Volume 129, Issue 15, 21 October 2008
 ARTICLES

 Theoretical Methods and Algorithms

Concentration fluctuations in fluid mixtures
View Description Hide DescriptionThe matrix of the Kirkwood–Buff theory of solutions describes number fluctuations of the component species. We show how, when the eigenvalues of the matrix are widely different in magnitude, the description of the fluctuations can be simplified by restriction to a lower dimensional subspace of composition space. This simplification entails a loss of accuracy, which is argued to be often acceptable. The development is illustrated by application to waterurea and water trifluoroethanol solutions. It is concluded that in these cases, the fluctuations of the components are coupled primarily by keeping the amount of void space in the solution almost constant.

Accurate and efficient calculation of van der Waals interactions within density functional theory by local atomic potential approach
View Description Hide DescriptionDensity functional theory(DFT) in the commonly used local density or generalized gradient approximation fails to describe van der Waals (vdW) interactions that are vital to organic, biological, and other molecular systems. Here, we propose a simple, efficient, yet accurate local atomic potential (LAP) approach, named , for including vdW interactions in the framework of DFT. The LAPs for H, C, N, and O are generated by fitting the potential energy curves of small molecule dimers to those obtained from coupled cluster calculations with single, double, and perturbatively treated triple excitations, CCSD(T). Excellent transferability of the LAPs is demonstrated by remarkable agreement with the JSCH–2005 benchmark database [P. Jurečka et al.Phys. Chem. Chem. Phys.8, 1985 (2006)], which provides the interaction energies of CCSD(T) quality for 165 vdW and hydrogenbonded complexes. For over 100 vdW dominant complexes in this database, our calculations give a mean absolute deviation from the benchmark results less than . The approach involves no extra computational cost other than standard DFT calculations and no modification of existing DFT codes, which enables straightforward quantum simulations, such as ab initio molecular dynamics, on biomolecular systems, as well as on other organic systems.

Incoherent control of locally controllable quantum systems
View Description Hide DescriptionAn incoherent control scheme for state control of locally controllable quantum systems is proposed. This scheme includes three steps: (1) amplitude amplification of the initial state by a suitable unitary transformation, (2) projective measurement of the amplified state, and (3) final optimization by a unitary controlled transformation. The first step increases the amplitudes of some desired eigenstates and the corresponding probability of observing these eigenstates, the second step projects, with high probability, the amplified state into a desired eigenstate, and the last step steers this eigenstate into the target state. Within this scheme, two control algorithms are presented for two classes of quantum systems. As an example, the incoherent control scheme is applied to the control of a hydrogen atom by an external field. The results support the suggestion that projective measurements can serve as an effective control and local controllability information can be used to design control laws for quantum systems. Thus, this scheme establishes a subtle connection between control design and controllability analysis of quantum systems and provides an effective engineering approach in controlling quantum systems with partial controllability information.

A formula for the minimal coordination number of a parallel bundle
View Description Hide DescriptionAn exact formula for the minimal coordination numbers of the parallel packed bundle of rods is presented based on an optimal thickening scenario. Hexagonal and square lattices are considered.

Breit interaction contribution to parity violating potentials in chiral molecules containing light nuclei
View Description Hide DescriptionThe importance of the Breit interaction for an accurate prediction of parity violating energy differences between enantiomers is studied within electroweak quantum chemical frameworks. Besides twoelectron orbitorbit and spinspin coupling contributions, the Breit interaction gives rise to the spinotherorbit coupling term of the Breit–Pauli Hamiltonian. The present numerical study demonstrates that neglect of this latter term leads in hydrogen peroxide to relative deviations in the parity violating potential by about 10%, whereas further relativistic corrections accounted for within a fourcomponent Dirac–Hartree–Fock–Coulomb (DHFC) framework remain smaller, below 5%. Thus, the main source of discrepancy between previous onecomponent based (coupled perturbed) Hartree–Fock (HF) and fourcomponent Dirac–Hartree–Fock results for parity violating potentials in is the neglect of the Breit contribution in DHFC. In heavier homologs of hydrogen peroxide the relative contribution of the spinotherorbit coupling term to decreases with increasing nuclear charge, whereas other relativistic effects become increasingly important. As shown for the series of molecules and for CHBrClF, to a good approximation these other relativistic influences on can be accounted for in onecomponent based HF calculations with the help of relativistic enhancement factors proposed earlier in the theory of atomic parity violation.

