An analytic potential energy function for the amide–amide and amide–water intermolecular hydrogen bonds in peptides

An analytic potential energy function is proposed and applied to evaluate the amide–amide and amide–water hydrogen‐bonding interaction energies in peptides. The parameters in the analytic function are derived from fitting to the potential energy curves of 10 hydrogen‐bonded training dimers. The analytic potential energy function is then employed to calculate the N? H…O?C, C? H…O?C, N? H…OH₂, and C?O…HOH hydrogen‐bonding interaction energies in amide–amide and amide–water dimers containing N‐methylacetamide, acetamide, glycine dipeptide, alanine dipeptide, N‐methylformamide, N‐methylpropanamide, N‐ethylacetamide and/or water molecules. The potential energy curves of these systems are therefore obtained, including the equilibrium hydrogen bond distances R(O…H) and the hydrogen‐bonding energies. The function is also applied to calculate the binding energies in models of β‐sheets. The calculation results show that the potential energy curves obtained from the analytic function are in good agreement with those obtained from MP2/6‐31+G** calculations by including the BSSE correction, which demonstrate that the analytic function proposed in this work can be used to predict the hydrogen‐bonding interaction energies in peptides quickly and accurately. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Potential energy function for cation–peptide interactions: An ab initio study

A potential energy function is developed to represent the interaction of small monovalent cations, Li⁺, Na⁺, and K⁺, with the backbone of polypeptides. The results are based on ab initio calculations up to the 6-31G* level of the interactions of the ions with acetamide and N-methylacetamide. Basis set superposition errors are corrected with the counterpoise method. A systematic overestimate of the bond polarities is taken into account by an empirical scaling procedure that uses the ratio of the experimental to ab initio dipole moment. The calculated binding energies obtained with this procedure show consistent convergence with different basis sets and are in good agreement with experimental data on cation–water and cation–dimethylformamide systems. Investigations of the calculated ab initio potential energy surface indicate that the cation–peptide interaction is dominated by electrostatics and includes a nonnegligible contribution from polarization of the peptide group by the ion. The induced polarization results in a steeper-than-Coulombic interaction and cannot be described by fixed ion–peptide partial charges electrostatics. Atomic polarizabilities located on the atoms of the ligand molecule are introduced to account for the induced polarization in the empirical energy function. A ～1/r⁴ attractive interaction appears in the potential function. The resulting radial and angular dependence of the potential energy surface is well reproduced. © 1995 by John Wiley & Sons, Inc.     

Third-order interaction approximation for linear polymer chains

Third-order interactions imposed by a pair of atoms separated by five bonds are taken into account in computations of the mean-square end-to-end distance and the mean-square radius of gyration for linear polymer chains. The statistical weight matrices are established on the basis of the rotational isomeric state model. The conformational energy of n-hexane is calculated as a function of the C? C bond rotation angles. The third-order interaction energy is obtained by comparison with that of n-pentane. The characteristic ratio of polymethylene is 6.6 in the third-order interaction approximation, which is in agreement with experimental data.     

Anab initio potential energy surface and dynamics calculations for vibrational excitation of I2 by He

We present newab initio calculations of the interaction potential and the elastic and inelastic cross sections for He scattering by I₂. The electronic structure calculations of the interaction potential are based on an extensive one-electron basis set (triple zeta plus ad set on each I, ans function plus ap set at the I₂ bond center, and quadruple zeta plus twop sets on He), a two-configuration-SCF orbital set, and a configuration interaction calculation based on all single and double excitations out of the two-configuration reference space. The calculations are performed at 16He-I₂ distances for nine combinations of I₂ vibrational displacement and orientation. A new form of analytic representation is presented that is particularly well suited to efficient and accurate fitting ofab initio interaction potentials that include vibrational displacements. Scattering calculations are performed by the vibrational close-coupling, rotational-infinite-order-sudden approximation with a converged vibrational basis.     

Influence of the Screening Function on Theoretical Calculations of the Structure Factor of Liquid Aluminum

Abstract

The structure factor S(k) of liquid aluminum is calculated using the Metropolis Monte Carlo method. The effective two-body ion-ion interaction used in the calculations are the Shaw optimized model and the local approximation suggested by Harrison calculated using two screening function in each case, the screening function of Vashishta and Singwi and that of Utsumi and Ichimaru. The calculated structure factors from each case are compared with experiment.     

