Boundary element solution of the linear Poisson-Boltzmann equation and a multipole method for the rapid calculation of forces on macromolecules in solution

The Poisson-Boltzmann equation is widely used to describe the electrostatic potential of molecules in an ionic solution that is treated as a continuous dielectric medium. The linearized form of this equation, applicable to many biologic macromolecules, may be solved using the boundary element method. A single-layer formulation of the boundary element method, which yields simpler integral equations than the direct formulations previously discussed in the literature, is given. It is shown that the electrostatic force and torque on a molecule may be calculated using its boundary element representation and also the polarization charge for two rigid molecules may be rapidly calculated using a noniterative scheme. An algorithm based on a fast adaptive multipole method is introduced to further increase the speed of the calculation. This method is particularly suited for Brownian dynamics or molecular dynamics simulations of large molecules, in which the electrostatic forces must be calculated for many different relative positions and orientations of the molecules. It has been implemented as a set of programs in C++, which are used to study the accuracy and speed of this method for two actin monomers.     

Comparison of the Aifrey-Price Q-e Scheme and a Simple Molecular Orbital Treatment of Copolymerization

A simple Huckel treatment of the transition states for the monomer-radical reactions in free radical copolymerization is developed. The resulting equations for the reactivity ratios are compared with those from the Q-e treatment of Alfrey and Price. It is concluded that the Q-e scheme can be regarded as a version of a molecular orbital approach.     

Lattice sum calculations for 1/rp interactions via multipole expansions and Euler summation

A method is developed here for doing multiple calculations of lattice sums when the lattice structure is kept fixed, while the molecular orientations or the molecules within the unit cells are altered. The approach involves a two‐step process. In the first step, a multipole expansion is factored in such a way as to separate the geometry from the multipole moments. This factorization produces a formula for generating geometry constants that uniquely define the lattice structure. A direct calculation of these geometry constants, for all but the very smallest of crystals, is computationally impractical. In the second step, an Euler summation method is introduced that allows for efficient calculation of the geometry constants. This method has a worst case computational complexity of O(( log N)²/N), where N is the number of unit cells. If the lattice sum is rapidly converging, then the computational complexity can be significantly less than N. Once the geometry constants have been calculated, calculating a lattice sum for a given molecule becomes computationally very fast. Millions of different molecular orientations or molecules can quickly be evaluated for the given lattice structure. © 2000 John Wiley & Sons, Inc. J Comput Chem 22: 208–215, 2001     

DNA-Mediated Self-Assembly and Metallization of Semiconductor Nanorods for the Fabrication of Nanoelectronic Interfaces

DNA nanostructures provide a powerful platform for the programmable assembly of nanomaterials. Here, this approach is extended to semiconductor nanorods that possess interesting electrical properties and could be utilized for the bottom-up fabrication of nanoelectronic building blocks. The assembly scheme is based on an efficient DNA functionalization of the nanorods. A complete coverage of the rod surface with DNA ensures a high colloidal stability while maintaining the rod size and shape. It furthermore supports the assembly of the nanorods at defined docking positions of a DNA origami platform with binding efficiencies of up to 90 % as well as the formation of nanorod dimers with defined relative orientations. By incorporating orthogonal binding sites for gold nanoparticles, defined metal-semiconductor heterostructures can be fabricated. Subsequent application of a seeded growth procedure onto the gold nanoparticles (AuNPs) allows for to establish a direct metal-semiconductor interface as a crucial basis for the integration of semiconductors in self-assembled nanoelectronic devices.     

Evaluating docked complexes with the HINT exponential function and empirical atomic hydrophobicities

Summary Methods that predict geometries of ligands binding to receptor molecules can facilitate ligand discovery and yield information on the factors governing complementarity. Here, the use of atomic hydrophobicities in evaluating binding modes has been examined with four ligand-receptor complexes of known structure. In each system, hundreds of hypothetical binding orientations were generated with DOCK and evaluated using the HINT (Hydropathic INTeractions) exponential function and atomic hydrophobic constants. In three of the four systems, the experimental binding mode received the best HINT score; in the fourth system, the experimental binding mode scored only slightly lower than a similar, apparently reasonable orientation. The HINT function may be generally useful as a scoring method in molecular docking.     

