Volume 121, Issue 8, 22 August 2004
 ARTICLES

 Theoretical Methods and Algorithms

Firstprinciples string molecular dynamics: An efficient approach for finding chemical reaction pathways
View Description Hide DescriptionA recently proposed approach, called “string method,” allows us to find minimum energy pathways connecting two metastable states of a system [W. E et al., Phys. Rev. B 66, 052301 (2002)]. So far this approach has been only used with empirical force field parametrizations of the atomic potential energy surface or in the context of macroscopic continuum models. Here we show that the string method can be efficiently combined with firstprinciples molecular dynamics to provide an accurate description of chemical reaction pathways and barriers. We illustrate the firstprinciples string molecular dynamics by applying it to the study of a surfacechemical reaction, for which extensive experimental and theoretical works are available, namely, the adsorption of on the reconstructed Si(100) surface.

Quantum statistics and classical mechanics: Real time correlation functions from ring polymer molecular dynamics
View Description Hide DescriptionWe propose an approximate method for calculating Kubotransformed realtime correlation functions involving positiondependent operators, based on path integral (ParrinelloRahman) molecular dynamics. The method gives the exact quantum mechanical correlation function at time zero, exactly satisfies the quantum mechanical detailed balance condition, and for correlation functions of the form and it gives the exact result for a harmonic potential. It also works reasonably well at short times for more general potentials and correlation functions, as we illustrate with some example calculations. The method provides a consistent improvement over purely classical molecular dynamics that is most apparent in the lowtemperature regime.

A general diagrammatic algorithm for contraction and subsequent simplification of secondquantized expressions
View Description Hide DescriptionWe present a general computer algorithm to contract an arbitrary number of secondquantized expressions and simplify the obtained analytical result. The functions that perform these operations are a part of the program Nostromo which facilitates the handling and analysis of the complicated mathematical formulas which are often encountered in modern quantumchemical models. In contrast to existing codes of this kind, Nostromo is based solely on the Goldstonediagrammatic representation of algebraic expressions in Fock space and has capabilities to work with operators as well as scalars. Each Goldstone diagram is internally represented by a line of text which is easy to interpret and transform. The calculation of matrix elements does not exploit Wick’s theorem in a direct way, but uses diagrammatic techniques to produce only nonzero terms. The identification of equivalent expressions and their subsequent factorization in the final result is performed easily by analyzing the topological structure of the diagrammatic expressions.

A prefactor free semiclassical initial value series representation of the propagator
View Description Hide DescriptionA new class of prefactor free semiclassical initial value representations (SCIVR) of the quantum propagator is presented. The derivation is based on the physically motivated demand, that on the average in phase space and in time, the propagator obey the exact quantum equation of motion. The resulting SCIVR series representation of the exact quantum propagator is also free of prefactors. When using a constant width parameter, the prefactor free SCIVR propagator is identical to the frozen Gaussian propagator of Heller [J. Chem. Phys. 75, 2923 (1981)]. A numerical study of the prefactor free SCIVR series is presented for scattering through a double slit potential, a system studied extensively previously by Gelabert et al. [J. Chem. Phys. 114, 2572 (2001)]. As a basis for comparison, the SCIVR series is also computed using the optimized Herman–Kluk SCIVR. We find that the sum of the zeroth order and the first order terms in the series suffice for an accurate determination of the diffraction pattern. The same exercise, but using the prefactor free propagator series needs also the second order term in the series, however the numerical effort is not greater than that needed for the Herman–Kluk propagator, since one does not need to compute the monodromy matrix elements at each point in time. The numerical advantage of the prefactor free propagator grows with increasing dimensionality of the problem.

A derivation of the mixed quantumclassical Liouville equation from the influence functional formalism
View Description Hide DescriptionWe show that the mixed quantumclassical Liouville equation is equivalent to linearizing the forwardbackward action in the influence functional. Derivations are provided in terms of either the diabatic or adiabatic basis sets. An application of the mixed quantumclassical Liouville equation for calculating the memory kernel of the generalized quantum master equation is also presented. The accuracy and computational feasibility of such an approach is demonstrated in the case of a twolevel system nonlinearly coupled to an anharmonic bath.

