Volume 132, Issue 8, 28 February 2010

A combined theoretical and solidstate nuclear magnetic resonance (NMR) study of the electronic structure of the uranyl ion in and rutherfordine is presented, the former representing a system with a hydrogenbonding environment around the uranyl oxygens and the latter exemplifying a uranyl environment without hydrogens. Relativistic density functional calculations reveal unique features of the U–O covalent bond, including the finding of chemical shift anisotropies that are among the largest for oxygen ever reported . Computational results for the oxygen electric field gradient tensor are found to be consistently larger in magnitude than experimental solidstate NMR measurements in a 7.05 T magnetic field indicate. A modified version of the Solomon theory of the twospin echo amplitude for a spin5/2 nucleus is developed and applied to the analysis of the echo signal of .
 COMMUNICATIONS


Communications: A nonperturbative quantum master equation approach to charge carrier transport in organic molecular crystals
View Description Hide DescriptionWe present a nonperturbative quantum master equation to investigate charge carriertransport in organic molecular crystals based on the Liouville space hierarchical equations of motion method, which extends the previous stochastic Liouville equation and generalized master equation methods to a full quantum treatment of the electronphonon coupling. Diffusive motion of charge carriers in a onedimensional model in the presence of nonlocal electronphonon coupling was studied, and two different charge carrierdiffusion mechanisms are observed for large and small average intermolecular couplings. The new method can also find applications in calculating spectra and energy transfer in various types of quantum aggregates where the perturbative treatments fail.

Communications: Adsorption of element 112 on the gold surface: Manybody wave function versus density functional theory
View Description Hide DescriptionThe applicability of the relativistic density functional theory (RDFT) with conventional generalized gradient and hybrid exchangecorrelation functionals to the description of the interactions of element 112 (Cn) and its lighter homolog Hg with a goldsurface is assessed. The comparison of Cn–Au (Hg–Au) bond properties for two simple models of adsorption complexes on Au(111) surface obtained by RDFT and accurate manybody calculations indicates a strong underestimation of binding energies by conventional RDFT schemes. This effect provides a possible explanation of the discrepancies between the RDFTbased theoretical and experimental data concerning the thermochromatographic registration of the decay chain element .

Communications: Development and characterization of a source of rotationally cold, enriched para
View Description Hide DescriptionIn an effort to develop a source of that is almost entirely in a single quantum state , we have successfully generated a plasma that is enriched to in para at a rotational temperature of 80 K. This enrichment is a result of the nuclear spin selection rules at work in hydrogenic plasmas, which dictate that only para will form from para, and that para can be converted to ortho by subsequent reaction with . This is the first experimental study in which the and nuclear spin selection rules have been observed at cold temperatures. The ions were produced from a pulsed solenoid valve source, cooled by supersonic expansion, and interrogated via continuouswave cavity ringdown spectroscopy.
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 ARTICLES

 Theoretical Methods and Algorithms

Efficient computation of free energy of crystal phases due to external potentials by errorbiased Bennett acceptance ratio method
View Description Hide DescriptionFree energy of crystal phases is commonly evaluated by thermodynamic integration along a reversible path that involves an external potential. However, this method suffers from the hysteresis caused by the differences in the center of mass position of the crystal phase in the presence and absence of the external potential. To alleviate this hysteresis, a constraint on the translational degrees of freedom of the crystal phase is imposed along the path and subsequently a correction term is added to the free energy to account for such a constraint. The estimation of the correction term is often computationally expensive. In this work, we propose a new methodology, termed as errorbiased Bennett acceptance ratio method, which effectively solves this problem without the need to impose any constraint. This method is simple to implement and it does not require any modification to the path. We show the applicability of this method in the computation of crystalmelt interfacial energy by cleaving wall method [R. L. Davidchack and B. B. Laird, J. Chem. Phys.118, 7651 (2003)] and bulk crystalmelt free energy difference by constrained fluid integration method [G. Grochola, J. Chem. Phys.120, 2122 (2004)] for a model potential of silicon.

