Volume 119, Issue 23, 15 December 2003
 ARTICLES

 Theoretical Methods and Algorithms

Quantum dynamics scattering study of reactions: A sevendimensional treatment for the reaction
View Description Hide DescriptionA timedependent wave packet approach is presented for the quantum dynamics study of the reaction system for zero total angular momentum. A sevendegreeoffreedom calculation is employed to study the chemical reaction of by treating as a linear molecule. Initial state selected reaction probabilities are presented for various initial rovibrational states. This study shows that the vibrational excitation of enhances the reaction probability, whereas the excitation of has only a small effect on the reactivity. An integral cross section is also reported for the initial ground states of and The theoretical and experimental results agree with each other very well when the calculated sevendimensional results are adjusted to account for the lower transition state barrier heights found in recent ab initio calculations.

A new approach to calculating the memory kernel of the generalized quantum master equation for an arbitrary system–bath coupling
View Description Hide DescriptionThe Nakajima–Zwanzig generalized quantum master equation provides a general, and formally exact, prescription for simulating the reduced dynamics of a quantum system coupled to a quantum bath. In this equation, the memory kernel accounts for the influence of the bath on the system’s dynamics. The standard approach is based on using a perturbative treatment of the system–bath coupling for calculating this kernel, and is therefore restricted to systems weakly coupled to the bath. In this paper, we propose a new approach for calculating the memory kernel for an arbitrary system–bath coupling. The memory kernel is obtained by solving a set of two coupled integral equations that relate it to a new type of twotime systemdependent bath correlation functions. The feasibility of the method is demonstrated in the case of an asymetrical twolevel system linearly coupled to a harmonic bath.

Recovery of the Smoluchowski–Collins–Kimball kinetics parameters from fluorescence quenching decays
View Description Hide DescriptionTimecorrelated singlephoton counting (TCSPC) is a timeresolved fluorescence technique capable of monitoring transient diffusionmediated kinetics. When the transients can be reliably quantified, TCSPC data can be used for extracting the underlying microscopic dynamics. In the present paper, we study the recovery of the Smoluchowski–Collins–Kimball model parameters from simulated fluorescence quenching decays. A Levenberg–Marquardt leastsquares optimization routine was used for the estimation of the sum of the diffusion coefficients of the fluorophore and quencher, the sum of their radii, and the intrinsic quenching rate coefficient k. The accuracy and precision of parameter estimation were parameterized by the dimensionless quantities and where τ is the fluorophore lifetime, and [Q] is the quencher concentration. The zerotime shift was an adjustable parameter. The best parameter estimates are obtained for longlived fluorophores at high quencher concentrations. The estimated R and D are more accurate as the intrinsic quenching rate k becomes faster, but the estimation of k is optimal when k and the diffusion controlled rate are comparable in value. The present study should be useful in planning and interpreting TCSPC experiments on nanosecond and picosecond time scales.

Absolute entropy and free energy of fluids using the hypothetical scanning method. I. Calculation of transition probabilities from local grand canonical partition functions
View Description Hide DescriptionThe hypothetical scanning (HS) method provides the absoluteentropy and free energy from a Boltzmann sample generated by Monte Carlo,molecular dynamics or any other exact simulation procedure. Thus far HS has been applied successfully to magnetic and polymer chain models; in this paper and the following one it is extended to fluid systems by treating a LennardJones model of argon. With HS a probability approximating the Boltzmann probability of system configuration i is calculated with a stepwise reconstruction procedure, based on adding atoms gradually layerbylayer to an initially empty volume, where they are replaced in their positions at i. At each step a transition probability (TP) is obtained from local grand canonical partition functions calculated over a limited space of the still unvisited (future) volume, the larger this space the better the approximation. is the product of the step TPs, where is an upper bound of the absoluteentropy, which leads to upper and lower bounds for the free energy. We demonstrate that very good results for the entropy and the free energy can be obtained for a wide range of densities of the argon system by calculating TPs that are based on only a very limited future volume.

