Volume 122, Issue 9, 01 March 2005
 COMMUNICATIONS


Continuous configuration timedependent selfconsistent field method for polyatomic quantum dynamical problems
View Description Hide DescriptionA new continuous configuration timedependent selfconsistent field method has been developed to study polyatomic dynamical problems by using the discrete variable representation for the reactionsystem, and applied to a reactionsystem coupled to a bath. The method is very efficient because the equations involved are as simple as those in the traditional single configuration approach, and can account for the correlations between the reactionsystem and bath modes rather well.

Accelerating quantum mechanical/molecular mechanical sampling using pure molecular mechanical potential as an importance function: The case of effective fragment potential
View Description Hide DescriptionAcceleration of sampling from a quantum mechanical/effective fragment mechanical (QM/EFP) potential is explored with effective fragment potential (EFP) as an importance function. EFP, generated on the fly, is found to be an excellent choice for an importance function for a QM/EFP potential. This technique is used to find nine stationary points of a blocked amino acid with twelve waters in a semiautomated way.

The stabilization of arginine’s zwitterion by dipolebinding of an excess electron
View Description Hide DescriptionThe arginine parent anion was generated by a newly developed, infrared desorptionelectron photoemission hybrid anion source. The photoelectron spectrum of the arginine anion was recorded and interpreted as being due to dipole binding of the excess electron. The results are consistent with calculations by Rak, Skurski, Simons, and Gutowski, who predicted the near degeneracy of arginine’s canonical and zwitterionic dipole bound anions. Since neutral arginine’s zwitterion is slightly less stable than its canonical form, this work also demonstrates the ability of an excess electron to stabilize a zwitterion, just as ions and solvent molecules are already known to do.

Novel method for selective probing of groundstate rotational dynamics of solutes in solvents
View Description Hide DescriptionWe introduce an optical pump/probe method that allows selective measurement of groundstaterotational dynamics of solutes in liquids. It relies on employing two successive pump pulses that are adjusted to create an optical anisotropy due to the orientational distribution of only the groundstatesolute molecules. Measurement on a dyesolvent system shows a large difference between the rotational diffusion rates of the ground state and the excited state of the dye molecules due to different solute–solvent interactions.

Isomer selective infrared spectroscopy of neutral metal clusters
View Description Hide DescriptionWe report experimental infrared spectra of neutral metal clusters in the gas phase. Multiple photondissociation of the argon complexes of niobiumclusters is used to obtain vibrational spectra in the region. The observed spectra for are different for different values of . This is explained by the presence of two isomers of that have different affinities towards Ar and the isomer specific infrared spectra are obtained. The structures of the isomers are determined by comparing the observed spectra with the outcome of densityfunctional theory calculations.
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 ARTICLES

 Theoretical Methods and Algorithms

Molecular wave packet interferometry and quantum entanglement
View Description Hide DescriptionWe study wave packet interferometry (WPI) considering the laser pulse fields both classical and quantum mechanically. WPI occurs in a molecule after subjecting it to the interaction with a sequence of phaselocked ultrashort laser pulses. Typically, the measured quantity is the fluorescence of the molecule from an excited electronic state. This signal has imprinted the interference of the vibrational wave packets prepared by the different laser pulses of the sequence. The consideration of the pulses as quantum entities in the analysis allows us to study the entanglement of the laser pulse states with the molecular states. With a simple model for the molecular system, plus several justified approximations, we solve for the fully quantum mechanical moleculeelectromagnetic field state. We then study the reduced density matrices of the molecule and the laser pulses separately. We calculate measurable corrections to the case where the fields are treated classically.

Mixed quantumclassical equilibrium
View Description Hide DescriptionWe present an analysis of the equilibrium limits of the two most widely used approaches for simulating the dynamics of molecular systems that combine both quantum and classical degrees of freedom. For a twolevel quantum system connected to an infinite number of classical particles, we derive a simple analytical expression for the equilibrium mean energy attained by the selfconsistentfield (Ehrenfest) method and show that it deviates substantially from Boltzmann. By contrast, “fewest switches” surface hopping achieves Boltzmann quantum state populations. We verify these analytical results with simulations.

