Efficient evaluation of short-range Hartree-Fock exchange in large molecules and periodic systems

We present an efficient algorithm for the evaluation of short-range Hartree-Fock exchange energies and geometry gradients in Gaussian basis sets. Our method uses a hierarchy of screening levels to eliminate negligible two-electron integrals whose evaluation is the fundamental computational bottleneck of the procedure. By applying our screening technique to the Heyd-Scuseria-Ernzerhof [J. Chem. Phys. 118, 8207 (2003)] short-range Coulomb hybrid density functional, we achieve a computational efficiency comparable with that of standard nonhybrid density functional calculations.     

Generalized extended empirical bond-order dependent force fields including nonbond interactions

We present a general approach for describing chemical processes (bond breaking and bond formation) in materials using force fields (FF) that properly describe multiple bonds at small distances while describing nonbond (Coulomb and van der Waals) interactions at long distances. This approach is referred to as the generalized extended empirical bond-order dependent FF. In this paper we use the Brenner empirical bond-order dependent FF for the short-range interactions and report applications on the energetics and structures of graphite crystal, dynamics of molecular crystals, and distortions of bucky tubes. Received: 7 August 1998 / Accepted: 26 October 1998 / Published online: 16 March 1999     

A short-range correlation energy density functional with multi-determinantal reference

We introduce a short-range correlation density functional defined with respect to a multi-determinantal reference which is meant to be used in a multi-determinantal extension of the Kohn–Sham scheme of density functional theory based on a long-range/short-range decomposition of the Coulomb electron–electron interaction. We construct the local density approximation for this functional and discuss its performance on the He atom.     

A genetic algorithm for the structural optimization of Morse clusters

This article describes the application of a genetic algorithm for the structural optimization of 19–50-atom clusters bound by medium-range and short-range Morse pair potentials. The GA is found to be efficient and reliable for finding the geometries corresponding to the previously published global minima [Doye JPK, Wales DJ (1997) J Chem Soc Faraday Trans 93: 4233]. Using the genetic algorithm, only a relatively small number of energy evaluations and minimizations are required to find the global minima. By contrast, a simple random search algorithm often cannot find the global minima of the larger clusters, even after many thousands of searches. Received: 27 October 1999 / Accepted: 7 December 1999 / Published online: 19 April 2000     

The properties of off-shell coulomb radial wavefunctions

Approximations to exact wave functions for the scattering of few-particle systems often involve components corresponding to the interaction of two of the particles “off the energy-shell”. Several examples arising in the collision of ions and photons with atoms are given. An expansion in partial waves leads to an off-shell radial wave function. The defining differential equation is solved here numerically with particular emphasis on the behaviour arising from two-body potentials of long-range Coulomb form. The transition to shell of the radial wave functions, Jost functions and solutions andT-matrix elements is discussed for both short-range and Coulomb potentials. It is shown that the approximation of a Coulomb potential by a shorter-range form involves little error when sufficiently far off the energy shell.     

Ab initio compact group model potentials for describing environment effects in cluster calculations

A method for the determination of ab initio group model potentials within the Hartree–Fock framework is reported. Following the theory of separability of many electron systems, a new way to incorporate the effect of complete chemical entities by means of polycenter compact model potentials is presented. The interaction between active and frozen electrons is partitioned as a sum of long- and short-range terms. The long-range term is described as the effect of −2e charges placed in the center of the charge of the frozen group molecular orbitals; the short-range one, the exchange and Pauli repulsion, is developed as a spectral representation in a nonorthogonal basis set. An algorithm to solve the problem associated with the rotation of the polycenter model potential is presented and implemented in an all-purpose quantum chemical program. In order to check the method, a group model potential for H₂O was obtained and tested. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1145–1152, 1999     

Ewald mesh method for quantum mechanical calculations

The Fourier transform Coulomb (FTC) method has been shown to be effective for the fast and accurate calculation of long-range Coulomb interactions between diffuse (low-energy cutoff) densities in quantum mechanical (QM) systems. In this work, we split the potential of a compact (high-energy cutoff) density into short-range and long-range components, similarly to how point charges are handled in the Ewald mesh methods in molecular mechanics simulations. With this linear scaling QM Ewald mesh method, the long-range potential of compact densities can be represented on the same grid as the diffuse densities that are treated by the FTC method. The new method is accurate and significantly reduces the amount of computational time on short-range interactions, especially when it is compared to the continuous fast multipole method.     

