Volume 140, Issue 2, 14 January 2014

Ultrashort soft and hard xray pulses are sensitive probes of structural dynamics on the picometer length and femtosecond time scales of electronic and atomic motions. Recent progress in generating such pulses has initiated new directions of condensed matter research, exploiting a variety of xray absorption, scattering, and diffraction methods to probe photoinduced structural dynamics. Atomic motion, changes of local structure and longrange order, as well as correlated electron motion and charge transfer have been resolved in space and time, providing a most direct access to the physical mechanisms and interactions driving reversible and irreversible changes of structure. This perspective combines an overview of recent advances in femtosecond xray diffraction with a discussion on ongoing and future developments.
 PERSPECTIVES


Perspective: Structural dynamics in condensed matter mapped by femtosecond xray diffraction
View Description Hide DescriptionUltrashort soft and hard xray pulses are sensitive probes of structural dynamics on the picometer length and femtosecond time scales of electronic and atomic motions. Recent progress in generating such pulses has initiated new directions of condensed matter research, exploiting a variety of xray absorption, scattering, and diffraction methods to probe photoinduced structural dynamics. Atomic motion, changes of local structure and longrange order, as well as correlated electron motion and charge transfer have been resolved in space and time, providing a most direct access to the physical mechanisms and interactions driving reversible and irreversible changes of structure. This perspective combines an overview of recent advances in femtosecond xray diffraction with a discussion on ongoing and future developments.
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 ARTICLES

 Theoretical Methods and Algorithms

Excitation energies with linear response density matrix functional theory along the dissociation coordinate of an electronpair bond in Nelectron systems
View Description Hide DescriptionTime dependent density matrix functional theory in its adiabatic linear response formulation delivers exact excitation energies ωα and oscillator strengths f α for twoelectron systems if extended to the socalled phase including natural orbital (PINO) theory. The LöwdinShull expression for the energy of twoelectron systems in terms of the natural orbitals and their phases affords in this case an exact phaseincluding natural orbital functional (PILS), which is nonprimitive (contains other than just J and K integrals). In this paper, the extension of the PILS functional to Nelectron systems is investigated. With the example of an elementary primitive NO functional (BBC1) it is shown that current density matrix functional theory ground state functionals, which were designed to produce decent approximations to the total energy, fail to deliver a qualitatively correct structure of the (inverse) response function, due to essential deficiencies in the reconstruction of the twobody reduced density matrix (2RDM). We now deduce essential features of an Nelectron functional from a wavefunction Ansatz: The extension of the twoelectron LöwdinShull wavefunction to the Nelectron case informs about the phase information. In this paper, applications of this extended LöwdinShull (ELS) functional are considered for the simplest case, ELS(1): one (dissociating) twoelectron bond in the field of occupied (including core) orbitals. ELS(1) produces high quality ωα(R) curves along the bond dissociation coordinate R for the molecules LiH, Li2, and BH with the two outer valence electrons correlated. All of these results indicate that response properties are much more sensitive to deficiencies in the reconstruction of the 2RDM than the ground state energy, since derivatives of the functional with respect to both the NOs and the occupation numbers need to be accurate.

Analysis of and remedies for unphysical ground states of the multireference averaged coupledpair functional
View Description Hide DescriptionA Multireference Configuration Interaction (MRCI) wavefunction includes both static and dynamic electron correlation. MRCI's wellknown flaw, a lack of size extensivity, can be ameliorated with the Multireference Averaged CoupledPair Functional (MRACPF). However, the original MRACPF is frequently unstable, sometimes producing unphysical results. The more Multireference Averaged Quadratic CoupledCluster and MRACPF2 functionals also occasionally exhibit unphysical behavior. We find that these instabilities are avoided crossings with unphysical solutions to the MRACPF equations. We present two approaches to avoid the undesirable unphysical solutions.

Nuclear quadrupole momentinduced CottonMouton effect in molecules
View Description Hide DescriptionNuclear magnetooptic effects could make important contributions to novel, highsensitivity, and highresolution spectroscopic and imaging methods that provide nuclear sitespecific structural and dynamic information on molecular and materials systems. Here we present a firstprinciples electronic structure formulation of nuclear quadrupole momentinduced CottonMouton effect in terms of response theory, as well as ab initio and densityfunctional theory calculations of this phenomenon for a series of molecular liquids: H2O, CH3NO2, CH3CH2OH, C6H6, C6H12 (cyclohexane), HI, XeF2, WF5Cl, and Pt(C2dtp)2. The roles of basisset convergence, electron correlation, and relativistic effects are discussed. The estimated order of magnitude of the overall ellipticities induced to linearly polarized light is 10^{−3}–10^{−7} rad/(M cm) for fully spin polarized nuclei. The cases with the largest presently obtained ellipticities should be detectable with modern instrumentation in the Voigt magnetooptic setup, particularly for the heavy nuclei.