Absolute entropy and free energy of fluids using the hypothetical scanning method. II. Transition probabilities from canonical Monte Carlo simulations of partial systems
View Description Hide DescriptionA variant of the hypothetical scanning (HS) method for calculating the absolute entropy and free energy of fluids is developed, as applied to systems of LennardJones atoms (liquid argon). As in the preceding paper (Paper I), a probability approximating the Boltzmann probability of system configuration i, is calculated with a reconstruction procedure based on adding the atoms gradually to an initially empty volume, where they are placed in their positions at i; in this process the volume is divided into cubic cells, which are visited layerbylayer, linebyline. At each step a transition probability (TP) is calculated and the product of all the TPs leads to At step k, cells have already been treated, where among them are occupied by an atom. A canonical metropolis Monte Carlo(MC) simulation is carried out over a portion of the still unvisited (future) volume thus providing an approximate representation of the as yet untreated (future) atoms. The TP of target cellk is determined from the number of visits of future atoms to this cell during the simulation. This MC version of HS, called HSMC, is based on a relatively small number of efficiency parameters; their number does not grow and their values are not changed as the number of the treated future atoms is increased (i.e., as the approximation improves); therefore, implementing HSMC for a relatively large number of future atoms (up to 40 in this study) is straightforward. Indeed, excellent results have been obtained for the free energy and the entropy.

Monte Carlo wavefunction approach to the quantumphase dynamics of a dissipative molecular system interacting with a singlemode amplitudesqueezed field
View Description Hide DescriptionWe investigate the quantumphase dynamics of a dissipative molecular system interacting with a singlemode amplitudesqueezed field (with a subPoissonian photonnumber distribution) using the Monte Carlo wavefunction method. As quantum dissipation, we consider molecular coherent (phase) and population relaxations, which are caused by nuclear vibration, and cavity relaxation (the dissipation of an internal single mode to outer mode). In this study, we elucidate the effects of these dissipations on the unique quantum dynamical behaviors of this coupled system, e.g., collapserevival behavior of Rabi oscillations, using the quasiprobability (Q function) distribution of a singlemode field and the offdiagonal molecular density matrix. It is found that although the amplitudesqueezed field exhibits a distinct revival with larger amplitudes of molecular population in the presence of the molecular phase and population relaxations as compared to the coherent field, a very slight cavity relaxation suppresses the revival of molecular population and the increase in the magnitude of offdiagonal molecular density matrices during the quiescent region in the amplitudesqueezed field case more significantly than in the coherent field case. These features are shown to be closely related to the difference in the dynamics of Q function distributions between amplitudesqueezed and coherent fields.

Heat capacity estimators for random series pathintegral methods by finitedifference schemes
View Description Hide DescriptionPrevious heat capacity estimators used in path integral simulations either have large variances that grow to infinity with the number of path variables or require the evaluation of first and secondorder derivatives of the potential. In the present paper, we show that the evaluation of the total energy by the Tmethod estimator and of the heat capacity by the TTmethod estimator can be implemented by a finite difference scheme in a stable fashion. As such, the variances of the resulting estimators are finite and the evaluation of the estimators requires the potential function only. By comparison with the task of computing the partition function, the evaluation of the estimators requires times more calls to the potential, where is the order of the difference scheme employed. Quantum Monte Carlo simulations for the cluster demonstrate that a second order centraldifference scheme should suffice for most applications.

Comparative assessment of a new nonempirical density functional: Molecules and hydrogenbonded complexes
View Description Hide DescriptionA comprehensive study is undertaken to assess the nonempirical metageneralized gradient approximation (MGGA) of Tao, Perdew, Staroverov, and Scuseria (TPSS) against 14 common exchangecorrelation energy functionals. Principal results are presented in the form of statistical summaries of deviations from experiment for the G3/99 test set (223 enthalpies of formation, 86 ionization potentials, 58 electron affinities, 8 proton affinities) and three additional test sets involving 96 bond lengths, 82 harmonic vibrational frequencies, and 10 hydrogenbonded complexes, all computed using the basis. The TPSS functional matches, or exceeds in accuracy all prior nonempirical constructions and, unlike semiempirical functionals, consistently provides a highquality description of diverse systems and properties. The computational cost of selfconsistent MGGA is comparable to that of ordinary GGA, and exact exchange (unavailable in some codes) is not required. A oneparameter global hybrid version of the TPSS functional is introduced and shown to give further improvement for most properties.

