Showing papers in "Journal of Computational Chemistry in 1999"

The GROMOS biomolecular simulation program package

Abstract: We present the newest version of the GROningen MOlecular Simulation program package, GROMOS96. GROMOS96 has been developed for the dynamic modelling of (bio)molecules using the methods of molecular dynamics, stochastic dynamics, and energy minimization as well as the path-integral formalism. An overview of its functionality is given, highlighting methodology not present in the last major release, GROMOS87. The organization of the code is outlined, and reliability, testing, and efficiency issues involved in the design of this large (73 000 lines of FORTRAN77 code) and complex package are discussed. Finally, we present two applications illustrating new functionality: local elevation simulation and molecular dynamics in four spatial dimensions.

Chemical reactivity indexes in density functional theory

Abstract: The theoretical description of charge distribution, and related properties, such as chemical reactivity descriptors of chemical compounds, has greatly benefited from the development of density functional theory (DFT) methods. Indeed, most concepts stemmed from DFT but, up to now, they have been used mostly within semiempirical MO methods, Hartree–Fock, or post-Hartree–Fock methods. During the last decade, however, DFT has enabled theoretical chemistry to predict accurately structures and energetics of clusters and molecules. Therefore, more attention should also now be paid to these reactivity descriptors determined directly from DFT calculations. In this work, chemical reactivity is explored in DFT through a functional Taylor expansion of energy that introduces various energy derivatives of chemical significance. This review summarizes their main features and examines the limitations of some indexes presently used for the characterization of reactivity. Also, several perspectives are given. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 129–154, 1999

MMFF VI. MMFF94s option for energy minimization studies

Abstract: This article describes the derivation of MMFF94s, which is the “s” (static) variant of MMFF94. MMFF94s incorporates altered out of plane bending parameters that yield planar (or nearly planar) energy-minimized geometries at unstrained delocalized trigonal nitrogen centers. Some experimental and most theoretical structures show appreciable puckering at nitrogen in isolated structures. However, condensed-phase effects or even strong intermolecular hydrogen bonding tends to reduce, but need not eliminate, such puckering; in contravention to results reported on the lower level Hartree–Fock surface, we show in the correlated LMP2/6-31G** calculations for the Watson–Crick guanine–cytosine base pair that one of the hydrogen-bonded NH2 groups remains appreciably puckered. The resultant MMFF94s geometries emulate the “time-averaged” structures typically observed in crystallographic and most other experimental structure determinations. MMFF94s also employs modified torsion parameters for interactions that involve such centers, but is identical to MMFF94 for other systems. Isolated instances are found in which MMFF94s fails to locate a (probably shallow) local minimum found on the MMFF94 and reference MP2/6-31G* surfaces. In general, however, MMFF94s describes conformation energies for delocalized trigonal nitrogen systems nearly as well as MMFF94 does. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 720–729, 1999

Approximate atomic surfaces from linear combinations of pairwise overlaps (lcpo)

Abstract: A fast analytical formula was derived for the calculation of approximate atomic and molecular van der Waals (vdWSA), and solvent-accessible surface areas (SASAs), as well as the first and second derivatives of these quantities with respect to atomic coordinates. This method makes use of linear combinations of terms composed from pairwise overlaps of hard spheres; therefore, we term this the LCPO method for linear combination of pairwise overlaps. For higher performance, neighbor-list reduction (NLR) was applied as a preprocessing step. Eighteen compounds of different sizes (8–2366 atoms) and classes (organic, proteins, DNA, and various complexes) were chosen as representative test cases. LCPO/NLR computed the SASA and first derivatives of penicillopepsin, a protein with 2366 atoms, in 0.87 s (0.22 s for the creation of the neighbor list, 0.35 s for NLR, and 0.30 s for SASA and first derivatives) on an SGI R10000/194 Mhz processor. This appears comparable to or better than timings reported previously for other algorithms. The vdWSAs were in good agreement with the numerical results: relative errors for total molecular surface areas ranged from 0.1 to 2.0% and average absolute atomic surface area deviations from 0.3 to 0.7 A2. For SASAs without NLR, the LCPO method exhibited relative errors in the range of 0.4–9.2% for total molecular surface areas and average absolute atomic surface area deviations of 2.0–2.7 A2; with NLR the relative molecular errors ranged from 0.1 to 7.8% and the average absolute atomic surface area deviation from 1.6 to 3.0 A2. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 217–230, 1999

