Comparison of overlap-based models for approximating the exchange-repulsion energy

Different ways of approximating the exchange-repulsion energy with a classical potential function have been investigated by fitting various expressions to the exact exchange-repulsion energy for a large set of molecular dimers. The expressions involve either the orbital overlap or the electron-density overlap. For comparison, the parameter-free exchange-repulsion model of the effective fragment potential (EFP) is also evaluated. The results show that exchange-repulsion energy is nearly proportional to both the orbital overlap and the density overlap. For accurate results, a distance-dependent correction is needed in both cases. If few parameters are desired, orbital overlap is superior to density overlap, but the fit to density overlap can be significantly improved by introducing more parameters. The EFP performs well, except for delocalized pi systems. However, an overlap expression with a few parameters seems to be slightly more accurate and considerably easier to approximate.     

Towards a force field based on density fitting

Total intermolecular interaction energies are determined with a first version of the Gaussian electrostatic model (GEM-0), a force field based on a density fitting approach using s-type Gaussian functions. The total interaction energy is computed in the spirit of the sum of interacting fragment ab initio (SIBFA) force field by separately evaluating each one of its components: electrostatic (Coulomb), exchange repulsion, polarization, and charge transfer intermolecular interaction energies, in order to reproduce reference constrained space orbital variation (CSOV) energy decomposition calculations at the B3LYP/aug-cc-pVTZ level. The use of an auxiliary basis set restricted to spherical Gaussian functions facilitates the rotation of the fitted densities of rigid fragments and enables a fast and accurate density fitting evaluation of Coulomb and exchange-repulsion energy, the latter using the overlap model introduced by Wheatley and Price [Mol. Phys. 69, 50718 (1990)]. The SIBFA energy scheme for polarization and charge transfer has been implemented using the electric fields and electrostatic potentials generated by the fitted densities. GEM-0 has been tested on ten stationary points of the water dimer potential energy surface and on three water clusters (n = 16,20,64). The results show very good agreement with density functional theory calculations, reproducing the individual CSOV energy contributions for a given interaction as well as the B3LYP total interaction energies with errors below kBT at room temperature. Preliminary results for Coulomb and exchange-repulsion energies of metal cation complexes and coupled cluster singles doubles electron densities are discussed.     

Does Förster theory predict the rate of electronic energy transfer for a model dyad at low temperature?

The use of the F?rster model to predict the dynamics of resonant electronic energy transfer (RET) in a model donor-acceptor dyad (a terphenyl-bridged perylene diimide (PDI)-terrylene diimide (TDI) dyad molecule) embedded at low temperature in a PMMA matrix is tested against experiment. The relevant ingredients involved in the F?rster rate for RET, namely electronic coupling, spectral overlap, and screening effects, are accounted for in a quantitative manner. Electronic couplings are obtained from time-dependent density functional theory calculations, and the effect of the PMMA environment is included both on the transition densities and on their interaction through the IEFPCM model. We find that the presence of the terphenyl bridge induces a slight delocalization of the PDI and TDI transition densities over the bridge originating in a 56% increase in the coupling and in the breakdown of the dipole-dipole approximation. The spectral overlap is determined on the basis of a detailed simulation of the homogeneously broadened donor emission and acceptor absorption line shapes determined by fitting the single molecule spectra measured at 1.2 K. The corresponding distribution of spectral overlap throughout the ensemble is then estimated by assuming an uncorrelated inhomogeneous line broadening for the donor and acceptor. Combining the calculated electronic couplings and spectral overlaps sampled from Monte Carlo realizations of the energetic disorder, we obtain a mean RET time (approximately 8 ps) and a distribution in reasonable agreement with experiment.     

Localized impurity states in the Hartree-Fock,LCAO approximation. I.

