Volume 129, Issue 22, 14 December 2008
 ARTICLES

 Theoretical Methods and Algorithms

Energy derivatives in quantum Monte Carlo involving the zerovariance property
View Description Hide DescriptionWe give an exact expression for the derivative of the expectation value of the energy that satisfies the zerovariance (ZV) principle when the wave function and its first derivatives are exact. The ZV principle was previously applied to the first energy derivative (“force”) within the variational Monte Carlo and mixedestimator diffusionMonte Carlo methods. We present a new expression for the force in pureestimator diffusionMonte Carlo that satisfies the ZV principle and can be evaluated much more efficiently than previous expressions while maintaining comparable accuracy. This expression is the sum of a pure expectation value and a variational expectation value, which separately satisfy the ZV principle. The bias in this force estimator is second order in the deviation of the trial wave function from the diffusionMonte Carlowave function. Results for small molecules demonstrate the accuracy of the method and its statistical efficiency.

Relativistic Jahn–Teller effect in tetrahedral systems
View Description Hide DescriptionIt is shown that states in tetrahedral systems exhibit a linear Jahn–Teller effect which is of purely relativistic origin (that is, it arises from the spinorbitcoupling operator). The electrostatic interactions give rise to a Jahn–Teller effect which is quadratic in the displacements. The Hamiltonian matrix in a diabatic spinelectron basis is derived by an expansion of the electrostatic electronic Hamiltonian and the Breit–Pauli spinorbit operator in powers of the Jahn–Teller active normal mode and taking account of symmetry selection rules for the matrix elements. The adiabatic potentialenergy functions of the system are doubly degenerate (Kramers degeneracy). For small displacements from the tetrahedral reference geometry, the adiabatic potentialenergysurfaces represent a double cone in fourdimensional space, which is a novel topography of Jahn–Teller potentialenergysurfaces. The topological phases of the adiabatic electronic wave functions are discussed.

Relativistic calculation of nuclear magnetic shielding tensor using the regular approximation to the normalized elimination of the small component. III. Introduction of gaugeincluding atomic orbitals and a finitesize nuclear model
View Description Hide DescriptionThe relativistic calculation of nuclear magnetic shielding tensors in hydrogen halides is performed using the secondorder regular approximation to the normalized elimination of the small component (SORANESC) method with the inclusion of the perturbation terms from the metric operator. This computational scheme is denoted as SORAMet. The SORAMet calculation yields anisotropies, , for the halogen nuclei in hydrogen halides that are too small. In the NESC theory, the small component of the spinor is combined to the large component via the operator , in which , is a nonunitary transformation operator, and is the velocity of light. The operator depends on the vector potential (i.e., the magnetic perturbations in the system) with the leading order and the magnetic perturbation terms of contribute to the Hamiltonian and metric operators of the system in the leading order . It is shown that the small for halogen nuclei found in our previous studies is related to the neglect of the perturbation operator of , which is independent of the external magnetic field and of the first order with respect to the nuclear magnetic dipole moment. Introduction of gaugeincluding atomic orbitals and a finitesize nuclear model is also discussed.

Using neural networks, optimized coordinates, and highdimensional model representations to obtain a vinyl bromide potential surface
View Description Hide DescriptionWe demonstrate that it is possible to obtain good potentials using highdimensional model representations (HDMRs) fitted with neural networks (NNs) from data in 12 dimensions and 15 dimensions. The HDMR represents the potential as a sum of lowerdimensional functions and our NNbased approach makes it possible to obtain all of these functions from one set of fitting points. To reduce the number of terms in the HDMR, we use optimized redundant coordinates. By using exponential neurons, one obtains a potential in sumofproducts form, which greatly facilitates quantum dynamics calculations. A 12dimensional (reference) potential surface for vinyl bromide is first refitted to show that it can be represented as a sum of twodimensional functions. To fit functions of the original coordinates, to improve the potential, a huge amount of data would be required. Redundant coordinates avoid this problem. They enable us to bypass the combinatorial explosion of the number of terms which plagues all HDMR and multimodetype methods. We also fit to a set of ab initio points for vinyl bromide in 15 dimensions [M. Malshe et al., J. Chem. Phys.127, 134105 (2007)] and show that it is possible to obtain a surface in sumofproducts form of quality similar to the quality of the fulldimensional fit. Although we obtain a fulldimensional surface, we limit the cost of the fitting by building it from fits of sixdimensional functions, each of which requires only a small NN.