Broken symmetry approach to calculation of exchange coupling constants for homobinuclear and heterobinuclear transition metal complexes

Abstract: The application of broken symmetry density functional calculations to homobinuclear and heterobinuclear transition metal complexes produces good estimates of the exchange coupling constants as compared to experimental data. The accuracy of different hybrid density functional theory methods was tested. A discussion is presented of the different methodological approaches that apply when a broken symmetry wave function is used with either Hartree–Fock or density functional calculations. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1391–1400, 1999

Improving efficiency of large time-scale molecular dynamics simulations of hydrogen-rich systems

Abstract: A systematic analysis is performed on the effectiveness of removing degrees of freedom from hydrogen atoms andror increasing hydrogen masses to increase the efficiency of molecular dynamics simulations of hydrogen-rich systems such as proteins in water. In proteins, high-frequency bond-angle vibrations involving hydrogen atoms limit the time step to 3 fs, which is already a factor of 1.5 beyond the commonly used time step of 2 fs. Removing these degrees of freedom from the system by constructing hydrogen atoms as dummy atoms, allows the time step to be increased to 7 fs, a factor of 3.5 compared with 2 fs. Additionally, a gain in simulation stability can be achieved by increasing the masses of hydrogen atoms with remaining degrees of freedom from 1 to 4 u. Increasing hydrogen mass without removing the high-frequency degrees of freedom allows the time step to be increased only to 4 fs, a factor of two, compared with 2 fs. The net gain in efficiency of sampling configurational space may be up to 15% lower than expected from the increase in time step due to the increase in viscosity and decrease in diffusion constant. In principle, introducing dummy atoms and increasing hydrogen mass do not influence thermodynamical properties of the system and dynamical properties are shown to be influenced only to a moderate degree. Comparing the maximum . time step attainable with these methods 7 fs to the time step of 2 fs that is routinely used in simulation, and taking into account the increase in viscosity and decrease in diffusion constant, we can say that a net gain in simulation efficiency of a factor of 3 to 3.5 can be achieved. Q 1999 John Wiley & Sons, Inc. J Comput Chem 20: 786)798, 1999

MMFF VII. Characterization of MMFF94, MMFF94s, and other widely available force fields for conformational energies and for intermolecular‐interaction energies and geometries

Abstract: This article provides extensive comparisons for the MMFF94, MMFF94s, CFF95, CVFF, MSI CHARMm, AMBER*, OPLS*, MM2*, and MM3* force fields to experimental and high-quality ab initio data for conformational energies and to scaled ab initio data for hydrogen-bonded complexes. Some comparisons are also presented for CHARMM 22. The tests of conformational energies consisted of two sets of comparisons to experiment and one more extensive set of comparisons to relatively high-quality ab initio data. As in the derivation of MMFF94, scaled HF/6-31G* energies and geometries were used to assess the reasonableness of the calculated intermolecular interaction energies and geometries. The comparisons for intermolecular interactions appear to be the first broadly based comparisons to appear in the chemical literature. Taken together, the comparisons reveal that most of the force fields make sizable errors and frequently produce qualitatively incorrect results for both conformational and intermolecular-interaction energies. For example, three of the force fields produce individual errors in conformational energy of more than 10 kcal/mol, and four rate thiophene as a stronger hydrogen-bond acceptor than ammonia. Only MMFF94 and MMFF94s perform consistently well. Some MMFF deficiencies are apparent, however, particularly for conformational energies of halocyclohexanes. These deficiencies, and others recently found for condensed-phase simulations, will need to be addressed in any future reparameterization of MMFF. The quantum-chemical data used in this work have been placed on the Computational Chemistry List web site. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 730-748, 1999.