One-electron energies and wave functions for deep trap impurity electrons in a crystal are calculated by the Hartree-Fock, single determinant method. The interactions arising from a many-electron single determinant crystal wave function, with automatic inclusion of exchange effects, are those which determine the one-electron functions and energies. The crystal plus impurity system has no translational symmetry and hence the Bloch theorem is not applicable for the solution of the essentially infinite Hartree-Fock eigenvalue matrix. Thus we develop a technique in which the Hamiltonian and overlap matrices are written in terms of bordered matrices, with the interaction of the impurity functions with the rest of the crystal environment contained in the bordering rows and columns. The resulting secular equation explicitly includes the effects of orthogonalization of the entire basis set, including the impurity functions. This technique could be used in an iterative calculation of the electronic structure of a small number of electrons, assuming that the rest of the electrons in the environment are fixed according to an initial estimate.     

Numerical instabilities in the computation of pseudopotential matrix elements

Steep high angular momentum Gaussian basis functions in the vicinity of a nucleus whose inner electrons are replaced by an effective core potential may lead to numerical instabilities when calculating matrix elements of the core potential. Numerical roundoff errors may be amplified to an extent that spoils any result obtained in such a calculation. Effective core potential matrix elements for a model problem are computed with high numerical accuracy using the standard algorithm used in quantum chemical codes and compared to results of the MOLPRO program. Thus, it is demonstrated how the relative and absolute errors depend an basis function angular momenta, basis function exponents and the distance between the off-center basis function and the center carrying the effective core potential. Then, the problem is analyzed and closed expressions are derived for the expected numerical error in the limit of large basis function exponents. It is briefly discussed how other algorithms would behave in the critical case, and they are found to have problems as well. The numerical stability could be increased a little bit if the type 1 matrix elements were computed without making use of a partial wave expansion.     

Ab initio calculations on the excited states of Na3 cluster to explore beyond Born-Oppenheimer theories: adiabatic to diabatic potential energy surfaces and nuclear dynamics

We perform ab initio calculation using quantum chemistry package (MOLPRO) on the excited states of Na(3) cluster and present the adiabatic PESs for the electronic states 2(2)E' and 1(2)A(1)', and the non-adiabatic coupling (NAC) terms among those states. Since the ab initio calculated NAC elements for the states 2(2)E' and 1(2)A(1)' demonstrate the numerical validity of so called "Curl Condition," such states closely form a sub-Hilbert space. For this subspace, we employ the NAC terms to solve the "adiabatic-diabatic transformation (ADT)" equations to obtain the functional form of the transformation angles and pave the way to construct the continuous and single valued diabatic potential energy surface matrix by exploiting the existing first principle based theoretical means on beyond Born-Oppenheimer treatment. Nuclear dynamics has been carried out on those diabatic surfaces to reproduce the experimental spectrum for system B of Na(3) cluster and thereby, to explore the numerical validity of the theoretical development on beyond Born-Oppenheimer approach for adiabatic to diabatic transformation.     

Force field validation for nucleic acid simulations: comparing energies and dynamics of a DNA dodecamer

Important questions exist regarding the quality of force fields used in molecular dynamics (MD) simulations and their interoperable use with other available MD implementations. NAMD is one of the most efficient and scalable parallel molecular dynamics codes for large-scale biomolecular simulations in the open source domain. It is the aim of this article to analyze and compare the dynamics of a benchmark DNA dodecamer d(CTTTTGCAAAAG)2 system, including its binding to a specific drug molecule arising from the use of various simulation protocols in NAMD using Amber98, with the dynamics arising from simulations of the same dodecamer using Amber98 in the AMBER package, one of the most well-established simulation codes for nucleic acids. Based upon a set of validation benchmarks, the details of which are discussed, we find that nucleic acid simulations using NAMD give meaningful results and that the essential features of the resulting dynamics are similar to those arising from the AMBER package. This sets the stage for reliable large-scale simulations of nucleic acids using NAMD.     

