Density functional calculation of intermolecular potentials

Calculations of intermolecular potentials following the density functional theory (DFT) turn out to be very complicated without using some appropriate approximations. Most often the following three approximations have been considered. In one approximation the disturbed charge distributions during collisions are reduced to sums of undisturbed charge distributions from the colliding species. In another approximation, the so-called local density approximation (LDA), one neglects the fact that the intermolecular potentials that depend on charge densities also depend on gradients in the densities. In a third approximation one assumes that the intermolecular potential can be considered as a sum of two terms: a term for the long-range geometry and a term for the short-range geometry. In this Article the three approximations mentioned will be discussed for numerical accuracy for calculations of potentials between inert gas atoms and for calculations of potentials between surfaces and inert gas atoms. In the discussion a few other approximations will be mentioned too.     

Nonuniform electro-osmotic flow on charged strips and its use in particle trapping

In this article, we investigate theoretically electro-osmotic flow set up by charged strips on an otherwise uncharged surface. Starting with a single-strip problem we demonstrate that for simple polynomial surface charge distributions several basic solutions can be derived in closed forms constituted by the analogous idea-flow solutions, which provide a more lucid way of revealing the flow features. These solutions reveal two types of flow topology: simple draining-in/pumping-out streaming and a pair of microvortices for symmetric and antisymmetric surface charge distributions, respectively. For an arbitrary surface charge distribution, more complicated flow structures can be found by the superposition of these basic solutions. We further extend the analysis to two uniformly charged strips and show how the flow characteristics vary with the strips' dimensions and surface zeta potentials. The far-field velocity behavior is also asymptotically identified and indicates that the hydrodynamic nature of the flow is typically long-range. An application to particle trapping with electro-osmotic vortices is also investigated theoretically for the first time. We show that in collaboration with short-range attraction effects the trapping can be facilitated by symmetric vortices with a converging stagnation point, but not by asymmetric vortices.     

Simulating the proton transfer in gramicidin A by a sequential dynamical Monte Carlo method

The large interest in long-range proton transfer in biomolecules is triggered by its importance for many biochemical processes such as biological energy transduction and drug detoxification. Since long-range proton transfer occurs on a microsecond time scale, simulating this process on a molecular level is still a challenging task and not possible with standard simulation methods. In general, the dynamics of a reactive system can be described by a master equation. A natural way to describe long-range charge transfer in biomolecules is to decompose the process into elementary steps which are transitions between microstates. Each microstate has a defined protonation pattern. Although such a master equation can in principle be solved analytically, it is often too demanding to solve this equation because of the large number of microstates. In this paper, we describe a new method which solves the master equation by a sequential dynamical Monte Carlo algorithm. Starting from one microstate, the evolution of the system is simulated as a stochastic process. The energetic parameters required for these simulations are determined by continuum electrostatic calculations. We apply this method to simulate the proton transfer through gramicidin A, a transmembrane proton channel, in dependence on the applied membrane potential and the pH value of the solution. As elementary steps in our reaction, we consider proton uptake and release, proton transfer along a hydrogen bond, and rotations of water molecules that constitute a proton wire through the channel. A simulation of 8 mus length took about 5 min on an Intel Pentium 4 CPU with 3.2 GHz. We obtained good agreement with experimental data for the proton flux through gramicidin A over a wide range of pH values and membrane potentials. We find that proton desolvation as well as water rotations are equally important for the proton transfer through gramicidin A at physiological membrane potentials. Our method allows to simulate long-range charge transfer in biological systems at time scales, which are not accessible by other methods.     

Long-Range multicenter integrals with slater functions: Gauss transform-based methods

The separation of the short- and long-range terms in the potentials generated by pairs of Slater functions is reformulated in the context of the Gauss transform method. Analytic expressions of the long-range potentials (in closed form) are derived for equal exponents and generalized (as expansion series) for different exponents. Additionally, the representation of these potentials from small sets of charges or lowest-order multipoles is examined, paying special attention to their values and optimal positions. Finally, numerical tests of the formal developments are presented. It is concluded that the long-range three- and four-center integrals can be calculated with high accuracy in a simple and relatively inexpensive manner. © John Wiley & Sons, Inc.     