A pseudobond parametrization for improved electrostatics in quantum mechanical/molecular mechanical simulations of enzymes
View Description Hide DescriptionThe pseudobond method is used in quantum mechanical/molecular mechanical (QM/MM) simulations in which a covalent bond connects the quantum mechanical and classical subsystems. In this method, the molecular mechanical boundary atom is replaced by a special quantum mechanical atom with one free valence that forms a bond with the rest of the quantum mechanical subsystem. This boundary atom is modified through the use of a parametrized effective core potential and basis set. The pseudobond is designed to reproduce the properties of the covalent bond that it has replaced, while invoking as small a perturbation as possible on the system. Following the work of Zhang [J. Chem. Phys.122, 024114 (2005)], we have developed new pseudobond parameters for use in the simulation of enzymatic systems. Our parameters yield improved electrostatics and deprotonation energies, while at the same time maintaining accurate geometries. We provide parameters for , , and pseudobonds, which allow the interface between the quantum mechanical and molecular mechanical subsystems to be constructed at either the bond of a given amino acid residue or along the peptide backbone. In addition, we demonstrate the efficiency of our parametrization method by generating residuespecific pseudobond parameters for a single amino acid. Such an approach may enable higher accuracy than general purpose parameters for specific QM/MM applications.

Optimization of expanded ensemble methods
View Description Hide DescriptionExpanded ensemble methods, designed to sample a range of an order parameter of interest, can be optimized to overcome the difficulties associated with traversing large freeenergy barriers or rugged landscapes. The optimization strategy of Trebst et al. [Phys. Rev. E70, 046701 (2004)] is based on finding suitable biasing weights for intertransitions that maximize the number of round trips that the system performs between the lower and upper bounds. In this work, this optimizedensemble methodology is extended by finding weights that minimize the mean roundtrip time (between the end states) for a Markovian walk. Applications are presented for an atomistically detailed model and for systems where one needs to sample a wide range of concentrations or compositions. A less rigorous method that implements a dual minimization (for both upward and downward trajectories) is found to be harder to converge but produce more round trips than a method based on a single minimization for all trajectories. While the proposed methods do not always minimize the true , they have performances that are either similar or better than those of the original optimizedensemble method and provide useful information to characterize deviations from Markovian dynamics in the sampling of the space.

A polarizable forcefield model for quantummechanicalmolecularmechanical Hamiltonian using expansion of point charges into orbitals
View Description Hide DescriptionWe present an ab initio polarizable representation of classical molecular mechanics (MM) atoms by employing an angular momentumbased expansion scheme of the point charges into partial wave orbitals. The charge density represented by these orbitals can be fully polarized, and for hybrid quantummechanicalmolecularmechanical (QM/MM) calculations, mutual polarization within the QM/MM Hamiltonian can be obtained. We present the mathematical formulation and the analytical expressions for the energy and forces pertaining to the method. We further develop a variational scheme to appropriately determine the expansion coefficients and then validate the method by considering polarizations of ions by the QM system employing the hybrid GROMACSCPMD QM/MM program. Finally, we present a simpler prescription for adding isotropic polarizability to MM atoms in a QM/MM simulation. Employing this simpler scheme, we present QM/MM energy minimization results for the classic case of a water dimer and a hydrogen sulfide dimer. Also, we present singlepoint QM/MM results with and without the polarization to study the change in the ionization potential of tetrahydrobiopterin in water and the change in the interaction energy of solvated (described by MM) with the heme described by QM. The model can be employed for the development of an extensive classical polarizable forcefield.

