Volume 128, Issue 15, 21 April 2008
 COMMUNICATIONS


Competing sigmatropic shift rearrangements in excited allyl radicals
View Description Hide DescriptionThe competition between rearrangement of the excited allyl radical via a 1,3 sigmatropic shift versus sequential 1,2 shifts has been observed and characterized using isotopic substitution, laser excitation, and molecular beam techniques. Both rearrangements produce a 1propenyl radical that subsequently dissociates to methyl plus acetylene. The 1,3 shift and 1,2 shift mechanisms are equally probable for , whereas the 1,3 shift is favored by a factor of 1.6 in . The translational energy distributions for the methyl and acetylene products of these two mechanisms are substantially different. Both of these allyl dissociation channels are minor pathways compared to hydrogen atom loss.

Dynamics of molecular diffusion of rhodamine 6G in silica nanochannels
View Description Hide DescriptionWe describe a method to study diffusion of rhodamine 6G dye in single silica nanochannels using arrays of silica nanochannels. Dynamics of the molecules inside single nanochannel is found from the change of the dye concentration in solution with time. A decrease in the dye diffusion coefficient relative to water was observed. In comparison to single fluorescent molecule studies, the presented method does not require fluorescence of the diffusing molecules.
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 ARTICLES

 Theoretical Methods and Algorithms

An atomic orbitalbased reformulation of energy gradients in secondorder Møller–Plesset perturbation theory
View Description Hide DescriptionA fully atomic orbital (AO)based reformulation of secondorder Møller–Plesset perturbation theory (MP2) energy gradients is introduced, which provides the basis for reducing the computational scaling with the molecular size from the fifth power to linear. Our formulation avoids any transformation between the AO and the molecular orbital (MO) basis and employs pseudodensity matrices similar to the AOMP2 energy expressions within the Laplace scheme for energies. The explicit computation of perturbed oneparticle density matrices emerging in the new AObased gradient expression is avoided by reformulating the Zvector method of Handy and Schaefer [J. Chem. Phys.81, 5031 (1984)] within a density matrixbased scheme.

Cooperativity between two types of hydrogen bond in and complexes
View Description Hide DescriptionHydrogenbonded clusters, , HCN–HCN, , , HNC–HNC, and , have been studied by using ab initio calculations. The optimized structures, harmonic vibrational frequencies, and interaction energies are calculated at the MP2 level with augccpVTZ basis set. The cooperative effects in the properties of these complexes are investigated quantitatively. A cooperativity contribution of around 10% relative to the total interaction energy was found in the complex. In the case of complex, the cooperativity contribution is about 15%. The cooperativity contribution in the singleelectron hydrogen bond is larger than that in the hydrogen bond of HCN–HCN and HNC–HNC complexes. NMRchemical shifts,charge transfers, and topological parameters also support such conclusions.

Explicitly correlated RMP2 for highspin openshell reference states
View Description Hide DescriptionWe present an explicitly correlated version of the highspin openshell RMP2 method. The theory is derived in a unitarily invariant form, which is suitable for the insertion of local approximations. It is demonstrated that the rapid basis set convergence of closedshell MP2F12 is also achieved in RMP2F12, and similar Ansätze and approximations can be employed. All integrals are computed using efficient density fitting approximations, and manyelectron integrals are avoided using resolution of the identity approximations. The performance of the method is demonstrated by benchmark calculations on a large set of ionization potentials,electron affinities and atomization energies. Using triplezeta basis sets RMP2F12 yields results that are closer to the basis set limit than standard RMP2 with augmented quintuplezeta basis sets for all properties. Different variants of perturbative corrections for the openshell Hartree–Fock treatment are described and tested.

Nonadiabatic electron wavepacket dynamics of molecules in an intense optical field: An ab initio electronic state study
View Description Hide DescriptionA theory of quantum electron wavepacket dynamics that nonadiabatically couples with classical nuclear motions in intense optical fields is studied. The formalism is intended to track the laserdriven electron wavepackets in terms of the linear combination of configurationstate functions generated with ab initio molecular orbitals. Beginning with the total quantum Hamiltonian for electrons and nuclei in the vector potential of classical electromagnetic field, we reduce the Hamiltonian into a mixed quantumclassical representation by replacing the quantum nuclear momentum operators with the classical counterparts. This framework gives equations of motion for electron wavepackets in an intense laser field through the time dependent variational principle. On the other hand, a generalization of the Newtonian equations provides a matrix form of forces acting on the nuclei for nonadiabatic dynamics. A meanfield approximation to the force matrix reduces this higher order formalism to the semiclassical Ehrenfest theory in intense optical fields. To bring these theories into a practical quantum chemical package for general molecules, we have implemented the relevant ab initio algorithms in it. Some numerical results in the level of the semiclassical Ehrenfesttype theory with explicit use of the nuclear kinematic (derivative) coupling and the velocity form for the optical interaction are presented.