Dynamics of coupled Bohmian and phasespace variables: A moment approach to mixed quantumclassical dynamics
View Description Hide DescriptionThe theoretical framework of the mixed quantumclassical description given by Burghardt and Parlant [J. Chem. Phys.120, 3055 (2004)] is detailed. A representation in terms of partial hydrodynamic moments is developed, the dynamics of which is determined by a hierarchy of equations derived from the quantum Liouville equation. Exact equations of motion are obtained, whose quantumclassical approximants are associated with a fluiddynamical trajectory representation which couples classical variables to quantum hydrodynamic variables. The latter evolve under a generalized hydrodynamic force which also depends upon the classical phasespace variables. The hydrodynamic moment description is shown to be closely connected to mixed quantumclassical phasespace methods.

Numerical study of the accuracy and efficiency of various approaches for Monte Carlo surface hopping calculations
View Description Hide DescriptionA onedimensional, twostate model problem with two wellseparated avoided crossing points is employed to test the efficiency and accuracy of a semiclassical surface hopping technique. The use of a onedimensional model allows for the accurate numerical evaluation of both fully quantummechanical and semiclassical transition probabilities. The calculations demonstrate that the surface hopping procedure employed accounts for the interference between different hopping trajectories very well and provides highly accurate transition probabilities. It is, in general, not computationally feasible to completely sum over all hopping trajectories in the semiclassical calculations for multidimensional problems. In this case, a Monte Carlo procedure for selecting important trajectories can be employed. However, the cancellation due to the different phases associated with different trajectories limits the accuracy and efficiency of the Monte Carlo procedure. Various approaches for improving the accuracy and efficiency of Monte Carlosurface hopping procedures are investigated. These methods are found to significantly reduce the statistical sampling errors in the calculations, thereby increasing the accuracy of the transition probabilities obtained with a fixed number of trajectories sampled.

Third and fourthorder perturbation corrections to excitation energies from configuration interaction singles
View Description Hide DescriptionComplete thirdorder and partial fourthorder Rayleigh–Schrödinger perturbation corrections to excitation energies from configuration interaction singles (CIS) have been derived and termed CIS(3) and . They have been implemented by the automated system TENSOR CONTRACTION ENGINE into parallelexecution programs taking advantage of spin, spatial, and index permutation symmetries and applicable to closed and openshell molecules. The consistent use of factorization, first introduced by HeadGordon et al. in the secondorder correction to CIS denoted CIS(D), has reduced the computational cost of CIS(3) and from and to and , respectively, with being the number of orbitals. It has also guaranteed the size extensivity of excitedstateenergies of these methods, which are in turn the sum of sizeintensive excitation energies and the groundstateenergies from the standard Møller–Plesset perturbation theory at the respective orders. The series CIS(D), CIS(3), and are usually monotonically convergent at values close to the accurate results predicted by coupledcluster singles and doubles (CCSD) with a small fraction of computational costs of CCSD for predominantly singly excited states characterized by a 90%–100% overlap between the CIS and CCSD wave functions. When the overlap is smaller, the perturbation theory is incapable of adequately accounting for the mixing of the CIS states through higherthansingles sectors of the Hamiltonian matrix, resulting in wildly oscillating series with often very large errors in . Hence, CIS(3) and have a rather small radius of convergence and a limited range of applicability, but within that range they can be an inexpensive alternative to CCSD.

Role of angular momentum conservation in unimolecular translational energy release: Validity of the orbiting transition state theory
View Description Hide DescriptionThe translational kinetic energy release distribution (KERD) for the halogen loss reaction of the bromobenzene and iodobenzene cations has been reinvestigated on the microsecond time scale. Two necessary conditions of validity of the orbiting transition state theory (OTST) for the calculation of kinetic energy release distributions (KERDs) have been formulated. One of them examines the central ioninduced dipole potential approximation. As a second criterion, an adiabatic parameter is derived. The lower the released translational energy and the total angular momentum, the larger the reduced mass, the rotational constant of the molecular fragment, and the polarizability of the released atom, the more valid is the OTST. Only the lowenergy dissociation of the iodobenzene ion (, where is the internal energy above the reaction threshold) is found to fulfill the criteria of validity of the OTST. The constraints that act on the dissociation dynamics have been studied by the maximum entropy method. Calculations of entropy deficiencies (which measure the deviation from a microcanonical distribution) show that the pair of fragments does not sample the whole of the phase space that is compatible with the mere specification of the internal energy. The major constraint that results from conservation of angular momentum is related to a reduction of the dimensionality of the dynamics of the translational motion to a twodimensional space. A second and minor constraint that affects the KERD leads to a suppression of small translational releases, i.e., accounts for threshold behavior. At high internal energies, the effects of curvature of the reaction path and of angular momentumconservation are intricately intermeddled and it is not possible to specify the share of each effect.

