Showing papers in "Journal of Computational Chemistry in 1990"

Determining atom-centered monopoles from molecular electrostatic potentials. The need for high sampling density in formamide conformational analysis

Abstract: An improved method for computing potential-derived charges is described which is based upon the CHELP program available from QCPE.1 This approach (CHELPG) is shown to be considerably less dependent upon molecular orientation than the original CHELP program. In the second part of this work, the CHELPG point selection algorithm was used to analyze the changes in the potential-derived charges in formamide during rotation about the CN bond. In order to achieve a level of rotational invariance less than 10% of the magnitude of the electronic effects studied, an equally-spaced array of points 0.3 A apart was required. Points found to be greater than 2.8 A from any nucleus were eliminated, along with all points contained within the defined VDW distances from each of the atoms. The results are compared to those obtained by using CHELP. Even when large numbers of points (ca. 3000) were sampled using the CHELP selection routine, the results did not indicate a satisfactory level of rotatational invariance. On the basis of these results, the original CHELP program was found to be inadequate for analyzing internal rotations.

MacroModel—an integrated software system for modeling organic and bioorganic molecules using molecular mechanics

Abstract: An integrated molecular modeling system for designing and studying organic and bioorganic molecules and their molecular complexes using molecular mechanics is described. The graphically controlled, atom-based system allows the construction, display and manipulation of molecules and complexes having as many as 10,000 atoms and provides interactive, state-of-the-art molecular mechanics on any subset of up to 1,000 atoms. The system semiautomates the graphical construction and analysis of complex structures ranging from polycyclic organic molecules to biopolymers to mixed molecular complexes. We have placed emphasis on providing effective searches of conformational space by a number of different methods and on highly optimized molecular mechanics energy calculations using widely used force fields which are supplied as external files. Little experience is required to operate the system effectively and even novices can use it to carry out sophisticated modeling operations. The software has been designed to run on Digital Equipment Corporation VAX computers interfaced to a variety of graphics devices ranging from inexpensive monochrome terminals to the sophisticated graphics displays of the Evans & Sutherland PS300 series.

Atomic charges derived from semiempirical methods

Abstract: It is demonstrated that semiempirical methods give electrostatic potential (ESP) derived atomic point charges that are in reasonable agreement with ab initio ESP charges. Furthermore, we find that MNDO ESP charges are superior to AM1 ESP charges in correlating with ESP charges derived from the 6-31G* basis set. Thus, it is possible to obtain 6-31G* quality point charges by simply scaling MNDO ESP charges. The charges are scaled in a linear (y = Mx) manner to conserve charge. In this way researchers desiring to carry out force field simulations or minimizations can obtain charges by using MNDO, which requires much less computer time than the corresponding 6-31G* calculation.

A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations

Abstract: A combined quantum mechanical (QM) and molecular mechanical (MM) potential has been developed for the study of reactions in condensed phases. For the quantum mechanical calculations semiempirical methods of the MNDO and AM1 type are used, while the molecular mechanics part is treated with the CHARMM force field. Specific prescriptions are given for the interactions between the QM and MM portions of the system; cases in which the QM and MM methodology is applied to parts of the same molecule or to different molecules are considered. The details of the method and a range of test calculations, including comparisons with ab initio and experimental results, are given. It is found that in many cases satisfactory results are obtained. However, there are limitations to this type of approach, some of which arise from the AM1 or MNDO methods themselves and others from the present QM/MM implementation. This suggests that it is important to test the applicability of the method to each particular case prior to its use. Possible areas of improvement in the methodology are discussed.

Compact contracted basis sets for third-row atoms: Ga-Kr

Abstract: The (14s11p5d) primitives basis set of Dunning for the third-row main group atoms Ga-Kr has been contracted (6s4p1d). The core functions have been relatively highly contracted while those which represent the valence region have been left uncontracted to maintain flexibility. Calculations with the (6s4p1d) contraction are reported for a variety of molecules involving third-row atoms. This basis set is found to satisfactorily reproduce experimental properties such as geometric configurations, dipole moments, and vibrational frequencies for a range of molecules. Comparisons are made with the performance of the uncontracted basis set. Polarization functions for the contracted basis set are reported and performance of the basis set with and without polarization functions is examined. A relaxation of the (6s4p1d) contraction to (9s6p2d) for higher level energy calculations is also presented.