Analysis of the Symmetry of Crystal Packing Forces by Methyl Proton Tunneling: A Strategy for the Unambiguous Assignment of the Magnetic Jahn – Teller Effect in Molecules

Intrinsic and extrinsic forces behind the distortion in metal atom clusters can be readily distinguished provided that the clusters are embedded in a suitable ligand environment and that the tunneling of the protons in the peripheral ligands is then analyzed by inelastic neutron scattering. For the [Cr₃O(OOCCH₃)₆(H₂O)₃]Cl⋅6 H₂O model system studied, the tunneling process is very sensitive to the local environment. Thus a tool is available to allow a better assessment of the cause of structural distortions.     

Brownian dynamics studies of dilute dispersions

The method of brownian dynamics of used to study the non-equilibrium properties of very dilute colloids electrostatically stabilised in dilute aqueous electrolyte. It is assumed that the colloid is a monodisperse system of structureless spherical particles embedded in a hydrodynamic continuum. Although the particles are interacting electrostatically through a screened Coulomb potential, the dilution is such that effects arising from coupling of hydrodynamic flow can be ignore. Studies of the self-diffusion coefficient and van Howe functions show that after an initial period, during which the particles move essentially independently, the flow properties of the colloids are significantly different from those expected on the basis of free brownian motion.     

Modeling the fragmentation dynamics of ionic clusters inside helium nanodroplets: the case of He100Ne4+

We present simulation results on the effect of a helium nanodroplet environment on the fragmentation dynamics of embedded molecular systems. The helium atoms are treated explicitly, with zero-point effects taken into account through an effective helium-helium interaction potential. The ionized neon tetramer is used as a model molecular system because, like all the small rare-gas clusters, it fragments extensively upon ionization. All the nonadiabatic effects between electronic states of the ionized neon cluster are taken into account. The results reveal a predominance of Ne2+ and HepNe2+ fragments and the absence of bare Ne+ fragments, in agreement with available experimental data. The neutral monomer fragments exhibit a rather wide kinetic energy distribution that can be fitted to the sum of two Boltzmann distributions, one with a low kinetic energy and the other with a higher kinetic energy. This indicates that cooling by helium atom evaporation is more efficient than was believed so far, as suggested by recent experimental results. Purely classical calculations are shown to strongly overestimate the amount of cage effect (cooling), clearly indicating the need to take into account zero-point effects.     

Comparison between the point-charge electrostatic model and the angular overlap model: The general case

The aim of this paper is to explore in detail the mathematical connection between the point-charge electrostatic model and the angular overlap model. More precisely, for any configuration nl^x in any symmetry, the matrix elements, and therefore the energy levels, as given by the angular overlap model restricted to the antibonding effects λ (for any of the possible λ's), are deduced from an effective potential constructed according to the point-charge electrostatic model. This allows us to give a mathematical proof of the equivalence between the point-charge electrostatic model and the angular overlap model taking into account all the antibonding effects λ. Finally, the sum rules for the angular overlap model are examined in the light of the formulae connecting the two models considered. Numerical tables for obtaining the results as given by the angular overlap model restricted to any of the antibonding effects from those as given by the point-charge electrostatic model are listed for the configurations nl^x with l = p, d, f and g.     

Substituent effects in parallel-displaced pi-pi interactions

High-quality quantum-mechanical methods are used to examine how substituents tune pi-pi interactions between monosubstituted benzene dimers in parallel-displaced geometries. The present study focuses on the effect of the substituent across entire potential energy curves. Substituent effects are examined in terms of the fundamental components of the interaction (electrostatics, exchange-repulsion, dispersion and induction) through the use of symmetry-adapted perturbation theory. Both second-order M?ller-Plesset perturbation theory (MP2) with a truncated aug-cc-pVDZ' basis and spin-component-scaled MP2 (SCS-MP2) with the aug-cc-pVTZ basis are found to mimic closely estimates of coupled-cluster with perturbative triples [CCSD(T)] in an aug-cc-pVTZ basis. Substituents can have a significant effect on the electronic structure of the pi cloud of an aromatic ring, leading to marked changes in the pi-pi interaction. Moreover, there can also be significant direct interactions between a substituent on one ring and the pi-cloud of the other ring.     

