Volume 129, Issue 12, 28 September 2008
 ARTICLES

 Theoretical Methods and Algorithms

Efficient and robust quantum Monte Carlo estimate of the total and spin electron densities at nuclei
View Description Hide DescriptionThe computational performance of two different variational quantum Monte Carlo estimators for both the electron and spin densities on top of nuclei are tested on a set of atomic systems containing also thirdrow species. Complications due to an unbounded variance present for both estimators are circumvented using appropriate sampling strategies. Our extension of a recently proposed estimator [Phys. Rev. A69, 022701 (2004)] to deal with heavy fermionic systems appears to provide improved computational efficiency, at least an order of magnitude, with respect to alternative literature approaches for our test set. Given the importance of an adequate sampling of the core region in computing the electron density at a nucleus, a further reduction in the overall simulation cost is obtained by employing accelerated sampling algorithms.

Laserinduced nuclear magnetic resonance splitting in hydrocarbons
View Description Hide DescriptionIrradiation of matter with circularly polarized light (CPL) shifts all nuclear magnetic resonance(NMR) lines. The phenomenon arises from the secondorder interaction of the electron cloud with the optical field, combined with the orbital hyperfine interaction. The shift occurs in opposite directions for right and left CPL, and rapid switching between them will split the resonance lines into two. We present ab initio and density functional theory predictions of laserinduced NMR splittings for hydrocarbon systems with different sizes: ethene, benzene, coronene, fullerene, and circumcoronene. Due to the computationally challenging nature of the effect, traditional basis sets could not be used for the larger systems. A novel method for generating basis sets, mathematical completeness optimization, was employed. As expected, the magnitude of the spectral splitting increases with the laser beam frequency and polarizability of the system. Massive amplification of the effect is also observed close to the optical excitation energies. A much larger laserinduced splitting is found for the largest of the present molecules than for the previously investigated noble gas atoms or small molecules. The laser intensity required for experimental detection of the effect is discussed.

Hybrid functionals with local range separation
View Description Hide DescriptionRangeseparated (screened) hybrid functionals provide a powerful strategy for incorporating nonlocal exact (Hartree–Focktype) exchange into density functional theory. Existing implementations of range separation use a fixed systemindependent screening parameter. Here, we propose a novel method that uses a positiondependent screening function. These locally rangeseparated hybrids add substantial flexibility for describing diverse electronic structures and satisfy a highdensity scaling constraint better than the fixed screening approximation does.

Determining quasidiabatic coupled electronic state Hamiltonians using derivative couplings: A normal equations based method
View Description Hide DescriptionA selfconsistent procedure for constructing a quasidiabatic Hamiltonian representing coupled electronic states in the vicinity of an arbitrary point in nuclear coordinate space is described. The matrix elements of the Hamiltonian are polynomials of arbitrary order. Employing a crude adiabatic basis, the coefficients of the linear terms are determined exactly using analytic gradient techniques. The remaining polynomial coefficients are determined from the normal form of a system of pseudolinear equations, which uses energy gradient and derivative coupling information obtained from reliable multireference configuration interactionwave functions. In a previous implementation energy gradient and derivative coupling information were employed to limit the number of nuclear configurations at which ab initio data were required to determine the unknown coefficients. Conversely, the key aspect of the current approach is the use of ab initio data over an extended range of nuclear configurations. The normal form of the system of pseudolinear equations is introduced here to obtain a leastsquares fit to what would have been an (intractable) overcomplete set of data in the previous approach. This method provides a quasidiabatic representation that minimizes the residual derivative coupling in a leastsquares sense, a means to extend the domain of accuracy of the diabatic Hamiltonian or refine its accuracy within a given domain, and a way to impose point group symmetry and hermiticity. These attributes are illustrated using the and states of the 1propynyl radical, .

