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7 Feb 2011

Volume 134, Issue 5, Articles (05xxxx)

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J. Chem. Phys. 134, 055101 (2011); http://dx.doi.org/10.1063/1.3541246 (12 pages)

Hiroshi Noguchi
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Communication: Driven Brownian transport in eccentric septate channels

M. Borromeo, F. Marchesoni, and P. K. Ghosh

J. Chem. Phys. 134, 051101 (2011); http://dx.doi.org/10.1063/1.3535559 (4 pages) | Cited 5 times

Online Publication Date: 1 February 2011

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In eccentric septate channels the pores connecting adjacent compartments are shifted off-axis, either periodically or randomly, so that straight trajectories parallel to the axis are not allowed. Driven transport of a Brownian particle in such a channel is characterized by a strong suppression of the current and its dispersion. For large driving forces, both quantities approach an asymptotic value, which can be analytically approximated in terms of the stationary distribution of the particle exit times out of a single channel compartment.
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05.40.Jc Brownian motion
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Stability, structural, and magnetic phase diagrams of ternary ferromagnetic 3d-transition-metal clusters with five and six atoms

G. Guzmán-Ramírez, J. Robles, A. Vega, and F. Aguilera-Granja

J. Chem. Phys. 134, 054101 (2011); http://dx.doi.org/10.1063/1.3533954 (9 pages)

Online Publication Date: 1 February 2011

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We report a theoretical investigation of free-standing Fe x Co y Ni z ternary clusters with x + y + z = 5 and 6. Our study is performed within density functional theory as implemented in the GAUSSIAN 03 set of programs and with the BPW91/SDD level of theory. We analyze the geometries, chemical order, local and total magnetic moments, binding energies, excess energies, and second difference in the energy in the whole range of composition, from which structural, magnetic, and stability phase diagrams are predicted for these cluster sizes. We determine the optimal stoichiometries for these clusters as regards the maximum total magnetic moment and stability.
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36.40.Ei Phase transitions in clusters
36.40.Mr Spectroscopy and geometrical structure of clusters
36.40.Cg Electronic and magnetic properties of clusters
61.46.Bc Structure of clusters (e.g., metcars; not fragments of crystals; free or loosely aggregated or loosely attached to a substrate)
64.70.kd Metals and alloys
75.75.-c Magnetic properties of nanostructures

Efficient implementation of the Hellmann–Feynman theorem in a diffusion Monte Carlo calculation

S. A. Vitiello

J. Chem. Phys. 134, 054102 (2011); http://dx.doi.org/10.1063/1.3532411 (6 pages)

Online Publication Date: 1 February 2011

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Kinetic and potential energies of systems of 4He atoms in the solid phase are computed at T = 0. Results at two densities of the liquid phase are presented as well. Calculations are performed by the multiweight extension to the diffusion Monte Carlo method that allows the application of the Hellmann–Feynman theorem in a robust and efficient way. This is a general method that can be applied in other situations of interest as well.
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67.80.B- Solid 4He

Time-optimal control of spin 1/2 particles in the presence of radiation damping and relaxation

Y. Zhang, M. Lapert, D. Sugny, M. Braun, and S. J. Glaser

J. Chem. Phys. 134, 054103 (2011); http://dx.doi.org/10.1063/1.3543796 (6 pages) | Cited 3 times

Online Publication Date: 1 February 2011

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We consider the time-optimal control of an ensemble of uncoupled spin 1/2 particles in the presence of relaxation and radiation damping effects, whose dynamics is governed by nonlinear equations generalizing the standard linear Bloch equations. For a single spin, the optimal control strategy can be fully characterized analytically. However, in order to take into account the inhomogeneity of the static magnetic field, an ensemble of isochromats at different frequencies must be considered. For this case, numerically optimized pulse sequences are computed and the dynamics under the corresponding optimal field is experimentally demonstrated using nuclear magnetic resonance techniques.
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75.30.Ds Spin waves

