Showing papers in "Molecular Physics in 2005"

The GAMESS-UK electronic structure package: algorithms, developments and applications

Abstract: A description of the ab initio quantum chemistry package GAMESS-UK is presented. The package offers a wide range of quantum mechanical wavefunctions, capable of treating systems ranging from closed-shell molecules through to the species involved in complex reaction mechanisms. The availability of a wide variety of correlation methods provides the necessary functionality to tackle a number of chemically important tasks, ranging from geometry optimization and transition-state location to the treatment of solvation effects and the prediction of excited state spectra. With the availability of relativistic ECPs and the development of ZORA, such calculations may be performed on the entire Periodic Table, including the lanthanides. Emphasis is given to the DFT module, which has been extensively developed in recent years, and a number of other, novel features of the program. The parallelization strategy used in the program is outlined, and detailed speedup results are given. Applications of the code in the areas ...

Molecular equilibrium geometries based on coupled-cluster calculations including quadruple excitations

Abstract: Using analytic gradient techniques and an additivity scheme for the various electron correlation contributions, i.e. core-correlation, contribution due to full treatment of triple excitations and contributions due to quadruple excitations calculated with different basis sets, the accuracy of computed geometrical parameters are analysed in comparison with experiment. For a test set of 12 closed-shell and 5 open-shell molecules, it is found that inclusion of quadruple excitations is essential to reach agreement with experiment. The mean error of 0.002 pm and the standard deviation of 0.040 pm of the present CCSD(T)/cc-pV6Z + core(CCSD(T)/cc-pCVQZ) + T/cc-pVTZ + Q/cc-pVDZ results for the closed-shell systems underline the importance of quadruple excitations, in particular, as corresponding calculations without quadruple excitations exhibit significantly larger error. Quadruples contributions for multiply bonded systems as well as the challenging F2 molecule are as large as 0.1 to 0.3 pm, while for single bon...

The performance of hybrid density functionals in solid state chemistry: the case of BaTiO3

Abstract: The performance of hybrid exchange functionals is investigated within the framework of Density Functional Theory (DFT), in describing the properties of cubic and tetragonal ferroelectric phases of BaTiO3. A variable fraction ξ of non-local HF exchange is mixed with Becke's GGA formulation, and coupled with the LYP correlation functional. Standard DFT functionals (LDA, PW, B3LYP) and uncorrelated HF are also added for comparison. Inclusion of the non-local HF exchange has a noticeable effect on the calculated electronic density, and several observables show clear trends as a function of the mixing parameter ξ; these include not only the band gap, but also lattice parameter and bulk modulus, structural distortions, relative ionic sizes, electronic polarizability and polarization of the tetragonal phase. In this context, it is shown that hybrid functionals yield results that are generally in better agreement with experiment than local (LDA and GGA) DFT formulations. A higher fraction of HF exchange than the ...

Fast electron correlation methods for molecular clusters in the ground and excited states

Abstract: An efficient and accurate electronic structure method for clusters of weakly interacting molecules has been proposed, on the basis of the pair-interaction method of Kitaura et al., and combined with density functional, many-body perturbation, coupled-cluster, equation-of-motion coupled-cluster, configuration-interaction singles, and time-dependent density functional theories. The method retains the one- and two-body (and, if necessary, also three-body) Coulomb, exchange, and correlation energies exactly and higher-order Coulomb energies in the leading order of multipole expansion (hence the dipole polarization or induction effects). The latter makes the combination of this method with existing implementations of any electronic structure theory extremely easy. It typically recovers the total energies within 0.001%, binding energies within a few kilocalories per mole, and excitation energies within a few hundredths of an electron volt of the conventional implementations. The size dependence of the computati...

Molecular dynamics in electronically excited states using time-dependent density functional theory

Abstract: We describe two different implementations of time-dependent density functional theory (TDDFT) for use in excited state molecular dynamics simulations. One is based on the linear response formulation (LR-TDDFT), whereas the other uses a time propagation scheme for the electronic wave functions (P-TDDFT). Photo-induced cis–trans isomerization of C=C, C=N and N=N double bonds is investigated in three model compounds, namely the 2,4-pentadiene-1-iminium cation (PSB), formaldimine and diimide. For formaldimine and diimide, the results obtained with both schemes are in agreement with experimental data and previously reported theoretical results. Molecular dynamics simulations yield new insights into the relaxation pathways in the excited state. For PSB, which is a model system for the retinal protonated Schiff base involved in the visual process, the forces computed from the LR-TDDFT S1 surface lead to an increased bond length alternation and, consequently, to single bond rotation. On the contrary, P-TDDFT dyna...