Spin-orbit relativistic long-range corrected time-dependent density functional theory for investigating spin-forbidden transitions in photochemical reactions

A long-range corrected (LC) time-dependent density functional theory (TDDFT) incorporating relativistic effects with spin-orbit couplings is presented. The relativistic effects are based on the two-component zeroth-order regular approximation Hamiltonian. Before calculating the electronic excitations, we calculated the ionization potentials (IPs) of alkaline metal, alkaline-earth metal, group 12 transition metal, and rare gas atoms as the minus orbital (spinor) energies on the basis of Koopmans' theorem. We found that both long-range exchange and spin-orbit coupling effects are required to obtain Koopmans' IPs, i.e., the orbital (spinor) energies, quantitatively in DFT calculations even for first-row transition metals and systems containing large short-range exchange effects. We then calculated the valence excitations of group 12 transition metal atoms and the Rydberg excitations of rare gas atoms using spin-orbit relativistic LC-TDDFT. We found that the long-range exchange and spin-orbit coupling effects significantly contribute to the electronic spectra of even light atoms if the atoms have low-lying excitations between orbital spinors of quite different electron distributions.     

Model potential approaches for describing the interaction of excess electrons with water clusters: incorporation of long-range correlation effects

In this work we focus on the binding of excess electrons to water clusters, a problem for which dispersion interactions, which originate from long-range correlation effects, are especially important. Two different model potential approaches, one using quantum Drude oscillators and the other using polarization potentials, are investigated for describing the long-range correlation effects between the weakly bound excess electron and the more tightly bound electrons of the monomers. We show that these two approaches are related in that the polarization potential models can be derived from the quantum Drude model approach by use of an adiabatic separation between the excess electron and the Drude oscillators. The model potential approaches are applied to clusters containing up to 45 water monomers. Where possible, comparison is made with the results of ab initio electronic structure calculations. Overall, the polarization potential approach is found to give electron binding energies in good agreement with those from the Drude model and ab initio calculations, with the greatest discrepancies being found for "cavity-bound" anion states.     

Isotropic periodic sum: a method for the calculation of long-range interactions

This work presents an accurate and efficient approach to the calculation of long-range interactions for molecular modeling and simulation. This method defines a local region for each particle and describes the remaining region as images of the local region statistically distributed in an isotropic and periodic way, which we call isotropic periodic images. Different from lattice sum methods that sum over discrete lattice images generated by periodic boundary conditions, this method sums over the isotropic periodic images to calculate long-range interactions, and is referred to as the isotropic periodic sum (IPS) method. The IPS method is not a lattice sum method and eliminates the need for a reciprocal space sum. Several analytic solutions of IPS for commonly used potentials are presented. It is demonstrated that the IPS method produces results very similar to that of Ewald summation, but with three major advantages, (1) it eliminates unwanted symmetry artifacts raised from periodic boundary conditions, (2) it can be applied to potentials of any functional form and to fully and partially homogenous systems as well as finite systems, and (3) it is more computationally efficient and can be easily parallelized for multiprocessor computers. Therefore, this method provides a general approach to an efficient calculation of long-range interactions for various kinds of molecular systems.     

Solid-liquid phase coexistence of the Lennard-Jones system through phase-switch Monte Carlo simulation

The phase-switch Monte Carlo method of Wilding and Bruce [Phys. Rev. Lett. 85, 5138 (2000)] is extended to enable calculation of solid-liquid phase coexistence for soft potentials. The method directly accesses coexistence information about a system while avoiding simulation of the interfacial region. Order parameters are introduced that allow one to define a path that connects liquid and crystalline phases. Transition matrix methods are employed to bias the sampling such that both phases are sampled in a rapid and efficient manner. Coexistence properties are determined through an analysis of specific volume probability distributions, which are generated naturally during a biased simulation. The approach is demonstrated with the Lennard-Jones system. Finite-size effects are examined and compared to those for the hard sphere system. In addition, two techniques are considered for accounting for long-range interactions. The methodology presented here is general and therefore provides a basis for its application to other soft systems.     