Understanding reactivity with Kohn–Sham molecular orbital theory: E2–SN2 mechanistic spectrum and other concepts

Abstract: On the basis of Kohn–Sham density functional (DFT) investigations on elementary organic and organometallic reactions, we show how a detailed understanding of the electronic structure of a reaction system can help recognize certain characteristics of the process, yielding valuable mechanistic concepts. The concept of the base as a selective catalyst in E2 eliminations, for example, leads to a straightforward explanation for the general preference for anti over syn stereochemistry in base-induced elimination reactions. Furthermore, electronic structure considerations provide the so-called E2–SN2 mechanistic spectrum, in terms of which one can interpret and understand the competition between elimination and substitution reactions and the shift, on solvation, of the reactivity from E2 to SN2. In addition, mechanistic concepts from organometallic and organic chemistry are linked as we argue that oxidative addition may be conceived, in some respect, as the organometallic analog of the frontside SN2 substitution. Finally, we introduce the ideas of “activation strain” of and “transition state interaction” between the deformed reactants in the activated complex, which together determine the activation energy, ΔE*=ΔE+ΔE. They prove to be helpful conceptual tools for understanding in detail how activation barriers and relative efficiencies of competing reaction mechanisms arise and how they may be affected (e.g., by changing reactants or by solvation). © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 114–128, 1999

Mixed ab initio QM/MM modeling using frozen orbitals and tests with alanine dipeptide and tetrapeptide

Abstract: Methodology is discussed for mixed ab initio quantum mechanics/molecular mechanics modeling of systems where the quantum mechanics (QM) and molecular mechanics (MM) regions are within the same molecule. The ab initio QM calculations are at the restricted Hartree–Fock level using the pseudospectral method of the Jaguar program while the MM part is treated with the OPLS force fields implemented in the IMPACT program. The interface between the QM and MM regions, in particular, is elaborated upon, as it is dealt with by “breaking” bonds at the boundaries and using Boys-localized orbitals found from model molecules in place of the bonds. These orbitals are kept frozen during QM calculations. Results from tests of the method to find relative conformational energies and geometries of alanine dipeptides and alanine tetrapeptides are presented along with comparisons to pure QM and pure MM calculations. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1468–1494, 1999

The DFT route to NMR chemical shifts

Abstract: An overview is given of the recent development and use of density functional methods in nuclear magnetic resonance (NMR) chemical-shift calculations. The available density functional theory (DFT) methods are discussed, and examples for their validation and application are given. Relativistic effects are also considered, with an emphasis on spin–orbit coupling. The systems discussed range from transition-metal complexes and clusters via biological systems and fullerenes to weakly bound van der Waals molecules. DFT results not published previously comprise spin–orbit effects on 31P chemical shifts in phosphorus halides, the orientation of the 31P-shift tensor in Ru4(PPh)(CO)13, δ(95Mo) data, 13C and endohedral chemical shifts for fullerenes and for C60H36, as well as the shielding surface of the Ne2 molecule. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 91–105, 1999

Solution of three-dimensional reference interaction site model and hypernetted chain equations for simple point charge water by modified method of direct inversion in iterative subspace

Abstract: We proposed a modified procedure of the direct inversion in the iterative subspace (DIIS) method to accelerate convergence in the integral equation theory of liquids. We update the DIIS basis vectors at each iterative step by using the approximate residual obtained in the DIIS extrapolation. The procedure is tested by solving the 3-dimensional (3-D) generalization of the reference interaction site model equation together with the hypernetted chain closure, as well as their 1-D version. We calculated the 3-D site distribution of water, represented by the simple point charge model, around one water molecule considered as a central particle. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 928–936, 1999

