Volume 123, Issue 16, 22 October 2005
 COMMUNICATIONS


Sizedependent structures of cluster ions with a methanol adsorbate: A combined study by photodissociation spectroscopy and densityfunctional theory calculation
View Description Hide DescriptionMethanol adsorption sites on ions were investigated. Photoexcitation to chargetransfer states of (methanol) predominantly produces two fragment ions: (methanol) (neutral NaI loss) and (neutral NaI and methanol loss), without forming (methanol loss). The relative intensities of these fragments are correlated with the geometries and binding energies.

Electronic excitedstate mixing in
View Description Hide DescriptionAb initio calculations that explicitly include spinorbit interactions are reported for the system of electronic states. A surprising curve crossing is observed for the , Tshaped geometry. Away from the geometry, the states mix, as expected. On the basis of these new results we propose a new mechanism for electronic energy transfer from highly vibrationally excited levels of the electronic state of the chlorine molecule. It is proposed that as long as vibrational predissociation of proceeds by direct coupling of the initial state to the continuum states the Ne atom does not sample geometries that efficiently quench the electronic state. However, when the vibrational dynamics changes to the intramolecular vibrational relaxation regime the Ne atom becomes quite effective at coupling the state with state.

Exchangecorrelation functional with broad accuracy for metallic and nonmetallic compounds, kinetics, and noncovalent interactions
View Description Hide DescriptionBy incorporating kineticenergy density in a balanced way in the exchange and correlational functionals and removing selfcorrelation effects, we have designed a density functional that is broadly applicable to organometallic, inorganometallic, and nonmetallic bonding, thermochemistry,thermochemical kinetics, and noncovalent interactions as well as satisfying the uniform electron gas limit. The average error is reduced by a factor of 1.3 compared with the best previously available functionals, but even more significantly, we find a functional that has a high accuracy for all four categories of interaction.

Oxygen adsorption at anionic free and supported Au clusters
View Description Hide DescriptionThe structure, stability, and adsorption properties of anionic clusters either free or supported at defected MgO(100) surfaces are investigated using densityfunctional theory.adsorption is strong whenever unpaired electrons are present, except for at some small, supported, planar, highbandgap clusters. These clusters have the unpaired electrons pinned by the Madelung potential of the support. Larger clusters (starting at ) become three dimensional and metallic. This ensures that while one cluster orbital is pinned to the defect, another orbital at comparable energy can undergo depletion, thus binding with charge transfer.

Energy relaxation versus spectral diffusion of the OHstretching vibration of HOD in liquidtosupercritical deuterated water
View Description Hide DescriptionThe dynamics of vibrational energy relaxation (VER) of the OHstretching vibration of HOD in liquidtosupercritical heavy water is studied as a function of temperature and solvent density by femtosecond midinfrared spectroscopy. Using the dielectric constant of the fluid both, the OHstretching absorption frequency and the VER rate, can be correlated phenomenologically with the average hydrogenbond connectivity within the random network. This correlation enables the identification of thermodynamic conditions under which spectraldiffusion due to hydrogenbond breakage/formation is much faster than VER.
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 ARTICLES

 Theoretical Methods and Algorithms

Molecular dynamics in the isothermalisobaric ensemble: The requirement of a “shell” molecule. I. Theory and phasespace analysis
View Description Hide DescriptionCurrent constant pressure moleculardynamics (MD) algorithms are not consistent with the recent reformulation of the isothermalisobaric ensemble. The ensemble partition function requires the use of a “shell” molecule to identify uniquely the volume of the system, thereby avoiding the redundant counting of configurations [e.g., G. J. M. Koper and H. Reiss, J. Phys. Chem.100, 422 (1996); D. S. Corti, Phys. Rev. E, 64, 016128 (2001)]. So far, only the Monte Carlo method has been updated to allow the system volume to be defined by a shell particle [D. S. Corti, Mol. Phys.100, 1887 (2002)]. A shell particle has yet to be incorporated into MD simulations. The proper modification of the MD algorithm is therefore the subject of this paper. Unlike Andersen’s method [H. C. Andersen, J. Chem. Phys.72, 2384 (1980)] where a piston of unknown mass serves to control the response time of volume fluctuations, the newly proposed equations of motion impose a constant external pressure via the introduction of a shell particle of known mass. Hence, the system itself sets the time scales for pressure and volume fluctuations. The new algorithm is subject to a number of fundamentally rigorous tests to ensure that the equations of motion sample phase space correctly. We also show that the Hoover algorithm [W. G. Hoover, Phys. Rev. A.31, 1695 (1985); 34, 2499 (1986)] does sample phase correctly, but only when periodic boundary conditions are employed.