Calculation of the nonlinear optical properties of molecules

Abstract: : A finite field method for the calculation of polarizabilities and hyperpolarizabilities is developed based on both an energy expansion and a dipole moment expansion. This procedure is implemented in the MOPAC semiempirical program. Values and components of the dipole moment (mu), polarizability (alpha), first hyperpolarizability (beta), and second hyperpolarizability (gamma) are calculated as an extension of the usual MOPAC run. Applications to benzene and substituted benzenes are shown as test cases utilizing both MNDO and AM1 Hamiltonians.

GEPOL: An improved description of molecular surfaces. I. Building the spherical surface set

Abstract: The algorithm used by the program GEPOL to compute the Molecular Surface (MS), as defined by Richards, is presented in detail. GEPOL starts like other algorithms from a set of spheres with van der Waals radii, centered on the atoms or group of atoms of the molecule. GEPOL computes the MS by first searching the spaces inaccessible to the solvent and consequently filling them with a new set of spheres. Here we study the behavior of the method with its parameters, presenting several examples of application.

A boundary element method for molecular electrostatics with electrolyte effects

Abstract: A boundary element method is developed to compute the electrostatic potential inside and around molecules in an electrolyte solution. A set of boundary integral equations are derived based on the integral formulations of the Poisson equation and the linearized Poisson-Boltzmann equation. The boundary integral equations are then solved numerically after discretizing the molecular surface into a number of flat triangular elements. The method is applied to a spherical molecule for which analytical solutions are available. Use is made of both constant and linearly varying unknowns over the boundary elements, and the method is tested for various values of parameters such as the dielectric constant of the molecule, ionic strength, and the location of the interior point charge. The use of the boundary integral method incorporating the nonlinear Poisson-Boltzmann equation is also briefly discussed.

Molecular mechanics (MM3) calculations on conjugated hydrocarbons

Abstract: 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.

Derivation of net atomic charges from molecular electrostatic potentials

Abstract: The dependence of net atomic charges, as derived from least-squares fitting to electrostatic potentials, on molecular orientation and potential site location is critically examined. A unique rotationally invariant algorithm, in which the charges may be constrained to reproduce the molecular dipole moment, is presented and the results for several basis sets compared to previous work. Significant improvements in dipole moments derived from the unconstrained charges are noted.

Semiempirical AM1 electrostatic potentials and AM1 electrostatic potential derived charges: A comparison with ab initio values

Abstract: Electrostatic potentials calculated from AM1 wave functions have been compared with ab initio STO-3G values and qualitative agreement has been found. Atomic charges derived from AM1 electrostatic potentials for both experimental and AM1 optimized geometries are of comparable quality with STO-3G potential derived charges. These results suggest that the AM1 electrostatic potential may be useful both in its own right and also for deriving atomic charges for use in molecular dynamics studies.

Monte Carlo simulations of liquid alkyl ethers with OPLS potential functions

Abstract: Intermolecular potential functions have been developed for use in computer simulations of alkyl ethers. The simple OPLS model was adopted and parameterized to yield good descriptions of bimolecular and ion-molecule complexes as well as to reproduce experimental thermodynamic properties of liquid ethers. The principal testing featured Monte Carlo statistical mechanics simulations for liquid dimethyl ether (DME), ethyl methyl ether (EME), diethyl ether (DEE), and tetrahydrofuran (THF). Average errors of 1–3% are obtained for the computed densities and heats of vaporization including results for THF at pressures up to 5000 atm. The torsional motion about the central CO bonds in EME and DEE was included in the simulations using rotational potential functions fit to results of molecular mechanics (MM2) calculations. The liquid-state environment is found to have negligible effect on the conformational equilibria.

Molecular mechanics. The MM3 force field for alkenes

Abstract: 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.

On the use of AM1 and MNDO wave functions to compute accurate electrostatic charges

Abstract: A new strategy to evaluate accurate electrostatic charges from semiempirical wave functions is reported. The rigorous quantum mechanical molecular electrostatic potentials computed from both MNDO and AM1 wave functions are fitted to the point-charge molecular electrostatic potential to obtain the electrostatic charges. The reliability of this strategy is tested by comparing the semiempirical electrostatic charges for 21 molecules with the semiempirical Mulliken charges and with the ab initio STO-3G and 6-31G* electrostatic charges. The ability of the dipoles derived from the semiempirical electrostatic and Mulliken charges as well as from the SCF charge distributions to reproduce the ab initio 6-31G* electrostatic dipoles and the gas phase experimental values is determined. The statistical analysis clearly point out the goodness of the semiempirical electrostatic charges, specially when the MNDO method is used. The excellent relationships found between the MNDO and 6-31G* electrostatic charges permit to define a scaling factor which allows to accurately reproduce the 6-31G* electrostatic charge distribution as well as the experimental dipoles from the semiempirical electrostatic charges.