Development of density functionals for thermochemical kinetics
View Description Hide DescriptionA density functional theoryexchangecorrelation functional for the exploration of reaction mechanisms is proposed. This functional, denoted BMK (BoeseMartin for Kinetics), has an accuracy in the 2 kcal/mol range for transition state barriers but, unlike previous attempts at such a functional, this improved accuracy does not come at the expense of equilibrium properties. This makes it a generalpurpose functional whose domain of applicability has been extended to transition states, rather than a specialized functional for kinetics. The improvement in BMK rests on the inclusion of the kinetic energy density together with a large value of the exact exchange mixing coefficient. For this functional, the kinetic energy density appears to correct “back” the excess exact exchange mixing for groundstate properties, possibly simulating variable exchange.

Calculation of exchangecorrelation potentials with auxiliary function densities
View Description Hide DescriptionThe use of Hermite Gaussian auxiliary function densities from the variational fitting of the Coulomb potential for the calculation of exchangecorrelation potentials is discussed. The basic working equations for the energy and gradient calculation are derived. The accuracy of this approximation for optimized structure parameters and bond energies are analyzed. It is shown that the quality of the approximation can be systematically improved by enlarging the auxiliary function set. Average errors of 0.5 kcal/mol are obtained with auxiliary function sets including and functions. The timings for a series of alkenes demonstrate a substantial performance improvement.

Propagators for the timedependent Kohn–Sham equations
View Description Hide DescriptionIn this paper we address the problem of the numerical integration of the timedependent Schrödinger equation In particular, we are concerned with the important case where is the selfconsistent Kohn–Sham Hamiltonian that stems from timedependent functional theory. As the Kohn–Sham potential depends parametrically on the timedependent density, is in general time dependent, even in the absence of an external timedependent field. The present analysis also holds for the description of the excited state dynamics of a manyelectron system under the influence of arbitrary external timedependent electromagnetic fields. Our discussion is separated in two parts: (i) First, we look at several algorithms to approximate where is a timeindependent operator [e.g., for some given time τ]. In particular, polynomial expansions, projection in Krylov subspaces, and splitoperator methods are investigated. (ii) We then discuss different approximations for the timeevolution operator, such as the midpoint and implicit rules, and Magnus expansions. Splitoperator techniques can also be modified to approximate the full timedependent propagator. As the Hamiltonian is time dependent, problem (ii) is not equivalent to (i). All these techniques have been implemented and tested in our computer code OCTOPUS, but can be of general use in other frameworks and implementations.

On the role of coupling in mode selective excitation using ultrafast pulse shaping in stimulated Raman spectroscopy
View Description Hide DescriptionThe coherence of two coupled twolevel systems, representing vibrational modes in a semiclassical model, is calculated in weak and strong fields for various coupling schemes and for different relative phases between initial state amplitudes. A relative phase equal to π projects the system into a dark state. The selective excitation of one of the two, twolevel systems is studied as a function of coupling strength and initial phases.

Pseudospectral approach to relativistic molecular theory
View Description Hide DescriptionThe efficient relativistic DiracHartreeFock (DHF) and DiracKohnSham (DKS) methods are proposed by an application of the pseudospectral (PS) approach. The present PSDHF/DKS method is a relativistic extension of the PSHF/KS method of Friesner, though we aim at higher numerical accuracy by elimination of superfluous arbitrariness. The relativistic PSDHF/DKS method is implemented into our REL4D programs. Several PS applications to molecular systems show that the relativistic PSDHF/DKS approach is more efficient than the traditional approach without a loss of accuracy. The present PSDKS method successfully assigns and predicts the photoelectron spectra of hexacarbonyl complexes of tungsten and seaborgium theoretically.

Delayed rejection variational Monte Carlo
View Description Hide DescriptionAn acceleration algorithm to address the problem of multiple time scales in variational Monte Carlo simulations is presented. After a first attempted move has been rejected, the delayed rejection algorithm attempts a second move with a smaller time step, so that even moves of the core electrons can be accepted. Results on Be and Ne atoms as test cases are presented. Correlation time and both average accepted displacement and acceptance ratio as a function of the distance from the nucleus evidence the efficiency of the proposed algorithm in dealing with the multiple time scales problem.