A method for analyzing the nonstationary nucleation and overall transition kinetics: A case of water
View Description Hide DescriptionWe present the statistical method as a direct extension of the mean firstpassage time concept to the analysis of molecular dynamics simulation data of a phase transformation. According to the method, the mean firstpassage time trajectories for the first (i = 1) as well as for the subsequent (i = 2, 3, 4,…) nucleation events should be extracted that allows one to calculate the timedependent nucleation rate, the critical value of the order parameter (the critical size), the waiting times for the nucleation events, and the growth law of the nuclei – i.e., all the terms, which are usually necessary to characterize the overall transition kinetics. There are no restrictions in the application of the method by the specific thermodynamic regions; and the nucleation rate parameters are extracted according to their basic definitions. The method differs from the WedekindBartell scheme and its modification [A. V. Mokshin and B. N. Galimzyanov, J. Phys. Chem. B116, 11959 (2012)], where the passagetimes for the first (largest) nucleus are evaluated only and where the average waiting time for the first nucleation event is accessible instead of the true steadystate nucleation time scale. We demonstrate an efficiency of the method by its application to the analysis of the vaportoliquid transition kinetics in water at the different temperatures. The nucleation rate/time characteristics and the droplet growth parameters are computed on the basis of the coarsegrained molecular dynamics simulation data.

Multilevel summation for dispersion: A lineartime algorithm for r ^{−6} potentials
View Description Hide DescriptionWe have extended the multilevel summation (MLS) method, originally developed to evaluate longrange Coulombic interactions in molecular dynamics simulations [R. D. Skeel, I. Tezcan, and D. J. Hardy, J. Comput. Chem.23, 673 (2002)], to handle dispersion interactions. While dispersion potentials are formally shortranged, accurate calculation of forces and energies in interfacial and inhomogeneous systems require longrange methods. The MLS method offers some significant advantages compared to the particleparticle particlemesh and smooth particle mesh Ewald methods. Unlike meshbased Ewald methods, MLS does not use fast Fourier transforms and is thus not limited by communication and bandwidth concerns. In addition, it scales linearly in the number of particles, as compared with the complexity of the meshbased Ewald methods. While the structure of the MLS method is invariant for different potentials, every algorithmic step had to be adapted to accommodate the r ^{−6} form of the dispersion interactions. In addition, we have derived error bounds, similar to those obtained by Hardy [“Multilevel summation for the fast evaluation of forces for the simulation of biomolecules,” Ph.D. thesis, University of Illinois at UrbanaChampaign, 2006] for the electrostatic MLS. Using a prototype implementation, we have demonstrated the linear scaling of the MLS method for dispersion, and present results establishing the accuracy and efficiency of the method.

Numerical approach to unbiased and driven generalized elastic model
View Description Hide DescriptionFrom scaling arguments and numerical simulations, we investigate the properties of the generalized elastic model (GEM) that is used to describe various physical systems such as polymers, membranes, singlefile systems, or rough interfaces. We compare analytical and numerical results for the subdiffusion exponent β characterizing the growth of the mean squared displacement ⟨(δh)^{2}⟩ of the field h described by the GEM dynamic equation. We study the scaling properties of the qth order moments ⟨δh^{ q }⟩ with time, finding that the interface fluctuations show no intermittent behavior. We also investigate the ergodic properties of the process h in terms of the ergodicity breaking parameter and the distribution of the time averaged mean squared displacement. Finally, we study numerically the driven GEM with a constant, localized perturbation and extract the characteristics of the average drift for a tagged probe.

Imaginary time correlations and the phaseless auxiliary field quantum Monte Carlo
View Description Hide DescriptionThe phaseless Auxiliary Field Quantum Monte Carlo (AFQMC) method provides a well established approximation scheme for accurate calculations of ground state energies of manyfermions systems. Here we address the possibility of calculating imaginary time correlation functions with the phaseless AFQMC. We give a detailed description of the technique and test the quality of the results for static properties and imaginary time correlation functions against exact values for small systems.