Density functional calculations on actinide compounds: Survey of recent progress and application to [UO2X4]2− (X=F, Cl, OH) and AnF6 (An=U, Np, Pu)

Abstract: The subject of this article, the application of density functional theory (DFT) to molecular systems containing actinide elements, is discussed in two parts. In the first part, a survey is given of DFT applications on actinide containing molecules. Various methodological developments are reviewed, including, among others, new relativistic effective core potentials ECP, and newly developed stable relativistic DFT methods. Actual DFT calculations of actinide molecular systems are discussed, covering the time from about 1991 to the present. In the second part, two different DFT-based relativistic methods are applied to some actinide molecules.

Fast computation, rotation, and comparison of low resolution spherical harmonic molecular surfaces

Abstract: A procedure that rapidly generates an approximate parametric representation of macromolecular surface shapes is described. The parametrization is expressed as an expansion of real spherical harmonic basis functions. The advantage of using a parametric representation is that a pair of surfaces can be matched by using a quasi-Newton algorithm to minimize a suitably chosen objective function. Spherical harmonics are a natural and convenient choice of basis function when the task is one of search in a rotational search space. In particular, rotations of a molecular surface can be simulated by rotating only the harmonic expansion coefficients. This rotational property is applied for the first time to the 3-dimensional molecular similarity problem in which a pair of similar macromolecular surfaces are to be maximally superposed. The method is demonstrated with the superposition of antibody heavy chain variable domains. Special attention is given to computational efficiency. The spherical harmonic expansion coefficients are determined using fast surface sampling and integration schemes based on the tessellation of a regular icosahedron. Low resolution surfaces can be generated and displayed in under 10 s and a pair of surfaces can be maximally superposed in under 3 s on a contemporary workstation. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 383–395, 1999

Global cluster geometry optimization by a phenotype algorithm with niches : location of elusive minima, and low-order scaling with cluster size

Abstract: The problem of global geometry optimization of clusters is addressed with a phenotype variant of the method of genetic algorithms, with several novel performance enhancements. The resulting algorithm is applied to Lennard–Jones clusters as benchmark system, with up to 150 atoms. The well-known, difficult cases involving nonicosahedral global minima can be treated reliably using the concept of niches. The scaling of computer time with cluster size is approximately cubic, which is crucial for future applications to much larger clusters. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 1752–1759, 1999

Full four‐component relativistic calculations of NMR shielding and indirect spin–spin coupling tensors in hydrogen halides

Abstract: Various methods for the inclusion of relativistic effects in the calculation of NMR parameters are discussed. Benchmark values for the NMR shieldings and indirect nuclear spin–spin coupling tensors for the hydrogen halides are calculated using the four-component relativistic random phase approximation method. Apart from recovering the well-known trend of increasing hydrogen isotropic shielding going from HF to HI, we also find a large effect on the anisotropy that decreases along this series. Inclusion of spin-orbit coupling in a nonrelativistic formalism suffices to recover both effects on the hydrogen shieldings but fails to reproduce the much larger effect on the halogen shieldings. This effect can be explained by considering the relativistic mass-velocity operator that contains correction terms to the nonrelativistic magnetic field operators. We recommend routine inclusion of the one-electron spin-orbit correction in calculations of hydrogen shieldings for hydrogens bonded to heavy atoms. For the heavy nucleus shielding one should include an additional mass-velocity correction. The relativistic effect on the indirect nuclear spin–spin coupling tensor is large and affects mainly the isotropic values; the effect on the anisotropy is small. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1262–1273, 1999

BLEEP—potential of mean force describing protein–ligand interactions: I. Generating potential