Self-assembly in block polyelectrolytes

Shuang Yang, Aleksey Vishnyakov, and Alexander V. Neimark

J. Chem. Phys. 134, 054104 (2011); http://dx.doi.org/10.1063/1.3532831 (8 pages) | Cited 3 times

Online Publication Date: 1 February 2011

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The self-consistent field theory (SCFT) complemented with the Poisson–Boltzmann equation is employed to explore self-assembly of polyelectrolyte copolymers composed of charged blocks A and neutral blocks B. We have extended SCFT to dissociating triblock copolymers and demonstrated our approach on three characteristic examples: (1) diblock copolymer (AB) melt, (2) symmetric triblock copolymer (ABA) melt, (3) triblock copolymer (ABA) solution with added electrolyte. For copolymer melts, we varied the composition (that is, the total fraction of A-segments in the system) and the charge density on A blocks and calculated the phase diagram that contains ordered mesophases of lamellar, gyroid, hexagonal, and bcc symmetries, as well as the uniform disordered phase. The phase diagram of charged block copolymer melts in the charge density – system composition coordinates is similar to the classical phase diagram of neutral block copolymer melts, where the composition and the Flory mismatch interaction parameter χAB are used as variables. We found that the transitions between the polyelectrolyte mesophases with the increase of charge density occur in the same sequence, from lamellar to gyroid to hexagonal to bcc to disordered morphologies, as the mesophase transitions for neutral diblocks with the decrease of χAB. In a certain range of compositions, the phase diagram for charged triblock copolymers exhibits unexpected features, allowing for transitions from hexagonal to gyroid to lamellar mesophases as the charge density increases. Triblock polyelectrolyte solutions were studied by varying the charge density and solvent concentration at a fixed copolymer composition. Transitions from lamellar to gyroid and gyroid to hexagonal morphologies were observed at lower polymer concentrations than the respective transitions in the similar neutral copolymer, indicating a substantial influence of the charge density on phase behavior.
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61.25.he Polymer solutions
61.25.hk Polymer melts and blends
64.75.Yz Self-assembly
64.60.-i General studies of phase transitions

Stiffness detection and reduction in discrete stochastic simulation of biochemical systems

Yang Pu, Layne T. Watson, and Yang Cao

J. Chem. Phys. 134, 054105 (2011); http://dx.doi.org/10.1063/1.3548838 (10 pages)

Online Publication Date: 1 February 2011

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Typical multiscale biochemical models contain fast-scale and slow-scale reactions, where “fast” reactions fire much more frequently than “slow” ones. This feature often causes stiffness in discrete stochastic simulation methods such as Gillespie's algorithm and the Tau-Leaping method leading to inefficient simulation. This paper proposes a new strategy to automatically detect stiffness and identify species that cause stiffness for the Tau-Leaping method, as well as two stiffness reduction methods. Numerical results on a stiff decaying dimerization model and a heat shock protein regulation model demonstrate the efficiency and accuracy of the proposed methods for multiscale biochemical systems.
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87.15.A- Theory, modeling, and computer simulation
02.50.Fz Stochastic analysis
87.14.E- Proteins
87.15.R- Reactions and kinetics

Sources of the deficiencies in the popular SPC/E and TIP3P models of water

Péter T. Kiss and András Baranyai

J. Chem. Phys. 134, 054106 (2011); http://dx.doi.org/10.1063/1.3548869 (5 pages) | Cited 2 times

Online Publication Date: 1 February 2011

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Motivated by the results of Vega et al. [J. Phys. Condens. Matter 20, 153101 (2008)] about the phase diagram of water, and by the results of Kiss and Baranyai [J. Chem. Phys. 131, 204310 (2009)] about the properties of gas-phase clusters, we carried out a comparative study of the structure modeled by SPC/E and TIP3P interactions in ambient liquid water. The gas-phase clusters of SPC/E and TIP3P models show erroneous structures, while TIP4P-type models, either polarizable or not, provide qualitatively correct results. The trimers of SPC/E and TIP3P are planar in gas phase, contrary to experimental and TIP4P-type models. The aim of this study was to see whether traces of these false geometries characteristic to SPC/E and TIP3P in gas phase can also be found in the liquid phase. For this purpose we selected trimers formed by adjacent neighbors of water molecules in the liquid and calculated their geometrical features. We determined angles formed by the HO bonds of the molecules with OO vectors and with the normal vector of the OOO plane in the selected trimers. Our results showed that, despite high temperature, the SPC/E and TIP3P water contains larger number of planar arrangements than other TIP4P-type models. Although structural differences presented in this study are small, they are accurately detectable. These results weaken the reliability of studies obtained by the SPC/E or TIP3P models even in the liquid phase.
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61.25.Em Molecular liquids
81.30.Dz Phase diagrams of other materials
61.50.Lt Crystal binding; cohesive energy
33.15.Kr Electric and magnetic moments (and derivatives), polarizability, and magnetic susceptibility