Polarization and bonding of the intrinsic characteristic contours of hydrogen and fluorine atoms of forming a hydrogen fluoride molecule based on an ab initio study
View Description Hide DescriptionThe spatial changing feature of the shapes and sizes of the system consisted of one hydrogen atom and one fluorine atom of forming a hydrogen fluoride molecule is investigated. We give formalism of the potential acting on an electron in a molecule and derive its concrete expression in Hartree–Fock selfconsistent molecular orbital theory including configuration interaction. The program of calculating the potential acting on an electron in a molecule is programmed and compiled in the framework of the MELD program package. We formulate briefly the approach of the molecular intrinsic characteristic contour (MICC) which is defined in terms of the classical turning points of electronic motion. The MICC for a molecular system is intrinsic and can be calculated by means of an ab initio CI method. Then, the polarization and bonding features of the intrinsic characteristic contours of hydrogen and fluorine atoms forming a hydrogen fluoride molecule are presented and discussed from ab initio calculations. Furthermore, electron density distribution as an added dimension has been demonstrated on the changing MICC and thus the vivid polarization and bonding features for a chemical process have been shown. It seems that at the early stage (internuclear distance the fluorine atom gives more enthusiastic with the sensitive and expanded polarization to welcome coupling with the hydrogen atom while the latter has little response even “shy” with shrinking a bit its size at the beginning of putting the two atoms into a system and it is only around the critical point, the contact point that both of them stretch their hands and arms to meet and then fuse together.

Polarization consistent basis sets. V. The elements Si–Cl
View Description Hide DescriptionPolarization consistent basis sets, optimized for density functional calculations, are proposed for the elements Si–Cl. Their performance for atomization energies, equilibrium geometries, harmonic vibrational frequencies, and associated infrared intensities is compared with other commonly used basis sets. Atomization energies can be predicted to within 0.01 kJ/mol per atom of the basis set limit by extrapolation of the pc2, 3, and 4 results. Equilibrium bond distances and harmonic vibrational frequencies can be calculated to within and 0.5 cm^{−1}, respectively, of the basis set limit. The basis sets are shown to give comparable or better accuracy than other alternatives, while containing fewer or equal number of primitive basis functions.

Analyzing intramolecular dynamics by fast Lyapunov indicators
View Description Hide DescriptionWe report an analysis of intramolecular dynamics of the highly excited planar carbonyl sulfide below and at the dissociation threshold by the fast Lyapunov indicator method. By mapping out the variety of dynamical regimes in the phase space of this molecule, we obtain the degree of regularity of the system versus its energy. We combine this stability analysis with a periodic orbit search, which yields a family of elliptic periodic orbits in the regular part of phase space and a family of inphase collinear hyperbolic orbits associated with the chaotic regime.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Theoretical study on isomeric stabilities of and its ionization potentials and electron affinities
View Description Hide DescriptionThe geometric structures and isomeric stabilities of various stationary points in neutral and its cation and anion are investigated at the coupledcluster singles, doubles (triples) [CCSD(T)] level of theory. For the geometrical survey, the basis sets used are of the Dunning’s correlation consistent basis sets of tripleζ quality (ccpVTZ) for the neutral and cation. For the anions, the ccpVTZ basis sets with diffuse functions (augccpVTZ) are used. The final energies are calculated by the use of the CCSD(T) level of theory with the augccpVTZ basis set at their optimized geometries. To lower lying neutrals and cations, the Dunning’s correlation consistent basis sets of quadrupleζ quality (ccpVQZ) are also applied. Both the global minima of the neutral and cation, N1 and C1 respectively, are silacyclopropenylidene conformers, having a CCSi ring with a double bond. No competitive stable isomers exist in the present neutral. In the cation, however, the second lowest lying isomer C2 lies 10.8 kJ/mol above the most stable C1. The vertical and adiabatic ionization potentials from the lowest lying neutral N1 are 9.83 and 8.97 eV, respectively, at the CCSD(T)/ccpVQZ level of theory. The electron addition to the N1 does not result in the anion with positive (real) electron affinities. On the other hand, the electron addition to the N2 isomer produces the global minimum anion A1 with the positive electron affinities of 1.13 eV. The second lowest lying anion isomer A2 with silylenylacetylene conformer, produced from an electron addition to the N3 neutral, very well competes with the A1 after the zeropoint vibrational energy corrections. The energy difference between the two lowest lying isomers of the neutral and its anion, N1 and A1, is only 0.39 eV.