Dynamic polarizability, dispersion coefficient C6 and dispersion energy in the effective fragment potential method

Abstract: The development of a fragment–fragment dispersion energy expression, for the general effective fragment potential (EFP2) method is presented. C6 dispersion coefficients, expressed in terms of the dynamic polarizabilties over the imaginary frequency range (α(iν)), were calculated for a set of homo and hetero dimers. Using these coefficients the dispersion energy has been calculated. The dispersion energy is expressed using a simple London series expansion terminated after the n=6 term and implemented using distributed localized molecular orbitals (LMOs). The EFP2 dispersion energy is compared to symmetry adapted perturbation theory (SAPT) values. From this comparison, it is apparent that one needs to include higher order terms in the dispersion energy. Adding an estimated C8 term to the C6 energy greatly improves the agreement with the benchmark SAPT energies.

Augmenting basis set for time-dependent density functional theory calculation of excitation energies: Slater-type orbitals for hydrogen to krypton

Abstract: Attention is given to the dual nature of the time-dependent density functional theory approach for predicting excitation spectra, namely its theoretical basis in dynamic polarizability and its practical implementation in computer programs as a single configuration interaction. A procedure for generating diffuse functions to be added to standard Slater-type orbital basis sets for H to Kr is proposed and tested on ten close-shell molecules. The database for comparing the performance of standard and augmented basis sets consists of the 15 lowest transitions to valence and Rydberg-like states for each of the molecules. The results of this computational study are very encouraging. The addition of new augmenting functions improves the performance of standard basis sets significantly. For example, the new augmented TZP basis set, about the same size as the standard TZ2P set (and considerably smaller than the large QZ4P set), led to an average absolute deviation of 150 predicted excitation energies of only 0.12 e...

Multiresolution quantum chemistry in multiwavelet bases: time-dependent density functional theory with asymptotically corrected potentials in local density and generalized gradient approximations

Abstract: A multiresolution solver for fully numerical linear response calculations of excitation states via the time-dependent Hartree–Fock and density functional theory (TD-HF/DFT) is presented. The linear response method Yanai et al. previously reported [J. Chem. Phys., submitted] was limited to the Tamm–Dancoff approximation and could only use the Hartree–Fock exchange and the local-spin density approximation (LSDA) with a crude asymptotic correction. The present development enables us to perform full TD-HF/DFT calculations employing generalized gradient approximation (GGA) exchange-correlation potentials as well as hybrid ones. The linear response of TD-HF/DFT is computed by means of iteratively solving the coupled integral equations with the Green's functions. In this study, Tozer and Handy's asymptotic correction (AC) is applied to existing DFT exchange-correlations, and is found numerically stable and efficient. Furthermore, the new hybrid exchange-correlation functional CAM-B3LYP, which was recently propos...

Development of a CAS-DFT method covering non-dynamical and dynamical electron correlation in a balanced way

Abstract: CAS-DFT (Complete Active Space Density Functional Theory) is presented as a method that allows an economical, simultaneous treatment of non-dynamical and dynamical correlation effects for electronic systems with multi-reference character. Central problems of CAS-DFT concern the effective coupling between wave function and DFT method, the double counting of dynamical correlation effects, the choice of the proper input quantities for the DFT functional, the balanced treatment of core and active orbital correlation, of equal-spin and opposite-spin correlation effects, and the inclusion of spin polarization to handle closed- and open-shell systems in a balanced way. We present CAS-DFT2(CS,SPP,FOS,DS) (CAS-DFT using level 2 for the distinction of core and active orbital correlations, carried out with the Colle–Salvetti functional, using the Stoll–Pavlidou–Preuss functional for equal-spin correlation corrections, including spin polarization in the scaling procedure, and correcting with the Davidson–Staroverov d...

Van der Waals interactions studied by density functional theory

Abstract: A new density functional theory (DFT) for calculations of van der Waals (vdW) complexes is presented. In this scheme, a long-range-corrected exchange-correlation functional is combined with a new damping method of the Andersson–Langreth–Lundqvist (ALL) vdW correlation functional for dealing with molecules containing various types of atoms. The long-range correction (LC) scheme for the exchange functional was used in this method. This LC-DFT+ALL method was applied to calculations of rare-gas dimers and vdW complexes, consisting of diatomic molecules and He atoms. The present method reproduces very accurate potential energy surfaces of these systems. In particular, for CO–He complexes, LC-DFT+ALL gives an equilibrium bending structure in agreement with experiment without using a particular basis function, while the collinear structure is given by conventional DFT and high-level ab initio molecular orbital methods without using a bond function. By comparing LC-DFT and ALL component energies, it was found tha...

