Volume 128, Issue 10, 14 March 2008
 COMMUNICATIONS


Electrophoretic size separation of particles in a periodically constricted microchannel
View Description Hide DescriptionThe size separation of Brownian particles with the same free mobility in an electrophoretic microchannel with alternating thick regions and narrow constrictions is studied theoretically. The electrophoreticmobility is field dependent and generally increases with field strength. In weak fields, Brownian diffusion dominates and the migration is controlled by the entrance effect. Therefore, smaller particles migrate faster than larger ones. In strong fields, however, the particle tends to follow electric field lines. Smaller particles are susceptible to Brownian motion and thus influenced by the nonuniform electric field in the well significantly. As a result, larger particles possess higher mobilities. Our simulation results agree with the experimental observations and provide guidance for efficient nanofluidic separation.

NMR chemical shifts of molecules encapsulated in single walled carbon nanotubes
View Description Hide DescriptionWe present density functional theory calculations of the nuclear magnetic resonance spectroscopy of molecules encapsulated within single walled carbon nanotubes.Ring currents in the nanotube induce shifts in the chemical shift of the nuclei comprising the encapsulated molecule. These changes in the chemical shifts are shown to have characteristic dependence on the chirality of the surrounding nanotubes.
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 ARTICLES

 Theoretical Methods and Algorithms

A fully relativistic method for calculation of nuclear magnetic shielding tensors with a restricted magnetically balanced basis in the framework of the matrix Dirac–Kohn–Sham equation^{a)}
View Description Hide DescriptionA new relativistic fourcomponent density functional approach for calculations of NMR shielding tensors has been developed and implemented. It is founded on the matrix formulation of the Dirac–Kohn–Sham (DKS) method. Initially, unperturbed equations are solved with the use of a restricted kinetically balanced basis set for the small component. The secondorder coupled perturbed DKS method is then based on the use of restricted magnetically balanced basis sets for the small component. Benchmark relativistic calculations have been carried out for the and heavyatom nuclear shielding tensors of the series , where spinorbit effects are known to be very pronounced. The restricted magnetically balanced basis set allows us to avoid additional approximations and/or strong basis set dependence which arises in some related approaches. The method provides an attractive alternative to existing approximate twocomponent methods with transformed Hamiltonians for relativistic calculations of chemical shifts and spinspin coupling constants of heavyatom systems. In particular, no picturechange effects arise in property calculations.

Finding reaction paths using the potential energy as reaction coordinate
View Description Hide DescriptionThe intrinsic reaction coordinate curve (IRC), normally proposed as a representation of a reaction path, is parametrized as a function of the potential energy rather than the arclength. This change in the parametrization of the curve implies that the values of the energy of the potential energy surface points, where the IRC curve is located, play the role of reaction coordinate. We use Carathéodory’s relation to derive in a rigorous manner the proposed parametrization of the IRC path. Since this Carathéodory’s relation is the basis of the theory of calculus of variations, then this fact permits to reformulate the IRC model from this mathematical theory. In this mathematical theory, the character of the variational solution (either maximum or minimum) is given through the Weierstrass function. As proposed by Crehuet and Bofill [J. Chem. Phys.122, 234105 (2005)], we use the minimization of the Weierstrass function, as a function of the potential energy, to locate an IRC path between two minima from an arbitrary curve on the potential energy surface, and then join these two minima. We also prove, from the analysis of the Weierstrass function, the mathematical bases for the algorithms proposed to locate the IRC path. The proposed algorithm is applied to a set of examples. Finally, the algorithm is used to locate a discontinuous, or broken, IRC path, namely, when the path connects two first order saddle points through a valleyridged inflection point.

Pseudospectral timedependent density functional theory
View Description Hide DescriptionTimedependent density functional theory (TDDFT) is implemented within the TammDancoff approximation (TDA) using a pseudospectral approach to evaluate twoelectron repulsion integrals. The pseudospectral approximation uses a split representation with both spectral basis functions and a physical space grid to achieve a reduction in the scaling behavior of electronic structure methods. We demonstrate here that exceptionally sparse grids may be used in the excitation energy calculation, following earlier work employing the pseudospectral approximation for determining correlation energies in wavefunctionbased methods with similar conclusions. The pseudospectral TDATDDFT method is shown to be up to ten times faster than a conventional algorithm for hybrid functionals without sacrificing chemical accuracy.

