Volume 127, Issue 8, 28 August 2007
 COMMUNICATIONS


Modespecific tunneling dynamics in the ground electronic state of tropolone
View Description Hide DescriptionThe mode specificity of protontransfer dynamics in the ground electronic state of tropolone has been explored at nearrotational resolution by implementing a fully coherent variant of stimulated emission pumping within the framework of twocolor resonantfourwave mixing spectroscopy. Three lowlying vibrational features, assigned to , , and , have been interrogated under ambient, bulkgas conditions, with term energies determined for the symmetric and antisymmetric (tunneling) components of each enabling the attendant tunnelinginduced bifurcations of 1.070(9), 0.61(3), and to be extracted. The dependence of tunneling rate (or hydron migration efficiency) on vibrational motion is discussed in terms of corresponding atomic displacements and permutationinversion symmetries for the tropolone skeleton.

Model for cage formation in colloidal suspension of laponite
View Description Hide DescriptionIn this paper we investigate glass transition in aqueous suspension of synthetic hectorite clay, laponite. We believe that upon dispersing laponite clay in water, the system comprises of clusters (agglomerates) of laponite dispersed in the same. Subsequent osmotic swelling of these clusters leads to an increase in their volume fraction. We propose that this phenomenon is responsible for slowing down of the overall dynamics of the system. As clusters fill up the space, the system undergoes glass transition. Along with the mode coupling theory, the proposed mechanism rightly captures various characteristic features of the system in the ergodic regime as it approaches glass transition.
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 ARTICLES

 Theoretical Methods and Algorithms

On the calculation of Mössbauer isomer shift
View Description Hide DescriptionA quantum chemical computational scheme for the calculation of isomer shift in Mössbauer spectroscopy is suggested. Within the described scheme, the isomer shift is treated as a derivative of the total electronic energy with respect to the radius of a finite nucleus. The explicit use of a finite nucleus model in the calculations enables one to incorporate straightforwardly the effects of relativity and electron correlation. The results of benchmark calculations carried out for several iron complexes as well as for a number of atoms and atomic ions are presented and compared with the available experimental and theoretical data.

Vibrational energy levels with arbitrary potentials using the EckartWatson Hamiltonians and the discrete variable representation
View Description Hide DescriptionAn effective and general algorithm is suggested for variational vibrational calculations of atomic molecules using orthogonal, rectilinear internal coordinates. The protocol has three essential parts. First, it advocates the use of the EckartWatson Hamiltonians of nonlinear or linear reference configuration. Second, with the help of an exact expression of curvilinear internal coordinates (e.g., valence coordinates) in terms of orthogonal, rectilinear internal coordinates (e.g., normal coordinates), any highaccuracy potential or force field expressed in curvilinear internal coordinates can be used in the calculations. Third, the matrix representation of the appropriate EckartWatson Hamiltonian is constructed in a discrete variable representation, in which the matrix of the potential energy operator is always diagonal, whatever complicated form the potential function assumes, and the matrix of the kinetic energy operator is a sparse matrix of special structure. Details of the suggested algorithm as well as results obtained for linear and nonlinear test cases including , , , , and are presented.

Assessment of timedependent density functional schemes for computing the oscillator strengths of benzene, phenol, aniline, and fluorobenzene
View Description Hide DescriptionIn present study the relevance of using the timedependent density functional theory (DFT) within the adiabatic approximation for computing oscillator strengths is assessed using different LDA, GGA, and hybrid exchangecorrelation (XC) functionals. In particular, we focus on the lowestenergy valence excitations, dominating the UV/visible absorption spectra and originating from benzenelike transitions, of several aromatic molecules: benzene, phenol, aniline, and fluorobenzene. The TDDFT values are compared to both experimental results obtained from gas phase measurements and to results determined using several ab initio schemes: random phase approximation (RPA), configuration interaction single (CIS), and a series of linear response coupledcluster calculations, CCS, CC2, and CCSD. In particular, the effect of the amount of HartreeFock (HF) exchange in the functional is highlighted, whereas a basis set investigation demonstrates the need of including diffuse functions. So, the hybrid XC functionals—and particularly BHandHLYP—provide values in good agreement with the highly correlated CCSD scheme while these can be strongly underestimated using pure DFT functionals. These results also display systematic behaviors: (i) larger and squares of the transition dipole moments are associated with larger excitation energies; (ii) these relationships present generally a linear character with in leastsquares fit procedures; (iii) larger amounts of HF exchange in the XC functional lead to larger , , as well as values; (iv) these increases in , , and are related to increased HOMOLUMO character; and (v) these relationships are, however, not universal since the linear regression parameters (the slopes and the intercepts at the origin) depend on the system under investigation as well as on the nature of the excited state.