STATISTICAL PROPERTIES OF LONG-RANGE CONTACTS IN GLOBULAR PROTEINS

The analysis of residue-residue contacts in protein structures can shed some light on our understanding of the folding and stability of proteins. In this paper, we study the statistical properties of long-range and short-range residue-residue contacts of 91 globular proteins using CSU software and analyze the importance of long-range contacts in globular protein structure. There are many short-range and long-range contacts in globular proteins, and it is found that the average number of long-range contacts per residue is 5.63 and the percentage of residue-residue contacts which are involved in long-range ones is 59.4%. In more detail, the distribution of long-range contacts in different residue intervals is investigated and it is found that the residues occurring in the interval range of 4-10 residues apart in the sequence contribute more long-range contacts to the stability of globular protein. The number of long-range contacts per residue, which is a measure of ability toform residue-residue contacts, is also calculated for 20 different amino acid residues. It is shown that hydrophobic residues (including Leu, Val, Ile, Met, Phe, Tyr, Cys and Trp) having a large number of long-range contacts easily form long-range contacts, while the hydrophilic amino acids (including Ala, Gly, Thr, His, Glu, Gln, Asp, Asn, Lys, Ser, Arg, and Pro) form long-range contacts with more difficulty. The relationship between the Fauchere-Pliska hydrophobicity scale (FPH) and the number of short-range and long-range contacts per residue for 20 amino acid residues is also studied. An approximately linear relationship between the Fauchere-Pliska hydrophobicity scale (FPH) and the number of long-range contacts per residue CL is found and can be expressed as     

Sensitive electrochemical monitoring of nucleic acids coupling DNA nanostructures with hybridization chain reaction

Methods based on metal nanotags have been developed for metallobioassay of nucleic acids, but most involve complicated labeling or stripping procedures and are unsuitable for routine use. Herein, we report the proof-of-concept of a novel and label-free metallobioassay for ultrasensitive electronic determination of human immunodeficiency virus (HIV)-related gene fragments at an ultralow concentration based on target-triggered long-range self-assembled DNA nanostructures and DNA-based hybridization chain reaction (HCR). The signal is amplified by silver nanotags on the DNA duplex. The assay mainly consists of capture probe, detection probe, and two different DNA hairpins. In the presence of target DNA, the capture probe immobilized on the sensor sandwiches target DNA with the 3′ end of detection probe. Another exposed part of detection probe at the 5′ end opens two alternating DNA hairpins in turn, and propagates a chain reaction of hybridization events to form a nicked double-helix. Finally, numerous silver nanotags are immobilized onto the long-range DNA nanostructures, each of which produces a strong electronic signal within the applied potentials. Under optimal conditions, the target-triggered long-range DNA nanostructures present good electrochemical behaviors for the detection of HIV DNA at a concentration as low as 0.5 fM. Importantly, the outstanding sensitivity can make this approach a promising scheme for development of next-generation DNA sensors without the need of enzyme labeling or fluorophore labeling.     

A simple algorithm to accelerate the computation of non-bonded interactions in cell-based molecular dynamics simulations

Cell lists are ubiquitous in molecular dynamics simulations--be it for the direct computation of short-range inter-atomic potentials, the short-range direct part of a long-range interaction or for the periodic construction of Verlet lists. The conventional approach to computing pairwise interactions using cell lists leads to a large number of unnecessary interparticle distance calculations. In this paper, an algorithm is presented which reduces the number of spurious distance calculations by first sorting the particles along the cell pair axis and then only interacting two particles if their distance along the axis is smaller than the cutoff distance of the interaction. This approach is shown to be more efficient than the conventional approach and similar approaches using smaller cells.     