Relation between exchangeonly optimized potential and Kohn–Sham methods with finite basis sets, and effect of linearly dependent products of orbital basis functions
View Description Hide DescriptionRecently, Staroverov, Scuseria, and Davidson [J. Chem. Phys.124, 141103 (2006)] presented examples of exchangeonly optimized effective potential (xOEP) calculations that yield exactly the Hartree–Fock (HF) total energy. Here, building on their work, arguments showing under which conditions xOEP methods, with finite basis sets, do or do not yield the HF ground stateenergy but a higher one, are given. While the orbital products of a complete basis are linearly dependent, the HF ground stateenergy can only be obtained via a finite basis set xOEP scheme in the case that all products of occupied and unoccupied orbitals emerging from the employed orbital basis set are linearly independent of each other. Further, exchange potentials leading to the HF ground stateenergy likely exhibit unphysical oscillations and do not represent a Kohn–Sham (KS) exchange potential as a functional derivative of the exchange energy. These findings appear to explain the seemingly paradoxical results of Staroverov et al. that certain finite basis set xOEP calculations lead to the HF ground stateenergy despite the fact that within a real space (or complete basis) representation, the xOEP ground stateenergy is always higher than the HF energy. Moreover, independent of whether or not the occupied and unoccupied orbital products are linearly dependent, it is shown that finite basis set xOEP methods only represent exact exchangeonly (EXX) KS methods, i.e., proper densityfunctional methods, if the orbital basis set and the auxiliary basis set representing the exchange potential are balanced to each other, i.e., if the orbital basis is comprehensive enough for a given auxiliary basis. Otherwise xOEP methods do not represent EXX KS methods and yield unphysical exchange potentials. The question whether a xOEP method properly represents a KS method with an exchange potential that is a functional derivative of the exchange energy is related to the problem of the definition of local multiplicative operators in finite basis representations. Plane wave calculations for bulk silicon illustrate the findings of this work.

Recursive inverse factorization
View Description Hide DescriptionA recursive algorithm for the inverse factorization of Hermitian positive definite matrices is proposed. The inverse factorization is based on iterative refinement [A.M.N. Niklasson, Phys. Rev. B70, 193102 (2004)] combined with a recursive decomposition of . As the computational kernel is matrixmatrix multiplication, the algorithm can be parallelized and the computational effort increases linearly with system size for systems with sufficiently sparse matrices. Recent advances in networktheory are used to find appropriate recursive decompositions. We show that optimization of the socalled network modularity results in an improved partitioning compared to other approaches. In particular, when the recursive inverse factorization is applied to overlap matrices of irregularly structured threedimensional molecules.

HartreeFock exchange computed using the atomic resolution of the identity approximation
View Description Hide DescriptionIn this work, we apply the atomic resolution of the identity (ARI) fitting approximation to the computation of HartreeFock exchange. The ARI approximation is a local modification of the RI approximation that produces an energy which is differentiable with respect to nuclear motion, unlike other local applications of RI. We justify empirically the use of locality and present timing comparisons of ARI, RI, and exact computation for one, two, and threedimensional carbon systems. ARI is found to reduce significantly the cost of RI for large systems, while retaining accuracy.

Application of geometric algebra for the description of polymer conformations
View Description Hide DescriptionIn this paper a Clifford algebrabased method is applied to calculate polymer chain conformations. The approach enables the calculation of the position of an atom in space with the knowledge of the bond length , valence angle , and rotation angle of each of the preceding bonds in the chain. Hence, the set of geometrical parameters yields all the position coordinates of the main chain atoms. Moreover, the method allows the calculation of side chain conformations and the computation of rotations of chain segments. With these features it is, in principle, possible to generate conformations of any type of chemical structure. This method is proposed as an alternative for the classical approach by matrix algebra. It is more straightforward and its final symbolic representation considerably simpler than that of matrix algebra. Approaches for realistic modeling by means of incorporation of energetic considerations can be combined with it. This article, however, is entirely focused at showing the suitable mathematical framework on which further developments and applications can be built.