The application of molecular similarity calculations

Abstract: A prescription for applying the method of molecular similarity calculations based on electrostatic potentials and fields is developed by consideration of a typical structure-activity series. Firm conclusions are drawn about the nature of the grid of points surrounding the molecules and about the choice of geometry, but options for point charges are less clearcut.

Comparative study of the molecular Electrostatic potential obtained from different wavefunctions. Reliability of the semiempirical MNDO wavefunction

Abstract: A systematic analysis of the molecular electrostatic potential (MEP) is presented. This study has been performed with a twofold purpose: first, to study the MEP dependence with regard to the quality of the basis set used to compute the ab initio SCF wavefunction and second, to develop and to assess a new strategy for computing isoelectrostatic potential maps using the semiempirical MNDO wavefunction. The only differences between this procedure and the ab initio SCF MEP computation lie in the freezing of the inner electrons and in the origin of the first-order density matrix. The statistical analysis of MEPs computed for a large number of molecules from MNDO wavefunction and ab initio SCF wavefunctions obtained using STO-3G, 4-31G, 6-31G, 4-31G*, 6-31G*, and 6-31G** basis sets points out the ability of any wavefunction to reproduce the general topological characteristics of the MEP surfaces. Nevertheless, split-valence basis sets including polarization functions are necessary to obtain accurate MEP minimum energy values. MNDO wavefunction tends to overestimate the MEP minima depth by a constant factor and shows an excellent ability to reflect the relative variation of MEP minima energies derived from a rather sophisticated (6-31G*) basis set, lacking of the shortcomings detected in the semiempirical CNDO approximation.

The nature of the N—H…O=C hydrogen bond: an Intermolecular Perturbation Theory study of the formamide/formaldehyde complex

Abstract: We have used Hayes-Stone Intermolecular Perturbation Theory (IMPT) to study the variation with distance and orientation of the various components of the interaction energy of the N H…O = C hydrogen bonded trans- formamide/formaldehyde complex, a model system for hydrogen bonding in proteins. The directionality of the total interaction energy is similar to that of the electrostatic component alone. We have analysed our data in terms of two model atom-atom intermolecular potentials, using an isotropic functional form and an anisotropic one. The anisotropic form gives an excellent representation of the IMPT potential energy surface, considerably better than the isotropic model, and is comprised entirely of theoretically justified, physically meaningful terms.

Computing the electric potential of biomolecules: application of a new method of molecular surface triangulation

Abstract: Une nouvelle methode est presentee pour definir une surface analytique lisse et triangulee pour des molecules biologiques. La surface produite par l'algorithme convient bien a la technique de polarisation de charge pour le calcul du potentiel electrostatique des molecules solvatees. Elle est aussi utilisee pour les calculs des surfaces et des volumes moleculaires. L'algorithme de triangulation peut etre utilise en combinaison avec les methodes electrostatiques pour calculer le potentiel electronique des molecules de forme arbitraire en solutions

Conserving energy during molecular dynamics simulations of water, proteins, and proteins in water

Abstract: Received 26 February 1990; accepted 29 May 1990Molecular dynamics simulations have been carried out for a series of systems of increasing complexityincluding: pure water, a model polypeptide (a-helical decaglycine) in vacuo, a protein (Pancreatic TrypsinInhibitor, PTI) in vacuo, and a fully solvated protein (PTI in water). The equations of motion were inte-grated using Andersen’s velocity version of the Verlet algorithm with internal contraints (the RATTLEalgorithm). The accuracy with which the equations of motion are integrated has been analyzed for sev-eral different simulation conditions. The effects of various nonbonded interaction truncation schemes onthe conservation of energy have been examined, including the use of atomic cutoffs, and (neutral group)residue cutoffs. The use of a smoothing function to eliminate the discontinuities in the potential at thecutoff leads to a significant improvement in the accuracy of the integration for each of the systems stud-ied. The accuracy with which the equations of motion are integrated using the RATTLE algorithm forpure water and for the sotvated protein are found to be comparable when the nonbonded interactions aretapered with a smoothing function at the cutoff.