Escorted free energy simulations

Suriyanarayanan Vaikuntanathan and Christopher Jarzynski

J. Chem. Phys. 134, 054107 (2011); http://dx.doi.org/10.1063/1.3544679 (11 pages) | Cited 3 times

Online Publication Date: 1 February 2011

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We describe a strategy to improve the efficiency of free energy estimates by reducing dissipation in nonequilibrium Monte Carlo simulations. This strategy generalizes the targeted free energy perturbation approach [C. Jarzynski, Phys. Rev. E 65, 046122 (2002)] to nonequilibrium switching simulations, and involves generating artificial, “escorted” trajectories by coupling the evolution of the system to updates in external work parameter. Our central results are: (1) a generalized fluctuation theorem for the escorted trajectories, and (2) estimators for the free energy difference ΔF in terms of these trajectories. We illustrate the method and its effectiveness on model systems.
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05.70.Ce Thermodynamic functions and equations of state
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
02.50.Ng Distribution theory and Monte Carlo studies
05.70.Ln Nonequilibrium and irreversible thermodynamics

A multiple replica approach to simulate reactive trajectories

Frédéric Cérou, Arnaud Guyader, Tony Lelièvre, and David Pommier

J. Chem. Phys. 134, 054108 (2011); http://dx.doi.org/10.1063/1.3518708 (16 pages)

Online Publication Date: 1 February 2011

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A method to generate reactive trajectories, namely equilibrium trajectories leaving a metastable state and ending in another one is proposed. The algorithm is based on simulating in parallel many copies of the system, and selecting the replicas which have reached the highest values along a chosen one-dimensional reaction coordinate. This reaction coordinate does not need to precisely describe all the metastabilities of the system for the method to give reliable results. An extension of the algorithm to compute transition times from one metastable state to another one is also presented. We demonstrate the interest of the method on two simple cases: A one-dimensional two-well potential and a two-dimensional potential exhibiting two channels to pass from one metastable state to another one.
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82.20.Rp State to state energy transfer
82.20.Fd Collision theories; trajectory models
82.20.Wt Computational modeling; simulation

Ring-polymer instanton method for calculating tunneling splittings

Jeremy O. Richardson and Stuart C. Althorpe

J. Chem. Phys. 134, 054109 (2011); http://dx.doi.org/10.1063/1.3530589 (11 pages) | Cited 3 times

Online Publication Date: 1 February 2011

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The semiclassical instanton expression for the tunneling splitting between two symmetric wells is rederived, starting from the ring-polymer representation of the quantum partition function. This leads to simpler mathematics by replacing functional determinants with matrix determinants. By exploiting the simple Hückel-like structure of the matrices, we derive an expression for the instanton tunneling splitting in terms of a minimum on the potential surface of a linear polymer. The latter is a section cut out of a ring polymer, consisting of an infinite number of beads, which describes a periodic orbit on the inverted potential surface. The approach is straightforward to generalize to multiple dimensions, and we demonstrate that it is computationally practical by carrying out instanton calculations of tunneling splittings in HO 2 and malonaldehyde in full dimensionality.
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36.20.Kd Electronic structure and spectra
31.50.-x Potential energy surfaces
31.15.bu Semi-empirical and empirical calculations (differential overlap, Hückel, PPP methods, etc.)

Cartesian coupled coherent states simulations: NenBr2 dissociation as a test case

Stewart K. Reed, Maykel L. González-Martínez, Jesús Rubayo-Soneira, and Dmitrii V. Shalashilin

J. Chem. Phys. 134, 054110 (2011); http://dx.doi.org/10.1063/1.3532407 (12 pages) | Cited 1 time

Online Publication Date: 2 February 2011

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In this article, we describe coupled coherent states (CCS) simulations of vibrational predissociation of weakly bounded complexes. The CCS method is implemented in the Cartesian frame in a manner that is similar to classical molecular dynamics. The calculated lifetimes of the vibrationally excited Ne-Br2(ν) complexes agree with experiment and previous calculations. Although the CCS method is, in principle, a fully quantum approach, in practice it typically becomes a semiclassical technique at long times. This is especially true following dissociation events. Consequently, it is very difficult to converge the quantum calculations of the final Br2 vibrational distributions after predissociation and of the autocorrelation functions. However, the main advantage of the method is that it can be applied with relative ease to determine the lifetimes of larger complexes and, in order to demonstrate this, preliminary results for tetra- and penta-atomic clusters are reported.
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31.15.bw Coupled-cluster theory
33.80.Gj Diffuse spectra; predissociation, photodissociation
36.40.Cg Electronic and magnetic properties of clusters
36.40.Mr Spectroscopy and geometrical structure of clusters
33.70.Ca Oscillator and band strengths, lifetimes, transition moments, and Franck-Condon factors
33.15.Mt Rotation, vibration, and vibration-rotation constants