Electronic excitation energies in solution at equation of motion CCSD level within a state specific polarizable continuum model approach
View Description Hide DescriptionWe present a study of excitation energies in solution at the equation of motioncoupled cluster singles and doubles (EOMCCSD) level of theory. The solvent effect is introduced with a state specific polarizable continuum model (PCM), where the solutesolvent interaction is specific for the state of interest. Three definitions of the excited state oneparticle density matrix (1PDM) are tested in order to gain information for the development of an integrated EOMCCSD/PCM method. The calculations show the accuracy of this approach for the computation of such property in solution. Solvent shifts between nonpolar and polar solvents are in good agreement with experiment for the test cases. The completely unrelaxed 1PDM is shown to be a balanced choice between computational effort and accuracy for vertical excitation energies, whereas the response of the ground state CCSD amplitudes and of the molecular orbitals is important for other properties, as for instance the dipole moment.

Quantum dynamics of the reaction in curvilinear coordinates: Fulldimensional and reduced dimensional calculations of reaction rates
View Description Hide DescriptionFulldimensional quantum dynamics calculations for the reaction using curvilinear coordinates are presented. A curvilinear coordinate system to describe reactions of the type is developed which facilitates efficient calculations using the multiconfigurational timedependent Hartree (MCTDH) approach. To describe the bending motion of the and atoms relative to the axis defined by the fragment, coordinates based on stereographic projection are introduced. These coordinates yield a kinetic energy operator free of singularities within the dynamically relevant region. Employing this curvilinear coordinate system, fulldimensional and reduced dimensional MCTDH calculations study the cumulative reaction probability (for ) and the thermal rate constant for the reaction on the JordanGilbert potential energy surface [J. Chem. Phys.102, 5669 (1995)]. The fulldimensional results agree very well with previous fulldimensional MCTDH results which used transition state based normal coordinates. The results of our eightdimensional (8D) calculations are in reasonable agreement with the fulldimensional ones. They deviate significantly from older 8D results of Zhang et al. [J. Chem. Phys.127, 234213 (2007)] but agree well with more recent results from the same group.

Identifying and correcting nonMarkov states in peptide conformational dynamics
View Description Hide DescriptionConformational transitions in proteins define their biological activity and can be investigated in detail using the Markov state model. The fundamental assumption on the transitions between the states, their Markov property, is critical in this framework. We test this assumption by analyzing the transitions obtained directly from the dynamics of a molecular dynamics simulated peptide valineprolinealanineleucine and states defined phenomenologically using clustering in dihedral space. We find that the transitions are Markovian at the time scale of and longer. However, at the time scale of 30–40 ps the dynamics loses its Markov property. Our methodology reveals the mechanism that leads to nonMarkov behavior. It also provides a way of regrouping the conformations into new states that now possess the required Markov property of their dynamics.

Size consistency of explicit functionals of the natural orbitals in reduced density matrix functional theory
View Description Hide DescriptionWe report a sizeinconsistency problem for several functionals within reduced density matrix functionaltheory. Being explicit functionals of the natural orbitals and occupation numbers, instead of the onebody reduced density matrix, many of the approximate functionals are not invariant under unitary transformations in the subspace of degenerate occupation numbers. One such transformation mixes the degenerate natural orbitals of identical independent subsystems, delocalizing them. Noninvariance under this transformation results in size inconsistency for some of the approximations while others avoid this pathology by favoring orbital localization.

Møller–Plesset perturbation theory gradient in the generalized hybrid orbital quantum mechanical and molecular mechanical method
View Description Hide DescriptionAn analytic gradient expression is formulated and implemented for the secondorder Møller–Plesset perturbation theory (MP2) based on the generalized hybrid orbital QM/MM method. The method enables us to obtain an accurate geometry at a reasonable computational cost. The performance of the method is assessed for various isomers of alanine dipepetide. We also compare the optimized structures of fumaramidederived [2]rotaxane and cAMPdependent protein kinase with experiment.