Corehole Hamiltonians and corrected equivalent core model for systems with equivalent atoms
View Description Hide DescriptionCore ionization in systems with several equivalent atoms gives rise to a set of neardegenerate corehole states each associated with the removal of an electron from one of the delocalized orbitals. The energy splitting between the corehole states is the intrinsic feature of core ionized systems and should not be neglected. The conventional equivalent core model (ECM) predicts strictly degenerate corehole states because the corehole is thought of as completely localized on one of the equivalent centers. This failure as well as several others inherent to the ECM are successfully removed in the framework of the corrected ECM presented in this paper. Two approaches are available in accordance with the two representations of the corehole, either delocalized or localized. The approximation is an excellent starting point in the localized representation. It must be modified, however, when the delocalized picture is used. To this end we introduce a system where is the magnitude of point charges added to the nuclear charges of equivalent atoms which share the loss of an electron upon core ionization. Systematic corrections improving the conventional ECM are obtained by establishing a connection between the ECM and corehole Hamiltonians. The corehole Hamiltonians, being ideally suited for description of core ionization, are derived both in the delocalized and localized representations. Numerical results are presented for

Similarity transformed semiclassical dynamics
View Description Hide DescriptionIn this article, we employ a recently discovered criterion for selecting important contributions to the semiclassical coherent state propagator [T. Van Voorhis and E. J. Heller, Phys. Rev. A 66, 050501 (2002)] to study the dynamics of many dimensional problems. We show that the dynamics are governed by a similarity transformed version of the standard classical Hamiltonian. In this light, our selection criterion amounts to using trajectories generated with the untransformed Hamiltonian as approximate initial conditions for the transformed boundary value problem. We apply the new selection scheme to some multidimensional Henon–Heiles problems and compare our results to those obtained with the more sophisticated Herman–Kluk approach. We find that the present technique gives nearquantitative agreement with the the standard results, but that the amount of computational effort is less than Herman–Kluk requires even when sophisticated integral smoothing techniques are employed in the latter.

A nonequilibrium Monte Carlo approach to potential refinement in inverse problems
View Description Hide DescriptionThe inverse problem for a disordered system involves determining the interparticle interaction parameters consistent with a given set of experimental data. Recently, Rutledge has shown [Phys. Rev. E 63, 021111 (2001)] that such problems can be generally expressed in terms of a grand canonical ensemble of polydisperse particles. Within this framework, one identifies a polydisperse attribute (“pseudospecies”) σ corresponding to some appropriate generalized coordinate of the system to hand. Associated with this attribute is a composition distribution measuring the number of particles of each species. Its form is controlled by a conjugate chemical potential distribution μ(σ) which plays the role of the requisite interparticle interaction potential. Simulation approaches to the inverse problem involve determining the form of μ(σ) for which matches the available experimental data. The difficulty in doing so is that μ(σ) is (in general) an unknown functional of and must therefore be found by iteration. At high particle densities and for high degrees of polydispersity, strong cross coupling between μ(σ) and renders this process computationally problematic and laborious. Here we describe an efficient and robust nonequilibrium simulation scheme for finding the equilibrium form of The utility of the method is demonstrated by calculating the chemical potential distribution conjugate to a specific lognormal distribution of particle sizes in a polydisperse fluid.

The Kramers’ restricted complete active space selfconsistentfield method for twocomponent molecular spinors and relativistic effective core potentials including spin–orbit interactions
View Description Hide DescriptionThe Kramers’ restricted complete active space selfconsistentfield (KRCASSCF) method based upon twocomponent molecular spinors and relativistic effective core potentials including spin–orbit interactions is implemented, employing the twostep approach, in which the expansion coefficients of configurations and molecular spinors are determined alternately. The present approach allows the influence of spin–orbit interactions to be taken into account in the optimization of oneelectron wave function space. Test calculations were performed for the Hg atom, anion, and cation with the closedshell electronic configuration, the ground state potential energy curves of homonuclear diatomic molecules, and over a wide range of internuclear distances, and the bond fission of a polyatomic molecule The results show that the KRCASSCF method properly describes the dissociation of molecules for the finestructure states. It is also evident that molecular properties are affected by optimized spinors for systems containing heavy atoms such as and at the CASSCF level of theory.

