Volume 122, Issue 8, 22 February 2005
 COMMUNICATIONS


Liquid–vapor and liquid–liquid phase equilibria of the Brodholt–Sampoli–Vallauri polarizable water model
View Description Hide DescriptionLiquid–vapor and liquid–liquid phase equilibria of the polarizable Brodholt–Sampoli–Vallauri water model have been investigated by Gibbs ensemble Monte Carlo computer simulations. The coexisting liquid and vapor densities and energy of vaporization of the model is found to be in a reasonable agreement with experimental data in the entire temperature range of liquid–vapor coexistence. The critical temperature and density of the model are found to be and , respectively, close to the experimental values of and . In the supercooled state two distinct liquid–liquid coexistence regions are observed. The existence of liquid–liquid phase separation of a polarizable water model is demonstrated for the first time.

Landing of sizeselected clusters on single crystal surfaces at room temperature
View Description Hide DescriptionMassselected clusters with impact energy less than per atom were deposited from the gas phase onto rutile titania single crystal surfaces at room temperature and imaged using ultrahigh vacuum scanning tunneling microscopy. Upon reaching the surface, Agmonomerssintered to form threedimensional islands of approximately 50 atoms in size, with an average measured height of and diameter of . This suggests that the monomers are highly mobile on the titania surface at room temperature. Dimers also sintered to form large clusters upon deposition, approximately 30 atoms in size, with an average height of and diameter of . Clusters formed from monomer deposition appeared approximately three times more frequently at step edges than clusters formed from dimer deposition, indicating that the surface mobility of deposited monomers is higher than that of deposited dimers. In sharp contrast to the deposition of monomers and dimers, the deposition of trimers resulted in a high density of very small clusters on the order of a few atoms in size, indicative of intact trimers on the surface, implying that deposited trimers have very limited mobility on the surface at room temperature.

A nonequilibrium molecular dynamics method for thermal conductivities based on thermal noise
View Description Hide DescriptionWe developed a nonequilibrium molecular dynamics (NEMD) method for calculating thermal conductivities. In contrast to other NEMD algorithms, here only the heat sink is localized, whereas the heat source can be uniformly distributed throughout the system. The noise due to cutting off the pair forces or to integration errors is such a uniform heat source. In traditional NEMD methods it is normally considered a nuisance factor. The new algorithm accounts for it and uses it. The algorithm is easy to derive, analyse and implement. Moreover, it circumvents the need to calculate energy fluxes. It is tested on the enhanced simplepoint charge model for liquid water and reproduces the known thermal conductivity of this model liquid of . It can be generalized to situations, where the thermal noise is replaced by another uniform heat source, or to the inverse situation, where the heat source is localized but the heat sink extends over the entire system.
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 ARTICLES

 Theoretical Methods and Algorithms

Local correlation measures in atomic systems
View Description Hide DescriptionThe phenomenon of electron correlation in atomic systems is examined and compared from the statistical, information theoretic, and energetic perspectives. Local correlationmeasures, based on the correlation coefficient, informationentropies, and idempotency measure, are compared to the correlation energy density. Analysis of these local measures reveals that the chemically significant valence region is responsible for the behavior of their respective global measures in contrast to the correlation energy density which has large contributions to the correlation energy from both the core and valence regions. These results emphasize the difference in the mechanisms inherent in the different perspectives, the similarity between the statistical, information entropic, and idempotency views, and provides further evidence for the use of information theoretic based quantities in studies of electron correlation.

Collective natural orbital occupancies of harmonium
View Description Hide DescriptionIn the harmonium atom, the collective occupancies of natural orbitals with different angular momenta can be rigorously studied for those values of the confinement strength that lead to groundstatewave functions with correlation factors given by polynomials of order. Analysis of two such cases, with equal to and , uncovers some interesting properties of , which turn out to be given by rational functions of with simple coefficients. In particular, contrary to naive expectations, the collective occupancies for actually decrease upon strengthening of correlation. The explicit formulas for matrices and can be readily utilized in testing, calibration, and benchmarking of approximate implementations of the density matrix functionaltheory (DMFT).