Significant reduction of on-site Coulomb energy U due to short-range correlation in an organic Mott insulator.

By carrying out a first-principles T-matrix calculation on multiple scatterings between electrons, we show that the intramolecular electron-electron interaction energy U, of a Mott insulator of the organic radical 1,3,5-trithia-2,4,6-triazapentalenyl (TTTA) is significantly reduced from the naive expectation value of the Coulomb interaction (7.3 eV and 5.3 eV, respectively, for the bare and screened Coulomb interactions) to 2.9 eV due to the short-range correlation. This result together with the intermolecular interaction energy D=1.3 eV explains the experimental optical gap (1.5 eV). The associated two-particle wavefunction clearly shows the Coulomb hole indicating that two electrons with antiparallel spins cannot approach because of the Coulomb repulsion. We also discuss the energetics and magnetics of this system.     

Étude théorique de la dynamique du réseau de PbTiO3 dans la phase quadratique

The lattice dynamics of lead titanate PbTiO₃ is discussed quantitatively using a shell model taking into account the electronic polarizabilities of the constituent ions, and including Coulomb and short-range interactions. Our calculations highlight the important role played by the anisotropic polarizability of oxygen and show good agreement between calculated and experimental dispersion curves.     

Etude theorique de la dynamique du réseau de batio3 en phase quadratique

The lattice dynamics of barium titanate BaTiO₃ is discussed quantitatively in the framework of a shell model taking into account the electronic polarizabilities of the constituent ions and including Coulomb and short-range interactions. The results of calculations point out the important role of the anisotropic oxygen polarizability. There is a good agreement between calculated and experimental dispersion curves.     

The Coulomb Hole of the Ne Atom

We analyze the Coulomb hole of Ne from highly-accurate CISD wave functions obtained from optimized even-tempered basis sets. Using a two-fold extrapolation procedure we obtain highly accurate results that recover 97 % of the correlation energy. We confirm the existence of a shoulder in the short-range region of the Coulomb hole of the Ne atom, which is due to an internal reorganization of the K-shell caused by electron correlation of the core electrons. The feature is very sensitive to the quality of the basis set in the core region and it is not exclusive to Ne, being also present in most of second-row atoms, thus confirming that it is due to K-shell correlation effects.     

A study of the effect of attenuation curvature on molecular correlation energies by introducing an explicit cutoff radius into two-electron integrals

We present a new attenuator function that can be applied to the Coulomb operator. Similar to the popular erf(omegar) attenuator, the function [erf(omega(r + r0)) + erf(omega(r - r0))]/2 divides the Coulomb potential into a singular short-range piece and a non-singular long-range piece. In our attenuator, omega controls the sharpness of the short-range/long-range division at r0. With r0 = 0, this reduces to erf(omegar), but the additional parameter allows more flexible adjustment of the potential, for physical and/or computational reasons. We present some illustrative results for a truncated MP2 method, where mean field effects are handled exactly and correlation is treated locally. This study indicates, somewhat expectedly, that the slope and curvature of the attenuated potential are more important than its value (a trivial constant may always be added to a potential). However, there are some surprising features of the data that suggest what bounds need to be put on the curvature of the attenuated potential in order to achieve reasonable physics. Conveniently, we find that our attenuator form has the ability to preserve the curvature of the Coulomb potential almost exactly at short range, allowing for the truncation of long-range interactions while preserving the local physics very well. The molecular integrals for the resultant operator can be done analytically over Gaussian basis functions, and the extensive algebraic manipulations necessary to evaluate them stably are shown.     