Statistically optimal analysis of samples from multiple equilibrium states
View Description Hide DescriptionWe present a new estimator for computing free energy differences and thermodynamic expectations as well as their uncertainties from samples obtained from multiple equilibrium states via either simulation or experiment. The estimator, which we call the multistate Bennett acceptance ratio estimator (MBAR) because it reduces to the Bennett acceptance ratio estimator (BAR) when only two states are considered, has significant advantages over multiple histogram reweighting methods for combining data from multiple states. It does not require the sampled energy range to be discretized to produce histograms, eliminating bias due to energy binning and significantly reducing the time complexity of computing a solution to the estimating equations in many cases. Additionally, an estimate of the statistical uncertainty is provided for all estimated quantities. In the large sample limit, MBAR is unbiased and has the lowest variance of any known estimator for making use of equilibrium data collected from multiple states. We illustrate this method by producing a highly precise estimate of the potential of mean force for a DNA hairpin system, combining data from multiple optical tweezer measurements under constant force bias.

The augmented Roothaan–Hall method for optimizing Hartree–Fock and Kohn–Sham density matrices
View Description Hide DescriptionWe present a novel method for the optimization of Hartree–Fock and Kohn–Sham energies that does not suffer from the flaws of the conventionally used twostep Roothaan–Hall (RH) with direct inversion in iterative subspace (DIIS) acceleration scheme, improving the reliability of the optimization while reducing its cost. The key to its success is the replacement of the two separate steps of each RH/DIIS iteration by a single concerted step that fully exploits the Hessian information available from the previous iterations. It is a trustregion based method and therefore by design converges to an energy minimum. Numerical examples are given to illustrate that the algorithm is robust and cost efficient, converging smoothly to a minimum also in cases when the RH/DIIS algorithm fails to converge or when it converges to a saddle point rather than to a minimum. The algorithm is based on matrix multiplications and becomes linearly scaling for sufficiently large systems.

On the simulated scaling based free energy simulations: Adaptive optimization of the scaling parameter intervals
View Description Hide DescriptionRecently, we developed a generalized ensemble based free energy simulation technique, the simulated scaling (SS) method [Li et al., J. Chem. Phys.126, 024106 (2007)]. In the SS simulations, random walks in the scaling parameter space are realized and free energy values can be conveniently estimated based on trial biasing weights. To improve free energy convergence in the SS simulations, we adopt a recent adaptive algorithm to systematically optimize the scaling parameter intervals; here, the optimization target is the roundtrip rate between two end chemical states. As demonstrated in our model studies on the solvation of chloride ion and methane,free energy convergence can be greatly improved when the roundtrip rates are accelerated.

Mixed timedependent densityfunctional theory/classical trajectory surface hopping study of oxirane photochemistry
View Description Hide DescriptionWe present a mixed timedependent densityfunctional theory (TDDFT)/classical trajectory surface hopping (SH) study of the photochemical ring opening in oxirane. Previous preparatory work limited to the symmetric CC ringopening pathways of oxirane concluded that the TammDancoff approximation (TDA) is important for improving the performance of TDDFT away from the equilibrium geometry. This observation is supported by the present TDDFT TDA/SH calculations which successfully confirm the main experimentally derived GomerNoyes mechanism for the photochemical CO ring opening of oxirane and, in addition, provide important statespecific information not easily accessible from experiments. In particular, we find that, while one of the lowest two excited states is photochemically relatively inert, excitation into the other excited state leads predominantly to rapid ring opening, cyclic. This is followed by hopping to the electronic ground state where hot dynamics leads to further reactions, namely, and . We note that, in the dynamics, we are not limited to following minimum energy pathways and several surface hops may actually be needed before products are finally reached. The performance of different functionals is then assessed by comparison of TDDFT and diffusion Monte Carlo potential energy curves along a typical TDDFT TDA/SH reaction path. Finally, although true conical intersections are expected to be absent in adiabatic TDDFT, we show that the TDDFT TDA is able to approximate a conical intersection in this system.