Linear response theory for the density matrix renormalization group: Efficient algorithms for strongly correlated excited states
View Description Hide DescriptionLinear response theory for the density matrix renormalization group (DMRGLRT) was first presented in terms of the DMRG renormalization projectors [J. J. Dorando, J. Hachmann, and G. K.L. Chan, J. Chem. Phys.130, 184111 (2009)]. Later, with an understanding of the manifold structure of the matrix product state (MPS) ansatz, which lies at the basis of the DMRG algorithm, a way was found to construct the linear response space for general choices of the MPS gauge in terms of the tangent space vectors [J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pižorn, H. Verschelde, and F. Verstraete, Phys. Rev. Lett.107, 070601 (2011)]. These two developments led to the formulation of the TammDancoff and random phase approximations (TDA and RPA) for MPS. This work describes how these LRTs may be efficiently implemented through minor modifications of the DMRG sweep algorithm, at a computational cost which scales the same as the groundstate DMRG algorithm. In fact, the mixed canonical MPS form implicit to the DMRG sweep is essential for efficient implementation of the RPA, due to the structure of the secondorder tangent space. We present ab initio DMRGTDA results for excited states of polyenes, the water molecule, and a [2Fe2S] ironsulfur cluster.

Dissecting molecular descriptors into atomic contributions in density functional reactivity theory
View Description Hide DescriptionDensity functional reactivity theory (DFRT) employs the electron density of a molecule and its related quantities such as gradient and Laplacian to describe its structure and reactivity properties. Proper descriptions at both molecular (global) and atomic (local) levels are equally important and illuminating. In this work, we make use of Bader's zeroflux partition scheme and consider atomic contributions for a few global reactivity descriptors in DFRT, including the densitybased quantification of steric effect and related indices. Earlier, we proved that these quantities are intrinsically correlated for atomic and molecular systems [S. B. Liu, J. Chem. Phys. 126, 191107 (2007); ibid. 126, 244103 (2007)]. In this work, a new basinbased integration algorithm has been implemented, whose reliability and effectiveness have been extensively examined. We also investigated a list of simple hydrocarbon systems and different scenarios of bonding processes, including stretching, bending, and rotating. Interesting changing patterns for the atomic and molecular values of these quantities have been revealed for different systems. This work not only confirms the strong correlation between these global reactivity descriptors for molecular systems, as theoretically proven earlier by us, it also provides new and unexpected changing patterns for their atomic values, which can be employed to understand the origin and nature of chemical phenomena.

Electron transfer in a twolevel system within a ColeDavidson vitreous bath
View Description Hide DescriptionWe study electron transfer (ET) in a two level quantum system coupled to a glassy viscous bath. The bath is modeled by the ColeDavidson (CD) spectral density. The ET in this model is compared to the ET in a normal DrudeDebye (DD) model. It is shown that at low temperatures and when the coupling to the bath is weak, the viscous bath preserves the quantum coherence for a longer time. However in the strong coupling regime, the tunneling rate is higher in the CD. In the classical high temperature limit the difference between the CD and DD models is negligible.

Stochastic, realspace, imaginarytime evaluation of thirdorder Feynman–Goldstone diagrams
View Description Hide DescriptionA new, alternative set of interpretation rules of Feynman–Goldstone diagrams for manybody perturbation theory is proposed, which translates diagrams into algebraic expressions suitable for direct Monte Carlo integrations. A vertex of a diagram is associated with a Coulomb interaction (rather than a twoelectron integral) and an edge with the trace of a Green's function in real space and imaginary time. With these, 12 diagrams of thirdorder manybody perturbation (MP3) theory are converted into 20dimensional integrals, which are then evaluated by a Monte Carlo method. It uses redundant walkers for convergence acceleration and a weight function for importance sampling in conjunction with the Metropolis algorithm. The resulting Monte Carlo MP3 method has lowrank polynomial size dependence of the operation cost, a negligible memory cost, and a naturally parallel computational kernel, while reproducing the correct correlation energies of small molecules within a few mE h after 10^{6} Monte Carlo steps.