Abstract: We have developed BLEEP (biomolecular ligand energy evaluation protocol), an atomic level potential of mean force (PMF) describing protein–ligand interactions The pair potentials for BLEEP have been derived from high-resolution X-ray structures of protein–ligand complexes in the Brookhaven Protein Data Bank (PDB), with a careful treatment of homology The use of a broad variety of protein–ligand structures in the derivation phase gives BLEEP more general applicability than previous potentials, which have been based on limited classes of complexes, and thus represents a significant step forward We calculate the distance distributions in protein–ligand interactions for all 820 possible pairs that can be chosen from our set of 40 different atom types, including polar hydrogen We then use a reverse Boltzmann methodology to convert these into energy-like pair potential functions Two versions of BLEEP are calculated, one including and one excluding interactions between protein and water The pair potentials are found to have the expected forms; polar and hydrogen bonding interactions show minima at short range, around 30 A, whereas a typical hydrophobic interaction is repulsive at this distance, with values above 40 A being preferred ©1999 John Wiley & Sons, Inc J Comput Chem 20: 1165–1176, 1999

Low-mode conformational search elucidated : application to c39h80 and flexible docking of 9-deazaguanine inhibitors into pnp

Abstract: We previously described a new conformational search method, termed low-mode search (LMOD), and discussed its utility for conformational searches performed on cycloalkanes and a cyclic penta-peptide.1 In this report, we discuss a rigorous implementation of mode following (c-LMOD) for conformational searching, and we demonstrate that for a conformational search involving cycloheptadecane, this rigorous implementation is capable of finding all of the previously known structures. To the best of our knowledge, this is the first computational proof that mode following can be used for conformational searches conducted on a complex molecular system. We show, however, that, as expected, it is generally inefficient to perform a conformational search in this manner. Nonetheless, c-LMOD has been shown to be an excellent method for conducting conformational analyses involving conformational interconversions, where the location of saddle points is important. We also describe refinement to our original LMOD procedure (l-LMOD) and discuss its utility for a difficult conformational search problem, namely locating the global minimum energy conformation of C39H80. For this search, l-LMOD combined with limited torsional Monte Carlo movement was able to locate the lowest energy structures yet reported, and significantly outperformed a pure torsional Monte Carlo and a genetic algorithm-based search. Furthermore, we also demonstrate the utility of l-LMOD combined with random translation/rotation of a ligand for the extremely difficult problem of docking flexible ligands into flexible protein binding sites on a system that includes 9-deaza-guanine-based inhibitors docked into the flexible biding site of PNP. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1671–1684, 1999

From Explicit to Implicit Density Functionals

Abstract: The concept of orbital- and eigenvalue-dependent exchange- . correlation xc energy functionals is reviewed. We show how such functionals can be derived in a systematic fashion via a perturbation expansion, utilizing the Kohn)Sham system as a noninteracting reference system. We demonstrate that the second-order contribution to this expansion of the xc-energy functional includes the leading term of the van der Waals interaction. The optimized- . potential method OPM , which allows the calculation of the multiplicative xc-potential corresponding to an orbital- and eigenvalue-dependent xc-energy functional via an integral equation, is discussed in detail. We examine an approximate analytical solution of the OPM integral equation, pointing out that, for eigenvalue-dependent functionals, the three paths used in the literature for the derivation of this approximation yield different results. Finally, a number of illustrative results, both for the exchange-only limit and for the combination of the exact exchange with various correlation functionals, are given. Q 1999 John Wiley & Sons, Inc. J Comput Chem 20: 31)50, 1999

United atom force field for phospholipid membranes: Constant pressure molecular dynamics simulation of dipalmitoylphosphatidicholine/water system

Abstract: We refined the united atom field for the simulations of phospholipid membranes. To validate this potential we performed 1000-ps constant pressure simulation of a dipalmitoylphosphatidicholine (DPPC) bilayer at T=50° C. The average area per head group (61.6±0.6) A2 obtained in our simulation agrees well with the measured one of (62.9±1.3) A2. The calculated SCD order parameters for the Sn-2 hydrocarbon tail also display a good agreement with the experiment. The conformations of head groups in our simulations of the liquid crystal phase are different than the ones observed in the crystal structure. ©1999 John Wiley & Sons, Inc. J Comput Chem 20, 531–545, 1999