Molecular dynamics simulations of ice growth from supercooled water

Abstract: The kinetics of ice growth on the secondary prismatic plane and the basal plane {0001} is studied by Molecular Dynamics simulations. The simulation system initially consists of a slab of ice in contact with a layer of water on one side, and vacuum on the other side. The remaining surface of the water layer is also facing vacuum. The time evolution of the system shows the crystallization of the liquid water and the evaporation of very few molecules at the free surfaces. The ice vapour interfaces are wet on both sides by identical thin layers of liquid water, strongly suggesting that the system has reached its equilibrium state. To analyse the results, we have developed a new method to discriminate whether a molecule belongs to the ice lattice or is in liquid state. Using this method to monitor the number of ice molecules as a function of time, we find that the freezing is much faster on the prismatic plane than on the basal plane. For the prismatic plane, irregularities in the surface of the solid phase ar...

Reflections on size-extensivity, size-consistency and generalized extensivity in many-body theory

Abstract: An overview is presented of the notions of size-extensivity and size-consistency, which play an important role in the discussion of many-body methods in physics and chemistry. We also introduce the concept of generalized extensivity, which has been used before implicitly in the literature, and provide an operational definition, which can be tested numerically in a similar way as size-consistency. A numerical example illustrates the concept of generalized extensivity as applied to the EOM-CCSD, STEOM-CCSD and extended-STEOM-CCSD electronic structure methods for excited states. In another line of thought it is argued that algebraic proofs are often more easily constructed than diagrammatic proofs to demonstrate proper separation into non-interacting fragments. The algebraic line of reasoning is illustrated for single reference methods and applied to discuss separability properties for a variety of Hilbert space multi-reference coupled cluster methods.

Accurate ab initio potential for argon dimer including highly repulsive region

Abstract: An ab initio potential has been developed for the argon dimer. This potential is based on coupled-cluster calculations with single, double, and non-iterated triple excitations in a sequence of very large basis sets, up to augmented sextuple-zeta quality and containing bond functions, followed by extrapolations to the complete basis set limit. The calculations included intermolecular distances as small as 0.25 A, where the interaction potential is of the order of 4 keV. The computed points were fitted by an analytic expression. The new potential has the minimum at 3.767 A with a depth of 99.27 cm−1 respectively, very close to experimental values of 3.761 ± 0.003 A and 99.2 ± 1.0 cm−1 respectively. The potential was used to compute the spectra of the argon dimer and the virial coefficients. The latter calculations suggest a possible revision of the established experimental reference results. From the agreement achieved with experimental values and from comparisons of the fit with available piecewise informa...

Quantum mechanical calculation of the OH vibrational frequency in crystalline solids

Abstract: The OH vibrational frequency of four crystalline compounds ranging from ionic (brucite, Mg(OH)2, and portlandite, Ca(OH)2) to semi-covalent (edingtonite, as representative of free surface OH groups in silica, and acid chabazite, as representative of acid zeolites) has been investigated at quantum mechanical level with the CRYSTAL program using the B3LYP hybrid functional. The OH vibration is calculated in two ways: (i) in the harmonic approximation, by diagonalizing the fully coupled dynamical matrix to yield the harmonic frequency ω h . (ii) at the anharmonic level, by decoupling the OH stretching mode from the bulk phonons and by numerically solving the one-dimensional Schrodinger equation associated with the OH potential energy to yield the fundamental ω01 and the first overtone ω02 frequencies. The harmonic and anharmonic frequencies differ by more than 150 cm−1. In the cases where direct comparison is possible (brucite, portlandite and edingtonite), the experimental and calculated frequencies differ ...

A comparison of density-functional-theory and coupled-cluster frequency-dependent polarizabilities and hyperpolarizabilities

Abstract: The frequency-dependent polarizabilities and hyperpolarizabilities of HF, CO, H2O and para-nitroaniline calculated by density-functional theory are compared with accurate coupled-cluster results. Whereas the local-density approximation and the generalized gradient approximation (BLYP) perform very similarly and overestimate polarizabilities and, in particular, the hyperpolarizabilities, hybrid density-functional theory (B3LYP) performs better and produces results similar to those obtained by coupled-cluster singles-and-doubles theory. Comparisons are also made for singlet excitation energies, calculated using linear response theory.