Design of topological indices: computer-oriented approach

A novel method is suggested for constructing topological indices (TIs) of molecular graphs which models human logic. This method is described in terms of a block scheme, consisting of the mutually connected elementary blocks. In each block the simple transformations of a molecular graph are fulfilled. A variant of the transformation is selected from the list of possible variants. Every TI is obtained as a result of the sequential execution of a number of operations, corresponding to some ‘walk’ on the block scheme. This walk can be selected both randomly and by the investigator. The suggested method can serve as a basis for the development of the respective computer program which may be used for the automatic construction of any number of TIs of differing nature. By this process one can also obtain the TIs that are unlikely to be constructed manually, due to their complexity. The set of obtained TIs may be used for building the structure–property models. In the case of an unsatisfactory result the obtained set of TIs may be changed using the described generator of TIs. A number of examples of application of the suggested approach for the building QSAR/QSPR models is given.     

On the performance of molecular polarization methods. II. Water and carbon tetrachloride close to a cation

Our initial study on the performance of molecular polarization methods close to a positive point charge [M. Masia, M. Probst, and R. Rey, J. Chem. Phys. 121, 7362 (2004)] is extended to the case in which a molecule interacts with a real cation. Two different methods (point dipoles and shell model) are applied to both the ion and the molecule. The results are tested against high-level ab initio calculations for a molecule (water or carbon tetrachloride) close to Li+, Na+, Mg2+, and Ca2+. The monitored observable is in all cases the dimer electric dipole as a function of the ion-molecule distance for selected molecular orientations. The moderate disagreement previously obtained for point charges at intermediate distances, and attributed to the linearity of current polarization methods (as opposed to the nonlinear effects evident in ab initio calculations), is confirmed for real cations as well. More importantly, it is found that at short separations the phenomenological polarization methods studied here substantially overestimate the dipole moment induced if the ion is described quantum chemically as well, in contrast to the dipole moment induced by a point-charge ion, for which they show a better degree of accord with ab initio results. Such behavior can be understood in terms of a decrease of atomic polarizabilities due to the repulsion between electronic charge distributions at contact separations. It is shown that a reparametrization of the Thole method for damping of the electric field, used in conjunction with any polarization scheme, allows to satisfactorily reproduce the dimer dipole at short distances. In contrast with the original approach (developed for intramolecular interactions), the present reparametrization is ion and method dependent, and corresponding parameters are given for each case.     

Indirect photolysis of organic compounds: prediction of OH reaction rate constants through molecular orbital calculations

The MOOH approach is a perturbational molecular orbital method to predict rate constants of indirect photolysis of organic compounds through reaction with OH radicals. It employs the semiempirical AM1 scheme as the underlying quantum chemical model. The original method introduced by Klamt has been reparametrized using an up-to-date set of 675 compounds with experimental rate constants and outperforms the prominent Atkinson increment scheme for this training set as well as for an extended set of 805 compounds, yielding an overall root-mean-square error of 0.32 log units. The discussion includes detailed comparative analyses of the model performances for individual compound classes. The present model calibration refers mainly to monofunctional compounds but performs already reasonably well for multifunctional compounds. For predictive applications, both the Atkinson scheme and the alternative, independent AM1-MOOH model can be used as components of a consensus modeling approach, arriving at increased confidence in cases where the different models agree.     

Use of locally dense basis sets for nuclear magnetic resonance shielding calculations

The locally dense basis set approach to the calculation of nuclear magnetic resonance shieldings is one in which a sufficiently large or dense set of basis functions is used for an atom or molecular fragment containing the resonant nucleus or nuclei of interest and fewer or attenuated sets of basis functions employed elsewhere. Provided the dense set is of sufficient size, this approach is capable of determining chemical shieldings nearly as well as a calculation with a balanced basis set of quality equal to the locally dense set, but with considerable savings of CPU time. Detailed comparisons are provided of locally dense and balanced calculations in the gauge including atomic orbital (GIAO) method for the individual principal values, the isotropic shieldings, and the tensor orientations for hydrogen, carbon, nitrogen, oxygen, fluorine, and phosphorus nuclei. It is seen that chemical functional groups can often define the appropriate molecular fragment to be taken locally dense. While the present test cases are for the most part small molecules, the value of the method is that it will allow calculations on systems that would otherwise presently be computationally expensive or inaccessible. © John Wiley & Sons, Inc.     