A smoothing monotonic convergent optimal control algorithm for nuclear magnetic resonance pulse sequence design
View Description Hide DescriptionThe past decade has demonstrated increasing interests in using optimal control based methods within coherent quantum controllable systems. The versatility of such methods has been demonstrated with particular elegance within nuclear magnetic resonance(NMR) where natural separation between coherent and dissipative spin dynamics processes has enabled coherent quantum control over long periods of time to shape the experiment to almost ideal adoption to the spin system and external manipulations. This has led to new design principles as well as powerful new experimental methods within magnetic resonance imaging, liquidstate and solidstate NMR spectroscopy. For this development to continue and expand, it is crucially important to constantly improve the underlying numerical algorithms to provide numerical solutions which are optimally compatible with implementation on current instrumentation and at same time are numerically stable and offer fast monotonic convergence toward the target. Addressing such aims, we here present a smoothing monotonically convergent algorithm for pulse sequencedesign in magnetic resonance which with improved optimization stability lead to smooth pulse sequence easier to implement experimentally and potentially understand within the analytical framework of modern NMR spectroscopy.

Statistics of tethered selfavoiding chains under spherical confinement and an external force
View Description Hide DescriptionWe compute the partition function of selfavoiding chains tethered inside a confining sphere using Monte Carlo simulations on a threedimensional lattice. Two cases are considered: (i) singletethered chains with one end anchored and one end free and (ii) doubletethered chains where both ends are tethered at a distance equal to the diameter of the sphere. The selfavoidance, confinement, and tethering constraints dramatically decrease the number of allowed configurations when compared with an unconstrained random coil, thereby affecting the sampling method used in the Monte Carlo procedure. The effect of an external applied force and the bias it introduces in the partition function are also investigated. Our method involves a decomposition of the partition function into the product of several terms that can be evaluated independently. For short chains, we demonstrate the validity of our approach through a direct evaluation of the partition function using an exact enumeration of the appropriate paths on the lattice. In the case of long chains, scaling laws for the behavior of the partition function are identified.

Gradientbased multiconfiguration Shepard interpolation for generating potential energy surfaces for polyatomic reactions
View Description Hide DescriptionThis paper describes and illustrates a way to construct multidimensional representations of reactive potential energy surfaces (PESs) by a multiconfiguration Shepard interpolation (MCSI) method based only on gradient information, that is, without using any Hessian information from electronic structure calculations. MCSI, which is called multiconfiguration molecular mechanics (MCMM) in previous articles, is a semiautomated method designed for constructing fulldimensional PESs for subsequent dynamics calculations (classical trajectories, full quantum dynamics, or variational transition state theory with multidimensional tunneling). The MCSI method is based on Shepard interpolation of Taylor series expansions of the coupling term of a electronically diabatic Hamiltonian matrix with the diagonal elements representing nonreactive analytical PESs for reactants and products. In contrast to the previously developed method, these expansions are truncated in the present version at the first order, and, therefore, no input of electronic structure Hessians is required. The accuracy of the interpolated energies is evaluated for two test reactions, namely, the reaction and the hydrogen atom abstraction from a model of tocopherol by methyl radical. The latter reaction involves 38 atoms and a 108dimensional PES. The mean unsigned errors averaged over a wide range of representative nuclear configurations (corresponding to an energy range of 19.5 kcal/mol in the former case and 32 kcal/mol in the latter) are found to be within 1 kcal/mol for both reactions, based on 13 gradients in one case and 11 in the other. The gradientbased MCMM method can be applied for efficient representations of multidimensional PESs in cases where analytical electronic structure Hessians are too expensive or unavailable, and it provides new opportunities to employ highlevel electronic structure calculations for dynamics at an affordable cost.