Efficient evaluation of analytic Fukui functions
View Description Hide DescriptionAn efficient method for the analytic evaluation of Fukui functions is proposed. Working equations are derived and numerical results are used to validate the method on medium size set of molecules. In addition to the obvious advantages of analytic differentiation, the proposed method is efficient enough to be considered a practical alternative to the finite difference formulation used routinely. The reliability of the approximations used here is demonstrated and discussed. Problems found in other methods for prediction of electrophilic centers are corrected automatically when using the new method.

NonMarkovian suppression of charge qubit decoherence in the quantum point contact measurement
View Description Hide DescriptionA nonequilibrium theory describing the charge qubit dynamics measured by a quantum point contact is developed based on Schwinger–Keldysh’s approach. Using the realtime diagrammatic technique, we derive the master equation to all orders in perturbation expansions. The nonMarkovian processes in the qubit dynamics is naturally taken into account. The qubit decoherence, in particular, the influence of the tunnelingelectron fluctuation in the quantum point contact with a longer correlation time comparing to the time scale of the qubit dynamics, is studied in the framework. We consider the Lorentziantype spectral density to characterize the channel mixture of the electrontunneling processes induced by the measurement, and determine the correlation time scale of the tunnelingelectron fluctuation. The result shows that as the quantum point contact is casted with a narrower profile of the spectral density, tunnelingelectrons propagate in a longer correlation time scale and lead to the nonMarkovian processes of the qubit dynamics. The qubitelectron in the charge qubit can be driven coherently. The quantum point contactmeasurement with the minimum deviation of the electrontunneling processes prevents the qubit state from the decoherence.

Multiple state transition path sampling
View Description Hide DescriptionWe developed a multiple state transition path sampling (TPS) approach in which it is possible to simultaneously sample pathways connecting a number of different stable states. Based on the original formulation of the TPS we have extended the path ensemble to include trajectories connecting not only two distinct stable states but any two states defined within a system. The multiple state TPS approach is useful in complex systems exhibiting a number of intermediate stable states that are interconnected in phase space. Combining this approach with transition interface sampling we can also directly obtain an expression for the rate constants of all possible transitions within the system.

Efficient solution of Poisson’s equation using discrete variable representation basis sets for Car–Parrinello ab initio molecular dynamics simulations with cluster boundary conditions
View Description Hide DescriptionAn efficient computational approach to perform Car–Parrinello ab initiomolecular dynamics (CPAIMD) simulations under cluster (free) boundary conditions is presented. The general approach builds upon a recent realspace CPAIMD formalism using discrete variable representation (DVR) basis sets [Y. Liu et al., Phys. Rev. B12, 125110 (2003);H.S. Lee and M. E. Tuckerman, J. Phys. Chem. A110, 5549 (2006)]. In order to satisfy cluster boundary conditions, a DVR based on sinc functions is utilized to expand the Kohn–Sham orbitals and electron density. Poisson’s equation is solved in order to calculate the Hartree potential via an integral representation of the singularity. Excellent convergence properties are achieved with respect to the number of grid points (or DVR functions) and the size of the simulation cell. A straightforward implementation of the present approach leads to near linear scaling of the computational cost with respect to the system size for the solution of Poisson’s equation. The accuracy and stability of CPAIMD simulations based on sinc DVR are tested for a model problem as well as for and a water dimer.