Implementation of the analytic energy gradient for the combined time-dependent density functional theory/effective fragment potential method: Application to excited-state molecular dynamics simulations

Noriyuki Minezawa (嶺澤範行), Nuwan De Silva, Federico Zahariev, and Mark S. Gordon (強首領真空)

J. Chem. Phys. 134, 054111 (2011); http://dx.doi.org/10.1063/1.3523578 (12 pages) | Cited 4 times

Online Publication Date: 2 February 2011

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Excited-state quantum mechanics/molecular mechanics molecular dynamics simulations are performed, to examine the solvent effects on the fluorescence spectra of aqueous formaldehyde. For that purpose, the analytical energy gradient has been derived and implemented for the linear-response time-dependent density functional theory (TDDFT) combined with the effective fragment potential (EFP) method. The EFP method is an efficient ab initio based polarizable model that describes the explicit solvent effects on electronic excitations, in the present work within a hybrid TDDFT/EFP scheme. The new method is applied to the excited-state MD of aqueous formaldehyde in the n-π* state. The calculated π*→n transition energy and solvatochromic shift are in good agreement with other theoretical results.
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71.15.Mb Density functional theory, local density approximation, gradient and other corrections
71.10.Li Excited states and pairing interactions in model systems
71.15.Pd Molecular dynamics calculations (Car-Parrinello) and other numerical simulations
78.55.Bq Liquids

Maximum likelihood-based analysis of single-molecule photon arrival trajectories

Marta Hajdziona and Andrzej Molski

J. Chem. Phys. 134, 054112 (2011); http://dx.doi.org/10.1063/1.3544494 (7 pages) | Cited 1 time

Online Publication Date: 2 February 2011

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In this work we explore the statistical properties of the maximum likelihood-based analysis of one-color photon arrival trajectories. This approach does not involve binning and, therefore, all of the information contained in an observed photon strajectory is used. We study the accuracy and precision of parameter estimates and the efficiency of the Akaike information criterion and the Bayesian information criterion (BIC) in selecting the true kinetic model. We focus on the low excitation regime where photon trajectories can be modeled as realizations of Markov modulated Poisson processes. The number of observed photons is the key parameter in determining model selection and parameter estimation. For example, the BIC can select the true three-state model from competing two-, three-, and four-state kinetic models even for relatively short trajectories made up of 2 × 103 photons. When the intensity levels are well-separated and 104 photons are observed, the two-state model parameters can be estimated with about 10% precision and those for a three-state model with about 20% precision.
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82.20.Uv Stochastic theories of rate constants
02.50.-r Probability theory, stochastic processes, and statistics

Explicitly time-dependent coupled cluster singles doubles calculations of laser-driven many-electron dynamics

Christian Huber and Tillmann Klamroth

J. Chem. Phys. 134, 054113 (2011); http://dx.doi.org/10.1063/1.3530807 (8 pages) | Cited 2 times

Online Publication Date: 2 February 2011

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We report explicitly time-dependent coupled cluster singles doubles (TD-CCSD) calculations, which simulate the laser-driven correlated many-electron dynamics in molecular systems. Small molecules, i.e., HF, H2O, NH3, and CH4, are treated mostly with polarized valence double zeta basis sets. We determine the coupled cluster ground states by imaginary time propagation for these molecules. Excited state energies are obtained from the Fourier transform of the time-dependent dipole moment after an ultrashort, broadband laser excitation. The time-dependent expectation values are calculated from the complex cluster amplitudes using the corresponding configuration interaction singles doubles wave functions. Also resonant laser excitations of these excited states are simulated, in order to explore the limits for the numerical stability of our current TD-CCSD implementation, which uses time-independent molecular orbitals to form excited configurations.
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31.15.bw Coupled-cluster theory
31.15.am Relativistic configuration interaction (CI) and many-body perturbation calculations
33.80.Rv Multiphoton ionization and excitation to highly excited states (e.g., Rydberg states)

A water-swap reaction coordinate for the calculation of absolute protein–ligand binding free energies

