Volume 137, Issue 10, 14 September 2012

A new multireference configuration interaction method using localised orbitals is proposed, in which a molecular system is divided into regions of unequal importance. The advantage of dealing with local orbitals, i.e., the possibility to neglect long range interaction is enhanced. Indeed, while in the zone of the molecule where the important phenomena occur, the interaction cut off may be as small as necessary to get relevant results, in the most part of the system it can be taken rather large, so that results of good quality may be obtained at a lower cost. The method is tested on several systems. In one of them, the definition of the various regions is not based on topological considerations, but on the nature, σ or π, of the localised orbitals, which puts in evidence the generality of the approach.
 COMMUNICATIONS


Communication: From graphite to diamond: Reaction pathways of the phase transition
View Description Hide DescriptionPhase transitions between carbon allotropes are calculated using the generalized solidstate nudged elastic band method. We find a new reaction mechanism between graphite and diamond with nucleation characteristics that has a lower activation energy than the concerted mechanism. The calculated barrier from graphite to hexagonal diamond is lower than to cubic diamond, resolving a conflict between theory and experiment. Transitions are calculated to three structures of cold compressed graphite: bct C4, M, and Zcarbon, which are accessible at the experimentally relevant pressures near 17 GPa.

Communication: Magnetic dipole transitions in the OH A ^{2}Σ^{+} ← X ^{2}Π system
View Description Hide DescriptionWe report on the observation of magnetic dipole allowed transitions in the wellcharacterized A ^{2}Σ^{+} − X ^{2}Π band system of the OH radical. A Stark decelerator in combination with microwave Rabi spectroscopy is used to control the populations in selected hyperfine levels of both Λdoublet components of the X ^{2}Π_{3/2}, v = 0, J = 3/2 ground state. Theoretical calculations presented in this Communication predict that the magnetic dipole transitions in the A ^{2}Σ^{+}, v = 1 ← X ^{2}Π, v = 0 band are weaker than the electric dipole transitions by a factor of 2.58 × 10^{3} only, i.e., much less than commonly believed. Our experimental data confirm this prediction.

Communication: Phase space wavelets for solving Coulomb problems
View Description Hide DescriptionRecently we introduced a phase space approach for solving the timeindependent Schrödinger equation using a periodic von Neumann basis with biorthogonal exchange (pvb) [A. Shimshovitz and D. J. Tannor, Phys. Rev. Lett.109, 070402 (2012)10.1103/PhysRevLett.109.070402]. Here we extend the approach to allow a wavelet scaling of the phase space Gaussians. The new basis set, which we call the wavelet pvb basis, is simple to implement and provides an appealing alternative to other wavelet approaches. For the 1D Coulomb problems tested in this paper, the method reduces the size of the basis relative to the Fourier grid method by a factor of 13–60. The savings in basis set size is predicted to grow steeply as the dimensionality increases.
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 ARTICLES

 Theoretical Methods and Algorithms

An adaptive weighted ensemble procedure for efficient computation of free energies and first passage rates
View Description Hide DescriptionWe introduce an adaptive weightedensemble procedure (aWEP) for efficient and accurate evaluation of firstpassage rates between states for twostate systems. The basic idea that distinguishes aWEP from conventional weightedensemble (WE) methodology is the division of the configuration space into smaller regions and equilibration of the trajectories within each region upon adaptive partitioning of the regions themselves into small grids. The equilibrated conditional/transition probabilities between each pair of regions lead to the determination of populations of the regions and the firstpassage times between regions, which in turn are combined to evaluate the first passage times for the forward and backward transitions between the two states. The application of the procedure to a nontrivial coarse–grained model of a 70residue calcium binding domain of calmodulin is shown to efficiently yield information on the equilibrium probabilities of the two states as well as their first passage times. Notably, the new procedure is significantly more efficient than the canonical implementation of the WE procedure, and this improvement becomes even more significant at low temperatures.

Multiscale multireference configuration interaction calculations for large systems using localized orbitals: Partition in zones
View Description Hide DescriptionA new multireference configuration interaction method using localised orbitals is proposed, in which a molecular system is divided into regions of unequal importance. The advantage of dealing with local orbitals, i.e., the possibility to neglect long range interaction is enhanced. Indeed, while in the zone of the molecule where the important phenomena occur, the interaction cut off may be as small as necessary to get relevant results, in the most part of the system it can be taken rather large, so that results of good quality may be obtained at a lower cost. The method is tested on several systems. In one of them, the definition of the various regions is not based on topological considerations, but on the nature, σ or π, of the localised orbitals, which puts in evidence the generality of the approach.