Turbo charging timedependent densityfunctional theory with Lanczos chains
View Description Hide DescriptionWe introduce a new implementation of timedependent densityfunctional theory which allows the entirespectrum of a molecule or extended system to be computed with a numerical effort comparable to that of a single standard groundstate calculation. This method is particularly well suited for large systems and/or large basis sets, such as plane waves or realspace grids. By using a superoperator formulation of linearized timedependent densityfunctional theory, we first represent the dynamical polarizability of an interactingelectron system as an offdiagonal matrix element of the resolvent of the Liouvillian superoperator. Oneelectron operators and density matrices are treated using a representation borrowed from timeindependent densityfunctional perturbation theory, which permits us to avoid the calculation of unoccupied Kohn–Sham orbitals. The resolvent of the Liouvillian is evaluated through a newly developed algorithm based on the nonsymmetric Lanczos method. Each step of the Lanczos recursion essentially requires twice as many operations as a single step of the iterative diagonalization of the unperturbed Kohn–Sham Hamiltonian. Suitable extrapolation of the Lanczos coefficients allows for a dramatic reduction of the number of Lanczos steps necessary to obtain well converged spectra, bringing such number down to hundreds (or a few thousands, at worst) in typical planewave pseudopotential applications. The resulting numerical workload is only a few times larger than that needed by a groundstate Kohn–Sham calculation for a same system. Our method is demonstrated with the calculation of the spectra of benzene, fullerene, and of chlorophyll a.

Quantum trajectories in complex space: Onedimensional stationary scattering problems
View Description Hide DescriptionOnedimensional timeindependent scattering problems are investigated in the framework of the quantum Hamilton–Jacobi formalism. The equation for the local approximate quantum trajectories near the stagnation point of the quantum momentum function is derived, and the first derivative of the quantum momentum function is related to the local structure of quantum trajectories. Exact complex quantum trajectories are determined for two examples by numerically integrating the equations of motion. For the soft potential step, some particles penetrate into the nonclassical region, and then turn back to the reflection region. For the barrier scattering problem, quantum trajectories may spiral into the attractors or from the repellers in the barrier region. Although the classical potentials extended to complex space show different pole structures for each problem, the quantum potentials present the same secondorder pole structure in the reflection region. This paper not only analyzes complex quantum trajectories and the total potentials for these examples but also demonstrates general properties and similar structures of the complex quantum trajectories and the quantum potentials for onedimensional timeindependent scattering problems.

Solving the electronnuclear Schrödinger equation of helium atom and its isoelectronic ions with the free iterativecomplementinteraction method
View Description Hide DescriptionOur previous paper [J. Chem. Phys.127, 224104 (2007)] revealed that the Schrödinger equation in the fixednucleus approximation could be very accurately solved for helium atom and its isoelectronic ions with the free iterativecomplementinteraction (ICI) method combined with the variation principle. In this report, the quantum effect of nuclear motion has further been variationally considered by the free ICI formalism for the Hamiltonian including masspolarization operator. We obtained for helium atom, which is over 40 digits in accuracy, similarly to the previous result for the fixednucleus level. Similar accuracy was also obtained for the helium isoelectronic ions. The present results may be regarded to be the nonrelativistic limits. We have further analyzed the physics of the free ICI wave function by applying it to an imaginary atom called “eneon,” , in which both of the quantum effect of nuclear motion and the threeparticle collisions are differently important from the helium and its isoelectronic ions. This revealed the accurate physics automatically generated by the free ICI formalism.

Solving the electron and electronnuclear Schrödinger equations for the excited states of helium atom with the free iterativecomplementinteraction method
View Description Hide DescriptionVery accurate variational calculations with the free iterativecomplementinteraction (ICI) method for solving the Schrödinger equation were performed for the singlet and triplet excited states of helium atom up to . This is the first extensive applications of the free ICI method to the calculations of excited states to very high levels. We performed the calculations with the fixednucleus Hamiltonian and movingnucleus Hamiltonian. The latter case is the Schrödinger equation for the electronnuclear Hamiltonian and includes the quantum effect of nuclear motion. This solution corresponds to the nonrelativistic limit and reproduced the experimental values up to five decimal figures. The small differences from the experimental values are not at all the theoretical errors but represent the physical effects that are not included in the present calculations, such as relativistic effect,quantum electrodynamic effect, and even the experimental errors. The present calculations constitute a small step toward the accurately predictive quantum chemistry.