Semiclassical initial value calculations of the collinear helium atom
View Description Hide DescriptionSemiclassical calculations using the HermanKluk initial value treatment are performed to determine energy eigenvalues of bound and resonance states of the collinear helium atom. Both the configuration (where the classical motion is fully chaotic) and the configuration (where the classical dynamics is nearly integrable) are treated. The classical motion is regularized to remove singularities that occur when the electrons collide with the nucleus. Very good agreement is obtained with quantum energies for bound and resonance states calculated by the complex rotation method.

Extrapolation of electron correlation energies to finite and complete basis set targets
View Description Hide DescriptionThe electron correlationenergy of twoelectron atoms is known to converge asymptotically as to the complete basis set limit, where is the maximum angular momentum quantum number included in the basis set. Numerical evidence has established a similar asymptotic convergence with the cardinal number of correlationconsistentbasis sets for coupled cluster singles and doubles (CCSD) and second order perturbation theory (MP2) calculations of molecules. The main focus of this article is to probe for deviations from asymptotic convergence behavior for practical values of by defining a trial function that for an effective exponent provides the correct energy, when extrapolating from results for two smaller basis sets, and . This analysis is first applied to “model” expansions available from analytical theory, and then to a large body of finite basis set results for 105 molecules containing H, C, N, O, and F, complemented by a smaller set of 14 molecules for which accurate complete basis set limits are available from MP2R12 and CCSDR12 calculations. is generally found to vary monotonically with the target of extrapolation, , making results for large but finite basis sets a useful addition to the limited number of cases where complete basis set limits are available. Significant differences in effective convergence behavior are observed between MP2 and CCSD (valence) correlationenergies, between hydrogenrich and hydrogenfree molecules, and, for He, between partialwave expansions and correlationconsistentbasis sets. Deviations from asymptotic convergence behavior tend to get smaller as increases, but not always monotonically, and are still quite noticeable even for . Finally, correlation contributions to atomization energies (rather than total energies) exhibit a much larger variation of effective convergence behavior, and extrapolations from small basis sets are found to be particularly erratic for molecules containing several electronegative atoms. Observed effects are discussed in the light of results known from analytical theory. A carefully calibrated protocol for extrapolations to the complete basis set limit is presented, based on a single “optimal” exponent for the entire set of molecules, and compared to similar approaches reported in the literature.

Acceleration of Monte Carlo simulations through spatial updating in the grand canonical ensemble
View Description Hide DescriptionA new grand canonical Monte Carlo algorithm for continuum fluid models is proposed. The method is based on a generalization of sequential Monte Carlo algorithms for lattice gas systems. The elementary moves, particle insertions and removals, are constructed by analogy with those of a lattice gas. The updating is implemented by selecting points in space (spatial updating) either at random or in a definitive order (sequential). The type of move, insertion or removal, is deduced based on the local environment of the selected points. Results on twodimensional squarewell fluids indicate that the sequential version of the proposed algorithm converges faster than standard grand canonical algorithms for continuum fluids. Due to the nature of the updating, additional reduction of simulation time may be achieved by parallel implementation through domain decomposition.

Ab initio study of singlemolecule rotation switch based on nonequilibrium Green’s function theory
View Description Hide DescriptionThe bistable molecular switches have been studied theoretically based on the firstprinciples calculation. The geometry structures of the switches studied in this paper can be triggered between two symmetrical structures by using an external applied electric field. characteristic curves of the different molecule configurations have been calculated, and distinguishability of these characteristic curves indicates a switching behavior, the performance of which can be improved significantly by some suitable donors and acceptors.

Evaluation of electronic correlation contributions for optical tensors of large systems using the incremental scheme
View Description Hide DescriptionA new method is developed to calculate the optical tensors of large systems based on available wave function correlation approaches (e.g., the coupled cluster ansatz) in the framework of the incremental scheme. The convergence behaviors of static first and secondorder polarizabilities with respect to the order of the incremental expansion are examined and discussed for the model system . The manybody increments of optical tensors originate from the dipoledipole coupling effects and the corresponding contributions to the incremental expansion are compared among local domains with different distances and orientations. The weight factors for increments of optical tensors are found to be tensorial in accordance with the structural symmetry as well as the polarization and the external electric field directions. The longterm goal of the proposed approach is to incorporate the sophisticated molecular correlation methods into the accurate wave function calculation of optical properties of large compounds or even crystals.