Fragmentation channels of large multicharged clusters

We address unifying features of fragmentation channels driven by long-range Coulomb or pseudo-Coulomb forces in clusters, nuclei, droplets, and optical molasses. We studied the energetics, fragmentation patterns, and dynamics of multicharged (A+)n (n=55, 135, 321) clusters. In Morse clusters the variation of the range of the pair-potential induced changes in the cluster surface energy and in the fissibility parameter X=E(Coulomb)2E(surface). X was varied in the range of X=1-8 for short-range interactions and of X=0.1-1.0 for long-range interactions. Metastable cluster configurations were prepared by vertical ionization of the neutral clusters and by subsequent structural equilibration. The energetics of these metastable ionic clusters was described in terms of the liquid drop model, with the coefficients of the volume and surface energies depending linearly on the Morse band dissociation energy. Molecular-dynamics simulations established two distinct fragmentation patterns of multicharged clusters that involve cluster fission into a small number of large, multicharged clusters for X<1 and Coulomb explosion into a large number of individual ions and small ionic fragments for X>1. The Rayleigh instability limit X=1 separates between spatially anisotropic fission and spatially isotropic Coulomb explosion. Distinct features of the fragmentation energetics and dynamics were unveiled. For fission of n=55 clusters, large kinetic and internal energies of the large fragments are exhibited and the characteristic fragmentation time is approximately 700 fs, while for Coulomb explosion the major energy content of the small fragments involves kinetic energy and the characteristic fragmentation time of approximately 300 fs is shorter. The Rayleigh (X=1) limit, leading to isotropic Coulomb explosion, is transcended by a marked enhancement of the Coulomb energy, which is realized for extremely ionized clusters in ultraintense laser fields, or by a dramatic reduction of the surface energy as is the case for the expansion of optical molasses.     

The non-equilibrium charge screening effects in diffusion-driven systems with pattern formation

The effects of non-equilibrium charge screening in mixtures of oppositely charged interacting molecules on surfaces are analyzed in a closed system. The dynamics of charge screening and the strong deviation from the standard Debye-Hückel theory are demonstrated via a new formalism based on computing radial distribution functions suited for analyzing both short-range and long-range spacial ordering effects. At long distances the inhomogeneous molecular distribution is limited by diffusion, whereas at short distances (of the order of several coordination spheres) by a balance of short-range (Lennard-Jones) and long-range (Coulomb) interactions. The non-equilibrium charge screening effects in transient pattern formation are further quantified. It is demonstrated that the use of screened potentials, in the spirit of the Debye-Hückel theory, leads to qualitatively incorrect results.     

TATB二聚体分子间作用力及其气相几何构型研究

采用对称性匹配微扰理论(SAPT)定量地求得TATB分子间的静电、交换排斥、诱导和色散等分子间作用能项, 从理论上揭示了TATB分子间作用本质; 在此基础上, 阐明了密度泛函在研究TATB二聚体时的适合性问题. 结果表明: (1)在有分子间氢键的TATB二聚体中, 库仑力足以与交换排斥力相抗衡, 起主导作用. (2)含分子间氢键的气相TATB二聚体的合理几何构型为平面型结构, 此结构的产生与色散力无关, 因此不管泛函是否含有近程色散作用, 均应预测到这种强极性的平面型结构. (3)在无分子间氢键的TATB二聚体中, 库仑力难以与交换排斥力相抗衡, 色散作用起到了关键作用; (4)在这种情况下, 未含有近程色散作用的密度泛函不可能给出合理构型. 恰好相反, 含有近程色散作用的密度泛函PBE0却能正确地预测到具有“平行重叠”结构且呈微弱极性的TATB二聚体, 色散力是导致这种构型产生的根本原因. “平行重叠”TATB二聚体是典型的色散体系, 其色散力占绝对主导地位并极有可能起源于两个TATB分子上π电子的相互作用. (5)对于所有TATB二聚体, 色散力或很显著或起主导作用. 由于密度泛函或未含有近程色散, 或只能部分地把近程色散表达出来, 这样使得当前所有密度泛函不可能精确求得这些二聚体的作用能.     