Corrections to the law of mass action and properties of the asymptotic state for reversible diffusionlimited reactions
View Description Hide DescriptionFor diffusionlimited reversible reactions we reexamine two fundamental concepts of classical chemical kinetics—the notion of “chemical equilibrium” and the “law of mass action.” We consider a general model with distancedependent reaction rates, such that any pair of particles, performing standard random walks on sites of a dimensional lattice and being at a distance apart of each other at time moment , may associate forming a particle at the rate . In turn, any randomly moving particle may spontaneously dissociate at the rate into a geminate pair of “born” at a distance apart of each other. Within a formally exact approach based on Gardiner’s Poisson representation method we show that the asymptotic state attained by such diffusionlimited reactions is generally not a true thermodynamic equilibrium, but rather a nonequilibrium steady state, and that the law of mass action is invalid. The classical concepts hold only in case when the ratio does not depend on for any .

Ab initio potentialenergy surfaces for complex, multichannel systems using modified novelty sampling and feedforward neural networks
View Description Hide DescriptionA neural network/trajectory approach is presented for the development of accurate potentialenergy hypersurfaces that can be utilized to conduct ab initiomolecular dynamics (AIMD) and Monte Carlo studies of gasphase chemical reactions, nanometric cutting, and nanotribology, and of a variety of mechanical properties of importance in potential microelectromechanical systems applications. The method is sufficiently robust that it can be applied to a wide range of polyatomic systems. The overall method integrates ab initio electronic structure calculations with importance sampling techniques that permit the critical regions of configuration space to be determined. The computed ab initio energies and gradients are then accurately interpolated using neural networks (NN) rather than arbitrary parametrized analytical functional forms, moving interpolation or leastsquares methods. The sampling method involves a tight integration of molecular dynamics calculations with neural networks that employ early stopping and regularization procedures to improve network performance and test for convergence. The procedure can be initiated using an empirical potential surface or direct dynamics. The accuracy and interpolation power of the method has been tested for two cases, the global potential surface for vinyl bromide undergoing unimolecular decomposition via four different reaction channels and nanometric cutting of silicon. The results show that the sampling methods permit the important regions of configuration space to be easily and rapidly identified, that convergence of the NN fit to the ab initio electronic structure database can be easily monitored, and that the interpolation accuracy of the NN fits is excellent, even for systems involving five atoms or more. The method permits a substantial computational speed and accuracy advantage over existing methods, is robust, and relatively easy to implement.

Characterizing the network topology of the energy landscapes of atomic clusters
View Description Hide DescriptionBy dividing potential energy landscapes into basins of attractions surrounding minima and linking those basins that are connected by transition state valleys, a network description of energy landscapes naturally arises. These networks are characterized in detail for a series of small LennardJones clusters and show behavior characteristic of smallworld and scalefree networks. However, unlike many such networks, this topology cannot reflect the rules governing the dynamics of network growth, because they are static spatial networks. Instead, the heterogeneity in the networks stems from differences in the potential energy of the minima, and hence the hyperareas of their associated basins of attraction. The lowenergy minima with large basins of attraction act as hubs in the network. Comparisons to randomized networks with the same degree distribution reveals structuring in the networks that reflects their spatial embedding.

Chemical reaction rates from ring polymer molecular dynamics
View Description Hide DescriptionWe show how the ringpolymer molecular dynamics method can be adapted to calculate approximate Kubotransformed fluxside correlation functions, and hence rate coefficients for condensed phase reactions. An application of the method to the standard model for a chemical reaction in solution—a quartic doublewell potential linearly coupled to a bath of harmonic oscillators—is found to give results of comparable accuracy to those of the classical Wigner model and the centroid molecular dynamics method. However, since the present method does not require that one evaluate the Wigner transform of a thermal flux operator or that one perform a separate path integral calculation for each molecular dynamics time step, we believe it will prove easier to apply to more general problems than either of these alternative techniques. We also present a (logarithmic) discretization scheme for the Ohmic bath in the systembath model that gives converged results with just nine bath modes—a surprisingly small number for a model of a condensed phase reaction. Finally, we present some calculations of the transmission through an Eckart barrier which show that the present method provides a satisfactory (although not perfect) description of the deep quantum tunneling regime. Part of the reason for the success of the method is that it gives the exact quantummechanical rate constant for the transmission through a parabolic barrier, as we demonstrate analytically in the Appendix.

Coupledcluster theory with simplified linear corrections: The CCSD(R12) model
View Description Hide DescriptionA simplified singlesanddoubles linear corrected coupledcluster model, denoted CCSD(R12), is proposed and compared with the complete singlesanddoubles linearcoupledcluster method CCSDR12. An orthonormal auxiliary basis set is used for the resolutionoftheidentity approximation to calculate threeelectron integrals needed in the linear Ansatz. Basisset convergence is investigated for a selected set of atoms and small molecules. In a large basis, the CCSD(R12) model provides an excellent approximation to the full linear energy contribution, whereas the magnitude of this contribution is significantly overestimated at the level of secondorder perturbation theory.