The Golden ratio, ionic and atomic radii and bond lengths

Abstract: This work arose from the author's finding that the ratio of the radius of hydrogen, estimated recently (C.H. Suresh, N. Koga, J. Phys. Chem. A, 105, 5940 (2001)) by density functional methods, to the ground state Bohr radius is the Golden ratio, which operates in a variety of natural phenomena. It is found that the Golden ratio indeed plays a quantitative role in atomic physics. The interesting results are (1) that it arises in atomic dimensions due to the electrostatic forces between negative and positive charges; (2) that the energy of atomic hydrogen is actually equivalent to the energy of the simplest atomic condenser with the Golden mean capacity; (3) that the origin of two terms in the Rydberg equation for absorption and emission is in fact in the ground state term; (4) that all atoms can be assigned definite values of cationic and anionic radii based on the Golden ratio and covalent radii; (5) that these radii are additive and explain quantitatively bond lengths like those of alkali halides, of hyd...

A ‘universal’ B3LYP-based method for gas-phase molecular properties: bond dissociation enthalpy, ionization potential, electron and proton affinity and gas-phase acidity

Abstract: The paper describes a density functional theory methodology using the B3LYP functional, with small correction terms introduced for open shell doublet states and closed-shell anions. The procedure is based on a B3LYP/6-31G(d) geometry optimization and frequency determination, followed by (RO)B3LYP/6-311 + G(2d,2p) single point energy calculations. Using a correction term of +8.368 kJ mol−1 for (doublet) radicals and + 4.184 kJ mol−1 for (closed shell) anions, close agreement is obtained with experiment (i.e. within 10 kJ mol−1) for a series of molecular properties. These include bond dissociation enthalpies for X–H, where X = functional groups containing C, N, O, F, S, and X–Y, where X and Y are binary combinations of the same five heavy atoms plus Si and Cl, ionization potentials, electron and proton affinities, and gas-phase acidities. Using locally dense basis sets the approach can be extended to bond dissociation enthalpy calculations of large molecules with only a small increase in error. Using the sa...

Temperatures: old, new and middle aged

Abstract: This study explores the various ways in which a ‘temperature’ can be introduced and calculated in a molecular simulation. We focus on the relatively recent formula of Rugh, and a simplified version called the ‘configurational’ temperature, T config, which became popular after Rugh's work. We derive formulae for these various ‘temperatures’ for the special case of the soft–sphere fluid, with the pair interaction, , where e and σ set the energy and length scales, respectively, and for different n values. We show with a number of simple test cases that the various prescriptions of temperature give the same result as the thermodynamic temperature at equilibrium. Although much of the current work uses the configurational temperature, Rugh's temperature, T R, has the advantage that it has the thermodynamic value in circumstances where the configurational temperature is not defined (such as in the limit of the ideal gas, where Rugh's temperature becomes the kinetic temperature). The configurational temperature i...

Towards a unified view of fluids

Abstract: It has traditionally been believed that, unlike normal fluids whose structural properties are determined primarily by the intermolecular short-range repulsive interactions, the properties of polar and associating fluids are strongly affected by the long-range Coulombic interactions. In the course of investigations to determine the primary driving forces governing the behaviour of various (non-simple) fluids, and hence to gain a deeper understanding of the molecular mechanisms leading to the development of theoretically based simple models and theory, extensive and systematic computer simulations have been performed on typical quadrupolar (carbon dioxide), dipolar (acetone and acetonitrile), and associating (hydrogen fluoride, methanol, and water) fluids using the available realistic effective pair potentials and their variants involving forces of different ranges. In addition to the main structural characteristics (one- and two-dimensional site–site correlation functions, local g factors, and radial slice...

Generalized equation of state for square-well potentials of variable range

Abstract: An equation of state for square-well fluids of short and long potential range λ is presented and compared with Gibbs ensemble and canonical Monte Carlo simulation data; vapour–liquid coexistence densities, vapour pressures, internal energies and contact radial distribution functions are examined. The equation is an extension of that presented in previous work for the reference monomer fluid in the SAFT-VR approach [GIL-VILLEGAS et al., 1997, J. chem. Phys., 106, 4168]. The Helmholtz free energy is written as a high-temperature expansion up to second order, where simple expressions are obtained for the mean attractive energy and the fluctuation term using the mean-value theorem and a mapping of radial distribution functions. In previous work the range of the square-well potential was limited to λ ≤ 1.8. In this work we show that the phase behaviour of such a fluid is far from the expected long-range limits given by the mean-field and van der Waals approximations. We extend the applicability of the equation...