Computation of vibrational energy levels and eigenstates of fluoroform using the multiconfiguration timedependent Hartree method
View Description Hide DescriptionA theoretical study of the vibrational spectrum of the molecule is carried out with the aid of the multiconfiguration timedependent Hartree (MCTDH) algorithm. In order to obtain the eigenvalues and the eigenstates, recent developments in the MCTDH improved relaxation method in a block form are exploited. Around 80 eigenvalues are reported, which are converged with a very high accuracy. The results obtained with our study are compared with those of a previous work using the wave operator sorting algorithm approach. The present investigation exemplifies the robustness and the accuracy of the improved relaxation method.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Internal energy of HCl upon photolysis of 2chloropropene at 193 nm investigated with timeresolved Fouriertransform spectroscopy and quasiclassical trajectories
View Description Hide DescriptionFollowing photodissociation of 2chloropropene at 193 nm, vibrationrotationally resolved emission spectra of HCl in the spectral region of were recorded with a stepscan timeresolved Fouriertransform spectrometer. All vibrational levels show a small low component corresponding to and a major high component corresponding to with average rotational energy of . The vibrational population of HCl is inverted at , and the average vibrational energy is . Two possible channels of molecular elimination producing or cannot be distinguished positively based on the observed internal energy distribution of HCl. The observed rotational distributions fit qualitatively with the distributions of both channels obtained with quasiclassical trajectories(QCTs), but the QCT calculations predict negligible populations for states at small . The observed vibrational distribution agrees satisfactorily with the total QCT distribution obtained as a weighted sum of contributions from both fourcenter elimination channels. Internal energy distributions of HCl from 2chloropropene and vinyl chloride are compared.

Vibrational signatures of hydrogen bonding in the protonated ammonia clusters
View Description Hide DescriptionThe gas phase vibrational spectroscopy of the protonated ammonia dimer , a prototypical system for strong hydrogen bonding, is studied in the spectral region from 330 to by combining infrared multiple photon dissociation and multidimensional quantum mechanical simulations. The fundamental transition of the antisymmetric proton stretching vibration is observed at and assigned on the basis of a sixdimensional model Hamiltonian, which predicts this transition at . Photodissociationspectra of the larger protonated ammonia clusters with are also reported for the range from 1050 to . The main absorption features can be assigned within the harmonic approximation, supporting earlier evidence that hydrogen bonding in these clusters is considerably weaker than for .

The remarkable influence of an “insignificant” quantity: How recoil orbital angular momentum determines product distributions and correlation in reactions
View Description Hide DescriptionReactions for which the reactant toproduct mass ratio is high, the wellknown processes, convert most of available energy to product rotation, while that disposed as recoil is often regarded as negligible. In angular momentum (AM) terms, however, this recoil orbital AM is shown to be a critical component of the overall AM balance. For products of light , the maximum value of is energy limited and as a result the formation of products in low rotational states is severely restricted. Here energy constraints on recoil orbital AM and the consequent restrictions on state populations are quantified using novel diagrammatic methods that illustrate how constraints on determine the states that are allowed or forbidden by the need to conserve energy and AM for each statetostate transition. The method accurately predicts j peaks from crossedbeam experiments, providing a quantitative and physically transparent rationale for the observed BaI rotational distributions. Extension to a wider range of reactions having shows that at least some are formally forbidden for each given reactant relative velocity or, more accurately, . The fraction of inaccessible product states for a given initial velocity rises rapidly with ( in ). The method is also used to demonstrate that recoil orbital AM will be strongly aligned parallel to product rotational AM for high , although this correlation is generally lost in the low region as the parallel vector requirement is relaxed.

A combined experimental/theoretical investigation of the nearinfrared photodissociation of
View Description Hide DescriptionWe report the collaborative experimental and theoretical study of the timeresolved recombination dynamics of photodissociated clusters. Excitation of the bare anionic chromophore to the dissociative state yields only and Br products. Interestingly, however, the addition of a few solvent molecules promotes recombination of the dissociating chromophore on the ground state, which correlates asymptotically with and I products. This process is studied experimentally using timeresolved, pumpprobe techniques and theoretically via nonadiabaticmolecular dynamics simulations. In sharp contrast to previous studies where more kinetic energy was released to the photofragments, the observed recombination times increase from picoseconds to nanoseconds with increasing cluster size up to . The recombination times then drop dramatically back to picoseconds for cluster sizes . This trend, seen both in experiment and theory, is explained by the presence of a solventinduced well on the state, the depth of which directly corresponds to the asymmetry of the solvation about the chromophore. The results seen for both the branching ratios and recombination times from experiment and theory show good qualitative agreement.