Christopher J. Woods, Maturos Malaisree, Supot Hannongbua, and Adrian J. Mulholland

J. Chem. Phys. 134, 054114 (2011); http://dx.doi.org/10.1063/1.3519057 (13 pages)

Online Publication Date: 3 February 2011

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The accurate prediction of absolute protein–ligand binding free energies is one of the grand challenge problems of computational science. Binding free energy measures the strength of binding between a ligand and a protein, and an algorithm that would allow its accurate prediction would be a powerful tool for rational drug design. Here we present the development of a new method that allows for the absolute binding free energy of a protein–ligand complex to be calculated from first principles, using a single simulation. Our method involves the use of a novel reaction coordinate that swaps a ligand bound to a protein with an equivalent volume of bulk water. This water-swap reaction coordinate is built using an identity constraint, which identifies a cluster of water molecules from bulk water that occupies the same volume as the ligand in the protein active site. A dual topology algorithm is then used to swap the ligand from the active site with the identified water cluster from bulk water. The free energy is then calculated using replica exchange thermodynamic integration. This returns the free energy change of simultaneously transferring the ligand to bulk water, as an equivalent volume of bulk water is transferred back to the protein active site. This, directly, is the absolute binding free energy. It should be noted that while this reaction coordinate models the binding process directly, an accurate force field and sufficient sampling are still required to allow for the binding free energy to be predicted correctly. In this paper we present the details and development of this method, and demonstrate how the potential of mean force along the water-swap coordinate can be improved by calibrating the soft-core Coulomb and Lennard-Jones parameters used for the dual topology calculation. The optimal parameters were applied to calculations of protein–ligand binding free energies of a neuraminidase inhibitor (oseltamivir), with these results compared to experiment. These results demonstrate that the water-swap coordinate provides a viable and potentially powerful new route for the prediction of protein–ligand binding free energies.
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87.15.R- Reactions and kinetics
87.15.kp Protein-ligand interactions
87.15.A- Theory, modeling, and computer simulation

Variational second order density matrix study of F3−: Importance of subspace constraints for size-consistency

Helen van Aggelen, Brecht Verstichel, Patrick Bultinck, Dimitri Van Neck, Paul W. Ayers, and David L. Cooper

J. Chem. Phys. 134, 054115 (2011); http://dx.doi.org/10.1063/1.3532409 (8 pages) | Cited 1 time

Online Publication Date: 3 February 2011

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Variational second order density matrix theory under “two-positivity” constraints tends to dissociate molecules into unphysical fractionally charged products with too low energies. We aim to construct a qualitatively correct potential energy surface for F3− by applying subspace energy constraints on mono- and diatomic subspaces of the molecular basis space. Monoatomic subspace constraints do not guarantee correct dissociation: the constraints are thus geometry dependent. Furthermore, the number of subspace constraints needed for correct dissociation does not grow linearly with the number of atoms. The subspace constraints do impose correct chemical properties in the dissociation limit and size-consistency, but the structure of the resulting second order density matrix method does not exactly correspond to a system of noninteracting units.
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31.15.E- Density-functional theory
31.50.-x Potential energy surfaces
33.15.Fm Bond strengths, dissociation energies

Efficient time-dependent density functional theory approximations for hybrid density functionals: Analytical gradients and parallelization

Taras Petrenko, Simone Kossmann, and Frank Neese

J. Chem. Phys. 134, 054116 (2011); http://dx.doi.org/10.1063/1.3533441 (14 pages) | Cited 3 times

Online Publication Date: 3 February 2011

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In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm–Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced “chain of spheres exchange” (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ∼26–29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ∼27–29 for 30 processors). The solution of the Z-vector equations shows a speedup of ∼24 on 30 processors. The parallelization efficiency for the Coulomb terms can be somewhat smaller (speedup ∼15–25 for 30 processors), but their contribution to the total calculation time is small. Thus, the parallel program completes a Becke3-Lee-Yang-Parr energy and gradient calculation on the Ag-TB2-helicate in less than 4 h on 30 processors. We also present the necessary extension of the Lagrangian formalism, which enables the calculation of the TDDFT excited state properties in the frozen-core approximation. The algorithms described in this work are implemented into the ORCA electronic structure system.
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31.15.ee Time-dependent density functional theory
33.15.Dj Interatomic distances and angles
33.20.Tp Vibrational analysis
33.15.Bh General molecular conformation and symmetry; stereochemistry
31.15.V- Electron correlation calculations for atoms, ions and molecules