Calculating electrostatic forces from grid-calculated potentials

Abstract: The accurate calculation of forces from finite difference potentials is very important, especially in the area of Brownian dynamics simulations. Test charge methods are typically used to calculate these forces. In these methods, the potential is calculated with one group of charges present, then the force on a second set of charges is calculated as the negative of the gradient of the potential times the charge. The test charge methods for calculating forces between solute molecules have been compared with more accurate methods and then regions of validity of the test charge methods explored. The test charge methods neglect certain reaction field effects. It is found for the simple charged systems studied that beyond a center-to-center separation of about twice the sum of the molecular radii the test charge approximations can be quite good. For polar molecules with no net charges, however, the corrections can be significant to even longer ranges.

A space-saving modification of Davidson's eigenvector algorithm

Abstract: A modification of Davidson's eigenvalue algorithm, based on the conjugate gradient method, is described. This method needs storage only for a few vectors (five to seven, depending on the implementation), making it practical for very large problems where disk storage is the limiting factor, without the necessity of restarting or discarding some expansion vectors. The convergence characteristics of the modified method are essentially identical with those of the original Davidson method if all expansion vectors are retained in the latter.

Combinatorial models and algorithms in chemistry. The expanded Wiener number—a novel topological index

Abstract: An expanded form of the Wiener number is suggested for characterization of molecular graphs and structure-property correlations. The simple, computer-oriented method for counting of the novel index is briefly discussed.

Relaxed potential energy surfaces of N‐linked oligosaccharides: The mannose‐α(1 → 3)‐mannose case

Abstract: We report calculations of potential energy surfaces where all the internal coordinates of the disaccharide Man-α(1 → 3)-Man-α-O-Me were relaxed and minimized through an extensive molecular mechanics scheme. Flexibility within the mannopyranose rings plays a crucial role. Introduction of the relaxed principle into the conformational description of the disaccharide does not greatly alter the overall shape of the low-energy domains but it reveals new local minima. However, its principle effect is the lowering of energy barriers in the potential energy surface. New conformational transitions about the glycosidic bonds appear, permiting pathways among the low energy sections. This occurs with only little variation of the classical 4C1 conformation of the mannopyranose residues. All the conformations observed in the solid state, along with those already predicted through the joint use of NMR and modeling techniques, fall into the populations of stable conformers calculated in the present work. Moreover, a satisfactory agreement is reached between previously observed NOE values, and the theoretical one, calculated from the averaging of more than 500 microstates. The present results reconciliate most of the apparently conflicting data previously reported; they provide strong support for the application of the concept of conformational averaging to solution behavior. Some limitations of the proposed methodology are also discussed.

Tautomeric equilibria of heterocyclic molecules.: a test of the semiempirical AM1 and MNDO-PM3 methods

Abstract: Tautomeric equilibria (mainly of the lactam-lactim type) for a rather large number of six-membered heterocyclic molecules are calculated by the semiempirical AM1, MNDO-PM3, and MNDO methods. Except for compounds with adjacent pyridine-like lone pairs both AM1 as well as MNDO-PM3 give rather reliable predictions for relative stabilities of the various tautomeric species–comparable to quite high level ab initio calculations. The known errors associated with MNDO in the treatment of heterocyclic tautomerism are thus largely corrected in AM1 as well as MNDO-PM3. For 2-hydroxypyridine-pyrid-2(1H)-one the effect of self-association is less satisfactorily described by MNDO-PM3 than by AM1. MNDO-PM3 calculated relative stabilities of methylated derivatives are, however, in considerably closer agreement with experimental values than those obtained by AM1. Ionization potentials, especially those for lone-pair orbitals, are overestimated by all three semiempirical methods. MNDO-PM3 results for nitrogen lone-pair orbital energies are slightly better than those obtained by the AM1 or MNDO method.

Protein structure prediction using a combination of sequence homology and global energy minimization I. Global energy minimization of surface loops

Abstract: A procedure has been developed for global energy minimization of surface loops of proteins in the presence of a fixed core. The ECEPP potential function has been modified to allow more accurate representations of hydrogen bond interactions and intrinsic torsional energies. A computationally efficient representation of hydration free energy has been introduced. A local minimization procedure has been developed that uses a cutoff distance, minimization with respect to subsets of degrees of freedom, analytical second derivatives, and distance constraints between rigid segments to achieve efficiency in applications to surface loops. Efficient procedures have been developed for deforming segments of the initial backbone structure and for removing overlaps. Global energy minimization of a surface loop is accomplished by generating a sequence (or a trajectory) of local minima, the component steps of which are generated by searching collections of local minima obtained by deforming seven‐residue segments of the surface loop. The search at each component step consists of the following calculations: (1) A large collection of backbone structures is generated by deforming a seven‐residue segment of the initial backbone structure. (2) A collection of low‐energy backbone structures is generated by applying local energy minimization to the resulting collection of backbone structures (interactions involving side chains that will be searched in this component step are not included in the energy). (3) One low‐energy side‐chain structure is generated for each of the resulting low‐energy backbone structures. (4) A collection of low‐energy local minima is generated by applying local energy minimization to the resulting collection of structures. (5) The local minimum with the lowest energy is retained as the next point of the trajectory. Applications of our global search procedure to surface segments of bovine pancreatic trypsin inhibitor (BPTI) and bovine trypsin suggest that component‐step searches are reasonably complete. The computational efficiency of component‐step searches is such that trajectories consisting of about 10 component steps are feasible using an FPS‐5200 array processor. Our procedure for global energy minimization of surface loops is being used to identify and correct problems with the potential function and to calculate protein structure using a combination of sequence homology and global energy minimization.

