Volume 124, Issue 3, 21 January 2006
 COMMUNICATIONS


Exact quantum dynamics of reaction: Crosssections, rate constants, and dependence on reactant rotation
View Description Hide DescriptionUsing an exact Chebyshev wave packet method, initial statespecified (, ) integral crosssections and rate constants are obtained for the title reaction on the latest ab initiopotential energy surface.Reaction probabilities up to are dependent on the reactant rotation and show mild oscillations superimposed on a broad background. Due to a barrier in the entrance channel, the cross sections increase with energy with clear thresholds and the rate constants vary with temperature in the Arrhenius form. The calculated canonical rate constant is in good agreement with the experimental measurements. Our results also indicate that the quasiclassical trajectory method underestimates the rate due to the neglect of tunneling, while the quantum statistical approach overestimates because of the short lifetime of the reaction intermediate.
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 ARTICLES

 Theoretical Methods and Algorithms

Dissipative dynamics of laser induced nonadiabatic molecular alignment
View Description Hide DescriptionNonadiabatic alignment induced by short, moderately intense laser pulses in molecules coupled to dissipative environments is studied within a nonperturbative density matrix theory. We focus primarily on exploring and extending a recently proposed approach [Phys. Rev. Lett.95, 113001 (2005)], wherein nonadiabatic laser alignment is used as a coherence spectroscopy that probes the dissipative properties of the solvent. To that end we apply the method to several molecular collision systems that exhibit sufficiently varied behavior to represent a broad variety of chemical environments. These include molecules in low temperature gas jets, in room temperature gas cells, and in dense liquids. We examine also the possibility of prolonging the duration of the field free (postpulse) alignment in dissipative media by a proper choice of the system parameters.

On the unphysical impact of complex absorbing potentials on the Hamiltonian and its remedy
View Description Hide DescriptionThe introduction of complex absorbing potentials as numerical tools to stabilize or increase the efficiency of calculations based on wavepacket propagation or on eigenvalue problems has the drawback of causing a modification of the Hamilton operator of the problem. In this work the consequences of such a modification are analyzed and the corrections required in order to properly describe the original physical process are derived. As an example, the decay of excited molecular states is considered: it is shown that the standard timeindependent expression for the decay spectrum loses its validity when a complex absorbing potential is introduced in the nuclear Hamilton operator of the problem. To remedy the situation, a new, very stable formula is derived and tested on relevant model studies. Numerical examples are discussed.

Construction of environment states in quantumchemical densitymatrix renormalization group calculations
View Description Hide DescriptionThe application of the quantumchemical densitymatrix renormalization group (DMRG) algorithm is cumbersome for complex electronic structures with many active orbitals. The high computational cost is mainly due to the poor convergence of standard DMRG calculations. A factor which affects the convergence behavior of the calculations is the choice of the startup procedure. In this startup step matrix representations of operators have to be calculated in a guessed manyelectron basis of the DMRG environment block. Different possibilities for the construction of these basis states exist, and we first compare four procedures to approximate the environment states using Slater determinants explicitly. These startup procedures are applied to DMRG calculations on a sophisticated test system: the chromium dimer. It is found that the converged energies and the rate of convergence depend significantly on the choice of the startup procedure. However, since already the most simple startup procedure, which uses only the HartreeFock determinant, is comparatively good, Slater determinants, in general, appear not to be a good choice as approximate environment basis states for convergence acceleration. Based on extensive test calculations it is demonstrated that the computational cost can be significantly reduced if the number of total states is successively increased. This is done in such a way that the environment states are built up stepwise from system states of previous truncated DMRG sweeps for slowly increasing values.

Coherent control of pumpprobe signals of helical structures by adaptive pulse polarizations
View Description Hide DescriptionThe simplification of the pumpprobe spectrum of excitons by purephasepolarization pulse shaping is investigated by a simulation study. The state of light is manipulated by varying the phases of two perpendicular polarization components of the pump, holding its total spectral and temporal intensity profiles fixed. Genetic and iterative Fourier transform algorithms are used to search for pulse phase functions that optimize the ratio of the signal at two frequencies. New features are extracted from the congested pumpprobe spectrum of a helical pentamer by selecting a combination of Liouville space pathways. Tensor components which dominate the optimized spectra are identified.

Densityfunctional theory with effective potential expressed as a mapping of the external potential: Applications to openshell molecules
View Description Hide DescriptionIn this paper we apply the directmapping densityfunctional theory(DFT) to openshell systems, in order to get manyelectron wave functions having the same transformation properties as the eigenstates of the exact Hamiltonians. Such a case is that of spin, where in order to get the magnetic properties, the manyparticle states must be eigenstates not only of but also of . In this theory the Kohn and Sham [Phys. Rev. A140, 1133 (1965)] potential is expressed directly as a mapping of the external potential. The total energies of the molecules calculated were satisfactory as their relative deviations from the exact HartreeFock ones were of the order of . This accuracy is much higher than that of the standard DFT in its local exchange potential approximation. This method does not need an approximate density as input, as the effective potential is derived directly from the external potential.