Half-projected and projected Hartree-Fock calculations for singlet ground states. II. Lithium hydride

The half-projected Hartree–Fock function (HPHF ) for singlet states is defined as a linear combination of two Slater determinants which contains only spin eigenstates with even spin quantum numbers. The possible uses of such an approach for determining molecular properties are investigated computing the potential energy curve, binding energy, force constant, and dipole moment variation corresponding to the lithium hydride ground state. Full projected and restricted Hartree–Fock calculations (PHF and RHF ) are performed simultaneously for comparison purposes. It is found that the HPHF model yields very satisfactory results, very close to those of the PHF scheme. Both models predict properly the molecular behavior as a function of nuclear separation, whereas the RHF one fails. A discussion is given in terms of configuration equivalents. It is concluded that the HPHF scheme seems to be useful for determining molecular properties specially in the case of large systems in which the more sophisticated methods are unmanageable.     

Evaluation of electronic correlation contributions for optical tensors of large systems using the incremental scheme

A new method is developed to calculate the optical tensors of large systems based on available wave function correlation approaches (e.g., the coupled cluster ansatz) in the framework of the incremental scheme. The convergence behaviors of static first- and second-order polarizabilities with respect to the order of the incremental expansion are examined and discussed for the model system Ga(4)As(4)H(18). The many-body increments of optical tensors originate from the dipole-dipole coupling effects and the corresponding contributions to the incremental expansion are compared among local domains with different distances and orientations. The weight factors for increments of optical tensors are found to be tensorial in accordance with the structural symmetry as well as the polarization and the external electric field directions. The long-term goal of the proposed approach is to incorporate the sophisticated molecular correlation methods into the accurate wave function calculation of optical properties of large compounds or even crystals.     

Evaluation of nonlinear quantum time correlation functions within the centroid dynamics formulation

A method to evaluate nonlinear centroid correlation functions is presented that is amenable to simple numerical computation. It can be implemented with the centroid molecular dynamics method for approximate quantum dynamics with no additional assumptions. Two nonlinear correlation functions are evaluated for a model potential using this scheme and compared with results from exact quantum calculations.     

Robust and accurate method for free-energy calculation of charged molecular systems

A new approach is presented to eliminate the problem of creation and/or annihilation of atoms in free-energy calculations of charged molecular systems. The method employs a damping potential in the Ewald summation scheme, which is an exact solution of the electrostatics for three-dimensional periodic systems. The proposed method enables entire molecules to be mutated from a noninteracting (ideal) state in an efficient and robust way, thus providing a means by which accurate absolute free energies of structurally complex molecules can be determined. This methodology will enable chemical and phase equilibria to be determined for large molecular species with significant charge distributions, e.g., biomolecules and drugs.     

Molecular density functional theory of solvation: from polar solvents to water

A classical density functional theory approach to solvation in molecular solvent is presented. The solvation properties of an arbitrary solute in a given solvent, both described by a molecular force field, can be obtained by minimization of a position and orientation-dependent free-energy density functional. In the homogeneous reference fluid approximation, limited to two-body correlations, the unknown excess term of the functional approximated by the angular-dependent direct correlation function of the pure solvent. We show that this function can be extracted from a preliminary MD simulation of the pure solvent by computing the angular-dependent pair distribution function and solving subsequently the molecular Ornstein-Zernike equation using a discrete angular representation. The corresponding functional can then be minimized in the presence of an arbitrary solute on a three-dimensional cubic grid for positions and Gauss-Legendre angular grid for orientations to provide the solvation structure and free-energy. This two-step procedure is proved to be much more efficient than direct molecular dynamics simulations combined to thermodynamic integration schemes. The approach is shown to be relevant and accurate for prototype polar solvents such as the Stockmayer solvent or acetonitrile. For water, although correct for neutral or moderately charged solute, it tends to underestimate the tetrahedral solvation structure around H-bonded solutes, such as spherical ions. This can be corrected by introducing suitable three-body correlation terms that restore both an accurate hydration structure and a satisfactory energetics.     