Effect of the nonlocal exchange on the performance of the orbitaldependent correlation functionals from secondorder perturbation theory
View Description Hide DescriptionAdding a fraction of the nonlocal exchange operator to the local orbitaldependent exchange potential improves the manybody perturbation expansion based on the Kohn–Sham determinant. The effect of such a hybrid scheme on the performance of the orbitaldependent correlation functional from the secondorder perturbation theory (PT2H) is investigated numerically. A small fraction of the nonlocal exchange is often sufficient to ensure the existence of the selfconsistent solution for the PT2H potential. In the He and Be atoms, including 37% of the nonlocal exchange leads to the correlation energies and electronic densities that are very close to the exact ones. In molecules, varying the fraction of the nonlocal exchange may result in the PT2H energy closely reproducing the CCSD(T) value; however such a fraction depends on the system and does not always result in an accurate electronic density. We also numerically verify that the “semicanonical” perturbation series includes most of the beneficial effects of the nonlocal exchange without sacrificing the locality of the exchange potential.

Selfconsistent generalized KohnSham local hybrid functionals of screened exchange: Combining local and rangeseparated hybridization
View Description Hide DescriptionWe present local hybrid functionals that incorporate a positiondependent admixture of shortrange (screened) nonlocal exact [HartreeFocktype (HF)] exchange. We test two limiting cases: screened local hybrids with no longrange HF exchange and longrangecorrected local hybrids with 100% longrange HF exchange. Longrangecorrected local hybrids provide the exact asymptotic exchangecorrelation potential in finite systems, while screened local hybrids avoid the problems inherent to longrange HF exchange in metals and smallbandgap systems. We treat these functionals selfconsistently using the nonlocal exchange potential constructed from KohnSham orbital derivatives. Generalized KohnSham calculations with screened and longrangecorrected local hybrids can provide accurate molecular thermochemistry and kinetics, comparable to existing local hybrids of fullrange exchange. Generalized KohnSham calculations with existing fullrange local hybrids provide results consistent with previous nonselfconsistent and “localized local hybrid” calculations. These new functionals appear to provide a promising extension of existing local and rangeseparated hybrids.

Linearized semiclassical initial value time correlation functions with maximum entropy analytic continuation
View Description Hide DescriptionThe maximum entropy analytic continuation (MEAC) method is used to extend the range of accuracy of the linearized semiclassical initial value representation (LSCIVR)/classical Wigner approximation for real time correlation functions. LSCIVR provides a very effective “prior” for the MEAC procedure since it is very good for short times, exact for all time and temperature for harmonic potentials (even for correlation functions of nonlinear operators), and becomes exact in the classical high temperature limit. This combined approach is applied here to two highly nonlinear dynamical systems, a pure quartic potential in one dimensional and liquid parahydrogen at two thermal state points (25 and 14 K under nearly zero external pressure). The former example shows the MEAC procedure to be a very significant enhancement of the LSCIVR for correlation functions of both linear and nonlinear operators, and especially at low temperature where semiclassical approximations are least accurate. For liquid parahydrogen, the LSCIVR is seen already to be excellent at , but the MEAC procedure produces a significant correction at the lower temperature . Comparisons are also made as to how the MEAC procedure is able to provide corrections for other trajectorybased dynamical approximations when used as priors.