Hydrogen-bonding-induced shifts of the excitation energies in nucleic acid bases: an interplay between electrostatic and electron density overlap effects

The theoretically calculated dimerization-induced shifts of the lowest excitation energies in two model systems, adenine-thymine and guanine-cytosine base pairs, are analyzed. The applied formalism is based on first principles and allows one to study the influence of the microscopic environment of a given molecule on its ground- [Wesolowski, T. A.; Warshel, A. J. Phys. Chem. 1993, 97, 8050] and excited-state [Casida, M. E.; Wesolowski, T. A. Int. J. Quantum Chem. 2004, 96, 577] properties. The assessment of the relative importance of such effects as (a) Coulomb interactions, (b) orbital interactions, (c) electronic polarization of the environment, and (d) electron density overlap effects is straightforward in this formalism. In the applied formalism, electron density overlap effects can be further decomposed into the exchange-correlation component which provides a small attractive contribution and the repulsive kinetic energy-dependent component. It is shown that the shifts can be attributed to the electrostatic interactions and the repulsive overlap-dependent term in the embedding potential. The electronic polarization of the environment plays a significant role (up to 30% of the total shift) only in transitions involving the orbitals localized on hydrogen bond donor groups. For all analyzed shifts, the contribution of the intermolecular orbital interactions is negligible. The analysis of this work provides strong evidence supporting the use of the widely applied embedding-molecule strategy in computational studies of chromophores in a condensed phase even in such cases where only one end of the hydrogen bond is included in the quantum mechanical part.     

ASEDock-docking based on alpha spheres and excluded volumes

ASEDock is a novel docking program based on a shape similarity assessment between a concave portion (i.e., concavity) on a protein and the ligand. We have introduced two novel concepts into ASEDock. One is an ASE model, which is defined by the combination of alpha spheres generated at a concavity in a protein and the excluded volumes around the concavity. The other is an ASE score, which evaluates the shape similarity between the ligand and the ASE model. The ASE score selects and refines the initial pose by maximizing the overlap between the alpha spheres and the ligand, and minimizing the overlap between the excluded volume and the ligand. Because the ASE score makes good use of the Gaussian-type function for evaluating and optimizing the overlap between the ligand and the site model, it can pose a ligand onto the docking site relatively faster and more effectively than using potential energy functions. The posing stage through the use of the ASE score is followed by full atomistic energy minimization. Because the posing algorithm of ASEDock is free from any bias except for shape, it is a very robust docking method. A validation study using 59 high-quality X-ray structures of the complexes between drug-like molecules and the target proteins has demonstrated that ASEDock can faithfully reproduce experimentally determined docking modes of various druglike molecules in their target proteins. Almost 80% of the structures were reconstructed within the estimated experimental error. The success rate of approximately 98% was attained based on the docking criterion of the root-mean-square deviation (RMSD) of non-hydrogen atoms (< or = 2.0 A). The markedly high success of ASEDock in redocking experiments clearly indicates that the most important factor governing the docking process is shape complementarity.     

Leveraging Material Properties in Fluorescence Anion Sensor Arrays: A General Approach