The structure of mixed monolayer films on Ru(0001)
View Description Hide DescriptionScanning tunneling microscopy(STM) and xray absorption spectroscopy(XAS) have been used to study the structures produced by water on Ru(0001) at temperatures above 140 K. It was found that while undissociated water layers are metastable below 140 K, heating above this temperature produces drastic transformations, whereby a fraction of the water molecules partially dissociate and form mixed structures.Xray photoelectron spectroscopy and XAS revealed the presence of hydroxyl groups with their O–H bond essentially parallel to the surface. STM images show that the mixed structures consist of long narrow stripes aligned with the three crystallographic directions perpendicular to the closepacked atomic rows of the Ru(0001) substrate. The internal structure of the stripes is a honeycomb network of Hbonded water and hydroxyl species. We found that the metastable low temperature molecular phase can also be converted to a mixed phase through excitation by the tunneling electrons when their energy is 0.5 eV or higher above the Fermi level. Structural models based on the STM images were used for density functional theory optimizations of the stripe geometry. The optimized geometry was then utilized to calculate STM images for comparison with the experiment.

Is it possible to determine rigorous magnetic Hamiltonians in spin systems from density functional theory calculations?
View Description Hide DescriptionThe variational energies of brokensymmetry single determinants are frequently used (especially in the Kohn–Sham density functional theory) to determine the magnetic coupling between openshell metal ions in molecular complexes or periodic lattices. Most applications extract the information from the solutions of and eigenvalues of magnetic spin momentum, assuming that a mapping of these energies on the energies of an Ising Hamiltonian is grounded. This approach is unable to predict the possible importance of deviations from the simplest form of the Heisenberg Hamiltonians. For systems involving magnetic centers, it cannot provide an estimate of neither the biquadratic exchange integral nor the threebody operator interaction that has recently been proven to be of the same order of magnitude [Phys. Rev. B70, 132412 (2007)]. The present work shows that one may use other brokensymmetry solutions of intermediate values of to evaluate the amplitude of these additional terms. The herederived equations rely on the assumption that an extended Hubbardtype Hamiltonian rules the interactions between the magnetic electrons. Numerical illustrations on a model problem of two molecules and a fragment of the lattice are reported. The results obtained using a variable percentage of Fock exchange in the BLYP functional are compared to those provided by elaborate wave function calculations. The relevant percentage of Fock exchange is system dependent but a mean value of 30% leads to acceptable amplitudes of the effective exchange interaction.

On the consistency, extremal, and global properties of counterdiabatic fields
View Description Hide DescriptionThe control of population transfer can be affected by the adiabatic evolution of a system under the influence of an applied field. If the field is too rapidly varying or too weak, the conditions for adiabatic transfer are not satisfactorily met. We report the results of an analysis of properties of counterdiabatic fields (CDFs) that restore the adiabatic dynamics of a system by suppressing diabatic effects as they are generated. We observe that a CDF is not unique and find the one that has minimum intensity, and we provide natural upper and lower bounds to the integrated intensity of a CDF in terms of integrals of the eigenvalues of the system Hamiltonian. For Hamiltonians that are separable with respect to their parameters, we prove that the time integral of an associated CDF is path independent. Finally we explain why and when, in the neighborhood of an avoided crossing, a CDF can be approximated by Lorentzian pulses.

Molecular transistors based on BDTtype molecular bridges
View Description Hide DescriptionIn this work we study the effect of electron correlations in molecular transistors with molecular bridges based on 1,4benzenedithiol (BDT) and 2nitro1,4benzenedithiol (nitroBDT) by using ab initio electron propagator calculations. We find that there is no gate field effect for the BDT based transistor in accordance with the experimental data. After verifying the computational method on the BDT molecule, we consider a transistor with a nitroBDT molecular bridge. From the electron propagator calculations, we predict strong negative differential resistance at small positive and negative values of sourcedrain voltages. The explanation of the peak and the minimum in the current is given in terms of the molecular orbital picture and switchon (off) properties due to the voltage dependencies of the Dyson poles (ionization potentials). When the current is off, the electronic states on both electrodes are populated resulting in the vanishing tunneling probability due to the Pauli principle. Besides the minimum and the maximum in the characteristics, we find a strong gate field effect in the conductance where the peak at and switches to the minimum at A similar behavior is discovered at the negative . Such a feature can be used for fast current modulation by changing the polarity of a gate field.