A quantum propagator for path-integral simulations of rigid molecules

Eva G. Noya, Carlos Vega, and Carl McBride

J. Chem. Phys. 134, 054117 (2011); http://dx.doi.org/10.1063/1.3544214 (8 pages) | Cited 1 time

Online Publication Date: 4 February 2011

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The expression for the quantum propagator for rigid tops, proposed by Müser and Berne [Phys. Rev. Lett. 77, 2638 (1996)], has been extended to asymmetric tops. Path-integral Monte Carlo simulations are provided that show that the quantum propagator proposed in this work exactly reproduces the rotational energy of free asymmetric tops as evaluated from the partition function. This propagator can subsequently be used in path-integral simulations of condensed phases if a rigid molecular model is used.
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33.20.Sn Rotational analysis
31.15.bt Statistical model calculations (including Thomas-Fermi and Thomas-Fermi-Dirac models)
02.70.Ss Quantum Monte Carlo methods
02.70.Uu Applications of Monte Carlo methods

Tensor decomposition in post-Hartree–Fock methods. I. Two-electron integrals and MP2

Udo Benedikt, Alexander A. Auer, Mike Espig, and Wolfgang Hackbusch

J. Chem. Phys. 134, 054118 (2011); http://dx.doi.org/10.1063/1.3514201 (12 pages) | Cited 4 times

Online Publication Date: 7 February 2011

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A new approximation for post-Hartree–Fock (HF) methods is presented applying tensor decomposition techniques in the canonical product tensor format. In this ansatz, multidimensional tensors like integrals or wavefunction parameters are processed as an expansion in one-dimensional representing vectors. This approach has the potential to decrease the computational effort and the storage requirements of conventional algorithms drastically while allowing for rigorous truncation and error estimation. For post-HF ab initio methods, for example, storage is reduced to O(d·R·n) with d being the number of dimensions of the full tensor, R being the expansion length (rank) of the tensor decomposition, and n being the number of entries in each dimension (i.e., the orbital index). If all tensors are expressed in the canonical format, the computational effort for any subsequent tensor contraction can be reduced to O(R2·n). We discuss details of the implementation, especially the decomposition of the two-electron integrals, the AO–MO transformation, the Møller–Plesset perturbation theory (MP2) energy expression and the perspective for coupled cluster methods. An algorithm for rank reduction is presented that parallelizes trivially. For a set of representative examples, the scaling of the decomposition rank with system and basis set size is found to be O(N1.8) for the AO integrals, O(N1.4) for the MO integrals, and O(N1.2) for the MP2 t2-amplitudes (N denotes a measure of system size) if the upper bound of the error in the ℓ2-norm is chosen as ε = 10−2. This leads to an error in the MP2 energy in the order of mHartree.
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31.15.xr Self-consistent-field methods
31.15.xp Perturbation theory
31.15.bw Coupled-cluster theory
31.15.ac High-precision calculations for few-electron (or few-body) atomic systems

Vibrational coupled cluster response theory: A general implementation

Peter Seidler, Manuel Sparta, and Ove Christiansen

J. Chem. Phys. 134, 054119 (2011); http://dx.doi.org/10.1063/1.3536499 (13 pages) | Cited 3 times

Online Publication Date: 7 February 2011

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The calculation of vibrational contributions to molecular properties using vibrational coupled cluster (VCC) response theory is discussed. General expressions are given for expectation values, linear response functions, and transition moments. It is shown how these expressions can be evaluated for arbitrary levels of excitation in the wave function parameterization as well as for arbitrary coupling levels in the potential and property surfaces. The convergence of the method is assessed by benchmark calculations on formaldehyde. Furthermore, excitation energies and infrared intensities are calculated for the fundamental vibrations of furan using VCC limited to up to two-mode and up to three-mode excitations, VCC[2] and VCC[3], as well as VCC with full two-mode and approximate three-mode couplings, VCC[2pt3].
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31.15.bw Coupled-cluster theory
33.20.Tp Vibrational analysis
33.20.Ea Infrared spectra
33.70.Ca Oscillator and band strengths, lifetimes, transition moments, and Franck-Condon factors