Fitting coupled potential energy surfaces for large systems: Method and construction of a 3state representation for phenol photodissociation in the full 33 internal degrees of freedom using multireference configuration interaction determined data
View Description Hide DescriptionA recently reported algorithm for representing adiabatic states coupled by conical intersections using a quasidiabatic state Hamiltonian in four and five atom systems is extended to treat nonadiabatic processes in considerably larger molecules. The method treats all internal degrees of freedom and uses electronic structure data from ab initio multireference configuration interaction wave functions with nuclear configuration selection based on quasiclassical surface hopping trajectories. The method is shown here to be able to treat ∼30 internal degrees of freedom including dissociative and large amplitude internal motion. Two procedures are introduced which are essential to the algorithm, a null space projector which removes basis functions from the fitting process until they are needed and a partial diagonalization technique which allows for automated, but accurate, treatment of the vicinity of extended seams of conical intersections of two or more states. These procedures are described in detail. The method is illustrated using the photodissociaton of phenol, C6H5OH( ) + hv → C6H5OH( , ) → C6H5O( , ) + H as a test case. Ab initio electronic structure data for the 1,2,3^{1}A states of phenol, which are coupled by conical intersections, are obtained from multireference first order configuration interaction wave functions. The design of bases to simultaneously treat large amplitude motion and dissociation is described, as is the ability of the fitting procedure to smooth the irregularities in the electronic energies attributable to the orbital changes that are inherent to nonadiabatic processes.
 Atoms, Molecules, and Clusters

Prediction of ^{1} P Rydberg energy levels of beryllium based on calculations with explicitly correlated Gaussians
View Description Hide DescriptionBenchmark variational calculations are performed for the seven lowest 1s ^{2}2s np (^{1} P), n = 2…8, states of the beryllium atom. The calculations explicitly include the effect of finite mass of ^{9}Be nucleus and account perturbatively for the massvelocity, Darwin, and spinspin relativistic corrections. The wave functions of the states are expanded in terms of allelectron explicitly correlated Gaussian functions. Basis sets of up to 12 500 optimized Gaussians are used. The maximum discrepancy between the calculated nonrelativistic and experimental energies of 1s ^{2}2s np (^{1} P) →1s ^{2}2s ^{2} (^{1} S) transition is about 12 cm^{−1}. The inclusion of the relativistic corrections reduces the discrepancy to bellow 0.8 cm^{−1}.

Photofragmentation spectroscopy of benzylium and 1phenylethyl cations
View Description Hide DescriptionThe electronic spectra of cold benzylium (C6H5CH2 ^{+}) and 1phenylethyl (C6H5CHCH3 ^{+}) cations have been recorded via photofragment spectroscopy. Benzylium and 1phenylethyl cations produced from electrosprayed benzylamine and phenylethylamine solutions, respectively, were stored in a cryogenically cooled quadrupole ion trap and photodissociated by an OPO laser, scanned in parts of the UV and visible regions (600–225 nm). The electronic states and active vibrational modes of the benzylium and 1phenylethyl cations as well as those of their tropylium or methyl tropylium isomers have been calculated with ab initio methods for comparison with the spectra observed. Sharp vibrational progressions are observed in the visible region while the absorption features are much broader in the UV. The visible spectrum of the benzylium cation is similar to that obtained in an argon tagging experiment [V. Dryza, N. Chalyavi, J. A. Sanelli, and E. J. Bieske, J. Chem. Phys. 137, 204304 (2012)], with an additional splitting assigned to Fermi resonances. The visible spectrum of the 1phenylethyl cation also shows vibrational progressions. For both cations, the second electronic transition is observed in the UV, around 33 000 cm^{−1} (4.1 eV) and shows a broadened vibrational progression. In both cases the S2 optimized geometry is nonplanar. The third electronic transition observed around 40 000 cm^{−1} (5.0 eV) is even broader with no apparent vibrational structures, which is indicative of either a fast nonradiative process or a very large change in geometry between the excited and the ground states. The oscillator strengths calculated for tropylium and methyl tropylium are weak. Therefore, these isomeric structures are most likely not responsible for these absorption features. Finally, the fragmentation pattern changes in the second and third electronic states: C2H2 loss becomes predominant at higher excitation energies, for both cations.

Electronic structure and reactivity in water splitting of the iron oxide dimers and their hexacarbonyls: A density functional study
View Description Hide DescriptionThe iron oxide dimers (FeO)2 and their peroxide isomers are studied with the B3LYP density functional as bare clusters and as hexacarbonyls. Among the bare clusters the planar fourmember ring structures are more stable than the nonplanar ones and the rhombic dioxide Fe2O2 with antiferromagnetically ordered electrons on iron centers is the global minimum. Water adsorption on the bare diiron dioxide is exothermic, but dissociation does not occur. Carbonylation favors a nonplanar Fe2O2 ring for both the dioxides and the peroxides and high electron density at the Fe centers is induced, evidenced by the natural charge distribution, the high proton affinity, and the values of global electronegativity and hardness. The iron dioxide hexacarbonyl Fe2O2(CO)6 is diamagnetic in the state of the global minimum. It is separated from the next lowlying triplet state by a small energy gap of 0.22 eV. Timedependent density functional theory methods were applied to examine electron excitations from the ground state to the lowlying triplet states in the hexacarbonyls and their adsorption complexes with water. Singlettotriplet state excitations occur via ligandtometal charge transfer in the hexacarbonyls; in the adsorption complexes excitations from the oxygen lone pairs to the adsorption center also occur and they appear in the IRvisible region. The lowest energy singlet and triplet state reaction paths for water splitting were followed. On the singlet potential energy surface (PES), water splitting is spontaneous, while for the triplet PES an activation barrier of 14.1 kJ mol^{−1} was determined.

