole

Validity of a force field with explicit treatment of electrostatic polarization in a form of inducible point dipoles for computing acidity constants was tested by calculating absolute pK(a) values of substituted phenols, methanol, and imidazole in water with the molecular dynamics technique. The last two systems were selected as tyrosine and histidine side-chain analogues, respectively. The solvent was represented by an explicit polarizable water model. Similar calculations were also performed with a modified OPLS-AA nonpolarizable force field. The resulting pK(a) values were compared with available experimental data. While the nonpolarizable force field yields errors of about 5 units in the absolute pK(a) values for the phenols and methanol, the polarizable force field produces the acidity constant values within a ca. 0.8 units accuracy. For the case of imidazole, the fixed-charges force field was capable of reproducing the experimental value of pK(a) (6.4 versus the experimental 7.0 units), but only at a cost of dramatically underestimating dimerization energy for the imidazolium-water complex. At the same time, the polarizable force field yields an even more accurate result of pK(a) = 6.96 without any sacrifice of the accuracy in the dimerization energy. It has also been demonstrated that application of Ewald summation for the long-range electrostatics is important, and substitution of a simple cutoff procedure with Born correction for ions can lead to underestimation of absolute pK(a) values by more than 5 units. The accuracy of the absolute acidity constants computed with the polarizable force field is very encouraging and opens road for further tests on more diverse organic molecules sets, as well as on proteins.     

Improved treatment of the protein backbone in empirical force fields

Empirical force field-based calculations of proteins, including protein-folding studies, have improved our understanding of the relationship of their structure to their biological function. However, limitations in the accuracy of empirical force fields in the treatment of the peptide backbone exist. Presented is a grid correction approach to improve the treatment of the peptide backbone phi/psi conformational energies. Inclusion of this correction with the CHARMM22 all-atom protein force field is shown to lead to significant improvement in the treatment of the conformational energies of both the peptide model compound, the alanine dipeptide, and of proteins in their crystal environment. The developed approach is suggested to lead to significant improvements in the accuracy of empirical force fields to treat peptides and proteins.     

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.     

Single-molecule force spectroscopy measurements of bond elongation during a bimolecular reaction

It is experimentally challenging to directly obtain structural information of the transition state (TS), the high-energy bottleneck en route from reactants to products, for solution-phase reactions. Here, we use single-molecule experiments as well as high-level quantum chemical calculations to probe the TS of disulfide bond reduction, a bimolecular nucleophilic substitution (S N2) reaction. We use an atomic force microscope in force-clamp mode to apply mechanical forces to a protein disulfide bond and obtain force-dependent rate constants of the disulfide bond reduction initiated by a variety of nucleophiles. We measure distances to the TS or bond elongation (Delta x), along a 1-D reaction coordinate imposed by mechanical force, of 0.31 +/- 0.05 and 0.44 +/- 0.03 A for thiol-initiated and phosphine-initiated disulfide bond reductions, respectively. These results are in agreement with quantum chemical calculations, which show that the disulfide bond at the TS is longer in phosphine-initiated reduction than in thiol-initiated reduction. We also investigate the effect of solvent environment on the TS geometry by incorporating glycerol into the aqueous solution. In this case, the Delta x value for the phosphine-initiated reduction is decreased to 0.28 +/- 0.04 A whereas it remains unchanged for thiol-initiated reduction, providing a direct test of theoretical calculations of the role of solvent molecules in the reduction TS of an S N2 reaction. These results demonstrate that single-molecule force spectroscopy represents a novel experimental tool to study mechanochemistry and directly probe the sub-?ngstr?m changes in TS structure of solution-phase reactions. Furthermore, this single-molecule method opens new doors to gain molecular level understanding of chemical reactivity when combined with quantum chemical calculations.     

Large kinetic isotope effects with unsymmetrical transition states

The results of a series of calculations for a wide, unrestricted variation in the force constants for the making and breaking bonds and their interaction constant are presented for the abstraction reactions of CH₂D₂ with Cl atoms. A wide range of asymmetrical force constants leads to a high kinetic isotope effect as has been pointed out by others for a more restricted range of consideration. These results pointedly contradict the assumed connection between a high kinetic isotope effect and a symmetrical transition state. It is found by examining the atomic displacements of the normal mode that the motion of the H or D atom in the real stretch of the transition state will often have little influence on the isotope effect because the mode can be dominated by end group motions. It is further found that a 3-center model multiplied by a constant factor to account for the contributions of the other vibrations is capable of very satisfactorily reproducing the more rigorous 6-center calculations.     

Normal coordinate and infrared band intensities of trichloronitromethane and trichloroacetate ions

Laser Raman and IR spectra in the region 50–3000 cm⁻¹ for trichloronitromethane and trichloroacetate ions were recorded. All observed vibrational bands have been assigned to normal modes. Normal coordinate analyses of these molecules have been carried out in the valence force-field approximation. A set of force constants was obtained leading to good agreement between observed and calculated frequencies. The relative displacements of the atoms resulting from normal coordinate calculations were used to compute the IR band intensity of each mode by the CNDO/2-MO procedure. The intensity calculations confirmed the assignments and supported the calculated force constants.