Freezing of Lennard-Jones-type fluids

Sergey A. Khrapak, Manis Chaudhuri, and Gregor E. Morfill

J. Chem. Phys. 134, 054120 (2011); http://dx.doi.org/10.1063/1.3552948 (5 pages) | Cited 4 times

Online Publication Date: 7 February 2011

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We put forward an approximate method to locate the fluid–solid (freezing) phase transition in systems of classical particles interacting via a wide range of Lennard-Jones-type potentials. This method is based on the constancy of the properly normalized second derivative of the interaction potential (freezing indicator) along the freezing curve. As demonstrated recently it yields remarkably good agreement with previous numerical simulation studies of the conventional 12-6 Lennard-Jones (LJ) fluid [S.A.Khrapak, M.Chaudhuri, G.E.Morfill, Phys. Rev. B 134, 052101 (2010)]. In this paper, we test this approach using a wide range of the LJ-type potentials, including LJ n–6 and exp–6 models, and find that it remains sufficiently accurate and reliable in reproducing the corresponding freezing curves, down to the triple-point temperatures. One of the possible application of the method—estimation of the freezing conditions in complex (dusty) plasmas with “tunable” interactions—is briefly discussed.
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64.70.dm General theory of the solid-liquid transition
61.20.-p Structure of liquids
52.27.Lw Dusty or complex plasmas; plasma crystals

Transition from patchlike to clusterlike inhomogeneity arising from hydrogen bonding in water

Dorota Swiatla-Wojcik and Joanna Szala-Bilnik

J. Chem. Phys. 134, 054121 (2011); http://dx.doi.org/10.1063/1.3552950 (10 pages) | Cited 4 times

Online Publication Date: 7 February 2011

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Assembling of water molecules via hydrogen bonding has been studied by molecular dynamics simulations using flexible potential model. The relationship between the number of H-bonds per molecule, nHB, the size of H-bonded nets, k, and the size of patches of four-bonded molecules, k4, has been examined for several thermodynamic states of water ranging from ambient to supercritical conditions. Two kinds of structural inhomogeneity have been found: the patchlike associated with the mean math HB > 2.0 and the clusterlike for math HB < 1.9. In compressed water up to ∼473 K patches coexist with less ordered nets, both constituting the gel-like H-bonded network. The size of patches steeply decreases with the increasing temperature and the decreasing density of water. The inhomogeneity resulting from the presence of patches disappears above 473 K. This feature is associated with the rapid increase in the fraction of unbound molecules and with the breakage of the gel-like network into a variety of H-bonded clusters leading to the clusterlike structural inhomogeneity. In contrast to the patchlike inhomogeneity an increase in temperature and a decrease in density make this kind of inhomogeneity more pronounced. A degree of connectivity of H-bonds has been characterized by a parameter Pg defined as the total fraction of molecules belonging to the H-bonded clusters of size k ≥ 5. The simulation-derived values of Pg agree well with the predictions of the random bond theory giving the explicit expression for Pg as a function of the mean nHB. Going from ambient to supercritical conditions, we have found that the patchlike inhomogeneity is connected with the very slight reduction in Pg, whereas the clusterlike inhomogeneity generates a steep linear decrease of Pg with the decreasing mean nHB. The self-diffusion coefficient calculated for the thermodynamic states of water showing the clusterlike inhomogeneity has occurred to be inversely proportional to the density. We have also found that the clusterlike inhomogeneity is associated with the linear correlation between Pg and the macroscopic properties of water: the static dielectric constant, the viscosity, and the density. The provided relationships allow one to estimate the degree of connectivity of hydrogen bonds from the measured macroscopic quantities.
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31.15.xv Molecular dynamics and other numerical methods
33.15.Fm Bond strengths, dissociation energies

The spin-free analogue of Mukherjee's state-specific multireference coupled cluster theory