Practical evaluation of condensed phase quantum correlation functions: A Feynman–Kleinert variational linearized path integral method
View Description Hide DescriptionWe report a new method for calculating the Wigner transform of the Boltzmann operator in the canonical ensemble. The transform is accomplished by writing the Boltzmann operator in a semiharmonic form, utilizing the variational centroid effective frequencies introduced by Feynman and Kleinert (FK). The approximate manybody Wigner transformedBoltzmann operator is then utilized with a linearized path integral (LPI) representation for correlation functions. It is shown that this new FKLPI method is capable of calculating quite accurately the short time behavior of linear and highly nonlinear correlation functions for low temperature LennardJones model systems and that it is vastly superior to classical dynamics. The feasibility of the FKLPI method for large systems is illustrated by considering a model liquid composed of 32 oxygen molecules with periodic boundary conditions. Initial conditions for molecular dynamics are obtained from its Boltzmann Wigner transform and the FKLPI method is shown to describe correctly the zeropoint motion of the liquid. The effective frequency representation of the Wigner transformed thermal density operator provides an efficient way of sampling nonclassical initial conditions for moleculardynamics simulations more generally. Applications to vibrational energy relaxation and rate constant calculations in complex molecular systems are discussed.

Selfconsistent density matrix algorithm for electronic structure and excitations of molecules and aggregates
View Description Hide DescriptionAn ab initio density matrix algorithm for electronic structure computations of manyelectron systems is proposed. The reduced singleelectron density matrices are derived by mapping the density functional theory nonlinear optical response functions onto an effective multilevel system. These density matrices are then used as a zeroth order iteration into selfconsistent equations whose solution should yield the exact energies and the complete set of (transition and diagonal) singleelectron density matrices. Higher order electron) density matrices are not computed explicitly. The linear and nonlinear optical response functions may be obtained at a low computational cost. Application is made to constructing an exciton Hamiltonian for molecular aggregates using density matrices of isolated molecules, avoiding electronic structure calculations of the entire aggregate.

A fastFourier transform method to solve continuumelectrostatics problems with truncated electrostatic interactions: Algorithm and application to ionic solvation and ion–ion interaction
View Description Hide DescriptionAn iterative algorithm based on fastFourier transforms is presented that solves the equations of continuum electrostatics for systems of heterogeneous dielectricpermittivity (e.g., solute cavity in a solvent) under periodic boundary conditions. The method makes explicit use of the charge–dipole and dipole–dipole interaction tensors, and is thus applicable both to Coulombic interactions (Ewald scheme) and cutoffbased electrostatic interactions described by any polynomial function (including a Coulombic term), as commonly used in molecular dynamics simulations. The latter case includes, in particular, straight truncation of Coulombic interactions and truncation including a reactionfield correction. After testing and validation by comparison with existing methods, the algorithm is used to investigate the effect of cutoff truncation and artificial periodicity in explicitsolvent simulations of ionic solvation and ion–ion interactions. Both cutoff truncation and artificial periodicity are found to significantly affect the polarization around a spherical ion and its solvation free energy. The nature and magnitude of the two perturbations are analyzed in detail, and approximate analytical correction terms are derived to be applied to the results of explicitsolvent simulations. Cutoff truncation induces strong alterations in the potential of mean force for the interaction between two spherical ions. The present observations based on continuum electrostatics help to rationalize artifacts previously reported from explicitsolvent simulations involving cutoff truncation and, in particular, the unphysical attraction of like charges and repulsion of opposite charges, and the corresponding alterations in the relative stabilities of contact, solventseparated, and free ion pairs.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Electron rescattering and the dissociative ionization of alcohols in intense laser light
View Description Hide DescriptionThe fragmentation dynamics of a series of alcohol molecules, from methanol and ethanol, through hexanol to dodecanol, has been studied by irradiating these molecules with 100 fs duration pulses of linearly and circularly polarized, infrared, intensityselected laser light. At laser intensities of the yields of singly and multiply charged atomic fragments from all these molecules are suppressed when circularly polarized light is used. This dependence of the fragmentation dynamics on polarization is rationalized using a simple electron rescattering model. Circular polarization switches “off” electron rescattering and leads to suppression of multiple ionization and molecular fragmentation. The degree of suppression depends upon the amount of energy transfer from the optical field to the molecule: the larger the energy transfer that is required for a particular fragmentation channel, the more marked is its suppression when circular polarization is used. The maximum kinetic energy that is released upon fragmentation appears to be more or less independent of the polarization state of the incident light. The observation that the actual values of kinetic energy released are less than Coulombic indicates that the enhanced ionization mechanism also holds for circularly polarized light.