Molecular dynamics in the isothermalisobaric ensemble: The requirement of a “shell” molecule. II. Simulation results
View Description Hide DescriptionThe results of a series of constant pressure and temperature moleculardynamics (MD) simulation studies based on the rigorous shell particle formulation of the isothermalisobaric ensemble are presented. These MD simulations validate the newly proposed constant pressure equations of motion in which a “shell” particle is used to define uniquely the volume of the system [M. J. Uline and D. S. Corti, J. Chem. Phys. (to be published), preceding paper]. Ensemble averages obtained with the new MD algorithm match the ensemble averages obtained using the previously derived shell particle Monte Carlo method [D. S. Corti, Mol. Phys.100, 1887 (2002)]. In addition, we also verify that the Hoover MD algorithm [W. G. Hoover, Phys. Rev. A31, 1695 (1985);34, 2499 (1986)] generates the correct ensemble averages, though only when periodic boundary conditions are employed. The extension of the shell particle MD algorithm to multicomponent systems is also discussed, in which we show for equilibrium properties that the identity of the shell particle is completely arbitrary when periodic boundary conditions are applied. Selfdiffusion coefficients determined with the shell particle equations of motion are also identical to those obtained in other ensembles. Finally, since the mass of the shell particle is known, the system itself, and not a piston of arbitrary mass, controls the time scales for internal pressure and volume fluctuations. We therefore consider the effects of the shell particle on the dynamics of the system. Overall, the shell particle MD algorithm is an effective simulation method for studying systems exposed to a constant external pressure and may provide an advantage over other existing constant pressure approaches when developing nonequilibrium MD methods.

Direct evaluation of multicomponent phase equilibria using flathistogram methods
View Description Hide DescriptionWe present a method for directly locating densitydriven phase transitions in multicomponent systems. Phase coexistence conditions are determined through manipulation of a total density probability distribution evaluated over a density range that includes both coexisting phases. Saturation quantities are determined through appropriate averaging of densitydependent mean values of a given property of interest. We discuss how to implement the method in both the grandcanonical and isothermalisobaric semigrand ensembles. Calculations can be conducted using any of the recently introduced flathistogram techniques. Here, we combine the general algorithm with a transitionmatrix approach to produce an efficient selfadaptive technique for determining multicomponent phase equilibriumproperties. To assess the performance of the new method, we generate phase diagrams for a number of binary and ternary LennardJones mixtures.

Efficient treatment of the Hartree interaction in the relativistic KohnSham problem
View Description Hide DescriptionWe elaborate the twocomponent DouglasKroll reduction of the DiracKohnSham problem of relativistic densityfunctional theory as introduced by Matveev and Rösch [J. Chem. Phys.118, 3997 (2003)]. That method retains corrections to the Coulomb selfinteraction (or Hartree) term of the energy functional that are due to the picture change. Using analytic expressions for the matrix elements, one is able to abandon the resolution of the identity approach for a crucial step of the relativistic transformation. Thus, a major source of uncertainties of the method is eliminated because basis sets no longer have to be extended by functions of higher angular momentum, previously required to ensure kinetic balance. This approach also relies on the electron chargedensity fitting scheme via an auxiliary basis set. An efficient approximate implementation results if one restricts the relativistic transformation to the spherically symmetric atomcentered auxiliary functions. It provides accurate results while simplifying greatly the expressions for the matrix elements of the relativistically transformed operators and significantly reducing the computational effort. We demonstrate the performance of the method for the fine structure of oneelectron levels of the Hg atom, the tensor shifts of , and the properties of the diatomic molecules , , PbO, and TlH.

On the accuracy of onecomponent pseudopotential spinorbit calculations
View Description Hide DescriptionImprovements on current onecomponent extraction procedures of spinorbit pseudopotentials are investigated for high accuracy computation of spinorbit couplingenergies. By means of the perturbationtheory formalism we first show that spinorbit pseudopotentials, extracted at the onecomponent selfconsistentfield level from a reference allelectron DiracCoulomb or DiracCoulombBreit calculation, include valence spinorbit polarization and relaxation effects. As a consequence the use of these pseudopotentials in uncontracted spinorbit configuration interaction (CI) with singles from the reference groundstate configuration gives rise to double counting of these spinorbit effects. Two new methods that avoid such double counting have been investigated. The first, socalled “explicit” method, calculates explicitly, by means of a fourcomponent spinorbit CI, the doublecounted spinorbit effects and removes them from the pseudopotentials. Due to the nonadditivity of the core and valence spinorbit effects as well as the socalled “pseudovariational collapse,” this method is shown to be cumbersome. In the second “implicit” method the spinorbit pseudopotential is extracted at the spinorbit polarized and relaxed level by means of a singleexcitation spinorbit CI calculation. Atomic tests on iodine demonstrate the ability of the latter method to solve the doublecounting problem.