Consistent modifications of SINDO1: I. Approximations and parameters

Abstract: A consistent modification, MSINDO, of the semiempirical MO method SINDO1 is presented. Different basis sets are used for one- and two-center interactions. The treatment of the core matrix elements in the nonorthogonal basis is retained with changes only for hydrogen and 3d orbitals. Orthogonalization corrections are now restricted to nonvanishing core matrix elements in the INDO approximation. The set of atomic parameters is increased, but bond parameters are no longer used. An automatic nonlinear least-squares algorithm with a restricted step constraint is used for the optimization of parameters. Heats of formation are adjusted with inclusion of zero-point energies obtained by a scaling procedure of the force constant matrix. The present version MSINDO provides significant improvements over previous versions. A brief comparison for ground-state properties of the elements H, C, N, O, F, and Na to Cl is given. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 563–571, 1999

Automatic Parameterization of Force Fields for Liquids by Simplex Optimization

Abstract: In this study we demonstrate an automatic method of force field development for molecular simulations. Parameter tuning is taken as an optimization problem in many dimensions. The parameters are automatically adapted to reproduce known experimental data such as the density and the heat of vaporization. Our method is more systematic than guessing parameters and, at the same time, saves human labor in parameterization. It was applied successfully to several molecular liquids. As a test, force fields for 2-methylpentane, tetrahydrofurane, cyclohexene, and cyclohexane were developed. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1009–1017, 1999

Importance of selecting proper basis set in quantum mechanical studies of potential energy surfaces of carbohydrates

Abstract: An extensive quantum mechanical study of a water dimer suggests that the introduction of a diffuse function into the basis set, which significantly reduces the basis set superposition error (BSSE) in the hydrogen bonding energy calculation, is the key to better calculations of the potential energy surfaces of carbohydrates. This article examines the potential energy surfaces of selected d-aldo- and d-ketohexoses (a total of 82 conformers) by quantum mechanics (QM) and molecular mechanics (MM) methods. In contrast to the results with a smaller basis set (B3LYP/6-31G** 5d), we found at the higher level calculation (B3LYP/6-311++G(2d,2p)//B3LYP/6-31G** 5d) that, in most cases, the furanose forms are less stable than the pyranose forms. These discrepancies are mainly due to the fact that intramolecular hydrogen bonding energies are overestimated in the lower level calculations. The higher level QM calculations of the potential energy surfaces of d-aldo- and d-ketohexoses now are more comparable to the MM3 results. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1593–1603, 1999

Vibrational spectra of nucleic acid bases and their Watson–Crick pair complexes

Abstract: The vibrational spectra of the nucleic acid bases adenine, thymine, guanine, and cytosine are calculated in the frame of density functional theory .DFT . In particular we use the Kohn)Sham scheme with gradient corrections for exchange and correlation to determine normal modes, frequencies, and intensities. The DFT results are found to be in good agreement with the experiment. Our computations provide assignments for IR, Raman, and neutron inelastic scattering spectroscopies; yield characteristic vibrational fingerprints of each compound for its identification in larger systems; and show general vibrational trends of nucleic acids. The Kohn)Sham scheme is further applied to obtain the spectra of the Watson)Crick pairs adenine-thymine and guanine- cytosine. A large number of monomeric vibrations are recognized in dimers; characteristic vibrations of pairs, which are mainly attributed to hydrogen bridges, are quantified according to changes in normal modes and frequency shifts. Binding and zero-point vibrational energies are analyzed to establish the stability of the complexes and discuss the quality of the energetic calculations. Q 1999 John Wiley & Sons, Inc. J Comput Chem 20: 511)530, 1999