Theoretical calculations of the Xe chemical shifts in cryptophane cages
View Description Hide DescriptionToward an understanding of the factors that affect the chemical shift in the Xe nuclear magnetic resonancespectrum of Xe atoms trapped in cages which may have applications as biosensors, we carry out calculations of Xe nuclear magnetic shielding using Hartree–Fock and density functional methods. The resulting values for various Xe positions within the cage can be described by an analytical function of Xe and cage atom coordinates. This shielding function is used in Monte Carlo canonical averaging of a Xe atom within cryptophane cages to investigate the dependence of the Xe chemical shifts on cage size (cryptophaneA versus cryptophaneE), isotopic substitution, and temperature. We compare our theoretical average Xe chemical shifts with the experimental values in four types of cryptophane cages, and with the temperature and isotopic dependence of Xe chemical shifts in cryptophaneA, and achieve a quantitative understanding of the factors that influence the Xe chemical shifts in these cages. The predicted effects on the Xe chemical shifts of mechanical distortion of the cryptophaneA cage provide some insight into the applications of Xe in cages as biosensors.

Laser spectroscopy of NiI: Ground and lowlying electronic states
View Description Hide DescriptionHighresolution laserinduced fluorescencespectrum of a jetcooled NiI molecule has been recorded in the near infrared and visible regions. The NiI molecule was produced by reacting laserablated nickel atom and methyl iodide Three electronic states have been identified that include the and two lowlying and excited states. Molecular transition bands of the system with 4–9, and the bands of the system with were observed and analyzed. Spectra of isotopic molecules confirmed the assignment of vibrational quantum number of the observed bands. Least squares fit of rotational transition lines yielded accurate molecular constants for the states studied. The bond length measured for the is 2.3479 Å and the equilibrium bond length, for the and are, respectively, 2.4834 and 2.5081 Å. With the use of a molecular orbital energy level diagram, we have examined the electronic configurations that give rise to the ground state for NiF, NiCl, and NiBr, but the state for NiI. This work represents the first spectroscopic study of the NiI molecule.

Density and binding forces: Rotational barrier of ethane
View Description Hide DescriptionThe possibility of extending the relationships between density, binding forces, and bonding energies to fine chemical effects is tested taking as an example the rotational barrier of ethane. Electron densities that reasonably fulfill the electrostatictheorem were obtained for several conformations using a Slater basis set. The analysis of these densities shows that the barrier is due to the internal forces acting on the H nuclei. Out of the staggered and eclipsed conformations, the clouds of the hydrogen atoms have a nonskeletal distortion that pull their nuclei toward the staggered conformation.

A comparative study of electron and positron scattering from chlorobenzene and chloropentafluorobenzene molecules
View Description Hide DescriptionTotal cross sections (TCSs) for electron and positronscattering from chlorobezene and chloropentafluorobenzene molecules have been measured by using the linear transmission timeofflight method. The impact energies are from 0.4 eV to 1000 eV and 0.2 to 1000 eV for positron and electron impacts, respectively, for scattering from molecules, and 0.8 eV to 600 eV for electron and 0.4 to 600 eV for positronscattering from molecules. Two resonance structures are observed in the electron TCSs at 0.8 eV and 2.5 eV, which merge to the single resonance at 1.6 eV of the molecule. This is an evidence of the splitting of the degenerate orbital of the molecule into two upon substitution of an H atom by the Cl atom. electron TCSs are lower than the positron TCSs at 2–4 eV, otherwise elsewhere, electron TCSs for both and are greater than positron TCSs by a factor of 1–2 at energies up to 30 eV. In the comparative studies of TCSs for with and and the magnitude of TCSs is found to be in the order of the molecular size over all energy ranges, except positron TCSs for and below 600 eV.