Efficient computation of transient solutions of the chemical master equation based on uniformization and quasiMonte Carlo
View Description Hide DescriptionA quasiMonte Carlo method for the simulation of discrete time Markov chains is applied to the simulation of biochemical reaction networks. The continuous process is formulated as a discrete chain subordinate to a Poisson process using the method of uniformization. It is shown that a substantial reduction of the number of trajectories that is required for an accurate estimation of the probability density functions(PDFs) can be achieved with this technique. The method is applied to the simulation of two model problems. Although the technique employed here does not address the typical stiffness of biochemical reaction networks, it is useful when computing the PDF by replication. The method can also be used in conjuncture with hybrid methods that reduce the stiffness.

Monte Carlo free energy calculations using electronic structure methods
View Description Hide DescriptionThe molecular mechanicsbased importance sampling function (MMBIF) algorithm [R. Iftimie, D. Salahub, D. Wei, and J. Schofield, J. Chem. Phys.113, 4852 (2000)] is extended to incorporate semiempiricalelectronic structure methods in the secondary Markov chain, creating a fully quantum mechanical Monte Carlo sampling method for simulations of reactive chemical systems which, unlike the MMBIF algorithm, does not require the generation of a systemspecific force field. The algorithm is applied to calculating the potential of mean force for the isomerizationreaction of HCN using thermodynamic integration. Constraints are implemented in the sampling using a modification of the SHAKE algorithm, including that of a fixed, arbitrary reaction coordinate. Simulation results show that sampling efficiency with the semiempirical secondary potential is often comparable in quality to force fields constructed using the methods suggested in the original MMBIF work. The semiempirical based importance sampling method presented here is a useful alternative to MMBIF sampling as it can be applied to systems for which no suitable MM force field can be constructed.

Nonadiabatic couplings from timedependent density functional theory. II. Successes and challenges of the pseudopotential approximation
View Description Hide DescriptionWe present extensive calculations of nonadiabatic couplings (NACs) between the electronically ground and excited states of molecules, using timedependent density functional theory (TDDFT) within (modified) linear response [C. Hu et al.J. Chem. Phys.127, 064103 (2007)]. Our approach is implemented in the pseudopotential framework, with the consideration of nonlinear core corrections. The features of either the ordinary Jahn–Teller conical intersections in (, Na, K, Cu,Ag,Au) trimers, or the elliptic Jahn–Teller conical intersections in , have been well reproduced. In particular, anticipated results for the collision near the avoided crossing are obtained, showing appealing improvement over the first, realtime, TDDFT calculation. The other important type of intersections, Renner–Teller glancing intersection, has also been studied for several typical molecular systems (, , , ), giving results in reasonable agreement with the theoretical model. Despite these successes, it is found that for some systems, including both Jahn–Teller and Renner–Teller systems, the pseudopotential scheme might give inaccurate results for some NAC components on nonhydrogen atoms. By trying different construction schemes of pseudopotentials, e.g., using local pseudopotentials, the results of NACs are found schemedependent and show improvement for some cases. Since there is much freedom in constructing ab initio nonlocal pseudopotentials, our findings on TDDFT calculation of NACs in the pseudopotential scheme might be helpful to give clues for constructing more “realistic” pseudopotentials.

Unbiased leap methods for stochastic simulation of chemically reacting systems
View Description Hide DescriptionThe leap method first developed by Gillespie [D. T. Gillespie, J. Chem. Phys.115, 1716 (2001)] can significantly speed up stochastic simulation of certain chemically reacting systems with acceptable losses in accuracy. Recently, several improved leap methods, including the binomial, multinomial, and modified leap methods, have been developed. However, in all these leap methods, the mean of the number of times, , that the reaction channel fires during a leap is not equal to the true mean. Therefore, all existing leap methods produce biased simulation results, which limit the simulation accuracy and speed. In this paper, we analyze the mean of based on the chemical master equation. Using this analytical result, we develop unbiased Poisson and binomial leap methods. Moreover, we analyze the variance of , and then develop an unbiased Poisson/Gaussian/binomial leap method to correct the errors in both the mean and variance of . Simulation results demonstrate that our unbiased leap method can significantly improve simulation accuracy without sacrificing speed.

Towards fast computations of correlated vibrational wave functions: Vibrational coupled cluster response excitation energies at the twomode coupling level
View Description Hide DescriptionAn efficient implementation of vibrational coupled clustertheory with twomode excitations and a twomode Hamiltonian is described. The algorithm is shown to scale cubically with respect to the number of modes which is identical to the scaling of the corresponding vibrational configuration interaction algorithm. This is achieved through the use of special intermediates. The same algorithm can also be used in vibrational Møller–Plesset calculations. To improve performance, screening techniques have been implemented as well. Test calculations on polyaromatic hydrocarbons with up to 264 coupled modes and model systems with up to 1140 modes are used to illustrate the various features of the algorithm.