Scalar relativistic allelectron density functional calculations on periodic systems
View Description Hide DescriptionScalar relativistic effects are included in periodic boundary conditions calculations with Gaussian orbitals. This approach is based on the thirdorder Douglas–Kroll–Hess approximation, allowing the treatment of all electrons on an equal footing. With this methodology, we are able to perform relativistic allelectron density functional calculations using the traditional local spindensity and generalized gradient approximations (GGA), as well as metaGGA and hybrid density functionals. We present benchmark results for the bulk metals Pd, Ag, Pt, and Au, and the large band gapsemiconductors AgF and AgCl.

Alchemical free energy calculations and multiple conformational substates
View Description Hide DescriptionThermodynamic integration (TI) was combined with (adaptive) umbrella sampling to improve the convergence of alchemical free energy simulations in which multiple conformational substates are present. The approach, which we refer to as nonBoltzmann TI (NBTI), was tested by computing the free energy differences between three fiveatomic model systems, as well as the free energy difference of solvation between leucine and asparagine. In both cases regular TI failed to give converged results, whereas the NBTI results were free from hysteresis and had standard deviations well below . We also present theoretical considerations that make it possible to compute free energy differences between simple molecules, such as the fiveatomic model systems, by numerical integration of the partition functions at the respective end points.

Quantum control of molecular motion including electronic polarization effects with a twostage toolkit
View Description Hide DescriptionA method for incorporating strong electric fieldpolarization effects into optimal control calculations is presented. A Born–Oppenheimertype separation, referred to as the electricnuclear Born–Oppenheimer (ENBO) approximation, is introduced in which variations of both the nuclear geometry and the external electric field are assumed to be slow compared with the speed at which the electronic degrees of freedom respond to these changes. This assumption permits the generation of a potential energy surface that depends not only on the relative geometry of the nuclei but also on the electric field strength and on the orientation of the molecule with respect to the electric field. The range of validity of the ENBO approximation is discussed in the paper. A twostage toolkit implementation is presented to incorporate the polarization effects and reduce the cost of the optimal control dynamics calculations. As an illustration of the method, it is applied to optimal control of vibrational excitation in a hydrogen molecule aligned along the field direction. Ab initio configuration interaction calculations with a large orbital basis set are used to compute the H–H interaction potential in the presence of the electric field. The significant computational cost reduction afforded by the toolkit implementation is demonstrated.

Is the Filinov integral conditioning technique useful in semiclassical initial value representation methods?
View Description Hide DescriptionThe utility of the Filinov integral conditioning technique, as implemented in semiclassical initial value representation (SCIVR) methods, is analyzed for a number of regular and chaotic systems. For nonchaotic systems of low dimensionality, the Filinov technique is found to be quite ineffective at accelerating convergence of semiclassical calculations since, contrary to the conventional wisdom, the semiclassical integrands usually do not exhibit significant phase oscillations in regions of large integrand amplitude. In the case of chaotic dynamics, it is found that the regular component is accurately represented by the SCIVR, even when using the Filinov integral conditioning technique, but that quantum manifestations of chaotic behavior was easily overdamped by the filtering technique. Finally, it is shown that the level of approximation introduced by the Filinov filter is, in general, comparable to the simpler ad hoc truncation procedure introduced by Kay [J. Chem. Phys.101, 2250 (1994)].

Laser control of electronic transitions of wave packet by using quadratically chirped pulses
View Description Hide DescriptionAn effective scheme is proposed for the laser control of wave packet dynamics. It is demonstrated that by using specially designed quadratically chirped pulses, fast and nearly complete excitation of wave packet can be achieved without significant distortion of its shape. The parameters of the laser pulse can be estimated analytically from the Zhu–Nakamura theory of nonadiabatic transition. If the wave packet is not too narrow or not too broad, then the scheme is expected to be utilizable for multidimensional systems. The scheme is applicable to various processes such as simple electronic excitation, pumpdump, and selective bond breaking, and it is actually numerically demonstrated to work well by taking diatomic and triatomic molecules (LiH, NaK, ) as examples.