Optimized virtual orbitals for correlated calculations: an alternative approach

Abstract: We propose an alternative formulation for creating the optimized virtual orbital space (OVOS). Our technique exploits and extends the method developed by Adamowicz and co-workers [L. Adamowicz, R.J. Bartlett. J. chem. Phys., 86, 6314 (1987); L. Adamowicz, R.J. Bartlett, A.J. Sadlej. J. chem. Phys., 88, 5749 (1988).]. The aim of the OVOS technique is to reduce the original SCF basis of the virtual molecular orbitals and to reduce the computer time in the coupled cluster (CC) and related highly sophisticated correlated methods. OVOS is created by using an invariant unitary rotation of the virtual orbitals subspace. New optimization functionals are proposed and implemented. The first type are ‘energy’ functionals. Their optimization leads to the minimal difference between the CCSD, CCD, or the second-order perturbation energy, MP2, in the original orbital basis and the OVOS basis, respectively. Alternatively, linearized ‘overlap’ functionals optimize the overlap between the correlated wave function in the fu...

Imaging the isotope effects in the ground state reaction of Cl CH4 and CD4

Abstract: The ground state reactions of Cl + CH4 and CD4 were studied in a crossed-beam experiment, in which the ground state methyl products were probed using a time-sliced velocity imaging technique. By taking the images over the energy range of chemical significance - from reaction threshold to about 10 kcal/mol, the reactive excitation functions as well as the dependences of product angular distributions and of the energy disposals on initial collision energies were obtained. Comparing the dynamical attributes of the two isotopic reactions revealed an interesting isotope effect in product angular distributions. The previous reduced-dimensional quantum scattering calculations of Yu and Nyman appear to reproduce this isotope effect rather well. Yet, a physical understanding of its origin awaits further theoretical investigations.

Heavy Rydberg states

Abstract: This paper discusses the nature of heavy Rydberg states, i.e. quantum states in molecular systems that are bound by the almost pure Coulomb potential between pairs of ions. A theoretical framework is developed in terms of mass–scaling laws for heavy Rydberg systems of certain reduced mass, so that the physics of electronic Rydberg states can be straightforwardly applied to heavier ion–pair systems, or any other system bound by a 1/r potential. The general description of such quantum systems is supported by an experimental investigation of the energy region near the H+H− ion–pair dissociation limit, using a 1 XUV + 1 UV laser excitation scheme. Such a scheme allows for preparation of a single intermediate rovibrational quantum state, from which the ion–pair threshold region can be explored with a narrowband Fourier–transform limited laser. Field–induced lowering of the H+H− dissociation limit was observed in the presence of an electric field. Using a combination of DC and pulsed electric fields two–photon ...

Rotation–vibration motion of pyramidal XY3 molecules described in the Eckart frame: Theory and application to NH3

Abstract: We present a new model for the rotation-vibration motion of pyramidal XY3 molecules, based on the Hougen–Bunker–Johns approach. Inversion is treated as a large-amplitude motion, while the small-amplitude vibrations are described by linearized stretching and bending coordinates. The rotation–vibration Schrodinger equation is solved variationally. We report three applications of the model to 14NH3 using an analytic potential function derived from high-level ab initio calculations. These applications address the J = 0 vibrational energies up to 6100 cm, the J≤2 energies for the vibrational ground state and the ν2, ν4, and 2ν2 excited vibrational states, and the J≤7 energies for the vibrational state. We demonstrate that also for four-atomic molecules, theoretical calculations of rotation–vibration energies can be helpful in the interpretation and assignment of experimental, high-resolution rotation–vibration spectra. Our approach incorporates an optimum inherent separation of different types of nuclear motio...

Developing a force field for simulation of poly(ethylene oxide) based upon ab initio calculations of 1,2-dimethoxyethane

Abstract: The relative conformational energies in the 1,2-dimethoxyethane (DME) molecule have been extensively studied using B3LYP and MP2 ab initio methods, employing a range of commonly used basis sets. These conformational energies have been used to fit new O–C–C–O and C–O–C–C torsional interaction parameters for the OPLS-AA force field. The resulting force field (DMEFF) shows some improvement in conformational populations, calculated from molecular dynamics simulation of bulk DME, compared to two other commonly used force fields. Extensive reverse-engineering of the OPLS-AA energy function has also allowed the development of additional sets of torsion parameters for these two dihedral types, resulting in a force field that reproduces the conformational behaviour of DME in the liquid phase extremely well.