Computing manybody wave functions with guaranteed precision: The firstorder MøllerPlesset wave function for the ground state of helium atom
View Description Hide DescriptionWe present an approach to compute accurate correlation energies for atoms and molecules using an adaptive discontinuous spectralelement multiresolution representation for the twoelectron wave function. Because of the exponential storage complexity of the spectralelement representation with the number of dimensions, a bruteforce computation of twoelectron (sixdimensional) wave functions with high precision was not practical. To overcome the key storage bottlenecks we utilized (1) a lowrank tensor approximation (specifically, the singular value decomposition) to compress the wave function, and (2) explicitly correlated R12type terms in the wave function to regularize the Coulomb electronelectron singularities of the Hamiltonian. All operations necessary to solve the Schrödinger equation were expressed so that the reconstruction of the fullrank form of the wave function is never necessary. Numerical performance of the method was highlighted by computing the firstorder MøllerPlesset wave function of a helium atom. The computed secondorder MøllerPlesset energy is precise to ∼2 microhartrees, which is at the precision limit of the existing general atomicorbitalbased approaches. Our approach does not assume special geometric symmetries, hence application to molecules is straightforward.

Fourier space approach to the classical density functional theory for multiYukawa and squarewell fluids
View Description Hide DescriptionWe present a Fourier space density functional approach for hard particles with attractive interactions, which is based on a previously developed twodimensional approach [S. Hlushak, W. Rżysko, and S. Sokołowski, J. Chem. Phys.131, 094904 (2009)10.1063/1.3213623] for hardsphere chains. The interactions are incorporated by means of a threedimensional Fourier image of the direct correlation function that is obtained from the firstorder meanspherical approximation. In order to improve the computational efficiency, we make extensive use of fast Fourier transforms for calculating density convolution integrals. A twodimensional implementation of the new density functional approach, based on the expansion of the functional around the bulk fluid density, is used to study structure and adsorption of two model fluids in narrow cylindrical pores. We also investigate two methods that improve the accuracy of the theory as compared to the conventional DFT approach, which expands the free energy functional around the bulk fluid density: One a variant of the reference fluid density functional theory used by Gillespie et al. [Phys. Rev. E68, 031503 (2003)10.1103/PhysRevE.68.031503], and the second a weighted density approach with energy route thermodynamics. Results from these two methods are compared to the conventional approach and also to the results of Monte Carlo simulations. We find that the method of Gillespie et al. and the weighted density approach with energy route thermodynamics yield significant improvement over the conventional approach.

Completenessoptimized basis sets: Application to groundstate electron momentum densities
View Description Hide DescriptionIn the current work we apply the completenessoptimization paradigm [P. Manninen and J. Vaara, J. Comput. Chem.27, 434 (2006)10.1002/jcc.20358] to investigate the basis set convergence of the moments of the groundstate electron momentum density at the selfconsistent field level of theory. We present a blackbox completenessoptimization algorithm that can be used to generate computationally efficient basis sets for computing any property at any level of theory. We show that the complete basis set (CBS) limit of the moments of the electron momentum density can be reached more cost effectively using completenessoptimized basis sets than using conventional, energyoptimized Gaussian basis sets. By using the established CBS limits, we generate a series of smaller basis sets which can be used to systematically approach the CBS and to perform calculations on larger, experimentally interesting systems.

Implicit ligand theory: Rigorous binding free energies and thermodynamic expectations from molecular docking
View Description Hide DescriptionA rigorous formalism for estimating noncovalent binding free energies and thermodynamic expectations from calculations in which receptor configurations are sampled independently from the ligand is derived. Due to this separation, receptor configurations only need to be sampled once, facilitating the use of binding free energy calculations in virtual screening. Demonstrative calculations on a hostguest system yield good agreement with previous free energy calculations and isothermal titration calorimetry measurements. Implicit ligand theory provides guidance on how to improve existing molecular docking algorithms and insight into the concepts of induced fit and conformational selection in noncovalent macromolecular recognition.