Observation of CH⋅⋅⋅π Interactions between Methyl and Carbonyl Groups in Proteins

Protein structure and function is dependent on myriad noncovalent interactions. Direct detection and characterization of these weak interactions in large biomolecules, such as proteins, is experimentally challenging. Herein, we report the first observation and measurement of long‐range “through‐space” scalar couplings between methyl and backbone carbonyl groups in proteins. These J couplings are indicative of the presence of noncovalent C−H⋅⋅⋅π hydrogen‐bond‐like interactions involving the amide π network. Experimentally detected scalar couplings were corroborated by a natural bond orbital analysis, which revealed the orbital nature of the interaction and the origins of the through‐space J couplings. The experimental observation of this type of CH⋅⋅⋅π interaction adds a new dimension to the study of protein structure, function, and dynamics by NMR spectroscopy.     

Observation of CH⋅⋅⋅π Interactions between Methyl and Carbonyl Groups in Proteins

Protein structure and function is dependent on myriad noncovalent interactions. Direct detection and characterization of these weak interactions in large biomolecules, such as proteins, is experimentally challenging. Herein, we report the first observation and measurement of long-range “through-space” scalar couplings between methyl and backbone carbonyl groups in proteins. These J couplings are indicative of the presence of noncovalent C−H⋅⋅⋅π hydrogen-bond-like interactions involving the amide π network. Experimentally detected scalar couplings were corroborated by a natural bond orbital analysis, which revealed the orbital nature of the interaction and the origins of the through-space J couplings. The experimental observation of this type of CH⋅⋅⋅π interaction adds a new dimension to the study of protein structure, function, and dynamics by NMR spectroscopy.     

Transferable scoring function based on semiempirical quantum mechanical PM6-DH2 method: CDK2 with 15 structurally diverse inhibitors

A semiempirical quantum mechanical PM6-DH2 method accurately covering the dispersion interaction and H-bonding was used to score fifteen structurally diverse CDK2 inhibitors. The geometries of all the complexes were taken from the X-ray structures and were reoptimised by the PM6-DH2 method in continuum water. The total scoring function was constructed as an estimate of the binding free energy, i.e., as a sum of the interaction enthalpy, interaction entropy and the corrections for the inhibitor desolvation and deformation energies. The applied scoring function contains a clear thermodynamical terms and does not involve any adjustable empirical parameter. The best correlations with the experimental inhibition constants (ln K _i) were found for bare interaction enthalpy (r ² = 0.87) and interaction enthalpy corrected for ligand desolvation and deformation energies (r ² = 0.77); when the entropic term was considered, however, the correlation becomes worse but still acceptable (r ² = 0.52). The resulting correlation based on the PM6-DH2 scoring function is better than previously published function based on various docking/scoring, SAR studies or advanced QM/MM approach, however, the robustness is limited by number of available experimental data used in the correlation. Since a very similar correlation between the experimental and theoretical results was found also for a different system of the HIV-1 protease, the suggested scoring function based on the PM6-DH2 method seems to be applicable in drug design, even if diverse protein–ligand complexes have to be ranked.     

Kinetics of partly diffusion-controlled reaction XXI: A simple algorithm for computing the apparent rate of reaction

Starting from Smoluchowski's hypothesis, a simple algorithm is developed in order to obtain the apparent rate constant at large values of time, t, with some physical and chemical processes, as in the case of diffusion controlled reactions. Some practical examples are illustrated, assuming nonuniform distribution function, space-dependent diffusion coefficient or short-range interaction leading to an asymptotic analytical expression of the form α + β/√t, where α and β are constants function of the system of interest.     

Radial limit of lithium revisited

Configuration interaction (CI) calculations are carried out for the ground state of lithium using a thoroughly optimized basis set of s-type Slater functions. They establish that the radial limit of the nonrelativistic energy of the ground ²S state of lithium is no higher than −7.448666443E_h. Thus, radial correlation accounts for 35.2% of the total correlation energy. The radial CI wave function predicts a significantly more accurate Fermi contact parameter than the Hartree-Fock wave function. However, the imbalanced treatment of electron correlation in the radial CI wave function leads to an excessively diffuse electron density that is worse than that of the Hartree-Fock wave function. © 1997 John Wiley & Sons, Inc.     