Effective solvent mediated potentials of Na+ and Cl- ions in aqueous solution: temperature dependence

The effective solvent-mediated potentials for Na(+) and Cl(-) ions in aqueous solution were calculated in a wide range of temperatures from 0 to 100 °C. The potentials have been determined using the inverse Monte Carlo approach, from the ion-ion radial distribution functions computed in 50 ns molecular dynamics simulations of ions and explicit water molecules. We further separated the effective potentials into a short-range part and an electrostatic long-range part represented by a coulombic potential with some dielectric permittivity. We adjusted the value of the dielectric permittivity to provide the fastest possible decay of the short-range potentials at larger distances. The obtained temperature dependence of the dielectric permittivity follows well the experimental data. We show also that the largest part of the temperature dependence of the effective potentials can be attributed to the temperature-dependent dielectric permittivity.     

Flexible, ab initio potential, and dipole moment surfaces for water. I. Tests and applications for clusters up to the 22-mer

We report full-dimensional, ab initio potential energy and dipole moment surfaces, denoted PES and DMS, respectively, for arbitrary numbers of water monomers. The PES is a sum of 1-, 2-, and 3-body potentials which can also be augmented by semiempirical long-range higher-body interactions. The 1-body potential is a spectroscopically accurate monomer potential, and the 2- and 3-body potentials are permutationally invariant fits to tens of thousands of CCSD(T)/aug-cc-pVTZ and MP2/aug-cc-pVTZ electronic energies, respectively. The DMS is a sum of 1- and 2-body DMS, which are covariant fits to tens of thousands MP2/aug-cc-pVTZ dipole moment data. We present the details of these new 2- and 3-body potentials and then extensive applications and tests of this PES are made to the structures, classical binding energies, and harmonic frequencies of water clusters up to the 22-mer. In addition, we report the dipole moment for these clusters at various minima and compare the results against available and new ab initio calculations.     

EMP as a similarity measure: a geometric point of view

Soft Coulomb potentials constructed by multiplying the classical potential by a Gaussian function (or a linear combination of them) permit to consider a wide family of distributions which limit with the classical potential when the exponent becomes infinite. Soft Coulomb potentials can be employed as potential operators with first order density functions in order to compute families of soft electrostatic molecular potentials (EMP) for any quantum object. The soft EMP family possesses two interesting computational features: being not only formally equivalent to classical EMP, but finite everywhere, even at the atomic nuclei. The structure of the soft Coulomb operator family yielding soft EMP can be easily related with a quantum similarity integral feature.     

Sensitivity analysis of thermodynamic properties of liquid water: a general approach to improve empirical potentials

A sensitivity analysis of bulk water thermodynamics is presented in an effort to understand the relation between qualitative features of molecular potentials and properties that they predict. The analysis is incorporated in molecular dynamics simulations and investigates the sensitivity of the Helmholtz free energy, internal energy, entropy, heat capacity, pressure, thermal pressure coefficient, and static dielectric constant to components of the potential rather than the parameters of a given functional form. The sensitivities of the properties are calculated with respect to the van der Waals repulsive and the attractive parts, plus short- and long-range Coulomb parts of three four site empirical water potentials: TIP4P, Dang-Chang and TTM2R. The polarization sensitivity is calculated for the polarizable Dang-Chang and TTM2R potentials. This new type of analysis allows direct comparisons of the sensitivities for different potentials that use different functional forms. The analysis indicates that all investigated properties are most sensitive to the van der Waals repulsive, the short-range Coulomb and the polarization components of the potentials. When polarization is included in the potentials, the magnitude of the sensitivity of the Helmholtz free energy, internal energy, and entropy with respect to this part of the potential is comparable in magnitude to the other electrostatic components. In addition similarities in trends of observed sensitivities for nonpolarizable and polarizable potentials lead to the conclusion that the complexity of the model is not of critical importance for the calculation of these thermodynamic properties for bulk water. The van der Waals attractive and the long-range Coulomb sensitivities are relatively small for the entropy, heat capacity, thermal pressure coefficient and the static dielectric constant, while small changes in any of the potential contributions will significantly affect the pressure. The analysis suggests a procedure for modification of the potentials to improve predictions of thermodynamic properties and we demonstrate this general approach for modifying potentials for one of the potentials.