Highly tunable spindependent electron transport through carbon atomic chains connecting two zigzag graphene nanoribbons
View Description Hide DescriptionMotivated by recent experiments of successfully carving out stable carbon atomic chains from graphene, we investigate a device structure of a carbon chain connecting two zigzag graphene nanoribbons with highly tunable spindependent transportproperties. Our calculation based on the nonequilibrium Green's function approach combined with the density functional theory shows that the transport behavior is sensitive to the spin configuration of the leads and the bridge position in the gap. A bridge in the middle gives an overall good coupling except for around the Fermi energy where the leads with antiparallel spins create a small transport gap, while the leads with parallel spins give a finite density of states and induce an evenodd oscillation in conductance in terms of the number of atoms in the carbon chain. On the other hand, a bridge at the edge shows a transport behavior associated with the spinpolarized edge states, presenting sharp pure αspin and βspin peaks beside the Fermi energy in the transmission function. This makes it possible to realize onchip interconnects or spintronic devices by tuning the spin state of the leads and the bridge position.
 Advanced Experimental Techniques

Zeroquantum stochastic dipolar recoupling in solid state nuclear magnetic resonance
View Description Hide DescriptionWe present the theoretical description and experimental demonstration of a zeroquantum stochastic dipolar recoupling (ZQSDR) technique for solid state nuclear magnetic resonance(NMR) studies of ^{13}Clabeled molecules, including proteins, under magicangle spinning (MAS). The ZQSDR technique combines zeroquantum recoupling pulse sequence blocks with randomly varying chemical shift precession periods to create randomly amplitude and phasemodulated effective homonuclear magnetic dipoledipole couplings. To a good approximation, couplings between different ^{13}C spin pairs become uncorrelated under ZQSDR, leading to spin dynamics (averaged over many repetitions of the ZQSDR sequence) that are fully described by an orientationdependent N × N polarization transfer rate matrix for an Nspin system, with rates that are inversely proportional to the sixth power of internuclear distances. Suppression of polarization transfers due to noncommutivity of pairwise couplings (i.e., dipolar truncation) does not occur under ZQSDR, as we show both analytically and numerically. Experimental demonstrations are reported for uniformly ^{13}Clabeled Lvaline powder (at 14.1 T and 28.00 kHz MAS), uniformly ^{13}Clabeled protein GB1 in microcrystalline form (at 17.6 T and 40.00 kHz MAS), and partially labeled ^{13}Clabeled protein GB1 (at 14.1 T and 40.00 kHz MAS). The experimental results verify that spin dynamics under ZQSDR are described accurately by rate matrices and suggest the utility of ZQSDR in structural studies of ^{13}Clabeled solids.

Rovibrationally selected ionmolecule collision study using the molecular beam vacuum ultraviolet laser pulsed field ionizationphotoion method: Charge transfer reaction of N_{2} ^{+}(X ^{2}Σ_{g} ^{+}; v^{+} = 0–2; N ^{+} = 0–9) + Ar
View Description Hide DescriptionWe have developed an ionmolecule reaction apparatus for stateselected absolute total cross section measurements by implementing a highresolution molecular beam vacuum ultraviolet (VUV) laser pulsed field ionizationphotoion (PFIPI) ion source to a doublequadrupole doubleoctopole ionguide mass spectrometer. Using the total cross section measurement of the stateselected N_{2} ^{+}(v^{+}, N ^{+}) + Ar charge transfer (CT) reaction as an example, we describe in detail the design of the VUV laser PFIPI ion source used, which has made possible the preparation of reactant N_{2} ^{+}(X ^{2}Σ_{g} ^{+}, v^{+} = 0–2, N ^{+} = 0–9) PFIPIs with high quantum state purity, high intensity, and high kinetic energy resolution. The PFIPIs and prompt ions produced in the ion source are shown to have different kinetic energies, allowing the clean rejection of prompt ions from the PFIPI beam by applying a retarding potential barrier upstream of the PFIPI source. By optimizing the width and amplitude of the pulsed electric fields employed to the VUVPFIPI source, we show that the reactant N_{2} ^{+} PFIPI beam can be formed with a laboratory kinetic energy resolution of ΔE_{lab} = ± 50 meV. As a result, the total cross section measurement can be conducted at centerofmass kinetic energies (E_{cm}’s) down to thermal energies. Absolute total rovibrationally selected cross sections σ(v^{+} = 0–2, N ^{+} = 0–9) for the N_{2} ^{+}(X ^{2}Σ_{g} ^{+}; v^{+} = 0–2, N ^{+} = 0–9) + Ar CT reaction have been measured in the E_{cm} range of 0.04–10.0 eV, revealing strong vibrational enhancements and E_{cm}dependencies of σ(v^{+} = 0–2, N ^{+} = 0–9). The thermochemical threshold at E_{cm} = 0.179 eV for the formation of Ar^{+} from N_{2} ^{+}(X; v^{+} = 0, N ^{+}) + Ar was observed by the measured σ(v^{+} = 0), confirming the narrow ΔE_{cm} spread achieved in the present study. The σ(v^{+} = 0–2; N ^{+}) values obtained here are compared with previous experimental and theoretical results. The theoretical predictions calculated based on the LandauZenerStückelberg formulism are found to be in fair agreement with the present measured σ(v^{+} = 1 or 2; N ^{+}). Taking into account of the experimental uncertainties, the measured σ(v^{+} = 1 or 2, N ^{+}) for N ^{+} = 0–9 at E_{cm} = 0.04–10.0 eV are found to be independent of N ^{+}.
 Atoms, Molecules, and Clusters