Excess electron states in reduced bulk anatase : Comparison of standard GGA, , and hybrid DFT calculations
View Description Hide DescriptionThe removal of lattice O atoms, as well as the addition of interstitial H atoms, in is known to cause the reduction in the material and the formation of “” ions. By means of electronic structure calculations we have studied the nature of such oxygen vacancy and hydrogen impurity states in the bulk of the anatase polymorph of . The spin polarized nature of these centers, the localized or delocalized character of the extra electrons, the presence of defectinduced states in the gap, and the polaronic distortion around the defect have been investigated with different theoretical methods: standard density functional theory(DFT) in the generalizedgradient approximation (GGA), methods as a function of the parameter, and two hybrid functionals with different admixtures of Hartree–Fock exchange. The results are found to be strongly dependent on the method used. Only or hybrid functionals are able to reproduce the presence of states at about 1 eV below the conduction band, which are experimentally observed in reduced titania. The corresponding electronic states are localized on levels, but partly delocalized solutions are very close in energy. These findings show the limited predictive power of these theoretical methods to describe the electronic structure of reduced titania in the absence of accurate experimental data.

Nonperturbative ab initio calculations in strong magnetic fields using London orbitals
View Description Hide DescriptionA selfconsistent field (SCF) Londonorbital computational scheme to perform gaugeorigin independent nonperturbative calculations for molecules in strong magnetic fields is presented. The crucial difference in the proposed approach with respect to commonorigin finitefield SCF implementations consists in the evaluation of molecular integrals over the fielddependent molecular basis functions, which is tantamount to computing molecular integrals in a hybrid Gaussian and planewave basis set. The implementation of a McMurchie–Davidson scheme for the calculation of the molecular integrals over London orbitals is discussed, and preliminary applications of the newly developed code to the calculation of fourthrank hypermagnetizabilities for a set of small molecules, benzene, and cyclobutadiene are presented. The nonperturbative approach is particularly useful for studying the highly nonlinear response of paramagnetic closedshell systems such as boron monohydride, or the electron response of cyclobutadiene.

Using the isotropic periodic sum method to calculate longrange interactions of heterogeneous systems
View Description Hide DescriptionIsotropic periodic sum (IPS) is a method for the calculation of longrange interactions in molecular simulation based on the homogeneity of simulation systems. Three IPS models, 3D IPS, 2D IPS, and 1D IPS have been developed for three common types of homogeneous systems. Based on the fact that 3D IPS can well describe the longrange interactions of a heterogeneous system if a local region larger than the homogeneity scale is used, this work presents a method based on 3D IPS to calculate longrange interactions for all kinds of simulation systems, including homogeneous, heterogeneous, and finite systems. Unlike the original 3D IPS method that uses a local region defined by the cutoff distance, this method uses a local region larger than that defined by the cutoff distance to reach the homogeneity scale. To efficiently calculate interactions within such a large local region, this method split longrange interactions into two parts, a cutoff part and a longrange part. The cutoff part is calculated by summing over atom pairs within a cutoff range (about ), and the longrange part is calculated using the discrete fast Fourier transform (DFFT) technique. This method is applied to electrostatic and van der Waals interactions for both periodic and nonperiodic systems. Example simulations demonstrate that this method can accurately and efficiently calculate longrange interactions for molecular simulation.

Generalization of the Gibbs–Kelvin–Köhler and Ostwald–Freundlich equations for a liquid film on a soluble nanoparticle
View Description Hide DescriptionA derivation of chemical equilibrium equations for a spherical thin film of solution around a solublesolidnanoparticle is presented. The equations obtained generalize the Gibbs–Kelvin–Köhler and Ostwald–Freundlich equations for a soluble particle immersed in the bulk phase. The generalized equations describe the dependence of the chemical potentials of a condensate and dissolved nanoparticle matter in the thin solutionfilm, the condensate saturated pressure, and the solubility of the nanoparticle matter on the film thickness, and the nanoparticle size with account of the disjoining pressure of the liquid film.