Molecular simulation of alkene adsorption in zeolites

Abstract: The adsorption isotherms of various alkenes and their mixtures in zeolites such as silicalite-1 (MFI-type), theta-1 (TON-type), and deca-dodecasil 3R (DDR-type) were calculated using the grand canonical Monte Carlo (GCMC) approach. Additionally, the adsorption of alkene–alkane mixtures was simulated. The GCMC approach was combined with the configurational-bias Monte Carlo (CBMC) method. Effective Lennard–Jones parameters for the interaction between the oxygen atoms of all-silica zeolites and the sp2-hybridized groups of linear alkenes were determined using a united atom force field. They were adjusted to the experimental adsorption data of silicalite-1 (MFI). The inflection behaviour of the 1-heptene isotherm was investigated in detail. It is shown that, in the inflection region, the 1-heptene molecules alter their end-to-end length depending on their location. The occurrence of a maximum in the mixture adsorption isotherms is attributed to two effects: entropic effects and non-ideality effects. From the ...

Fermi-Amaldi model for exchange-correlation: atomic excitation energies from orbital energy differences

Abstract: Motivated by recent work on asymptotic correct exchange-correlation potentials, this paper investigates properties of the Fermi-Amaldi model for the exchange-correlation potential. It compares atomic excitation energies for Hydrogen through Argon to orbital energy differences computed using the exact Kohn-Sham potential and the Fermi-Amaldi approximation to the Kohn-Sham potential. While the Fermi-Amaldi model is not a particularly good model for the exchange-correlation energy, its eigenvalue spectrum is semi-quantitatively correct for alkali metals and alkaline earths. However, it is not accurate for p-block atoms, which suggests that the Fermi-Amaldi model may not be a superior choice for asymptotically correcting exchange-correlation potentials. It is suggested that asymptotic correction involving the Fukui function would give better results.

Anharmonic force fields and thermodynamic functions using density functional theory

Abstract: The very good performance of modern density functional theory for molecular geometries and harmonic vibrational frequencies has been well established. We investigate the performance of density functional theory (DFT) for quartic force fields, vibrational anharmonicity and rotation–vibration coupling constants, and thermodynamic functions beyond the RRHO (rigid rotor–harmonic oscillator) approximation of a number of small polyatomic molecules. Convergence in terms of basis set, integration grid and the numerical step size for determining the quartic force field by using central differences of analytical second derivatives has been investigated, as well as the performance of various exchange-correlation functionals. DFT is found to offer a cost-effective approach with manageable scalability for obtaining anharmonic molecular properties, and particularly as a source for anharmonic zero-point and thermal corrections for use in conjunction with benchmark ab initio thermochemistry methods.

Accurate local approximations to the triples correlation energy: formulation, implementation and tests of 5th-order scaling models

Abstract: Local models for the triples part of the MP4 or CCSD(T) energy are formulated in terms of atom-labelled functions to describe the occupied and virtual orbital spaces. These models retain triple substitutions in which at most one of the three orbital replacements involves a change of atom. This reduces the number of triple substitutions from scaling with the 6th power of molecule size to scaling with the 4th power, and reduces the computational cost from 7th order to 5th order. Non-locality in the triple substitutions is dominated by terms in which an electron is scattered twice, while the other two singly scattered electrons exhibit non-locality that is similar to that seen in double substitutions. Two non-iterative computational models are designed around this observation. The first, ionic2, allows for non-locality only in the doubly-scattered electron, and recovers around 95% of the triples correlation energy (in the large-molecule limit). The second, ionic*, also approximately accounts for the effect o...

The excluded volume of hard sphero-zonotopes

Abstract: Excluded volume effects can account for most ordering transitions in simple liquids and liquid crystals. Starting with the work of Onsager, this has been demonstrated in the case of liquid crystals for a number of simple convex bodies, e.g. sphero-cylinders, for which the orientation-dependent pair-excluded volume could be written down analytically. However, in recent years, experiments and simulations have been reported on ordering transitions in suspensions of more complex convex colloids. For these systems, theoretical understanding is hampered by the fact that no analytical expressions for the pair-excluded volume were available. Here we show that it is possible to obtain explicit expressions for the pair-excluded volume of a much larger class of convex bodies: the so-called sphero-zonotopes. These bodies are obtained by ‘padding’ a special class of convex polytopes with a blanket of uniform thickness. The resultant family of particles encompasses a wide range of shapes that have been considered as mo...