New constraints upon the electronelectron repulsion energy functional of the oneelectron reduced density matrix
View Description Hide DescriptionThree strict constraints upon the electronelectron repulsion energy functional of the oneelectron reduced density matrix (the 1matrix) are obtained by combining its invariance and stationary properties with the extended Koopmans’ theorem. The constraints relate the quantities derived from the functional pertaining to an electron system with those of its electron congener. Together with the representability requirement for the 1matrix of the congener, identities involving the electronelectron repulsion energies of the two systems and their derivatives with respect to the 1matrices seriously narrow down the choices for potential approximate densitymatrix functionals. This fact is well illustrated in the case of twoelectron systems, where the validity of the new constraints is confirmed and found to originate from a nontrivial cancellation among different terms. Thus, the constraints provide a new tool for the construction and testing of new functionals that complements the previously known conditions such as the reproduction of the homogeneous gas energies and momentum distributions, convexity, and the representability of the associated 2matrices.

Fast evaluation of polarizable forces
View Description Hide DescriptionPolarizability is considered to be the single most significant development in the next generation of force fields for biomolecular simulations. However, the selfconsistent computation of induced atomic dipoles in a polarizable force field is expensive due to the cost of solving a large dense linear system at each step of a simulation. This article introduces methods that reduce the cost of computing the electrostatic energy and force of a polarizable model from about 7.5 times the cost of computing those of a nonpolarizable model to less than twice the cost. This is probably sufficient for the routine use of polarizable forces in biomolecular simulations. The reduction in computing time is achieved by an efficient implementation of the particlemesh Ewald method, an accurate and robust predictor based on leastsquares fitting, and nonstationary iterative methods whose fast convergence is accelerated by a simple preconditioner. Furthermore, with these methods, the selfconsistent approach with a larger timestep is shown to be faster than the extended Lagrangian approach. The use of dipole moments from previous timesteps to calculate an accurate initial guess for iterative methods leads to an energy drift, which can be made acceptably small. The use of a zero initial guess does not lead to perceptible energy drift if a reasonably strict convergence criterion for the iteration is imposed.

Improvement of semiempirical response properties with chargedependent response density
View Description Hide DescriptionThe present work outlines a new method for treatment of chargedependentpolarizability in semiempirical quantum models for use in combined quantummechanical/molecular mechanical simulations of biological reactions. The method addresses a major shortcoming in the performance of conventional semiempirical models for these simulations that is tied to the use of a localized minimal atomicorbital basis set. The present approach has the advantages that it uses a density basis that retains a set of linearresponse equations, does not increase the atomicorbital basis, and avoids the problem of artificial charge transfer and scaling of the polarizability seen in related models that allow atomic charges to fluctuate. The model introduces four new atombased parameters and has been tested with the modified neglect of differential overlap dorbital Hamiltonian against and ions and shown to decrease the dipole moment and polarizability errors by factors of 2 and 10, respectively, with respect to densityfunctional results. The method performs impressively for a variety of charge states (from to ), and offers a potentially powerful extension in the design of next generation semiempirical quantum models for accurate simulations of highly charged biological reactions.

Coarsegrained freeenergyfunctional treatment of quasistatic multiscale processes in heterogeneous materials
View Description Hide DescriptionA new treatment of quasistatic (reversible) multiscale processes in heterogeneous materials at nonzero temperature is presented. The system is coarse grained by means of a finiteelement mesh. The coarsegrained freeenergy functional (of the positions of the nodes of the mesh) appropriate to the thermodynamicstate variables controlled in the relevant process is minimized. Tests of the new procedure on a LennardJonesium crystal yield thermomechanical properties in good agreement with the “exact” atomistic results.

About the calculation of exchange coupling constants using densityfunctional theory: The role of the selfinteraction error
View Description Hide DescriptionThe effect of the correction of the selfinteraction error on the calculation of exchange coupling constants with methods based on densityfunctional theory has been tested in simple model systems. The inclusion of the selfinteraction correction cancels the nondynamical correlation energy contributions simulated by the commonly used functionals. Hence, such correction should be important in the accurate determination of exchange coupling constants. We have also tested several recent functionals to calculate exchange coupling constants in transitionmetal complexes, such as metaGGA functionals or new formulations of hybrid functionals. The influence of the basis set and of the use of pseudopotentials on the calculated values has also been evaluated for a Fe(III) dinuclear complex in which the paramagnetic centers bear several unpaired electrons.