Localized Hartree product treatment of multiple protons in the nuclearelectronic orbital framework
View Description Hide DescriptionAn approximation for treating multiple quantum nuclei within the nuclearelectronic orbital (NEO) framework for molecular systems is presented. In the approximation to NEOHartree–Fock, the nuclear wave function is represented by a Hartree product rather than a Slater determinant, corresponding to the neglect of the nuclear exchange interactions. In the approximation to NEOdensity functional theory, the nuclear exchangecorrelation functional is chosen to be the diagonal nuclear exchange interaction terms, thereby eliminating the nuclear selfinteraction terms. To further enhance the simplicity and computational efficiency, the nuclear molecular orbitals or Kohn–Sham orbitals are expanded in terms of localized nuclear basis sets. These approximations are valid because of the inherent localization of the nuclear orbitals and the numerical insignificance of the nuclear exchange interactions in molecular systems. Moreover, these approximations lead to substantial computational savings due to the reduction in both the number of integrals that must be calculated and the size of the matrices that must be diagonalized. These nuclear Hartree product approximation (HPA) methods scale linearly with the number of quantum protons and are highly parallelizable. Applications to a water hexamer, glycine dimer, and 32water cluster, where all hydrogen nuclei are treated quantum mechanically, illustrate the accuracy and computational efficiency of the nuclear HPA methods. These strategies will facilitate the implementation of explicitly correlated NEO methods for molecular systems with multiple quantum protons.

Compatibility between shape equation and boundary conditions of lipid membranes with free edges
View Description Hide DescriptionOnly some special open surfaces satisfying the shape equation of lipid membranes can be compatible with the boundary conditions. As a result of this compatibility, the first integral of the shape equation should vanish for axisymmetric lipid membranes, from which two theorems of nonexistence are verified: (i) there is no axisymmetric open membrane being a part of torus satisfying the shape equation; (ii) there is no axisymmetric open membrane being a part of a biconcave discodal surface satisfying the shape equation. Additionally, the shape equation is reduced to a secondorder differential equation while the boundary conditions are reduced to two equations due to this compatibility. Numerical solutions to the reduced shape equation and boundary conditions agree well with the experimental data [A. Saitoh et al., Proc. Natl. Acad. Sci. U.S.A.95, 1026 (1998)].

Extraction of statetostate reactive scattering attributes from wave packet in reactant Jacobi coordinates
View Description Hide DescriptionThe matrix for a scattering system provides the most detailed information about the dynamics. In this work, we discuss the calculation of matrix elements for the , type reaction. Two methods for extracting matrix elements from a single wave packet in reactant Jacobi coordinates are reviewed and compared. Both methods are capable of extracting the statetostate attributes for both product channels from a single wave packet propagation. It is shown through the examples of , , and reactions that such reactant coordinate based methods are easy to implement, numerically efficient, and accurate. Additional efficiency can be gained by the use of a shaped grid with twodimensional fast Fourier transform.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Search for production in the reaction
View Description Hide DescriptionDeuterium bromide (DBr) is expanded from a pulsed jet into a vacuum and a synchronized pulsed laser causes photodissociation of some of the DBr molecules to produce primarily groundstate bromine atoms and fast D atoms. The latter collide with the cold DBr molecules and react to produce molecular deuterium via two possible channels, the adiabatic channel and the nonadiabatic channel , which are asymptotically separated in energy by the spinorbit splitting (0.457 eV) of the bromine atom. Ion images are recorded for , , and for various collision energies. For the nonadiabatic production of spinorbitexcited in the reaction for the conditions studied we estimate that this channel contributes 1% or less.

Valence ionized states of iron pentacarbonyl and cyclopentadienyl cobalt dicarbonyl studied by symmetryadapted clusterconfiguration interaction calculation and collisionenergy resolved Penning ionization electron spectroscopy
View Description Hide DescriptionValence ionized states of iron pentacarbonyl and cyclopentadienyl cobalt dicarbonyl have been studied by ultraviolet photoelectron spectroscopy, twodimensional Penning ionizationelectron spectroscopy (2DPIES), and symmetryadapted clusterconfiguration interaction calculations. Theory provided reliable assignments for the complex ionization spectra of these molecules, which have metalcarbonyl bonds. Theoretical ionization energies agreed well with experimental observations and the calculated wave functions could explain the relative intensities of PIES spectra. The collisionenergy dependence of partial ionization cross sections (CEDPICS) was obtained by 2DPIES. To interpret these CEDPICS, the interaction potentials between the molecules and a Li atom were examined in several coordinates by calculations. The relation between the slope of the CEDPICS and the electronic structure of the ionized states, such as molecular symmetry and the spatial distribution of ionizing orbitals, was analyzed. In , an attractive interaction was obtained for the equatorial CO, while the interaction for the axial CO direction was repulsive. For , the interaction potential in the direction of both Co–C–O and Co–Cp ring was attractive. These anisotropic interactions and ionizing orbital distributions consistently explain the relative slopes of the CEDPICS.