Refined theoretical study of radiative association: Cross sections and rate constants for the formation of SiN
View Description Hide DescriptionRadiative association of silicon mononitride (SiN) in its two lowest molecular electronic states is studied through quantum and classical dynamics. Special attention is paid to the behavior of the cross section at high collision energies. A modified expression for the semiclassical cross section is presented which excludes transitions to continuum states. This gives improved agreement with quantum mechanical perturbation theory at high energies. The high energy cross section is overestimated if conventional semiclassical theory is used. The modified semiclassical theory should be valid in general for radiative association transitions from an upper to a lower electronic state. We also implement a quantum dynamical optical potential method with the same type of modification. The rate coefficient is calculated using Breit–Wigner theory and the modified semiclassical formula for the resonance and direct contributions, respectively, for temperatures from 10 K to 20 000 K. A rapid decrease in the rate constant for formation of ground state SiN is observed above 2000 K which was not seen previously.

Cold collisions of polyatomic molecular radicals with Sstate atoms in a magnetic field: An ab initio study of He + collisions
View Description Hide DescriptionWe develop a rigorous quantum mechanical theory for collisions of polyatomic molecular radicals with Sstate atoms in the presence of an external magnetic field. The theory is based on a fully uncoupled spacefixed basis set representation of the multichannel scattering wave function. Explicit expressions are presented for the matrix elements of the scattering Hamiltonian for spin1/2 and spin1 polyatomic molecular radicals interacting with structureless targets. The theory is applied to calculate the cross sections and thermal rate constants for spin relaxation in lowtemperature collisions of the prototypical organic molecule methylene [] with He atoms. To this end, two accurate threedimensional potential energy surfaces (PESs) of the He– complex are developed using the stateoftheart coupledcluster method including single and double excitations along with a perturbative correction for triple excitations and large basis sets. Both PESs exhibit shallow minima and are weakly anisotropic. Our calculations show that spin relaxation in collisions of CH_{2}, CHD, and CD_{2} molecules with He atoms occurs at a much slower rate than elasticscattering over a large range of temperatures (1 μK–1 K) and magnetic fields (0.01–1 T), suggesting excellent prospects for cryogenic helium buffergas cooling of groundstate ortho molecules in a magnetic trap. Furthermore, we find that orthoCH_{2} undergoes collisioninduced spin relaxation much more slowly than paraCH_{2}, which indicates that magnetic trapping can be used to separate nuclear spin isomers of openshell polyatomic molecules.