Rotationally resolved studies of and the exciton coupled origin regions of diphenylmethane and the isotopologue
View Description Hide DescriptionRotationally resolved microwave and ultraviolet spectra of jetcooled diphenylmethane (DPM) and DPM have been obtained in , , and electronic states using Fouriertransform microwave and UV laser/molecular beam spectrometers. The and states of both isotopologues have been well fit to asymmetric rotor Hamiltonians that include only Watson distortion parameters. The transition dipole moment (TDM) orientations of DPM and DPM are perpendicular to the symmetry axes with 66(2)%:34(2)% hybridtype character, establishing the lower exciton origin as a completely delocalized, antisymmetric combination of the zeroorder locally excited states of the toluenelike chromophores. In contrast, the rotational structures of the origin bands at and , respectively, display type branch transitions and lack the central type branch features that characterize the origins, indicating TDM orientations parallel to the symmetry axes as anticipated for the upper exciton levels. However, rotational fits were not possible in line with expectations from previous work [N. R. Pillsbury, J. A. Stearns, C. W. Müller, T. S. Zwier, and D. F. Plusquellic, J. Chem. Phys.129, 114301 (2008)] where the origins were found to be largely perturbed through vibronic interactions with the symmetric, antisymmetric torsional, and butterfly levels in close proximity. Predictions from a dipoledipole coupling model and ab initio theories are shown to be in fair agreement with the observed TDM orientations and exciton splitting. The need to include outofringplane dipole coupling terms indicates that inplane models are not sufficient to fully account for the excitonic interactions in this bichromophore.

Formation of evennumbered hydrogen cluster cations in ultracold helium droplets
View Description Hide DescriptionNeutral hydrogen clusters are grown in ultracold helium nanodroplets by successive pickup of hydrogen molecules. Evennumbered hydrogen cluster cations are observed upon electronimpact ionization with and without attached helium atoms and in addition to the familiar oddnumbered . The helium matrix affects the fragmentation dynamics that usually lead to the formation of overwhelmingly oddnumbered . The use of highresolution mass spectrometry allows the unambiguous identification of evennumbered up to by their mass excess that distinguishes them from , mixed , and background ions. The large range in size of these hydrogen cluster ions is unprecedented, as is the accuracy of their definition. Apart from the previously observed magic number , pronounced drops in the abundance of evennumbered cluster ions are seen at and 114, which suggest icosahedral shell closures at and . Possible isomers of are identified at the quadratic configuration interaction with inclusion of single and double excitations (QCISD)/augccpVTZ level of theory

Ab initio characterization of the conical intersections involved in the photochemistry of phenol
View Description Hide DescriptionThe nature of the vibronic interactions between the , the , and the states at the and conical intersections has been investigated by accurate ab initio calculations. Potential energy surfaces have been constructed at the completeactivespace selfconsistentfield and multireference configurationinteraction (MRCI) levels of theory along each of the ten normal coordinates of symmetry that potentially can be coupling modes at these conical intersections. The OH torsion was found to be by far the strongest coupling mode in each case. As for benzene, a “channel three” radiationless decay mechanism associated with a prefulvenic conical intersection, , was found to exist in phenol. The reaction path connecting the prefulvenic form of phenol with the minimumenergy structure of the state was computed at different levels of theory. The barrier to be overcome for the opening of the prefulvenic decay channel is estimated as at the MRCI level, that is, about above the energy of . With sufficient excess energy in the state, the prefulvenic decay mechanism can be in competition with the hydrogen detachment process.