Internuclear distance and effects of Born–Oppenheimer breakdown for PtS, determined from its pure rotational spectrum
View Description Hide DescriptionPlatinum monosulfide PtS has been prepared in its ground electronic state by laser ablation of Pt in the presence of The rotational spectra of eight isotopic species have been measured with a cavity pulsed jet Fouriertransform microwave spectrometer.Spectral analysis using a multiisotopomer Dunhamtype expression produced values for and along with large values for Born–Oppenheimer breakdown (BOB) parameters for both atoms of the molecule. The BOB parameters are rationalized in terms of the molecular electronic structure and nuclear field shift effects. A large negative nuclear spinrotation constant has been rationalized in terms of the electronnucleus dipoledipole hyperfine constant. The equilibrium bond length in the Born–Oppenheimer approximation has been evaluated.

Experimental and theoretical studies of charge transfer and deuterium ion transfer between and
View Description Hide DescriptionThe charge transfer and deuterium ion transfer reactions between and have been studied using the crossed beam technique at relative collision energies below one electron volt and by density functional theory(DFT) calculations. Both direct and rearrangement charge transfer processes are observed, forming and respectively. Independent of collision energy, deuterium ion transfer accounts for approximately 20% of the reactive collisions. Between 22 and 36 % of charge transfer collisions occur with rearrangement. In both charge transfer processes, comparison of the internal energy distributions of products with the photoelectron spectrum of shows that FranckCondon factors determine energy disposal in these channels. DFT calculations provide evidence for transient intermediates that undergo H/D migration with rearrangement, but with minimal modification of the product energy distributions determined by long range electron transfer. The cross section for charge transfer with rearrangement is approximately larger than predicted from the RiceRamspergerKasselMarcus isomerization rate in transient complexes, suggesting a nonstatistical mechanism for H/D exchange. DFT calculations suggest that reactive trajectories for deuterium ion transfer follow a pathway in which a deuterium atom from approaches the πcloud of ethylene along the perpendicular bisector of the C–C bond. The product kinetic energy distributions exhibit structure consistent with vibrational motion of the Datom in the bridged product perpendicular to the C–C bond. The reaction quantitatively transforms the reaction exothermicity into internal excitation of the products, consistent with mixed energy release in which the deuterium ion is transferred in a configuration in which both the breaking and the forming bonds are extended.

Experimental studies of the dynamics of the bondforming reactions of with using positionsensitive coincidence spectroscopy
View Description Hide DescriptionThe dynamics of the product channels forming and following the collisions of with have been investigated with a new positionsensitive coincidence experiment at a centerofmass collision energy of 5.6 eV. The results show the formation of occurs via the formation of a doubly charged collision complex which subsequently undergoes a charge separating dissociation to form and The monocation subsequently fragments to form The lifetimes of the collision complex and the ion are at least of the order of their rotational period. The kinetic energy release in this reaction indicates that it involves the ground state of and forms the ground electronic states of and HF. The mechanism for forming involves the direct and rapid abstraction of a hydride ion from by The resulting ion subsequently fragments to on a time scale at least comparable with its rotational period.

electronic relaxation dynamics probed via timeresolved photoelectron imaging
View Description Hide DescriptionAnion timeresolved photoelectron imaging has been used to investigate the electronic relaxation dynamics of following excitation of the and transitions at 607 and 498 nm, respectively. Analysis of evolving photodetachment energy distributions reveals differing relaxation pathways from these prepared states. Specifically, the level relaxes on a time scale of 620±30 fs to vibrationally hot (∼2.0 eV) anion ground state both directly and indirectly through vibrationally excited levels of the intermediatelying state that decay with a time scale of 2300±200 fs. In contrast, the level relaxes much more quickly (<100 fs) to vibrationally hot (∼2.5 eV) anion ground state directly and with transient population accumulation in the and electronic levels, as determined by spectral and timescale analyses. This work also presents the experimental observation of the optically inaccessible state, which is found to have an electronic term value of 1.41±0.05 eV.

Extremely narrow peaks in predissociation of sodium dimer due to rovibronic coupling
View Description Hide DescriptionIn sodium dimer the and electronic states are coupled; the coupling of the two states is due to vibrational motion while the nonadiabaticinteraction between the and the states—in particular, the state—is mediated by rotational interaction. The resulting vibronic problem is studied in some detail. The bound vibrational states of the and states lie in the dissociation continuum of the state and become resonances due to the prevailing nonadiabatic coupling. The resonances are calculated using the complex scaling method and the available ab initio adiabatic potential energy curves. It is demonstrated that the resonances associated with rotational nonadiabatic coupling are narrower by several orders of magnitude than those that emerge from the vibrational nonadiabatic coupling. The predissociation cross section is computed and compared with experiment.