Partitioning of Dyes,Free Anthraquinones,and Tanshinones in Aqueous Two-Phase Systems of Cationic/Anionic Surfactants

The partition behaviors of some dyes, anthraquinones, and tanshiones in two kinds of aqueous two-phase systems (ATPSs) have been investigated. The partition constants (K) of ionic dyes and rhein in the first kind of ATPSs are dependent on hydrophobic and electrostatic interactions. A correlation for K as a function of the concentration ratio of total surfactant ions and surface net charge ratio of aggregates between the two coexisting phases has been proposed. Almost 100% of water-insoluble electroneutral extract accumulates in surfactant-rich phase of the first kind of ATPS due to hydrophobic interaction. K of emodin in the second kind of ATPSs is correlated by the same model regardless of electrostatic interaction.     

A molecule on the surface or inside a spherical nanoparticle: the computation of the interaction energy in terms of the dielectric continuum model

The electrostatic interaction energy between a charged or polar molecule and a spherical polarizable nanoparticle is studied within the advanced dielectric continuum model proposed previously. The molecule can be located either inside or outside the nanoparticle or in the vicinity of its boundary surface. The nanoparticle and its environment are considered as a polarizable medium and described in terms of a nonuniform dielectric continuum approximation with a position-dependent dielectric permittivity function e(r) \varepsilon (r) , where r is the position vector. A special construction of this function accounts for the proper treatment of sophisticated boundary effects. Test computations are performed for a number of sample molecules.     

The application of the λ parameter method to calculation of the interaction energies between two plane parallel double layers for symmetric electrolytes

The λ parameter method had successfully been applied to calculate the interaction energies between two plane parallel double layers for symmetric electrolytes. When y ₀ and |y _d | ≤ 20, the number of the series terms required to obtain the interaction energies with six significant digits is not more than 4. If we regard the interaction energies as the function of the hyperbolic function tanh (y ₀/2) instead of tanh(y ₀/4), then calculating it with the aid of λ parameter method, we can obtain above results at once. This enables one to avoid the mathematical complexity of other methods.     

An atom-in-molecules and electron-localization-function study of the interaction between O2 and VxOy+/VxOy (x = 1, 2, y = 1–5) clusters

 The most stable structures of V _x O _y ⁺/V _x O _y (x=1, 2, y=1–5) clusters and their interaction with O₂ are determined by density functional calculations, the B3LYP functional with the 6-31G* basis set. The nature of the bonding of these clusters and the interaction with O₂ have been studied by topological analysis in the framework of both the atoms-in-molecules theory of Bader and the Becke–Edgecombe electron localization function. Bond critical points are localized by means of the analysis of the electron density gradient field, ∇ρ(r), and the electron localization function gradient field, ∇η(r). The values of the electron density properties, i.e., electron density, ρ(r), Laplacian of the electron density, ∇²ρ(r), and electron localization function, η(r), allow the nature of the bonds to be characterized, and linear correlation is found for the results obtained in both gradient fields. Vanadium-oxygen interactions are characterized as unshared-electron interactions, and linear correlation is observed between the electron density properties and the V–O bond length. In contrast, O₂ units involve typical shared-electron interactions, as for the dioxygen molecule. Four different vanadium–oxygen interactions are found and characterized: a molecular O₂ interaction, a peroxo O₂ ²⁻ interaction, a superoxo O₂ ⁻ interaction and a side-on O₂ ⁻ interaction. Received: 15 October 2001 / Accepted: 30 January 2002 / Published online: 24 June 2002     

Thermodynamics of Transfer of Some Alkyl Acetates from Water to Water–Ethanol Mixtures