Infrared spectroscopy of hydrated naphthalene cluster anions
View Description Hide DescriptionWe present infrared spectra of massselected C_{10}H_{8} ^{−}·(H_{2}O)_{ n }·Ar_{ m } cluster anions (n = 1–6) obtained by Ar predissociation spectroscopy. The experimental spectra are compared with predicted spectra from density functional theory calculations. The OH groups of the water ligands are involved in Hbonds to other water molecules or to the π system of the naphthalene anion, which accommodates the excess electron. The interactions in the water network are generally found to be more important than those between water molecules and the ion. For 2 ≤ n ≤ 4 the water molecules form single layer water networks on one side of the naphthalene anion, while for n = 5 and 6, cage and multilayer structures become more energetically favorable. For cluster sizes with more than 3 water molecules, multiple conformers are likely to be responsible for the experimental spectra.

The water hexamer: Threebody interactions, structures, energetics, and OHstretch spectroscopy at finite temperature
View Description Hide DescriptionUsing a newly developed and recently parameterized classical empirical simulation model for water that involves explicit threebody interactions, we determine the eleven most stable isomers of the water hexamer. We find that the lowest energy isomer is one of the cage structures, in agreement with farIR and microwave experiments. The energy ordering for the binding energies is cage > glove > book > bag > chair > boat > chaise, and energies relative to the cage are in good agreement with CCSD(T) calculations. The threebody contributions to the cage, book, and chair are also in reasonable agreement with CCSD(T) results. The energy of each isomer results from a delicate balance involving the number of hydrogen bonds, the strain of these hydrogen bonds, and cooperative and anticooperative threebody interactions, whose contribution we can understand simply from the form of the threebody interactions in the simulation model. Oxygenoxygen distances in the cage and book isomers are in good agreement with microwave experiments. Hydrogenbond distances depend on both donor and acceptor, which can again be understood from the threebody model. Fully anharmonic OHstretch spectra are calculated for these lowenergy structures, and compared with shifted harmonic results from ab initio and density functional theory calculations. Replicaexchange molecular dynamics simulations were performed from 40 to 194 K, which show that the cage isomer has the lowest free energy from 0 to 70 K, and the book isomer has the lowest free energy from 70 to 194 K. OHstretch spectra were calculated between 40 and 194 K, and results at 40, 63, and 79 K were compared to recent experiments, leading to reassignment of the peaks in the experimental spectra. We calculate local OHstretch cumulative spectral densities for different donoracceptor types and compare to analogous results for liquid water.

Radical ions with nearly degenerate ground state: Correlation between the rate of spinlattice relaxation and the structure of adiabatic potential energy surface
View Description Hide DescriptionParamagnetic spinlattice relaxation (SLR) in radical cations (RCs) of the cycloalkane series in liquid solution was studied and analyzed from the point of view of the correlation between the relaxation rate and the structure of the adiabatic potential energy surface (PES) of the RCs. SLR rates in the RCs formed in xray irradiated nhexane solutions of the cycloalkanes studied were measured with the method of timeresolved magnetic field effect in the recombination fluorescence of spincorrelated radical ion pairs. Temperature and, for some cycloalkanes, magnetic field dependences of the relaxation rate were determined. It was found that the conventional Redfield theory of the paramagneticrelaxation as applied to the results on cyclohexane RC, gave a value of about 0.2 ps for the correlation time of the perturbation together with an unrealistically high value of 0.1 T in field units for the matrix element of the relaxation transition. The PES structure was obtained with the DFT quantumchemical calculations. It was found that for all of the cycloalkanes RCs considered, including low symmetric alkylsubstituted ones, the adiabatic PESes were surfaces of pseudorotation due to avoided crossing. In the RCs studied, a correlation between the SLR rate and the calculated barrier height to the pseudorotation was revealed. For RCs with a higher relaxation rate, the apparent activation energies for the SLR were similar to the calculated heights of the barrier. To rationalize the data obtained it was assumed that the vibronic states degeneracy, which is specific for JahnTeller active cyclohexane RC, was approximately kept in the RCs of substituted cycloalkanes for the vibronic states with the energies above and close to the barrier height to the pseudorotation. It was proposed that the effective spinlattice relaxation in a radical with nearly degenerate lowlying vibronic states originated from stochastic crossings of the vibronic levels that occur due to fluctuations of the interaction between the radical and the solvent. The magnitude of these fluctuations, ∼100 cm^{−1}, determines the upper scale of the unperturbed splitting between the vibronic states, for which the manifestation of this paramagneticrelaxation mechanism could be expected. Our estimate for the relaxation rate derived using standard LandauZener model of nonadiabatic transitions at the level crossing agrees with the experimental data. This paramagneticrelaxation mechanism can also be operative in paramagnetic species of other types such as linear radicals, radicals with threefold degeneracy, paramagnetic centers in crystals, etc. It looks likely that the proposed SLR mechanism can be quenched by a fast vibrational relaxation in radicals.