A relativistic timedependent density functional study of the excited states of the mercury dimer
View Description Hide DescriptionIn previous works on Zn2 and Cd2 dimers we found that the longrange corrected CAMB3LYP gives better results than other density functional approximations for the excited states, especially in the asymptotic region. In this paper, we use it to present a timedependent density functional (TDDFT) study for the groundstate as well as the excited states corresponding to the (6s ^{2} + 6s6p), (6s ^{2} + 6s7s), and (6s ^{2} + 6s7p) atomic asymptotes for the mercury dimer Hg2. We analyze its spectrum obtained from allelectron calculations performed with the relativistic DiracCoulomb and relativistic spinfree Hamiltonian as implemented in DIRACPACKAGE. A comparison with the literature is given as far as available. Our result is excellent for the most of the lower excited states and very encouraging for the higher excited states, it shows generally good agreements with experimental results and outperforms other theoretical results. This enables us to give a detailed analysis of the spectrum of the Hg2 including a comparative analysis with the lighter dimers of the group 12, Cd2, and Zn2, especially for the relativistic effects, the spinorbit interaction, and the performance of CAMB3LYP and is enlightened for similar systems. The result shows, as expected, that spinfree Hamiltonian is less efficient than DiracCoulomb Hamiltonian for systems containing heavy elements such as Hg2.

Parity violation in nuclear magnetic resonance frequencies of chiral tetrahedral tungsten complexes NWXYZ (X, Y, Z = H, F, Cl, Br or I)
View Description Hide DescriptionDensity functional theory within the twocomponent quasirelativistic zerothorder regular approximation (ZORA) is used to predict parity violation shifts in ^{183}W nuclear magnetic resonance shielding tensors of chiral, tetrahedrally bonded tungsten complexes of the form NWXYZ (X, Y, Z = H, F, Cl, Br or I), as well as for the heavier systems NWHAtF and NWH(117)F for comparison. The calculations reveal that submHz accuracy is required to detect such tiny effects in this class of compounds, and that parity violation effects are very sensitive to the choice of ligands.

Investigating the significance of zeropoint motion in small molecular clusters of sulphuric acid and water
View Description Hide DescriptionThe nucleation of particles from trace gases in the atmosphere is an important source of cloud condensation nuclei, and these are vital for the formation of clouds in view of the high supersaturations required for homogeneous water droplet nucleation. The methods of quantum chemistry have increasingly been employed to model nucleation due to their high accuracy and efficiency in calculating configurational energies; and nucleation rates can be obtained from the associated free energies of particle formation. However, even in such advanced approaches, it is typically assumed that the nuclei have a classical nature, which is questionable for some systems. The importance of zeropoint motion (also known as quantum nuclear dynamics) in modelling small clusters of sulphuric acid and water is tested here using the path integral molecular dynamics method at the density functional level of theory. The general effect of zeropoint motion is to distort the mean structure slightly, and to promote the extent of proton transfer with respect to classical behaviour. In a particular configuration of one sulphuric acid molecule with three waters, the range of positions explored by a proton between a sulphuric acid and a water molecule at 300 K (a broad range in contrast to the confinement suggested by geometry optimisation at 0 K) is clearly affected by the inclusion of zero point motion, and similar effects are observed for other configurations.

The permanent electric dipole moment of thorium sulfide, ThS
View Description Hide DescriptionNumerous rotational lines of the {18.26}1X ^{1}Σ^{+} band system of thorium sulfide, ThS, were recorded near 547.6 nm at a resolution of approximately 30 MHz. Measurements were made under fieldfree conditions, and in the presence of a static electric field. The fieldfree spectrum was analyzed to produce rotational and Λdoubling parameters. The Stark shifts induced by the electric field were analyzed to determine permanent electric dipole moments, , of 4.58(10) D and 6.72(5) D for the X ^{1}Σ^{+} (v = 0) and {18.26}1 states, respectively. The results are compared with the predictions of previous and new electronic structure calculations for ThS, and the properties of isovalent ThO.