Application of variational reduceddensitymatrix theory to organic molecules
View Description Hide DescriptionVariational calculation of the twoelectron reduceddensity matrix (2RDM), using a new firstorder algorithm [D. A. Mazziotti, Phys. Rev. Lett.93, 213001 (2004)], is applied to mediumsized organic molecules. The calculations reveal systematic trends in the accuracy of the energy with wellknown chemical concepts such as hybridization, electronegativity, and atomic size. Furthermore, correlation energies from hydrocarbon chains indicate that the calculation of the 2RDM subject to twopositivity conditions is size extensive, that is, the energy grows linearly with the number of electrons. Because organic molecules have a welldefined set of functional groups, we employ the trends in energy accuracy of the functional groups to design a correction to the 2RDM energy for an arbitrary organic molecule. We apply the 2RDM calculations with the functionalgroup correction to a large set of organic molecules with different functional groups. Energies with millihartree accuracy are obtained both at equilibrium and nonequilibrium geometries.

Stationary phase evaluations of quantum rate constants
View Description Hide DescriptionWe compute the quantum rate constant based on two extended stationary phase approximations to the imaginarytime formulation of the quantum rate theory. The optimized stationary phase approximation to the imaginarytime fluxflux correlation function employs the optimized quadratic reference system to overcome the inaccuracy of the quadratic expansion in the standard stationary phase approximation, and yields favorable agreements with instanton results for both adiabatic and nonadiabatic processes in dissipative and nondissipative systems. The integrated stationary phase approximation to the twodimensional barrier free energy is particularly useful for adiabatic processes and demonstrates consistent results with the imaginarytime fluxflux correlation function approach. Our stationary phase methods do not require calculation of tunneling paths or stability matrices, and work equally well in the hightemperature and the lowtemperature regimes. The numerical results suggest their general applicability for calibration of imaginarytime methods and for the calculation of quantum rate constants in systems with a large number of degrees of freedom.

Testing wave packet dynamics in computing radiative association cross sections
View Description Hide DescriptionA timedependent wave packet method is used to compute cross sections for radiative recombination reactions using the as a test case. Cross sections are calculated through standard timetoenergy mapping of the timedependent transition moment and a useful method is introduced to deal with the low collision energy regime. Results are in quantitative agreement over the whole energy range with previous timeindependent results for the same system [I. Baccarelli, L. Andric, T. Grozdanov, and R. McCarroll, J. Chem. Phys.117, 3013 (2002)], thereby suggesting that the method can be of help in computing radiative association cross sections for more complicated systems.

Electron correlation in Hooke’s law atom in the highdensity limit
View Description Hide DescriptionClosedform expressions for the first three terms in the perturbation expansion of the exact energy and Hartree–Fock energy of the lowest singlet and triplet states of the Hooke’s law atom are found. These yield elementary formulas for the exact correlationenergies ( and ) of the two states in the highdensity limit and lead to a pair of necessary conditions on the exact correlation kernel in Hartree–Fock–Wigner theory.

Multireference configuration interaction based electronic Floquet states for molecules in an intense radiation field: Theory and application to
View Description Hide DescriptionA multireference configuration interaction (CI) method which includes single and double excitations based description of adiabatic Floquet states for the electronic structure of a molecule in an intense laser field is introduced. Using a variant of a recently introduced configuration state function (CSF) based TableCI methodology, it is shown that the multiple states of several irreducible representations required for a good description of lowlying Floquet states can be obtained using modifications of computational molecular electronic structure techniques. In particular, formulas for all components of the transition dipole moment matrix elements within the CSFbased TableCI method are derived and presented. Moreover, the flexibility of the recently introduced macroconfiguration description of model and external configuration spaces is shown to lead to multiple potential energy surfaces of sufficiently uniform quality to allow construction of useful Floquet states. The formalism and computer programs developed are demonstrated on in a field. In analogy with , the , , , and states are of relevance, although the pattern of couplings is shown to be more complex. A hitherto unnoticed metastable state, which correlates asymptotically with , is described.