Two definitions of the hopping time in a confined fluid of finite particles
View Description Hide DescriptionWe consider a fluid of hard disks diffusing in a flat long narrow channel of width approaching from above the doubled diameter of the disks. In this limit, the disks can pass their neighbors only rarely, in a mean hopping time growing to infinity, so the disks start by diffusing anomalously. We study the hopping time, which is the crucial parameter of the theory describing the subsequent transition to normal diffusion. We show that two different definitions of this quantity, based either on the mean first passage time calculated from solution of the Fick–Jacobs equation, or coming from transition state theory, are incompatible. They have different physical interpretation and also, they give different dependencies of the hopping time on the width of the channel.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Quantifying the effects of the selfinteraction error in density functional theory: When do the delocalized states appear? II. Ironoxo complexes and closedshell substrate molecules
View Description Hide DescriptionEffects of the selfinteraction error (SIE) in approximate density functional theory have several times been reported and quantified for the dissociation of charged radicals, charge transfer complexes, polarizabilities, and for transition states of reactions involving maingroup molecules. In the present contribution, effects of the SIE in systems composed of a catalytic transition metal complex and a closedshell substrate molecule are investigated. For this type of system, effects of the SIE have not been reported earlier. It is found that although the best density functionals (e.g., B3LYP) are capable of accurate predictions of structure, thermodynamics, and reactivity of such systems, there are situations and systems for which the magnitude of the SIE can be large, and for which the effects can be severe for the modeling of chemical reactivity. The largest energetic effect reported here is the artificial stabilization of a catalystsubstrate complex by as much as . Also, the disappearance of significant energy barriers for hydrogen atom transfer in certain systems are reported. In line with earlier work, it is found that the magnitude of the SIE is related to the energetics of electron transfer between the metal catalyst and the substrate molecule. It is suggested that these problems might be circumvented by the inclusion of counterions or point charges that would alter the energetics of electron transfer. It is also pointed out that the effects of SIE in the modeling of transition metal reactivity need to be investigated further.

Imaging the paircorrelated dynamics and isotope effects of the reaction
View Description Hide DescriptionBy using a timesliced (ion) velocityimaging technique, the title reaction was investigated to interrogate the paircorrelated dynamics of HCl (DCl) in concomitance with the or groundstate product under the crossedbeam conditions. Product paircorrelated excitation functions, vibrational branching ratios, and angular distributions were obtained over a wide range of collision energies, from 2 to 22 kcal/mol. Two distinct reaction mechanisms were uncovered. Both the dominant groundstatereaction of and the reaction forming the same product pairs from bendexcited reactants proceed through direct mechanisms, which shift from a rebound dynamics near thresholds to a peripheral dynamics at higher . Reactivity of forming the product pairs from groundstate reactants is small, yet shows dynamics pattern characteristics of a resonant reaction pathway. Significant spinorbit reactivity of was discovered, and its mechanism appears to be also mediated by the resonant reaction pathway. Comparing the dynamical attributes of the H and Datom transfer channels, remarkable isotope effects are found—in line with the previous findings in the and reactions.

Measurement of absolute transition dipole moment functions of the and transitions in NaK using Autler–Townes spectroscopy and calibrated fluorescence
View Description Hide DescriptionWe describe a twolaser experiment using opticaloptical double resonance fluorescence and Autler–Townes (AT) splittings to determine the NaK , absolute transitiondipole moment functions. Resolved and fluorescence was recorded with the frequencies of a titaniumsapphire laser (L1) and a ring dye laser (L2) fixed to excite particular double resonance transitions. The coefficients of a trial transitiondipole moment function were adjusted to match the relative intensities of resolved spectral lines terminating on the lower and levels. These data provide a relative measure of the functions over a broad range of . Next, L2 was tuned to either the or transition and focused to an intensity large enough to split the levels via the AT effect. L1 was scanned over the or transition to probe the AT line shape, which was fit using density matrix equations to yield an absolute value for , where and represent the upper and lower levels, respectively, of the coupling laser (L2) transition. Finally, the values of were used to place the relative functions obtained with resolved fluorescence onto an absolute scale. We compare our experimental transitiondipole moment functions to the theoretical work of Magnier et al. [J. Mol. Spectrosc.200, 96 (2000)].