Vinylphosphineborane: Synthesis, gas phase infrared spectroscopy, and quantum chemical vibrational calculations
View Description Hide DescriptionBoth experimental and theoretical investigations are reported on the infrared spectrum of vinylphosphineborane , a donoracceptor complex. The gas phase infrared spectra have been recorded at resolution. This first primary unsaturated phosphineborane synthesized up to now is kinetically very unstable in the gas phase and decomposes rapidly into two fragments: the free vinylphosphine and the monoborane which dimerizes to form the more stable diborane . Spectra of free and compounds were also recorded to assign some vibration modes of the complex in very dense spectral regions. The analysis was completed by carrying out quantum mechanical calculations by density functional theory method at the level. Anharmonic frequencies and infrared intensities of the two predicted gauche and syn conformers of the vinylphosphineborane complex were calculated in the region with the use of a variational approach, implemented in the P_ANHAR_V1.2 code. Because of the relatively weak interaction between the vinylphosphine and the monoborane, the vibrations of the complex can easily be subdivided into modes localized in the and moieties and into “intermolecular” modes. Localized modes are unambiguously correlated with the modes of the isolated monomers. Therefore, they are described in terms of the monomer vibrations, and the complexation shifts are defined as to make the effect of the complexation precise on each localized mode. In this objective, anharmonic frequencies and infrared intensities of the monomer and the stable gauche and syn conformers of the free vinylphosphine were obtained at the same level of theory. In the gas phase, only the syn form of the complex was observed and assigned. All theoretically predicted frequencies and complexation shifts in magnitude and direction are in good agreement with experiment. By infrared spectroscopy assisted by quantum chemical calculations, the consequences of the complexation of an unsaturated phosphine by borane on the physicochemical properties of the formed 12atom complex have been efficiently evaluated.

Quantum dynamics of the reaction at low temperatures
View Description Hide DescriptionWe report quantum dynamics calculations of the reaction on two different representations of the electronic ground state potential energy surface (PES) using a timeindependent quantum formalism based on hyperspherical coordinates. Calculations show that several excited vibrational levels of the product molecule are populated in the reaction. Rate coefficients evaluated using both PESs were found to be very sensitive to the energy resolution of the reaction probability, especially at temperatures lower than 100 K. It is found that the rate coefficient remains largely constant in the temperature range of 10–39 K, in agreement with the conclusions of a recent experimental study [Carty et al., J. Phys. Chem. A110, 3101 (2006)]. This is in contrast with the timeindependent quantum calculations of Xu et al. [J. Chem. Phys.127, 024304 (2007)] which, using the same PES, predicted nearly two orders of magnitude drop in the rate coefficient value from 39 to 10 K. Implications of our findings to oxygen chemistry in the interstellar medium are discussed.

Measurement of the electron attachment rates for and at in a magnetized Q machine plasma
View Description Hide DescriptionElectron attachment rates for and were measured in a magnetized Q machineplasma at an electron temperature of and with neutral gas pressures of . The rate constants for attachment to and were and , respectively.

Theoretical study of unimolecular decomposition of allene cations
View Description Hide DescriptionAb initio coupled clusters and multireference perturbation theory calculations with geometry optimization at the density functional or complete active space selfconsistentfield levels have been carried out to compute ionizationenergies and to unravel the dissociation mechanism of allene and propyne cations, . The results indicate that the dominant decomposition channel of the monocation is , endothermic by 37.9 kcal/mol and occurring via a barrier of 43.1 kcal/mol, with possible minor contributions from and . For the dication, the competing reaction channels are predicted to be , , and , with dissociation energies of , 8.5, and 3.0 kcal/mol, respectively. The calculations reveal a roaming mechanism for the loss, where a neutral fragment is formed first, then roams around and abstracts a proton from the remaining molecular fragment before leaving the dication. According to Rice–Ramsperger–Kassel–Marcus calculations of energydependent rate constants for individual reaction steps, relative product yields vary with the available internal energy, with being the major product just above the dissociation threshold of 69.6 kcal/mol, in the energy range of 70–75 kcal/mol, and taking over at higher energies. The trication is found to be not very stable, with dissociation thresholds of 18.5 and 3.7 kcal/mol for allene and propyne, respectively. Various products of Coulomb explosion of , , , , and are highly exothermic (by 98–185 kcal/mol). The tetracation of is concluded to be unstable and therefore no more than three electrons can be removed from this molecule before it falls apart. The theoretical results are compared to experimental observations of Coulomb explosions of allene and propyne.