Multireference Brillouin–Wigner coupled cluster method with singles, doubles, and triples: Efficient implementation and comparison with approximate approaches
View Description Hide DescriptionWe have developed an efficient implementation of the multireference Brillouin–Wigner coupled cluster method with full iterative treatment of connected singles, doubles, and triples. Its computational costs are too high for applications to larger molecules; however, it can be used as a useful tool for benchmarking approximate methods. Performance of the method has been tested on the ground and lowlying excited states of the oxygen molecule and on the singlettriplet gap in methylene; the results are in good agreement with experimental data.

Analytical solution for optimal squeezing of wave packet of a trapped quantum particle
View Description Hide DescriptionOptimal control problem with a goal to squeeze wave packet of a trapped quantum particle is considered and solved analytically using adiabatic approximation. The analytical solution that drives the particle into a highly localized final state is presented for a case of an infinite well trapping potential. The presented solution may be applied to increase the resolution of atom lithography.

The KohnSham kinetic energy density as indicator of the electron localization: Atomic shell structure
View Description Hide DescriptionIn this report, it is shown that the KohnSham (KS) kinetic energy density (KED) contains the average local electrostatic potential (ALEP) and the average local ionizationenergy (ALIE); the shell structure in atomic systems is presented as one application of the KSKED. By writing the KSKED from the KS equations, this quantity was divided in three contributions: orbital, Coulomb, and exchange correlation. By studying several closed and open shell atoms, the shell structure was established by the maxima presented by the Coulomb contribution and the minima in the orbital contribution of the KSKED. The exchangecorrelation contribution to the KSKED does not show maxima or minima, but this quantity shows bumps where the division between shells is expected. The results obtained in this work were compared with other shell structure indicators such as the electron localization function, the ALEP, the ALIE, and the radial distribution function. The most important result in this work is related to the fact that even when the ALEP and the ALIE functions were built with different arguments to each other, they are contained in the KSKED. In this way, the KSKED shows its importance to reveal the electron localization in atomic systems.

Adaptive minimum action method for the study of rare events
View Description Hide DescriptionAn adaptive minimum action method is proposed for computing the most probable transition paths between stable equilibria in metastable systems that do not necessarily have an underlying energy function, by minimizing the action functional associated with such transition paths. This new algorithm uses the moving mesh strategy to adaptively adjust the grid points over the time interval of transition. Numerical examples are presented to demonstrate the efficiency of the adaptive minimum action method.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Zero kinetic energy photoelectron spectroscopy of tetracene using laser desorption for vaporization
View Description Hide DescriptionFar infrared (FIR) spectroscopy of polycyclic aromatic hydrocarbons is of particular interest to astrophysics since vibrational modes in this range are representative of the molecular size and shape. This information is hence important for identification of chemical compositions and for modeling of the IR spectrum observed in the outer space. In this work, we report neutral and cation FIR spectroscopy of tetracene vaporized from a laser desorption source. Results from twocolor resonantly enhanced multiphoton ionization and twocolor zero kinetic energy photoelectron spectroscopy will be presented. Several skeletal vibrational modes of the first electronically excited state of the neutral species and those of the cation are assigned, with the aid of ab initio and density functional calculations. The adiabatic ionization potential is determined to be . Interestingly, all observed vibrational modes can be rationalized based on a simple Hückle calculation, i.e., by observing the addition or elimination of nodal planes due to electronic excitation and/or ionization. Limited by the Franck–Condon principle and the rigidity of the molecular frame of tetracene, only IR forbidden modes are observed in this work.

Electronic spectrum of TaO and its hyperfine structure
View Description Hide DescriptionThe band at and the band at of tantalum oxide (TaO) were recorded by laser excitation spectroscopy using a hollow cathode sputtering source to generate the molecules. The hyperfine structure arising from the nucleus was measured at subDoppler resolution using the technique of intermodulated fluorescence spectroscopy. The hyperfine structure was assigned and fitted in order to derive accurate values for the magnetic dipole and electric quadrupole interactions. The magnetic hyperfine constant for the ground electronic state was also calculated using the density functional theory as , in good agreement with the experimental value of . This result suggests that the ground state of TaO is well described by a pure electronic configuration, where the unpaired electron is located in a Ta orbital.