 The solubility of methyl acetate (MeOAc), ethyl acetate (EtOAc), 1-propyl acetate(1-PrOAc), 1-butyl acetate (1-BuOAc), 2-methyl-1-propyl acetate (iso-BuOAc), 2-butyl acetate (sec-BuOAc), 2-methyl-2-propyl acetate (tert-BuOAc), 1-pentyl acetate (1-PeOAc), and 1-hexyl acetate(1-HeOAc) in 2.5, 5.0, 7.5, and 10.0 weight per cent of ethanol in water were determined at 298.2 K. The solubility of the same compounds, except for tert-BuOAc, 1-PeOAc, and 1-HeOAc, was determined as a function of temperature at 10.0 weight per cent of ethanol in water. From the solubility measurements the standard Gibbs energy (), enthalpy (), and entropy () of transfer were determined. The calculated thermodynamic functions show that the predominant factors in the transfer of alkyl acetate molecules are the transfer of the cavity and the hydrophobic interaction of the non-polar alkyl chain. Scaled particle theory calculations were used to determine the thermodynamics of cavity transfer, which were combined with the experimental total transfer quantities to obtain the corresponding interaction transfer quantities. It was found that the Gibbs energy of interaction for the transfer is negative, whereas the enthalpy and entropy of interaction for the transfer are positive; almost complete compensation of enthalpy and entropy components occurs.     

All-pair wave function and reduced variational equation for electronic systems

A new type of wave function is proposed for atomic and molecular systems. This all-pair function is constructed of N(N – 1)/2 identical geminals for N electrons. For systems with the highest multiplicity this is the full space part of the wave function. For closed shell systems it has to be multiplied by a Slater determinant according to the antisymmetry condition. In the case of maximal multiplicity a reduced variational equation is derived for the geminal. This equation is independent of the dimensionality of the system and contains the particle number as a multiplicative factor only. The method is extended to the closed shell case where a restriction has to be fulfilled. The reduction of the variational equation can be done only approximately. The use of identical geminals can be treated as a first approximation. An extension of the method, called the pair interdependent configuration interaction (PICI), is proposed. The special features of the method are discussed briefly.     

Liquid–liquid phase separation in multicomponent polymer solutions. IX. Concentration-dependent pair interaction parameter from critical miscibility data on the system polystyrene–cyclohexane

Critical miscibility data obtained from measurements of phase-volume ratios have been used to calculate the concentration dependence of the pair interaction parameter for the system polystyrene–cyclohexane. The measured temperature and concentration ranges are 11–30°C and 4–18% polymer by weight, respectively. With the Gibbs free energy of mixing expressed in polymer segment mole fractions, x^*, the pair interaction parameter is g(x^*, T) = 0.4961 + 71.92/T + 0.2312x^* + 0.0750x^*2. In a polymer volume fraction formulation the parameter is g(φ, T) = 0.4099 + 90.65/T + 0.2064 φ + 0.0518 φ², which approximates to χ(φ, T) = 0.2035 + 90.65/T + 0.3092 φ + 0.1554 φ². Comparison of the temperature and concentration dependence with that obtained by other authors shows very good agreement, even when extensive extrapolations in temperature and concentration are applied. The present function is believed to be the most accurate. Solutions of mixtures of two narrow-distribution polystyrenes in cyclohexane show separation into three liquid phases under the exact conditions predicted by theoretical calculation with the present pair-interaction function.     

Memory effect on the inelastic interaction of electrons moving parallel to a solid surface

It is generally assumed that two successive inelastic interactions between an electron and a solid are independent of each other. In other words, the electron has no memory of its previous interaction. However, the previous interaction of the electron generates a potential that should influence its succeeding inelastic interaction. The aim of this work is to establish a model to account for the memory effect of an electron between two successive inelastic interactions. On the basis of the dielectric response theory, formulae for differential inverse inelastic mean free paths (DIIMFPs) and inelastic mean free paths (IMFPs) considering the memory effect were derived for electrons moving parallel to a solid surface by solving the Poisson equation and applying suitable boundary conditions. These mean free paths were then calculated with the extended Drude dielectric function for a Cu surface. It was found that the DIIMFP and the IMFP with the memory effect for electron energy E lay between the corresponding values without the memory effect for electron energy E and previous energy E₀. The memory effect increased with increasing electron energy loss, E₀ ? E, in the previous inelastic interaction. Copyright © 2005 John Wiley & Sons, Ltd.