Targeted excited state algorithms
View Description Hide DescriptionTo overcome the limitations of the traditional stateaveraging approaches in excited state calculations, where one solves and represents all states between the ground state and excited state of interest, we have investigated a number of new excited state algorithms. Building on the work of van der Vorst and Sleijpen [SIAM J. Matrix Anal. Appl.17, 401 (1996)], we have implemented harmonic Davidson and stateaveraged harmonic Davidson algorithms within the context of the density matrix renormalization group (DMRG). We have assessed their accuracy and stability of convergence in completeactivespace DMRG calculations on the lowlying excited states in the acenes ranging from naphthalene to pentacene. We find that both algorithms offer increased accuracy over the traditional stateaveraged Davidson approach, and, in particular, the stateaveraged harmonic Davidson algorithm offers an optimal combination of accuracy and stability in convergence.

Tensor product approximation with optimal rank in quantum chemistry
View Description Hide DescriptionTensor product decompositions with optimal separation rank provide an interesting alternative to traditional Gaussiantype basis functions in electronic structure calculations. We discuss various applications for a new compression algorithm, based on the Newton method, which provides for a given tensor the optimal tensor product or socalled best separable approximation for fixed Kronecker rank. In combination with a stable quadrature scheme for the Coulomb interaction, tensor product formats enable an efficient evaluation of Coulomb integrals. This is demonstrated by means of best separable approximations for the electron density and Hartree potential of small molecules, where individual components of the tensor product can be efficiently represented in a wavelet basis. We present a fairly detailed numerical analysis, which provides the basis for further improvements of this novel approach. Our results suggest a broad range of applications within density fitting schemes, which have been recently successfully applied in quantum chemistry.

Selfconsistent field tightbinding model for neutral and (multi) charged carbon clusters
View Description Hide DescriptionA semiempirical model for carbon clusters modeling is presented, along with structural and dynamical applications. The model is a tightbinding scheme with additional one and twocenter distancedependent electrostatic interactions treated selfconsistently. This approach, which explicitly accounts for charge relaxation, allows us to treat neutral and (multi) charged clusters not only at equilibrium but also in dissociative regions. The equilibrium properties, geometries, harmonic spectra, and relative stabilities of the stable isomers of neutral and singly charged clusters in the range , for and , are found to reproduce the results of ab initio calculations. The model is also shown to be successful in describing the stability and fragmentation energies of dictations in the range and allows the determination of their Coulomb barriers, as examplified for the smallest sizes . We also present timedependent meanfield and linear response optical spectra for the and clusters and discuss their relevance with respect to existing calculations.

Phase quantization of chaos in the semiclassical regime
View Description Hide DescriptionSince the early stage of the study of Hamilton chaos, semiclassical quantization based on the loworder WentzelKramersBrillouin theory, the primitive semiclassical approximation to the Feynman path integrals (or the socalled Van Vleck propagator), and their variants have been suffering from difficulties such as divergence in the correlation function, nonconvergence in the trace formula, and so on. These difficulties have been hampering the progress of quantum chaos, and it is widely recognized that the essential drawback of these semiclassical theories commonly originates from the erroneous feature of the amplitude factors in their applications to classically chaotic systems. This forms a clear contrast to the success of the EinsteinBrillouinKeller quantization condition for regular (integrable) systems. We show here that energy quantization of chaos in semiclassical regime is, in principle, possible in terms of constructive and destructive interference of phases alone, and the role of the semiclassical amplitude factor is indeed negligibly small, as long as it is not highly oscillatory. To do so, we first sketch the mechanism of semiclassical quantization of energy spectrum with the Fourier analysis of phase interference in a time correlation function, from which the amplitude factor is practically factored out due to its slowly varying nature. In this argument there is no distinction between integrability and nonintegrability of classical dynamics. Then we present numerical evidence that chaos can be indeed quantized by means of amplitudefree quasicorrelation functions and Heller’s frozen Gaussian method. This is called phase quantization. Finally, we revisit the work of Yamashita and Takatsuka [Prog. Theor. Phys. Suppl.161, 56 (2007)] who have shown explicitly that the semiclassical spectrum is quite insensitive to smooth modification (rescaling) of the amplitude factor. At the same time, we note that the phase quantization naturally breaks down when the oscillatory nature of the amplitude factor is comparable to that of the phases. Such a case generally appears when the Planck constant of a large magnitude pushes the dynamics out of the semiclassical regime.