On the nature of bonding in a stable neutral diborene
View Description Hide DescriptionWe report the bonding interactions within and [R] as a ligand in a newly synthesized stable neutral diborene. By using theoretical analyses, we have found the nature of the bonding, and, more importantly, the key to realize multiple bonds for chemical elements. With character of almost equal covalency and ionicity, the stabilizing orbital interaction term, , of , is mainly given by symmetry orbital interactions; the donoracceptor interaction is weak and contributes small to . In the weak donoracceptor interaction, the backdonation is stronger than the donation. Thus, in effect, the bond emerges in the dipole. Inspection of the correlation lines of the orbital correlation diagram for the bonding indicates that the strength of the bonding orbitals in the central BB unit is weakened due to the coordination of the carbenes, and the center is unstabilized by the carbene ligand. This is contrary to the conventional view on the mechanism of coordination and the Dewar–Chatt–Duncanson model. However this unstabilizing effect should be responsible for the stability of the double bond in the stable neutral diborene. This is because the very short bond lengths arising from multiple bonds will lead to a very strong Pauli repulsion, and, ultimately, destruction of chemical bonds. It can therefore be concluded that, actually, to prevent the very short bond lengths is the true reason for the successful realization of multiple bonds for maingroup elements such as boron.

The HOOH UV spectrum: Importance of the transition dipole moment and torsional motion from semiclassical calculations on an ab initio potential energy surface
View Description Hide DescriptionThe absorption cross section of HOOH, a starting point for larger ROOH, was calculated using the “Wigner method.” Calculations use the Wigner transform of ground statewave functions and classical approximations for excited statewave functions. Potential energy and transition dipole moment surfaces were calculated using the equationofmotion coupledcluster singles and doubles method over an extended Franck–Condon region. The first two O–O stretches and the first five HOOH torsional levels are included. This study also addresses two fundamental questions about ROOH photodissociation. The long wavelength excited state preference has been measured from dynamics experiments, but a Franck–Condon overlap explanation has not been directly verified. A moderate barrier to HOOH torsional motion and excited state dynamics affect the temperature dependence in the UVspectrum. Based on these initial findings for HOOH, photodissociation of large ROOH cannot be eliminated as an important factor for ozone and particulate matter production seen in both ambient and laboratory studies.

Sevendegreeoffreedom, quantum scattering dynamics study of the reaction
View Description Hide DescriptionA quantum scattering dynamics, timedependent wavepacket propagation method is applied to study the reaction of on the Xie–Braams–Bowman potential energy surface. The reduceddimensional, sevendegreeoffreedom approach is employed in this calculation by fixing one Jacobi and one torsion angle related to at the lowest saddle point geometry of on the potential energy surface. Initial state selected reaction probabilities are presented for various initial rovibrational states. The ground statereaction probability shows no threshold for this reaction, in other words, this reaction can occur without an activation barrier. The vibrational excitation shows that the stretching motion of only has a small effect on the reaction probability; the vibrational excitation of HD in hinders the reactivity. By contrast, rotational excitation of greatly enhances the reactivity with the reaction probability increased double or triple at high rotational states compared to the ground state. Reactive resonances, seen in all the initial state selected reaction probabilities, are also found in the integral cross section for the ground state of and . The thermal rate coefficient is also calculated and is found to be in semiquantitative agreement with experiment; however, quantum scattering approaches including more degrees of freedom, especially including all the angles, are necessary to study this reaction in the future.