Density fitting of twoelectron integrals in extended systems with translational periodicity: The Coulomb problem
View Description Hide DescriptionDensity fitting approach to Coulomb integrals for infinite systems with translational periodicity is reformulated in direct space. Despite of the Coulomb infinite decay of some integrals, directspace calculation is shown to be feasible. Moreover, we show that the directspace ansatz is completely equivalent to our previous formulation in reciprocal space. Computational demands scale linearly with the number of unit cells. In addition, directspace treatment has some practical advantages over the reciprocalspace formulation. The efficiency of our scheme is demonstrated on systems with translational periodicity in one dimension. Computation time takes only a small fraction of the conventional calculation with exact integrals. We show that for infinite systems auxiliary basis sets of equally good quality as for molecules can be constructed in a systematic way.

Relativistic smallcore energyconsistent pseudopotentials for the alkalineearth elements from Ca to Ra
View Description Hide DescriptionSmallcore tenvalence electron energyconsistent scalar and twocomponent relativistic pseudopotentials for the alkalineearth elements from Ca to Ra are presented. The accuracy and reliability of these pseudopotentials are discussed in terms of their ability to reproduce allelectron calculated and experimental dipole polarizabilities and ionization potentials.

Semiempirical hybrid density functional with perturbative secondorder correlation
View Description Hide DescriptionA new hybrid density functional for general chemistry applications is proposed. It is based on a mixing of standard generalized gradient approximations (GGAs) for exchange by Becke (B) and for correlation by Lee, Yang, and Parr (LYP) with HartreeFock (HF) exchange and a perturbative secondorder correlation part (PT2) that is obtained from the KohnSham (GGA) orbitals and eigenvalues. This virtual orbitaldependent functional contains only two global parameters that describe the mixture of HF and GGA exchange and of the PT2 and GGA correlation, respectively. The parameters are obtained in a leastsquaresfit procedure to the set of heat of formations. Opposed to conventional hybrid functionals, the optimum is found to be quite large (53% with ) which at least in part explains the success for many problematic molecular systems compared to conventional approaches. The performance of the new functional termed B2PLYP is assessed by the standard benchmark set, a second test suite of atoms, molecules, and reactions that are considered as electronically very difficult (including transitionmetal compounds, weakly bonded complexes, and reaction barriers) and comparisons with other hybrid functionals of GGA and metaGGA types. According to many realistic tests, B2PLYP can be regarded as the best general purpose density functional for molecules (e.g., a mean absolute deviation for the two test sets of only 1.8 and compared to about 3 and , respectively, for the best other density functionals). Very importantly, also the maximum and minium errors (outliers) are strongly reduced (by about ). Furthermore, very good results are obtained for transition state barriers but unlike previous attempts at such a good description, this definitely comes not at the expense of equilibrium properties. Preliminary calculations of the equilibrium bond lengths and harmonic vibrational frequencies for diatomic molecules and transitionmetal complexes also show very promising results. The uniformity with which B2PLYP improves for a wide range of chemical systems emphasizes the need of (virtual) orbitaldependent terms that describe nonlocal electron correlation in accurate exchangecorrelation functionals. From a practical point of view, the new functional seems to be very robust and it is thus suggested as an efficient quantum chemical method of general purpose.

A reversible minimumtominimum mapping method for the calculation of freeenergy differences
View Description Hide DescriptionA general method is introduced for the calculation of the freeenergy difference between two systems, 0 and 1, with configuration spaces , of the same dimensionality. The method relies upon establishing a bijective mapping between disjoint subsets of and corresponding disjoint subsets of , and averaging a function of the ratio of configurational integrals over and with respect to the probability densities of the two systems. The mapped subsets and need not span the entire configuration spaces and . The method is applied for the calculation of the excess chemical potential in a LennardJones (LJ) fluid. In this case, is the configuration space of a real molecule plus one idealgas molecule system, while is the configuration space of a real molecule system occupying the same volume. and are constructed from hyperspheres of the same radius centered at minimumenergy configurations of a set of “active” molecules lying within distance from the idealgas molecule and the last real molecule, respectively. An algorithm is described for sampling and given a point in or in . The algorithm encompasses three steps: “quenching” (minimization with respect to the activemolecule degrees of freedom), “mutation” (gradual conversion of the idealgas molecule into a real molecule, with simultaneous minimization of the energy with respect to the activemolecule degrees of freedom), and “excitation” (generation of points on a hypersphere centered at the activemolecule energy minimum). These steps are also carried out in reverse, as required by the bijective nature of the mapping. The mutation step, which establishes a reversible mapping between energy minima with respect to the active degrees of freedom of systems 0 and 1, ensures that excluded volume interactions emerging in the process of converting the idealgas molecule into a real molecule are relieved through appropriate rearrangement of the surrounding active molecules. Thus, the insertion problem plaguing traditional methods for the calculation of chemical potential at high densities is alleviated. Results are presented at two state points of the LJ system for a variety of radii of the active domain. It is shown that the estimated values of are correct in all cases and subject to an order of magnitude lower statistical uncertainty than values based on the same number of Widom [J. Chem. Phys.39, 2808 (1963)] insertions at high fluid densities. Optimal settings for the new algorithm are identified and distributions of the quantities involved in it [number of active molecules, energy at the sampled minima of systems 0 and 1, and freeenergy differences between subsets and that are mapped onto each other] are explored.