Coulomb effects in binding of heme in gas-phase ions of myoglobin

Coulomb effects in binding of heme in gas-phase holomyoglobin ions are studied. Positive and negative ions are formed from solution myoglobin with Fe(2+) (ferromyoglobin) and Fe(3+) (ferrimyoglobin). The energy that must be added to the resulting holomyoglobin ions to cause heme loss has been measured by triple-quadrupole tandem mass spectrometry. With negative ions, neutral heme is lost regardless of the charge state of Fe in solution. It is likely that the Fe(3+) is reduced to Fe(2+) in the negative electrospray process. With positive ions, predominantly neutral heme loss is observed with ions formed from ferromyoglobin in solution, and positive heme loss with ions formed from ferrimyoglobin in solution. The energies required to induce neutral heme loss are similar for positive and negative ions. The energies required to induce charged heme loss from positive holomyoglobin ions are significantly less. Coulomb repulsion between the charged heme and charged protein appears to lower the barrier for heme loss. These results are consistent with a simple model potential with a long-range Coulomb repulsion and short-range attraction between the heme and protein.     

Role of short-range electrostatics in torsional potentials

A force field needs to decide if it should contain a torsional potential or not. A helpful guide to this decision should come from a quantum mechanical energy partitioning. Here we analyze the energy profiles of eight simple molecules (ethane, hydrogen peroxide, hydrazine, methanol, acetaldehyde, formamide, acetamide and N-methylacetamide) subject to rotation around a torsion angle. Coulomb interaction energies between all atom pairs in a molecule are monitored during the rotation. Atoms are defined as finite electron density fragments by quantum chemical topology, a method that enables well-defined short-range interactions (1-2, 1-3 and 1-4). Energy profiles of Coulomb interaction energies mostly counteract the ab initio energy profiles. This and future work strives to settle ambiguities in current force field design.     

Continuum solutions of the Klein-Gordon equation

We construct explicit solutions of the Klein-Gordon equation for continuum states. The role of the energy in the single-particle Klein-Gordon theory is elucidated. Special emphasis is laid on the determination of resonance states in the continuum for overcritical potentials. As examples for long-range interactions we depict solutions for the Coulomb potential of a point-like nucleus as well as an extended nucleus. The square-well potential and the exponential potential are treated to exemplify peculiarities of short-range interactions. We also derive continuum solutions for a scalar interaction of square-well type. Finally we discuss the behaviour of a spin-0 particle in an external homogeneous magnetic field.     

Protein interactions studied by SAXS: effect of ionic strength and protein concentration for BSA in aqueous solutions

We have studied a series of samples of bovine serum albumin (BSA) solutions with protein concentration, c, ranging from 2 to 500 mg/mL and ionic strength, I, from 0 to 2 M by small-angle X-ray scattering (SAXS). The scattering intensity distribution was compared to simulations using an oblate ellipsoid form factor with radii of 17 x 42 x 42 A, combined with either a screened Coulomb, repulsive structure factor, SSC(q), or an attractive square-well structure factor, SSW(q). At pH = 7, BSA is negatively charged. At low ionic strength, I < 0.3 M, the total interaction exhibits a decrease of the repulsive interaction when compared to the salt-free solution, as the net surface charge is screened, and the data can be fitted by assuming an ellipsoid form factor and screened Coulomb interaction. At moderate ionic strength (0.3-0.5 M), the interaction is rather weak, and a hard-sphere structure factor has been used to simulate the data with a higher volume fraction. Upon further increase of the ionic strength (I >or= 1.0 M), the overall interaction potential was dominated by an additional attractive potential, and the data could be successfully fitted by an ellipsoid form factor and a square-well potential model. The fit parameters, well depth and well width, indicate that the attractive potential caused by a high salt concentration is weak and long-ranged. Although the long-range, attractive potential dominated the protein interaction, no gelation or precipitation was observed in any of the samples. This is explained by the increase of a short-range, repulsive interaction between protein molecules by forming a hydration layer with increasing salt concentration. The competition between long-range, attractive and short-range, repulsive interactions accounted for the stability of concentrated BSA solution at high ionic strength.