Rydberg energies using excited state density functional theory
View Description Hide DescriptionWe utilize excited statedensity functional theory (eDFT) to study Rydberg states in atoms. We show both analytically and numerically that semilocal functionals can give quite reasonable Rydbergenergies from eDFT, even in cases where time dependent density functional theory (TDDFT) fails catastrophically. We trace these findings to the fact that in eDFT the Kohn–Sham potential for each state is computed using the appropriate excited state density. Unlike the ground state potential, which typically falls off exponentially, the sequence of excited state potentials has a component that falls off polynomially with distance, leading to a Rydbergtype series. We also address the rigorous basis of eDFT for these systems. Perdew and Levy have shown using the constrained search formalism that every stationary density corresponds, in principle, to an exact stationary state of the full manybody Hamiltonian. In the present context, this means that the excited stateDFT solutions are rigorous as long as they deliver the minimum noninteracting kinetic energy for the given density. We use optimized effective potential techniques to show that, in some cases, the eDFT Rydberg solutions appear to deliver the minimum kinetic energy because the associated density is not pure state representable. We thus find that eDFT plays a complementary role to constrained DFT: The former works only if the excited state density is not the ground state of some potential while the latter applies only when the density is a ground state density.

Quantum streamlines within the complex quantum Hamilton–Jacobi formalism
View Description Hide DescriptionQuantum streamlines are investigated in the framework of the quantum Hamilton–Jacobi formalism. The local structures of the quantum momentum function (QMF) and the Pólya vector field near a stagnation point or a pole are analyzed. Streamlines near a stagnation point of the QMF may spiral into or away from it, or they may become circles centered on this point or straight lines. Additionally, streamlines near a pole display eastwest and northsouth opening hyperbolic structure. On the other hand, streamlines near a stagnation point of the Pólya vector field for the QMF display general hyperbolic structure, and streamlines near a pole become circles enclosing the pole. Furthermore, the local structures of the QMF and the Pólya vector field around a stagnation point are related to the first derivative of the QMF; however, the magnitude of the asymptotic structures for these two fields near a pole depends only on the order of the node in the wave function. Two nonstationary states constructed from the eigenstates of the harmonic oscillator are used to illustrate the local structures of these two fields and the dynamics of the streamlines near a stagnation point or a pole. This study presents the abundant dynamics of the streamlines in the complex space for onedimensional timedependent problems.

An improved variational approach to offdiagonal excitonphonon coupling
View Description Hide DescriptionA stateoftheart variational wave function incorporating Jastrowtype excitonphonon correlations, the globallocal Ansatz, is utilized to elucidate excitonphonon correlations in a generalized form of the Holstein Hamiltonian with the simultaneous presence of diagonal and offdiagonal excitonphonon coupling. Much lowered groundstateenergies are found for the globallocal Ansatz when compared with the previously studied Toyozawa Ansatz. A threedimensional phase diagram spanned by the transfer integral and two forms of excitonphonon coupling is given to illustrate polaronic selftrapping near the zone center.

The Prigogine–Defay ratio and the microscopic theory of supercooled liquids
View Description Hide DescriptionPrigogine–Defay ratios and, more recently, their frequency extension have been proposed to be a measure of the number of nonmacroscopic processes involved in the relaxation dynamics of supercooled liquids. We show that the microscopic theory of the Navier–Stokes equations of those liquids provides a consistent thermodynamic framework in which all possible dynamical Prigogine–Defay ratios can be expressed in terms of the same relaxation functions and that these ratios provide less information than the microscopic theory itself. The latter shows that more than one relaxation process is certainly always involved in this relaxation dynamics, whatever is the molecular dynamics, or experimental, technique used to determine the latter.

Partial multicanonical algorithm for molecular dynamics and Monte Carlo simulations
View Description Hide DescriptionPartial multicanonical algorithm is proposed for molecular dynamics and Monte Carlo simulations. The partial multicanonical simulation samples a wide range of a part of the potentialenergy terms, which is necessary to sample the conformational space widely, whereas a wide range of total potential energy is sampled in the multicanonical algorithm. Thus, one can concentrate the effort to determine the weight factor only on the important energy terms in the partial multicanonical simulation. The partial multicanonical, multicanonical, and canonical molecular dynamics algorithms were applied to an alanine dipeptide in explicit water solvent. The canonical simulation sampled the states of , , , and . The multicanonical simulation covered the state as well as these states. The partial multicanonical simulation also sampled the state in addition to the states that were sampled by the multicanonical simulation. In the partial multicanonical simulation, furthermore, backbone dihedral angles and rotated more frequently than those in the multicanonical and canonical simulations. These results mean that the partial multicanonical algorithm has a higher sampling efficiency than the multicanonical and canonical algorithms.