On the calculation of time correlation functions by potential scaling
View Description Hide DescriptionWe present and analyze a general method to calculate time correlation functions from molecular dynamics on scaled potentials for complex systems for which simulation is affected by broken ergodicity. Depending on the value of the scaling factor, correlations can be calculated for times that can be orders of magnitude longer than those accessible to direct simulations. We show that the exact value of the time correlation functions of the original system (i.e., with unscaled potential) can be obtained, in principle, using an actionreweighting scheme based on a stochastic pathintegral formalism. Two tests (involving a bistable potential model and a dipeptide bondvector orientational relaxation) are exemplified to showcase the strengths, as well as the limitations of the approach, and a procedure for the estimation of the timedependent standard deviation error is outlined.

Quantum computing based on vibrational eigenstates: Pulse area theorem analysis
View Description Hide DescriptionIn a recent paper [D. Babikov, J. Chem. Phys.121, 7577 (2004)], quantum optimal control theory was applied to analyze the accuracy of quantum gates in a quantum computer based on molecular vibrational eigenstates. The effects of the anharmonicity parameter of the molecule, the target time of the pulse, and the penalty function on the accuracy of the qubit transformations were investigated. We demonstrate that the effects of all the molecular and laserpulse parameters can be explained utilizing the analytical pulse area theorem, which originates from the standard twolevel model. Moreover, by analyzing the difference between the optimal control theory results and those obtained using the pulse area theorem, it is shown that extremely high quantum gate fidelity can be achieved for a qubit system based on vibrational eigenstates.

Generalmodelspace stateuniversal coupledcluster methods for excited states: Diagonal noniterative triple corrections
View Description Hide DescriptionThe recently developed multireference, generalmodelspace, stateuniversal coupledcluster approach considering singles and doubles (GMS SU CCSD) has been extended to account perturbatively for triples, similar to the ubiquitous singlereference CCSD(T) method. The effectiveness of this extension in handling of excited states and its ability to account for the static and nondynamic correlation effects when considering spin and/or spacesymmetry degenerate levels within the spinorbital formalism is examined on the example of lowlying excitation energies of the , , and CO molecules and a comparison is made with the CCSD method used for the same puropose. It is shown that while the triple corrections are very effective in improving the absolute energies, they have only a modest effect on the corresponding excitation energies, which may be even detrimental if both the ground and excitedstate levels cannot be given a balanced treatment. While the triple corrections help to avoid the symmetrybreaking effects arising due to the use of the spinorbital formalism, they are much less effective in this regard than the CCSD approach.

Chiralityinduced signals in coherent multidimensional spectroscopy of excitons
View Description Hide DescriptionThe nonlocal second and thirdorder susceptibilities of an isotropic ensemble of aggregates are calculated by solving the nonlinear exciton equations which map the system into coupled anharmonic oscillators. Both electric and magnetic contributions are included using the minimalcoupling Hamiltonian. The various tensor components are evaluated to first order in the optical wave vector . Additional structural information about the interchromophore distances, which is not accessible through zerothorder contributions (the dipole approximation), is contained to the first order in . New resonant second and thirdorder signals predicted for chiral molecules provide multidimensional extensions of circular dichroism spectroscopy. Numerical simulations demonstrate the sensitivity of thirdorder signals to the secondary structural motiffs of peptides.

Quantummechanical evaluation of the Boltzmann operator in correlation functions for large molecular systems: A multilayer multiconfiguration timedependent Hartree approach
View Description Hide DescriptionIt is shown that the Boltzmann operator in time correlation functions for complex molecular systems can be evaluated in a numerically exact way employing the multilayer formulation of the multiconfiguration timedependent Hartree theory in combination with Monte Carlo importance sampling techniques. The performance of the method is illustrated by selected applications to photoinduced intervalence electron transferreactions in the condensed phase. Furthermore, the validity of approximate schemes to evaluate the Boltzmann is discussed.