Ab initio calculation of the ratio of magnetic circular dichroism
View Description Hide DescriptionA procedure for calculating the magnetic circular dichroism ratio from density functional theory calculations is discussed. The method is simplified considerably through the application of group theory and the irreducibletensor method and only requires integrals of the magnetic dipole moment operator over a few orbitals and published tables of symmetry factors. The implementation of the method is tested through application to several small and mediumsized molecules.

LocalMP2 electron correlation method for nonconducting crystals
View Description Hide DescriptionRigorous methods for the postHF (HF—Hartree–Fock) determination of correlation corrections for crystalline solids are currently being developed following different strategies. The CRYSTAL program developed in Torino and Daresbury provides accurate HF solutions for periodic systems in a basis set of Gaussian type functions; for insulators, the occupied HF manifold can be represented as an antisymmetrized product of well localized Wannier functions. This makes possible the extension to nonconducting crystals of local correlation linear scaling techniques as successfully and efficiently implemented in Stuttgart’s MOLPRO program. These methods exploit the fact that dynamic electron correlation effects between remote parts of a molecule (manifesting as dispersive interactions in intermolecular perturbation theory) decay as an inverse sixth power of the distance between these fragments, that is, much more quickly than the Coulomb interactions that are treated already at the HF level. Translational symmetry then permits the crystalline problem to be reduced to one concerning a cluster around the reference zero cell. A periodic local correlation program (CRYSCOR) has been prepared along these lines, limited for the moment to the solution of secondorder MøllerPlesset equations. Exploitation of point group symmetry is shown to be more important and useful than in the molecular case. The computational strategy adopted and preliminary results concerning five semiconductors with tetrahedral structure (C, Si, SiC, BN, and BeS) are presented and discussed.

Operator splitting algorithm for isokinetic SLLOD molecular dynamics
View Description Hide DescriptionWe apply an operator splitting method to develop a simulation algorithm that has complete analytical solutions for the Gaussian thermostated SLLOD equations of motion [D. J. Evans and G. P. Morriss, Phys. Rev. A30, 1528 (1984)] for a system under shear. This leads to a homogeneous algorithm for performing both equilibrium and nonequilibrium isokinetic molecular dynamics simulation. The resulting algorithm is computationally efficient. In particular, larger integration time steps can be used compared to simulations with regular Gaussian thermostated SLLOD equations of motion. The utility and accuracy of the algorithm are demonstrated through application to the Weeks–Chandler–Anderson fluid. Although strict conservation of the kinetic energy suppresses thermal fluctuations in the system, this algorithm does not allow simulations at lower shear rates than those normally afforded by older nonequilibrium molecular dynamics simulations.

The merits of the frozendensity embedding scheme to model solvatochromic shifts
View Description Hide DescriptionWe investigate the usefulness of a frozendensity embedding scheme within densityfunctional theory [J. Phys. Chem.97, 8050 (1993)] for the calculation of solvatochromic shifts. The frozendensity calculations, particularly of excitation energies have two clear advantages over the standard supermolecule calculations: (i) calculations for much larger systems are feasible, since the timeconsuming timedependent density functional theory (TDDFT) part is carried out in a limited molecular orbital space, while the effect of the surroundings is still included at a quantum mechanical level. This allows a large number of solvent molecules to be included and thus affords both specific and nonspecific solvent effects to be modeled. (ii) Only excitations of the system of interest, i.e., the selected embedded system, are calculated. This allows an easy analysis and interpretation of the results. In TDDFT calculations, it avoids unphysical results introduced by spurious mixings with the artificially too low chargetransfer excitations which are an artifact of the adiabatic localdensity approximation or generalized gradient approximation exchangecorrelation kernels currently used. The performance of the frozendensity embedding method is tested for the wellstudied solvatochromic properties of the excitation of acetone. Further enhancement of the efficiency is studied by constructing approximate solvent densities, e.g., from a superposition of densities of individual solvent molecules. This is demonstrated for systems with up to 802 atoms. To obtain a realistic modeling of the absorption spectra of solvated molecules, including the effect of the solvent motions, we combine the embedding scheme with classical molecular dynamics (MD) and CarParrinello MD simulations to obtain snapshots of the solute and its solvent environment, for which then excitation energies are calculated. The frozendensity embedding yields estimated solvent shifts in the range of , in good agreement with experimental values of between 0.19 and .