Selfconsistent effective local potentials
View Description Hide DescriptionAn effective local potential (ELP) is a multiplicative operator whose deviation from a given nonlocal potential has the smallest variance evaluated with a prescribed singledeterminant wave function. ELPs are useful in density functional theory as alternatives to optimized effective potentials (OEPs) because they do not require special treatment in finite basis set calculations as OEPs do. We generalize the idea of varianceminimizing potentials by introducing the concept of a selfconsistent ELP (SCELP), a local potential whose deviation from its nonlocal counterpart has the smallest variance in terms of its own KohnSham orbitals. A semianalytical method for computing SCELPs is presented. The OEP, ELP, and SCELP techniques are applied to the exactexchangeonly KohnSham problem and are found to produce similar results for manyelectron atoms.

Semiclassical description of electronically nonadiabatic dynamics via the initial value representation
View Description Hide DescriptionThe initial value representation (IVR) of semiclassical (SC) theory is used in conjunction with the MeyerMiller/StockThoss description of electronic degrees of freedom in order to treat electronically nonadiabatic processes. It is emphasized that the classical equations of motion for the nuclear and electronic degrees of freedom that emerge in this description are precisely the Ehrenfest equations of motion (the force on the nuclei is the force averaged over the electronic wave function) but that the trajectories given by these equations of motion do not have the usual shortcomings of the traditional Ehrenfest model when they are used within the SCIVR framework. For example, in the traditional Ehrenfest model (a mixed quantumclassical approach) the nuclear motion emerges from a nonadiabatic encounter on an averagepotential energy surface (a weighted average according to the population in the various electronic states), while the SCIVR describes the correct correlation between electronic and nuclear dynamics, i.e., the nuclear motion is on one potential energy surface or the other depending on the electronic state. Calculations using forwardbackward versions of SCIVR theory are presented to illustrate this behavior. An even more approximate version of the SCIVR, the linearized approximation (LSCIVR), is slightly better than the traditional Ehrenfest model, but since it cannot describe quantum coherence effects, the LSCIVR is also not able to describe the correct correlation between nuclear and electronic dynamics.

Local control theory applied to molecular photoassociation
View Description Hide DescriptionLocal control theory (LCT) is employed to achieve molecular photoassociation with shaped laser pulses. Within LCT, the control fields are constructed from the response of the system to the perturbation which makes them accessible to a straightforward interpretation. This is shown regarding the groundstate collision of and atoms. Different objectives are defined, which aim at the formation of vibrational cold or hot associated molecules, respectively. Results are presented for wave scattering, where the rotational degree of freedom is ignored and also for full scale calculations including rotations, in order to describe more realistic conditions.

Cluster algorithm to perform parallel Monte Carlo simulation of atomistic systems
View Description Hide DescriptionWe propose an efficient algorithm to perform Monte Carlo simulations of dense systems using multiple particle moves. The method is intended to be used in the atomistic simulation of complex systems, where the computing requirements for a single simulation run make advisable the use of parallel computing. The algorithm is based on the use of steps in which all the particle positions of the system are perturbed simultaneously. A division of the system in clusters of particles is performed, using a bonding criterion which makes feasible that the acceptance or rejection of the new particle coordinates can be carried out independently for each cluster.

Decoupling of the Dirac equation correct to the third order for the magnetic perturbation
View Description Hide DescriptionA twocomponent relativistic theory accurately decoupling the positive and negative states of the Dirac Hamiltonian that includes magnetic perturbations is derived. The derived theory eliminates all of the odd terms originating from the nuclear attraction potential and the firstorder odd terms originating from the magnetic vector potential , which connect the positive states to the negative states. The electronic energy obtained by the decoupling is correct to the third order with respect to due to the rule. The decoupling is exact for the magnetic shielding calculation. However, the calculation of the diamagneticproperty requires both the positive and negative states of the unperturbed Hamiltonian. The derived theory is applied to the relativistic calculation of nuclear magnetic shieldingtensors of HX systems at the HartreeFock level. The results indicate that such a substantially exact decoupling calculation well reproduces the fourcomponent DiracHartreeFock results.

Variational calculation of static and dynamic vibrational nonlinear optical properties
View Description Hide DescriptionThe vibrational configuration interaction method used to obtain static vibrational (hyper)polarizabilities is extended to dynamic nonlinear optical properties in the infinite optical frequency approximation. Illustrative calculations are carried out on and . The former molecule is weakly anharmonic while the latter contains a strongly anharmonic umbrella mode. The effect on vibrational (hyper)polarizabilities due to various truncations of the potential energy and propertysurfaces involved in the calculation are examined.