Coarse graining of master equations with fast and slow states
View Description Hide DescriptionWe propose a general method for simplifying master equations by eliminating from the description rapidly evolving states. The physical recipe we impose is the suppression of these states and a renormalization of the rates of all the surviving states. In some cases, this decimation procedure can be analytically carried out and is consistent with other analytical approaches, such as in the problem of the random walk in a double well potential. We discuss the application of our method to nontrivial examples: diffusion in a lattice with defects and a model of an enzymatic reaction outside the steady state regime.

A novel algorithm for creating coarsegrained, density dependent implicit solvent models
View Description Hide DescriptionImplicit solvent simulations are those in which solvent molecules are not explicitly simulated, and the solutesolute interaction potential is modified to compensate for the implicit solvent effect. Implicit solvation is well known in Brownian dynamics of dilute solutions but offers promise to speed up many other types of molecular simulations as well, including studies of proteins and colloids where the local density can vary considerably. This work examines implicit solvent potentials within a more general coarsegraining framework. While a pairwise potential between solute sites is relatively simple and ubiquitous, an additional parametrization based on the local solute concentration has the possibility to increase the accuracy of the simulations with only a marginal increase in computational cost. We describe here a method in which the radial distribution function and excess chemical potential of solute insertion for a system of Lennard–Jones particles are first measured in a fully explicit, allparticle simulation, and then reproduced across a range of solute particle densities in an implicit solvent simulation.

Extrapolating potential energy surfaces by scaling electron correlation: Isomerization of bicyclobutane to butadiene
View Description Hide DescriptionThe recently proposed potential energy surface (PES) extrapolation scheme, which predicts smooth molecular PESs corresponding to larger basis sets from the relatively inexpensive calculations using smaller basis sets by scaling electron correlation energies [A. J. C. Varandas and P. Piecuch, Chem. Phys. Lett.430, 448 (2006)], is applied to the PESs associated with the conrotatory and disrotatory isomerization pathways of bicyclo[1.1.0]butane to buta1,3diene. The relevant electronic structure calculations are performed using the completely renormalized coupledcluster method with singly and doubly excited clusters and a noniterative treatment of connected triply excited clusters, termed CRCC(2,3), which is known to provide a highly accurate description of chemical reaction profiles involving biradical transition states and intermediates. A comparison with the explicit CRCC(2,3) calculations using the large correlationconsistent basis set of the ccpVQZ quality shows that the ccpVQZ PESs obtained by the extrapolation from the smaller basis set calculations employing the ccpVDZ and ccpVTZ basis sets are practically identical, to within fractions of a millihartree, to the true ccpVQZ PESs. It is also demonstrated that one can use a similar extrapolation procedure to accurately predict the complete basis set (CBS) limits of the calculated PESs from the results of smaller basis set calculations at a fraction of the effort required by the conventional pointwise CBS extrapolations.

On the relationship between quantum control landscape structure and optimization complexity
View Description Hide DescriptionIt has been widely observed in optimal control simulations and experiments that state preparation is surprisingly easy to achieve, regardless of the dimension of the systemHilbert space. In contrast, simulations for the generation of targeted unitary transformations indicate that the effort increases exponentially with . In order to understand such behavior, the concept of quantum control landscapes was recently introduced, where the landscape is defined as the physical objective, as a function of the control variables. The present work explores how the local structure of the control landscape influences the effectiveness and efficiency of quantum optimal control search efforts. Optimizations of state and unitary transformation preparation using kinematiccontrol variables (i.e., the elements of the action matrix) are performed with gradient, genetic, and simplex algorithms. The results indicate that the search effort scales weakly, or possibly independently, with for state preparation, while the search effort for the unitary transformation objective increases exponentially with . Analysis of the mean path length traversed during a search trajectory through the space of action matrices and the local structure along this trajectory provides a basis to explain the difference in the scaling of the search effort with for these control objectives. Much more favorable scaling for unitary transformation preparation arises upon specifying an initial action matrix based on state preparation results. The consequences of choosing a reduced number of control variables for state preparation is also investigated, showing a significant reduction in performance for using fewer than variables, which is consistent with the topological analysis of the associated landscape.

Higher excitations for an exponential multireference wavefunction Ansatz and singlereference based multireference coupled cluster Ansatz: Application to model systems , , and
View Description Hide DescriptionThis article reports on the convergence of the exponential multireference wavefunctionAnsatz (MRexpT) [J. Chem. Phys.123, 84102 (2005)] and the singlereference based multireference coupled clusterAnsatz [J. Chem. Phys.94, 1229 (1991)] with respect to higher cluster excitations. The approaches are applied to the , , and model systems according to the recently published analysis by Evangelista et al. [J. Chem. Phys.125, 154113 (2006)]. The results show both MRexpT and SRMRCC to be highly accurate although SRMRCC shows problems due to its lack of Fermi vacuum invariance (symmetry breaking).