Fourier–Legendre expansion of the oneelectron density matrix of groundstate twoelectron atoms
View Description Hide DescriptionThe density matrix of a spherically symmetric system can be expanded as a Fourier–Legendre series of Legendre polynomials. Application is here made to harmonically trapped electron pairs (i.e., Moshinsky’s and Hooke’s atoms), for which exact wavefunctions are known, and to the helium atom, using a nearexact wavefunction. In the present approach, generic closed form expressions are derived for the series coefficients of . The series expansions are shown to converge rapidly in each case, with respect to both the electron number and the kinetic energy. In practice, a twoterm expansion accounts for most of the correlation effects, so that the correlated density matrices of the atoms at issue are essentially a linear functions of . For example, in the case of Hooke’s atom, a twoterm expansion takes in 99.9% of the electrons and 99.6% of the kinetic energy. The correlated density matrices obtained are finally compared to their determinantal counterparts, using a simplified representation of the density matrix , suggested by the Legendre expansion. Interestingly, twoparticle correlation is shown to impact the angular delocalization of each electron, in the oneparticle space spanned by the and variables.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Microwave spectroscopy of the PBr radical in the state
View Description Hide DescriptionThe microwave spectrum of the PBr radical in the ground electronic state has been observed by a source modulated spectrometer. The PBr radical was generated in a free space cell by an ac∕dc glow discharge in a mixture of with He and∕or . A spectrum with three spin components for each of the two isotopomers, and , was observed. The spectrum showed hyperfine splitting caused by interactions due to both bromine and phosphorus nuclei. The molecular constants including the magnetic hyperfine and nuclear quadrupolehyperfineinteraction constants were determined by analyzing the observed spectrum. The spin density of the unpaired electrons was estimated from the observed hyperfine coupling constants to be 85.4% and 16.3% on the phosphorus and bromine atoms, respectively.

Using small angle xray scattering to measure the homogeneous nucleation rates of propanol, butanol, and pentanol in supersonic nozzle expansions
View Description Hide DescriptionIn our earlier publication [M. Gharibeh et al., J. Chem. Phys.122, 094512 (2005)] we determined the temperatures and partial pressures corresponding to the maximum nucleation rate for a series alcohols (; ) during condensation in a supersonic nozzle. Although we were able to determine the characteristic time corresponding to the peak nucleation rate, we were unable to measure the number density of the aerosol and, thus, unable to directly quantify the nucleation rate . In this paper we report the results of our pioneering small angle xray scattering (SAXS) experiments of alcohol droplets formed in a supersonic nozzle together with a new series of complementary pressure trace measurements. By combining the SAXS and pressure trace measurement data we determine the nucleation rates as a function of temperature and supersaturation.

Theoretical study of the emission spectrum of
View Description Hide DescriptionThe emission spectrum of has been calculated by means of exact dynamics calculations and an accurate potential energy surface for the state. The potential energy surface has been obtained by electronic structure calculations employing the internally contracted multireference configuration interaction method plus Davidson correction and the augmented correlation consistent polarized quadruple zeta basis set. The calculated spectrum, based on energies as well as intensities, agrees well with the measured one. Despite the two asymmetric potential wells of the potential energy surface, the spectrum is best described by a assignment in terms of symmetric stretch, bending, and antisymmetric stretch quantum numbers. The barrier separating the two wells is merely of the order of with the consequence that only the two lowest states, (0,0,0) and (0,0,1), show a tunneling splitting. Essential for the correct assignment of the spectrum is the pronounced negative anharmonicity of the antisymmetric stretch mode. Excitation of the symmetric stretch mode is not directly seen in the main part of the spectrum.