SCF, MP2, and CEPA-1 calculations on the OH..O hygrogen bonded complexes (H 2 O) 2 and (H 2 O--H 2 CO)

Abstract: Counterpoise corrected ab initio calculations are reported for (H2O)2 and H2O-H2CO. Geometry searches were done in the moment-optimized basis DZP' at the SCF, MP2, and CEPA-1 levels of theory, followed by more accurate single-point calculations in basis ESPB, which includes bondfunctions to saturate the dispersion energy. The final equilibrium binding energies obtained are −4.7 ±0.3 kcal/mol for a near-linear (H2O)2 structure and −4.6 ±0.3 kcal/mol for a strongly bent HOH ‥ OCH2 structure. The energy difference between these systems is much smaller than in all previous ab initio work. Cyclic (C2h) and bifurcated (C2v) transition structures for (H2O)2 are located at 1.0 ±0.1 kcal/mol and 1.9 ±0.3 kcal/mol above the global minimum, respectively. A new partitioning scheme is presented that rigorously partitions the MP2 correlation interaction energy in intra and intermolecular (dispersion) contributions. These terms are large (up to 2 kcal/mol) but of opposite sign for most geometries studied and hence their overall effect upon the final structures is relatively small. The relative merits of the MP2 and CEPA-1 approaches are discussed are discussed and it is concluded that for economical reasons MP2 is to be preferred, especially for larger systems.

A critical comparison of MINDO/3, MNDO, AM1, and PM3 for a model problem carbon clusters C 2 -C 10 : An ad hoc reparametrization of MNDO well suited for the accurate prediction of their spectroscopic constants

Abstract: Dissociation energies and potential energy surface features for the carbon clusters C2 to C10 are compared with ab initio or experimental results for the semiempirical methods MINDO/3, MNDO, AM1, and PM3. Quite surprisingly, MINDO/3 gives a rather good account of the various structures and electronic states, unlike the other three methods. MINDO/3 tends towards systematic overestimates of binding energies, the other methods to systematic gross underestimates. Reparametrization of the diatomic parameters α, βs, and βp for exact reproduction of the experimental data for C3 results in much improved values for binding energies, but fails to correct the state splittings. Also reparametrizing Uss, Upp, ζs, and ζp to reproduce the ab initio linear-rhombic energy difference in C4 results in a much improved description of the other states. For the linear structures, computed harmonic frequencies with the latter parameters are in surprisingly good agreement with experimental or correlated ab initio data, where available; experimental values are consistently overestimated by about 40 cm−1. Other results are comparable in quality to good ab initio treatments. The experimental IR bands at 2128 and 1892 cm−1, formerly assigned to C9, should be reassigned to linear C7. The intense 1997 cm−1 feature almost certainly belongs to C9; bands at 1952 and 1197 cm−1 both belong to linear C6. Tentative assignments of bands in the 1600–1850 cm−1 region to various cyclic structures of C6, C8, and C10 have been made. As such, this suggests a new and promising procedure for the theoretical study of large molecules in general, and of large clusters in particular.

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

Abstract: 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.

Comments on a comparison of AM1 with the recently developed PM3 method

Abstract: A reparameterized version (PM3) of AM1 has recently been reported and the results for several hundred molecules compared with those from AM1 itself. The comparison implied that PM3 represents a significant improvement over the earlier treatment. The apparently poor performance of AM1 is, however, due to the inclusion of “AM1 results” for elements (A1,P,S) for which AM1 parameters were unavailable. If these are omitted, PM3 is seen to be only marginally better than AM1. Since this conclusion refers only to a specific set of stable molecules, it is not clear whether even this small improvement will apply to other species or studies of reactions. It is in any case insufficient to justify the confusion caused by the release of the new treatment.