A theoretical study of molecular conduction. II. A HartreeFock approach to transmission probability
View Description Hide DescriptionIn this paper, we discuss molecular conductivity based on Green’s function methods. In our calculations, we adopted the selfenergy formalism to accommodate semiinfinite electrodes connected to a molecule, and the selfenergy was obtained from the surfaceGreen’s function of the electrodes. We adopted the formalism of the surfaceGreen’s function derived by Sanvito et al. [Phys. Rev. B59, 11936 (1999)] and Krstic et al. [Phys. Rev. B66, 205319 (2002)], and although their formalisms for the surfaceGreen’s function were different, we were able to demonstrate that these formalisms are mathematically identical. We analyzed the electron transmission probability by using the spectrum expression of Green’s function, instead of using the inverse matrix of the effective Hamiltonian that includes an isolated molecule and the electrodes. Finally, we calculated the transmission probability of benzenedithiol based on the HartreeFock method and analyzed the disappearance of the transmission probability due to the orbital interference.

Efficient method for the calculation of time and frequencyresolved fourwave mixing signals and its application to photonecho spectroscopy
View Description Hide DescriptionAn efficient method has been developed for the calculation of thirdorder time and frequencyresolved optical signals. To obtain the general fourwave mixing signal, seven auxiliary density matrices have to be propagated in time. For the special cases of twopulse photonecho and transientgrating signals, two or three density matrices, respectively, are required. The method is limited to weak laser fields (it is thus valid within the thirdorder perturbation theory) but allows for any pulse durations and automatically accounts for pulseoverlap effects. To illustrate the method, we present the explicit derivation of the threepulse photonecho signal. Any other thirdorder optical signal can be calculated in the same manner. As an example, two and threepulse photonecho and transientgrating signals for a weakly damped displaced harmonic oscillator have been calculated.

Theoretical studies on magnetic circular dichroism by the finite perturbation method with relativistic corrections
View Description Hide DescriptionA theoretical method for calculating magnetic circular dichroism(MCD) of molecules is presented. We examined the numerical accuracy and the stability of the finite perturbation (FP) method and the sumoverstate (SOS)perturbation method. The relativistic effects are shown to be important for the MCDspectra of molecules containing heavy elements. Calculations using the FP and the SOS methods were carried out for ethylene, para and orthobenzoquinone, showing that the FP method is superior to the SOS method, as expected. The relativistic effect was examined using the secondorder DouglasKroll Hamiltonians for the halogen molecules , , , and . The Faraday terms of and were strongly affected by the relativistic effects, while the effect was negligible for and .

A regularized and renormalized electrostatic coupling Hamiltonian for hybrid quantummechanical–molecularmechanical calculations
View Description Hide DescriptionWe describe a regularized and renormalized electrostatic coupling Hamiltonian for hybrid quantummechanical (QM)–molecularmechanical (MM) calculations. To remedy the nonphysical QM/MM Coulomb interaction at short distances arising from a point electrostatic potential (ESP) charge of the MM atom and also to accommodate the effect of polarized MM atom in the coupling Hamiltonian, we propose a partialwave expansion of the ESP charge and describe the effect of a wave expansion, extended over the covalent radius , of the MM atom. The resulting potential describes that, at short distances, large scale cancellation of Coulomb interaction arises intrinsically from the localized expansion of the MM point charge and the potential selfconsistently reduces to at zero distance providing a renormalization to the Coulomb energy near interatomic separations. Employing this renormalized Hamiltonian, we developed an interface between the CarParrinello moleculardynamics program and the classical moleculardynamics simulation program Groningen machine for chemical simulations. With this hybrid code we performed QM/MM calculations on water dimer, imidazole carbon monoxide complex, and imidazoleheme complex with interacting with another imidazole. The QM/MM results are in excellent agreement with experimental data for the geometry of these complexes and other computational data found in literature.

On the origins of approximations for stochastic chemical kinetics
View Description Hide DescriptionThis paper considers the derivation of approximations for stochastic chemical kinetics governed by the discrete master equation. Here, the concepts of (1) partitioning on the basis of fast and slow reactions as opposed to fast and slow species and (2) conditional probability densities are used to derive approximate, partitioned master equations, which are Markovian in nature, from the original master equation. Under different conditions dictated by relaxation time arguments, such approximations give rise to both the equilibrium and hybrid (deterministic or Langevin equations coupled with discrete stochastic simulation) approximations previously reported. In addition, the derivation points out several weaknesses in previous justifications of both the hybrid and equilibrium systems and demonstrates the connection between the original and approximate master equations. Two simple examples illustrate situations in which these two approximate methods are applicable and demonstrate the two methods’ efficiencies.