Exact analytical loop closure in proteins using polynomial equations

Abstract: Loop closure in proteins has been studied actively for over 25 years. Using spherical geometry and polynomial equations, several loop-closure problems in proteins are solved exactly by reducing them to the determination of the real roots of a polynomial. Loops of seven, eight, and nine atoms are treated explicitly, including the tripeptide and disulfide-bonded loop-closure problems. The number of valid loop closures can be evaluated by the method of Sturm chains, which counts the number of real roots of a polynomial. Longer loops can be treated by three methods: by sampling enough dihedral angles to reduce the problem to a soluble loop-closure problem; by applying the loop-closure algorithm hierarchically; or by decimating the chain into independently moving rigid elements that can be reconnected using loop-closure algorithms. Applications of the methods to docking, homology modeling and NMR problems are discussed. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 819–844, 1999

Topological analysis of electron density in depleted homopolar chemical bonds

Abstract: Except for the case of van der Waals interactions, homopolar bonds are covalent and therefore a concentration of the electron density is expected at the bond midpoint. Many experimental and theoretical studies have reported standard deformation density maps and molecular density minus spherical atoms densities, which show a depletion of electron density between formally covalently bonded atoms. For example, electron deficits are found in the theoretical map of the FF bond in F2, in the experimental map of the NN bond in carbonohydrazide, and in the experimental and theoretical maps of the OO bond in 1,2,7,8-tetraaza-4,5,10,11-tetraoxatricyclo[6.4.1.1]tetradecane. Other partitioning schemes, such as subtraction of valence state atoms rather than spherical atoms from the total density, have been proposed to interpret these unexpected features. In the present work we examine these electronically depleted covalent bonds on the basis of the topological analysis of the electron localization function (ELF) of theoretically calculated electron densities. The attractors of ELF determine basins that are either core or valence basins. The valence basins are characterized by the number of core basins with which they share a common boundary, and this number is called the synaptic order. Disynaptic valence basins have been found for the FF bond in F2, for the NN bond in carbonohydrazide and for the OO bond in 1,2,7,8-tetraaza-4,5,10,11- tetraoxatricyclo[6.4.1.1]tetradecane. In the case of F2, polarization functions increase the V(F, F′) basin population, whereas accounting for the Coulomb correlation lowers this basin population. The results calculated for F2 are compared with those obtained for other diatomic molecules, such as N2 and O2, and the ELF picture of the bond compared with the molecular orbital analysis. In the case of carbonohydrazyde, the V(N, N′) basin population is the lowest among all the populations of the disynaptic valence basins present in the molecule, in good agreement with the experimental observations. Analogous results are obtained for the V(O, O′) basin population in 1,2,7,8-tetraaza-4,5,10,11- tetraoxatricyclo[6.4.1.1]tetradecane. Population fluctuation analysis indicates a strong delocalization of the electron density toward lone pairs and adjacent bonds. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1517–1526, 1999

Optimization and analysis of force field parameters by combination of genetic algorithms and neural networks

Abstract: In search of a force field description for tripod metal templates, tripodM [tripod=RC(CH2X)(CH2Y)(CH2Z); X, Y, Z=PR′R″] force field parameters, p, were optimized by the use of genetic algorithms (GA) with the structures of ten compounds, tripodMo(CO)3, serving as the database. It was found that the evaluation of the fitness criterion, based on the root‐mean‐square deviation (rms) between observed and calculated structures by force field methods, is actually the time‐consuming step under this optimization protocol. It is shown now how this time‐consuming step may in part be substituted by using a trained neural network (NN) as the evaluating function. The network is trained on the basis of parameter vectors that have been evaluated previously with respect to their corresponding rms values during several preceding generations of a GA run. The network function, rms=f(p), thus built up is able to calculate the rms corresponding to a specific parameter vector within milliseconds, whereas obtaining the same result by molecular mechanics methods takes several minutes for the problem at hand and with the equipment used. Therefore, significant time savings may be expected using a combination of GA optimization and NN simulation In addition, the simulated function, rms=f(p), allows for insights into the dependence of the rms value on specific parameters or combinations thereof. Kohonen mapping is used as a tool to visualize such dependence. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 455–471, 1999