Quantum fluctuation of electronic wavepacket dynamics coupled with classical nuclear motions
View Description Hide DescriptionAn ab initio electronic wavepacket dynamics coupled with the simultaneous classical dynamics of nuclear motions in a molecule is studied. We first survey the dynamical equations of motion for the individual components. Reflecting the nonadiabatic dynamics that electrons can respond to nuclear motions only with a finite speed, the equations of motion for nuclei include a force arising from the kinematic (nuclear momentum) coupling from electron cloud. To materialize these quantum effects in the actual ab initio calculations, we study practical implementation of relevant electronic matrix elements that are related to the derivatives with respect to the nuclear coordinates. Applications of the present scheme are performed in terms of the configuration state functions (CSF) using the canonical molecular orbitals as basis functions without transformation to particular diabatic basis. In the CSF representation, the nonadiabatic interaction due to the kinematic coupling is anticipated to be rather small, and instead it should be well taken into account through the offdiagonal elements of the electronic Hamiltonian matrix. Therefore it is expected that the nonadiabatic dynamics based on this CSF basis neglecting the kinematic coupling may work. To verify this anticipation and to quantify the actual effects of the kinematic coupling, we compare the dynamics with and without the kinematiccoupling terms using the same CSF set. Applications up to the fifth electronically excited states in a nonadiabatic collision between and shows that the overall behaviors of these two calculations are surprisingly similar to each other in an average sense except for a fast fluctuation reflecting the electronic time scale. However, at the same time, qualitative differences in the collision events are sometimes observed. Therefore it turns out after all that the kinematiccoupling terms cannot be neglected in the CSFbasis representation. The present applications also demonstrate that the nonadiabatic electronic wavepacket dynamics within ab initio quantum chemical calculation is feasible.

Comparison of two genres for linear scaling in density functional theory: Purification and density matrix minimization methods
View Description Hide DescriptionTwo classes of linearscaling methods to replace diagonalization of the oneparticle Hamiltonian matrix in density functional theory are compared to each other. Purification takes a density matrix with the correct eigenfunctions and corrects the occupation numbers; density matrix minimization takes a density matrix with correct occupation numbers and corrects the eigenfunctions by rotating the orbitals. Computational comparisons are performed through modification of the MondoSCF program on water clusters and the protein endothelin. A purification scheme and a density matrix minimization scheme, based on the 1,2contracted Schrödinger equation [D. A. Mazziotti, J. Chem. Phys.115, 8305 (2001)] are implemented in large systems.

Correlation and response functions with nonMarkovian dissipation: A reduced Liouvillespace theory
View Description Hide DescriptionBased on a recently developed quantum dissipation formulation [R. X. Xu and Y. J. Yan, J. Chem. Phys.116, 9196 (2002)], we present a reduced Liouvillespace approach to evaluate the response and correlation functions of dissipative systems. The weak systembath interaction is treated properly for its effects on the initial state, the evolution, and the correlation between coherent driving and nonMarkovian dissipation. Numerical demonstration shows this correlated effect cannot be neglected even in the calculation of linear response quantities that do not explicitly depend on external fields. Highlighted in this paper is also the proper choice of theory among various formulations in the weak systembath interaction regime.

Orbitaloptimized coupledcluster theory does not reproduce the full configurationinteraction limit
View Description Hide DescriptionIt is shown that due to the mixing of the usual projection approach of coupled cluster with variational orbital optimization, orbitaloptimized coupled cluster (OCC) fails to reproduce the full configurationinteraction (full CI) limit when the cluster operator becomes complete. It is pointed out that the fulfillment of the projected singles equations, which define the orbital gradient in Brueckner coupled cluster (BCC), is mandatory for a correct behavior. As numerical examples we present general OCC and BCC calculations up to the full CI limit on and an activespace model of ozone. The observed deviations of OCC from full CI are of the order of the correlation error obtained in calculations with up to quadruples excitations. Thus the failure of OCC may be considered tolerable in more approximate calculations but clearly prohibitive for any benchmark application. For applications to activespace models a hybrid approach for OCC is suggested in which for active particlehole rotations the Brueckner orbital gradient is employed, whereas for the remaining orbital rotations the variational orbital gradient is retained.

Correlated holes and their relationships with reduced density matrices and cumulants
View Description Hide DescriptionThis paper describes a matrix formulation for the correlated hole theory within the framework of the domainaveraged model in many electron systems (atoms, molecules, condensed matter, etc.). General relationships between this quantity and oneparticle reduced density matrices for any independent particle or correlated state functions are presented. This formulation turns out to be suitable for computational purposes due to the straightforward introduction of cumulants of twoparticle reduced density matrices within the quantum field structure. Numerical calculations in selected simple molecular systems have been performed in order to determine preliminary correlated values for such a quantity.