Reconciling semiclassical and Bohmian mechanics. II. Scattering states for discontinuous potentials
View Description Hide DescriptionIn a previous paper [B. Poirier, J. Chem. Phys.121, 4501 (2004)] a unique bipolar decomposition, , was presented for stationary bound states of the onedimensional Schrödinger equation, such that the components and approach their semiclassical WKB analogs in the large action limit. Moreover, by applying the MadelungBohm ansatz to the components rather than to itself, the resultant bipolar Bohmian mechanical formulation satisfies the correspondence principle. As a result, the bipolar quantum trajectories are classicallike and well behaved, even when has many nodes or is wildly oscillatory. In this paper, the previous decomposition scheme is modified in order to achieve the same desirable properties for stationary scattering states. Discontinuous potential systems are considered (hard wall, step potential, and square barrier/well), for which the bipolar quantum potential is found to be zero everywhere, except at the discontinuities. This approach leads to an exact numerical method for computing stationary scattering states of any desired boundary conditions, and reflection and transmission probabilities. The continuous potential case will be considered in a companion paper [C. Trahan and B. Poirier, J. Chem. Phys.124, 034116 (2006), following paper].

Reconciling semiclassical and Bohmian mechanics. III. Scattering states for continuous potentials
View Description Hide DescriptionIn a previous paper [B. Poirier, J. Chem. Phys.121, 4501 (2004)] a unique bipolar decomposition was presented for stationary bound states of the onedimensional Schrödinger equation, such that the components and approach their semiclassical WKB analogs in the largeaction limit. The corresponding bipolar quantum trajectories, as defined in the usual Bohmian mechanical formulation, are classicallike and well behaved, even when has many nodes or is wildly oscillatory. A modification for discontinuous potential stationary scattering states was presented in a second, companion paper [C. Trahan and B. Poirier, J. Chem. Phys.124, 034115 (2006), previous paper], whose generalization for continuous potentials is given here. The result is an exact quantum scattering methodology using classical trajectories. For additional convenience in handling the tunneling case, a constantvelocitytrajectory version is also developed.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Doppler effect in fluorine KAuger line produced in electroninduced core ionization of
View Description Hide DescriptionAn experimental evidence is reported on the observation of the Doppler effect in fluorine Auger line emitted from a coreionized molecule under an impact of electrons. The emitting source of the Auger line is found to acquire a kinetic energy of . We propose that such large energy is released from the Coulomb repulsion taking place between and fragment ions under influence of an intense focusing field of the incident electrons. In the presence of the Coulomb field of these ions, the Auger line obtains a polarization.

Spectroscopic analysis of small organic molecules: A comprehensive nearedge xrayabsorption finestructure study of ringcontaining molecules
View Description Hide DescriptionWe report highresolution C nearedge xrayabsorption finestructure (NEXAFS)spectra of the ringcontaining molecules benzene , 1,3 and 1,4cyclohexadiene , cyclohexene , cyclohexane , styrene , and ethylbenzene which allow us to examine the gradual development of delocalization of the corresponding electron systems. Due to the high experimental resolution, vibrational progressions can be partly resolved in the spectra. The experimental spectra are compared with theoreticalNEXAFSspectra obtained from densityfunctional theory calculations where electronic finalstate relaxation is accounted for. The comparison yields very good agreement between theoreticalspectra and experimental results. In all cases, the spectra can be described by excitations to  and type finalstate orbitals with valence character, while finalstate orbitals of Rydberg character make only minor contributions. The lowest C excitation energy is found to agree in the (experimental and theoretical)spectra of all molecules except for 1,3cyclohexadiene where an energy smaller by about 0.6 eV is obtained. The theoretical analysis can explain this result by different binding properties of this molecule compared to the others.

A systematic multireference perturbationtheory study of the lowlying states of
View Description Hide DescriptionThe three known lowestenergy isomers of , two cyclic singlets ( and ) and a linear triplet , have been reinvestigated using multireference secondorder perturbation theory (MRPT2). The dependence of the relative energies of the isomers upon the quality of the basis sets and the sizes of the reference active spaces is explored. When using a completeactivespace selfconsistentfield reference wave function with 12 electrons in 11 orbitals [CASSCF (12, 11)] together with basis sets that increase in size up to the correlationconsistent polarized corevalence quadruple zeta basis set (ccpCVQZ), the MRPT2 method consistently predicts the linear triplet to be the most stable isomer. A new parallel direct determinant MRPT2 code has been used to systematically explore reference spaces that vary in size from CASSCF (8,8) to full optimized reaction space [FORS or CASSCF (16,16)] with the ccpCVQZ basis. It is found that the relative energies of the isomers change substantially as the active space is increased. At the best level of theory, MRPT2 with a full valence FORS reference, the isomer is predicted to be more stable than and by 4.7 and , respectively.