Effect of laser pulse shaping parameters on the fidelity of quantum logic gates
View Description Hide DescriptionThe effect of varying parameters specific to laser pulse shaping instruments on resulting fidelities for the ACNOT_{1}, NOT_{2}, and Hadamard_{2}quantum logic gates are studied for the diatomic molecule ^{12}C^{16}O. These parameters include varying the frequency resolution, adjusting the number of frequency components and also varying the amplitude and phase at each frequency component. A time domain analytic form of the original discretized frequency domain laser pulse function is derived, providing a useful means to infer the resulting pulse shape through variations to the aforementioned parameters. We show that amplitude variation at each frequency component is a crucial requirement for optimal laser pulse shaping, whereas phase variation provides minimal contribution. We also show that high fidelity laser pulses are dependent upon the frequency resolution and increasing the number of frequency components provides only a small incremental improvement to quantum gate fidelity. Analysis through use of the pulse area theorem confirms the resulting population dynamics for one or two frequency high fidelity laser pulses and implies similar dynamics for more complex laser pulse shapes. The ability to produce high fidelity laser pulses that provide both population control and global phase alignment is attributed greatly to the natural evolution phase alignment of the qubits involved within the quantum logic gate operation.

Spectroscopy and dynamics of the predissociated, quasilinear S_{2} state of chlorocarbene
View Description Hide DescriptionIn this work, we report on the spectroscopy and dynamics of the quasilinear S_{2} state of chlorocarbene, CHCl, and its deuterated isotopologue using opticaloptical double resonance (OODR) spectroscopy through selected rovibronic levels of the S_{1} state. This study, which represents the first observation of the S_{2} state in CHCl, builds upon our recent examination of the corresponding state in CHF, where pronounced mode specificity was observed in the dynamics, with predissociation rates larger for levels containing bending excitation. In the present work, a total of 14 S_{2} state vibrational levels with angular momentum ℓ = 1 were observed for CHCl, and 34 levels for CDCl. The range of ℓ in this case was restricted by the pronounced RennerTeller effect in the lowlying S_{1} levels, which severely reduces the fluorescence lifetime for levels with K _{ a } > 0. Nonetheless, by exploiting different intermediate S_{1} levels, we observed progressions involving all three fundamental vibrations. For levels with long predissociation lifetimes, rotational constants were determined by measuring spectra through different intermediate J levels of the S_{1} state. Plots of the predissociationlinewidth (lifetime) vs. energy for various S_{2} levels show an abrupt onset, which lies near the calculated threshold for elimination to form C(^{3}P) + HCl on the triplet surface. Our experimental results are compared with a series of high level ab initio calculations, which included the use of a dynamically weighted fullvalence CASSCF procedure, focusing maximum weight on the state of interest (the singlet and triplet states were computed separately). This was used as the reference for subsequent Davidsoncorrected MRCI(+Q) calculations. These calculations reveal the presence of multiple conical intersections in the singlet manifold.

Structures of N_{2}Ar, O_{2}Ar, and O_{2}Xe dimers studied by Coulomb explosion imaging
View Description Hide DescriptionWe use intense femtosecond laser pulses to multiply ionize and directly image the structures of N_{2}Ar, O_{2}Ar, and O_{2}Xe dimers by coincidently measuring the momenta of the fragment ions. All these dimers are found to have an equilibrium Tshaped structure in which the bond of the diatomic molecule is perpendicular to the dimer axis. The equilibrium distance between the raregas atom and the centerofmass of the diatomic molecule is estimated to be R_{N2–Ar} ∼ 3.86 Å, R_{O2–Ar} ∼ 3.65 Å, and R_{O2–Xe} ∼ 4.07 Å, respectively. For the Tshaped N_{2}Ar dimer, both sequential and direct tripleionizationinduced threebody breakups are observed. In contrast to N_{2}Ar dimer, other structures are found to coexist with the dominating Tshaped one for O_{2}Ar and O_{2}Xe.