Magnetism and local order

A simple electronic structure scheme based upon a combination of the molecular clusters and tight binding formulation is proposed that is not only quantitative but also enables electronic structure studies in a computationally efficient manner. As a first application, we use the new scheme to study the magnetic moment of Fe and Ni in a wide range of environments where the local coordination of the magnetic atom changes from two to as many as twelve. This is achieved by considering configurations such as linear chain, crystallographic surfaces of various orientations, thin films and bulk. The magnetic moment is shown to increase with decreasing coordination due to narrowing of electron bands. Its implications for the magnetic moments of small Fe and Ni clusters are discussed.     

A general and efficient pseudopotential Fourier filtering scheme for real space methods using mask functions

A scheme for the Fourier filtering of pseudopotentials in real space calculations is proposed, in order to reduce the artifact of positional energy dependence ("egg box" effect). It is based on an improved version of the mask function method poposed by Wang [Phys. Rev. B 64, 201107/1 (2001)]. It is easy to implement, efficient, and accurate. By using atom-centered compensation charges, the local part of the pseudopotential becomes short ranged and can be filtered on the same footing as the nonlocal parts. A major advantage of the approach is that a generic set of parameters can be used for different pseudopotentials. A balanced parameter set is derived and validated. In this context a strategy to monitor the extent of grid dependence is introduced. It is found that, given a sufficiently fine grid spacing is used to represent the atomic valence density, the positional energy dependence can be reduced below 0.1 mhartree for all investigated atoms. On the example of a D(3h) symmetric Si(5) cluster and the C(60) molecule it is demonstrated that the artificial symmetry breaking of both bond lengths and orbital energies can substantially be reduced by the filtering scheme.     

A new hierarchical parallelization scheme: generalized distributed data interface (GDDI), and an application to the fragment molecular orbital method (FMO)

A two-level hierarchical scheme, generalized distributed data interface (GDDI), implemented into GAMESS is presented. Parallelization is accomplished first at the upper level by assigning computational tasks to groups. Then each group does parallelization at the lower level, by dividing its task into smaller work loads. The types of computations that can be used with this scheme are limited to those for which nearly independent tasks and subtasks can be assigned. Typical examples implemented, tested, and analyzed in this work are numeric derivatives and the fragment molecular orbital method (FMO) that is used to compute large molecules quantum mechanically by dividing them into fragments. Numeric derivatives can be used for algorithms based on them, such as geometry optimizations, saddle-point searches, frequency analyses, etc. This new hierarchical scheme is found to be a flexible tool easily utilizing network topology and delivering excellent performance even on slow networks. In one of the typical tests, on 16 nodes the scalability of GDDI is 1.7 times better than that of the standard parallelization scheme DDI and on 128 nodes GDDI is 93 times faster than DDI (on a multihub Fast Ethernet network). FMO delivered scalability of 80-90% on 128 nodes, depending on the molecular system (water clusters and a protein). A numerical gradient calculation for a water cluster achieved a scalability of 70% on 128 nodes. It is expected that GDDI will become a preferred tool on massively parallel computers for appropriate computational tasks.     

Fixed closest distance of approach dipole potential mapping: An effective alternative to the monopole isopotential approach

It has been shown that an easier procedure to the study of molecular electrostatic potentials than the prevalent monopole isopotential approach is to use a dipole as the mapping device: allow the dipole to move on a geometrical surface enclosing the molecule such that the distance between the surface and the nearest atoms of the molecule (closest distance of approach) is fixed, say at 2 Å, calculate the electrostatic interaction energy between the molecule and the dipole at different points of the surface, and let the dipole orient itself along the minimum energy direction and treat these minimum energies as the desired electrostatic potentials. Thus the favorable binding sites of a given molecule for other species along with their relative orientations can be obtained. This procedure has been applied to the nucleic acid bases using the necessary input data from two independent sources. Thus success of the procedure in predicting important features of molecular electrostatic potentials has been demonstrated.     

Coherent control of molecular torsion

We propose a coherent, strong-field approach to control the torsional modes of biphenyl derivatives, and develop a numerical scheme to simulate the torsional dynamics. By choice of the field parameters, the method can be applied either to drive the torsion angle to an arbitrary configuration or to induce free internal rotation. Transient absorption spectroscopy is suggested as a probe of torsional control and the usefulness of this approach is numerically explored. Several consequences of our ability to manipulate molecular torsional motions are considered. These include a method for the inversion of molecular chirality and an ultrafast chiral switch.