Toward the description of van der Waals interactions within density functional theory

Abstract: On the basis of the adiabatic connection formula we propose several approximations for the total correlation energy functional, which, in the limit of two separated neutral subsystems, correctly reproduce the van der Waals R−6 behavior. We have calculated the corresponding van der Waals coefficients as well as total correlation energies, thus demonstrating the feasibility of a “seamless” functional. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 12–22, 1999

Consistent modifications of SINDO1: II. Applications to first‐ and second‐row elements

Abstract: A statistical evaluation of ground state properties for first‐row and second‐row elements is presented. The present version MSINDO is compared with the previous version SINDO1 and other standard semiempirical methods. Significant improvements are achieved for heats of formation, bond lengths, bond angles, and ionization energies by MSINDO, which is now again competitive with other semiempirical methods. An extrapolation to bulk properties is given for ionic clusters of NaCl and MgO to demonstrate the transferability of the parameterization to large systems. Improvements for the electronic structure of compounds containing second‐row elements are demonstrated with the MO diagram of an NaCl cluster with an F‐center defect. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 572–578, 1999

BLEEP—potential of mean force describing protein–ligand interactions: II. Calculation of binding energies and comparison with experimental data

Abstract: We have developed BLEEP (biomolecular ligand energy evaluation protocol), an atomic level potential of mean force (PMF) describing protein–ligand interactions. Here, we present four tests designed to assess different attributes of BLEEP. Calculating the energy of a small hydrogen‐bonded complex allows us to compare BLEEP's description of this system with a quantum‐chemical description. The results suggest that BLEEP gives an adequate description of hydrogen bonding. A study of the relative energies of various heparin binding geometries for human basic fibroblast growth factor (bFGF) demonstrates that BLEEP performs excellently in identifying low‐energy binding modes from decoy conformations for a given protein–ligand complex. We also calculate binding energies for a set of 90 protein–ligand complexes, obtaining a correlation coefficient of 0.74 when compared with experiment. This shows that BLEEP can perform well in the difficult area of ranking the interaction energies of diverse complexes. We also study a set of nine serine proteinase–inhibitor complexes; BLEEP's good performance here illustrates its ability to determine the relative energies of a series of similar complexes. We find that a protocol for incorporating solvation does not improve correlation with experiment. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1177–1185, 1999

PRODOCK: Software Package for Protein Modeling and Docking

Abstract: A new software package, PRODOCK, for protein modeling and flexible docking is presented. The protein system is described in internal coordinates with an arbitrary level of flexiblity for the proteins or ligands. The protein is represented by an all-atom model with the ECEPPr 3o r A MBER IV force field, depending on whether the ligand is a peptidic molecule or not. PRODOCK is based on a new residue data dictionary that makes the programming easier and the definition of molecular flexibility more straigthforward. Two versions of the dictionary have been constructed for the ECEPPr3 and AMBER IV geometry, respectively. The global optimization of the energy function is carried out with the scaled collective variable Monte Carlo method plus energy minimization. The incorporation of a local minimization during the conformational sampling has been shown to be very important for distinguishing low-energy nonnative conformations from native structures. To make the Monte Carlo minimization method efficient for docking, a new grid-based energy evaluation technique using Bezier splines has been incorporated. This article includes some techniques and simulation tools that significantly improve the efficiency of flexible docking simulations, in particular forwardrbackward polypeptide chain generation. A comparative study to illustrate the advantage of using quaternions over Euler angles for the rigid-body rotational variables is presented in this paper. Several applications of the program PRODOCK are also discussed. Q 1999 John Wiley & Sons, Inc. J Comput Chem 20: 412)427, 1999