As the demand for probes suitable for sensor development increases, investigation of approaches that utilize known successful receptors gains in general importance. This study describes a two‐prong approach that can be used as a guide to developing sensors from known receptors. First, the conversion of a simple receptor, calix[4]pyrrole, into a fluorescent probe to establish a ratiometric signal is described. Secondly, the sensors that employ an output from a single ratiometric calix[4]pyrrole probe are fabricated by using poly(ether‐urethane) hydrogel copolymers. These hydrogels are designed to absorb, internalize and transport aqueous electrolytes. A sensor array of ten different poly(ether‐urethane) matrices with varying comonomer proportions were doped with a single probe and were exposed to eight different anions: acetate, benzoate, fluoride, chloride, phosphate, pyrophosphate, hydrogen sulfide, and cyanide, eight urine samples and anti‐inflammatory drugs (NSAIDs). The poly(ether‐urethane) matrices comprise different proportions of anion‐binding urethane moieties and different hydrophilicity given by the ratio between ethylene glycol ether and butylene glycol ether. This diversity in the hydration behavior provides different environment polarity, in which the recognition and self‐assembly processes display enough diverse behavior to allow for unique response of the probe to the analytes. Furthermore, a single probe is shown to recognize eight different aqueous anions and eight urine samples when embedded in ten different polyurethanes in an array that displays 100 % classification accuracy. To demonstrate the potential of the concept for quantitative studies, an estimation of non‐steroidal anti‐inflammatory drugs ibuprofen and diclofenac in water and in saliva was performed. A limit of detection of 0.1 ppm and a dynamic range of 0.1–0.6 and 0.05–60 ppm was observed, respectively. Given the general difficulty of chemosensors to recognize aqueous anions, the fact that one probe recognizes eight different analytes attests to an enormous effect of the polymer environment on the recognition process. This method could be used to generate a variety of sensor arrays for various analyses including species that are difficult to recognize, such as small‐molecule‐ and inorganic anions.     

Ion selectivity using membranes comprising functionalized carbon nanotubes

In this paper, we use applied mathematical modelling to investigate the transportation of ions inside functionalized carbon nanotubes, and in particular the transport of sodium and chloride ions. This problem is important for future ion transport and detection, and also arises in ion diffusion inside complex biological channels. Some important future applications of the system for a solvent are ultra-sensitive biosensors and electrolytes for alkaline fuel cells. We model the interactions between the ions and the nanotube by the Lennard-Jones potential and the interactions between the ions and the functional group by the Coulomb potential, while the atomic interactions between the ions is modeled by both the Lennard-Jones and Coulomb potentials. We further assume that the carbon atoms, the charge of the functional group, and the ions are all evenly distributed on the surface of the nanotube, the entry of the nanotube and the envisaged ionic surface, respectively, so that we may use the continuous approximation to calculate the corresponding potential energies. For nanotubes located in salt water, the molecular effects arising from the bulk solution can be extracted from MD simulation studies. Assuming that the solvent is absent, we first determine the acceptance radii for the sodium or chloride ion entering the nanotube, both with and without a functional group, and we then determine the equilibrium positions of two identical ions inside the nanotube. Finally, the transportation time of an intruding ion through the nanotube is deduced from the total axial force. In the presence of a solvent, the molecular effects arising from the bulk solution are examined and we establish that the presence of a solvent stabilizes the selectivity of the ions.     

Anisotropy resolved multidimensional emission spectroscopy (ARMES): A new tool for protein analysis

Structural analysis of proteins using the emission of intrinsic fluorophores is complicated by spectral overlap. Anisotropy resolved multidimensional emission spectroscopy (ARMES) overcame the overlap problem by the use of anisotropy, with chemometric analysis, to better resolve emission from different fluorophores. Total synchronous fluorescence scan (TSFS) provided information about all the fluorophores that contributed to emission while anisotropy provided information about the environment of each fluorophore. Here the utility of ARMES was demonstrated via study of the chemical and thermal denaturation of human serum albumin (HSA).     

Molecular dynamics search for magic numbers for silver and copper clusters

Isothermal molecular dynamics is used to find the magic numbers corresponding to clusters of fcc transition metals: silver and copper. To that end, we use both our own computer program with a tight-binding potential and well-known LAMMPS software whose standard package is designed to model metal systems by the embedded atom method. Regardless of the choice between two relaxation techniques (lowtemperature relaxation at 1 K and the variant involving a gradual temperature decrease with subsequent relaxation at 1 K), magic number 13 is detected that corresponds to the first term of the Chini series. At the same time, other magic numbers are also found that belong and do not belong to this series.