Electron attachment to and
View Description Hide DescriptionAn experimental study has been made of thermal electron attachment to the transitionmetal trifluorophosphine complexes and using a flowingafterglow Langmuirprobe apparatus. Both complexes are efficient at electron attachment, although the rate constants are somewhat less than collisional. The rate constant for electron attachment to is at room temperature, about a factor of 2 less than collisional. The activation energy is for the attachment reaction. The rate constant for electron attachment to is at room temperature, and the activation energy is . For both complexes, a ligand is lost on electron attachment, and only the ion is observed in the negativeion mass spectrum. Density functional calculations were carried out on and various fragments in order to describe the thermochemistry of the attachment reaction.

Fragmentation of metastable ions with microsecond lifetimes in competition with autodetachment
View Description Hide DescriptionFragmentation of metastable ions formed in low energy electron attachment to has been investigated. The dissociation reaction has been observed and after electron attachment in a timeofflight and a double focusing two sector field mass spectrometer, respectively. Metastable dissociation is observed with maximum intensity at between the peak at zero and the peak at . The kinetic energy released in dissociation is low, with a most probable value of . The lifetime of decreases as the electron energy increases, but it is not possible to fit this decrease with statistical Rice–Ramsperger–Kassel/quasiequilibrium theory. Metastable dissociation of appears to compete with autodetachment of the electron at all electron energies.

Excited states of the water molecule: Analysis of the valence and Rydberg character
View Description Hide DescriptionThe excited states of the water molecule have been analyzed by using the extended quantumchemical multistate CASPT2 method, namely, MSCASPT2, in conjunction with large oneelectron basis sets of atomic natural orbital type. The study includes 13 singlet and triplet excited states, both valence and , , and members of the Rydberg series converging to the lowest ionization potential and the  and Rydberg members converging to the second lowlying state of the cation, . The research has been focused on the analysis of the valence or Rydberg character of the lowlying states. The computation of the state of water at different geometries indicates that it has a predominant Rydberg character at the equilibrium geometry of the molecule but it becomes progressively a valence state described mainly by the oneelectron promotion, as expected from a textbook of general chemistry, upon elongation of the O–H bonds. The described valenceRydberg mixing is established to be originated by a molecular orbital (MO) Rydbergization process, as suggested earlier by R. S. Mulliken [Acc. Chem. Res.9, 7 (1976)]. The same phenomenon occurs also for the state whereas a more complex behavior has been determined for the state, where both MO Rydbergization and configurational mixing take place. Similar conclusions have been obtained for the triplet states of the molecule.

Infrared–vacuum ultraviolet–pulsed field ionization–photoelectron study of using a highresolution infrared laser
View Description Hide DescriptionBy using a highresolution single mode infraredoptical parametric oscillator laser to prepare in single rotational levels of the (symmetric C–H stretching) vibrational state, we have obtained rovibrationally resolved infrared–vacuum ultraviolet–pulsed field ionization–photoelectron (IRVUVPFIPE) spectra of the band, where and represent the respective rotational quantum numbers of and . The IRVUVPFIPE spectra observed for and 1 are found to have nearly identical structures. The IRVUVPFIPE spectra for and (7, 0) are also consistent with the previous selected IRVUVPFIPE measurements. The analysis of these spectra indicates that the photoionization cross section of depends strongly on but not on and . This observation lends strong support for the major assumption adopted for the semiempirical simulation scheme, which has been used for the simulation of the origin bands observed in VUVPFIPE study of polyatomic molecules. Using the statetostate photoionization cross sections determined in this IRVUV study, we have obtained excellent simulation of the VUVPFIPE origin band of , yielding more precise and .

Dynamics at conical intersections: The influence of O–H stretching vibrations on the photodissociation of phenol
View Description Hide DescriptionComparing the recoil energy distributions of the fragments from onephoton dissociation of phenol with those from vibrationally mediated photodissociation shows that initial vibrational excitation strongly influences the disposal of energy into relative translation. The measurements use velocity map ion imaging to detect the Hatom fragments and determine the distribution of recoil energies.Dissociation of phenol molecules with an initially excited O–H stretching vibration produces significantly more fragments with low recoil energies than does onephoton dissociation at the same total energy. The difference appears to come from the increased probability of adiabatic dissociation in which a vibrationally excited molecule passes around the conical intersection between the dissociative state and the ground state to produce electronically excited phenoxyl radicals. The additional energy deposited in electronic excitation of the radical reduces the energy available for relative translation.