Dipayan Datta and Debashis Mukherjee

J. Chem. Phys. 134, 054122 (2011); http://dx.doi.org/10.1063/1.3537740 (16 pages) | Cited 14 times

Online Publication Date: 7 February 2011

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In this paper, we develop a rigorously spin-adapted version of Mukherjee's state-specific multireference coupled cluster theory (SS-MRCC, also known as Mk-MRCC) [U. S. Mahapatra, B. Datta, and D. Mukherjee, J. Chem. Phys. 110, 6171 (1999)] for reference spaces comprising open-shell configurations. The principal features of our approach are as follows: (1) The wave operator Ω is written as Ω = ∑μΩμ|ϕμ〉cμ, where {ϕμ} is the set of configuration state functions spanning a complete active space. (2) In contrast to the Jeziorski–Monkhorst Ansatz in spin-orbital basis, we write Ωμ as a power series expansion of cluster operators Rμ defined in terms of spin-free unitary generators. (3) The operators Rμ are either closed-shell-like n hole-n particle excitations (denoted as Tμ) or they involve valence (active) destruction operators (denoted as Sμ); these latter type of operators can have active–active scatterings, which can also carry the same active orbital labels (such Sμ’s are called to have spectator excitations). (4) To simulate multiple excitations involving powers of cluster operators, we allow the Sμ’s carrying the same active orbital labels to contract among themselves. (5) We exclude Sμ’s with direct spectator scatterings. (6) Most crucially, the factors associated with contracted composites are chosen as the inverse of the number of ways the Sμ’s can be joined among one another leading to the same excitation. The factors introduced in (6) have been called the automorphic factors by us. One principal thrust of this paper is to show that the use of the automorphic factors imparts a remarkable simplicity to the final amplitude equations: the equations consist of terms that are at most quartic in cluster amplitudes, barring only a few. In close analogy to the Mk-MRCC theory, the inherent linear dependence of the cluster amplitudes leading to redundancy is resolved by invoking sufficiency conditions, which are exact spin-free analogues of the spin-orbital based Mk-MRCC theory. This leads to manifest size-extensivity and an intruder-free formulation. Our formalism provides a relaxed description of the nondynamical correlation in presence of dynamical correlation. Pilot numerical applications to doublet systems, e.g., potential energy surfaces for the first two excited 2A' states of asymmetric H2S+ ion and the ground 2Σ+state of BeH radical are presented to assess the viability of our formalism over an wide range of nuclear geometries and the manifest avoidance of intruder state problem.
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31.15.bw Coupled-cluster theory
31.50.Df Potential energy surfaces for excited electronic states

Calculation of spin-current densities using gauge-including atomic orbitals

Stefan Taubert, Dage Sundholm, and Jonas Jusélius

J. Chem. Phys. 134, 054123 (2011); http://dx.doi.org/10.1063/1.3549567 (12 pages) | Cited 4 times

Online Publication Date: 7 February 2011

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The gauge-including magnetically induced current method for calculating the components of the current-density tensor using gauge-including atomic orbitals has been extended to treating open-shell molecules. The applicability of the method is demonstrated by calculations of first-order induced current densities on cyclobutadiene, Al3, and B3 at correlated ab initio levels of theory. For comparison, current-density calculations were also performed on the lowest closed-shell singlet state of cyclobutadiene as well on the closed-shell Al 3− and B3− anions. The ring-current susceptibilities of the open-shell species are computed at the Hartree-Fock self-consistent-field, second-order Møller– Plesset perturbation theory, and coupled-cluster singles and doubles levels, whereas for the closed-shell systems also density functional theory calculations were employed. Explicit values for the current strengths caused by α and β electrons as well as the difference, representing the spin current, were obtained by numerical integration of the current-density contributions passing a plane perpendicular to the molecular ring. Comparisons of the present results to those recently obtained for the lowest triplet state of biphenyl emphasize that electron correlation effects must be considered for obtaining an accurate description of spin-current densities.
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31.15.xr Self-consistent-field methods
31.15.xp Perturbation theory
31.15.bw Coupled-cluster theory
31.15.V- Electron correlation calculations for atoms, ions and molecules
31.15.E- Density-functional theory

Statistical approaches to forcefield calibration and prediction uncertainty in molecular simulation

Fabien Cailliez and Pascal Pernot

J. Chem. Phys. 134, 054124 (2011); http://dx.doi.org/10.1063/1.3545069 (14 pages) | Cited 1 time

Online Publication Date: 7 February 2011

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Calibration of forcefields for molecular simulation should account for the measurement uncertainty of the reference dataset and for the model inadequacy, i.e., the inability of the force-field/simulation pair to reproduce experimental data within their uncertainty range. In all rigour, the resulting uncertainty of calibrated force-field parameters is a source of uncertainty for simulation predictions. Various calibration strategies and calibration models within the Bayesian calibration/prediction framework are explored in the present article. In the case of Lennard-Jones potential for Argon, we show that prediction uncertainty for thermodynamical and transport properties, albeit very small, is larger than statistical simulation uncertainty.
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31.15.bt Statistical model calculations (including Thomas-Fermi and Thomas-Fermi-Dirac models)
02.50.-r Probability theory, stochastic processes, and statistics
34.20.-b Interatomic and intermolecular potentials and forces, potential energy surfaces for collisions
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