Volume 125, Issue 20, 28 November 2006
 COMMUNICATIONS


Stability and structure of oligomers and polymers made of xenon and hydrocarbons: Theoretical predictions
View Description Hide DescriptionCalculations at B3LYP level predict the existence of three carbon chain oligomers containing branches: , , and . The geometries and NBO charges of the groups in the species are similar to those of the experimental known molecule, and are insensitive to the length of the carbon chain. The structures of the xenon oligomers are very similar to their hydrocarbon precursors. The energetics for is calculated to assess the stability of these polymers. Similar to , is kinetically stable and protected by a high barrier of against dissociation to , and is energetically more stable by than the products, which strongly supports the existence of the molecule. Extrapolation of the results for the oligomers suggests the existence of an extended polymer. A strategy for preparation is proposed.

Manyelectron selfinteraction error in approximate density functionals
View Description Hide DescriptionOne of the most important challenges in density functional theory(DFT) is the proper description of fractional charge systems relating to the selfinteraction error (SIE). Traditionally, the SIE has been formulated as a oneelectron problem, which has been addressed in several recent functionals. However, these recent oneelectron SIEfree functionals, while greatly improving the description of thermochemistry and reaction barriers in general, still exhibit many of the difficulties associated with SIE. Thus we emphasize the need to surpass this limit and shed light on the manyelectron SIE. After identifying the sufficient condition for functionals to be free from SIE, we focus on the symptoms and investigate the performance of most popular functionals. We show that these functionals suffer from manyelectron SIE. Finally, we give a SIE classification of density functionals.

Bursts in singlefile motion mediated conduction
View Description Hide DescriptionWe present a cellular automaton (CA) model of particles in a singlefile motion with free particle exchange at the boundaries of a onedimensional channel connected to two infinite reservoirs in order to study the selftransmission of particles with excluded mutual passage. The parallel, local and homogeneous rule sets of the CA algorithm consider two different interactions of varying strength between particles, without any specific particlechannel interaction. CA model results suggest that one hallmark of singlefile motion is the conduction bursts at a particular time scale, which have thus far only been discovered for hydrogen bond networked water translocation. The cumulative transport probabilities of particles through singlefile channels of different length follow a single profile, which can be obtained through proper scaling of time. The universal features of our results suggest new experiments in singlefile channel with fluids other than water.

Molecular orientation and alignment of rubbed poly(vinyl cinnamate) surfaces
View Description Hide DescriptionWe observed that weakly and strongly rubbed polyvinylcinnamate surfaces align liquid crystalfilms perpendicular and parallel to the rubbing direction, respectively. Surfacespecific sumfrequency vibrational spectroscopy was used to probe molecular orientations and alignments of the rubbed surfaces and provide a molecularlevel understanding of the observation.
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 ARTICLES

 Theoretical Methods and Algorithms

Markovian approximation in a coarsegrained description of atomic systems
View Description Hide DescriptionThe Markovian assumption stating that memory effects can be neglected is a crucial assumption in the theory of coarsegraining. We investigate the coarsegraining of a onedimensional chain of oscillators where the atoms are grouped into clusters or blobs. When the interaction between oscillators is through Hookean springs, the cluster dynamics is nonMarkovian, as has been recently noted by Cubero and Yaliraki [J. Chem. Phys.122, 03418 (2005)]. When the oscillators interact through a nonlinear potential of the LennardJones type, the dynamics turns out to be Markovian. The different behavior in both types of interactions is attributed to the persistence of sound waves in the harmonic case, which are strongly suppressed in the nonlinear case.

A graphtheoretic method for detecting potential Turing bifurcations
View Description Hide DescriptionThe conditions for diffusiondriven (Turing) instabilities in systems with two reactive species are well known. General methods for detecting potential Turing bifurcations in larger reaction schemes are, on the other hand, not well developed. We prove a theorem for a graphtheoretic condition originally given by Volpert and Ivanova [Mathematical Modeling (Nauka, Moscow, 1987) (in Russian), p. 57] for Turing instabilities in a massaction reactiondiffusion system involving substances. The method is based on the representation of a reaction mechanism as a bipartite graph with two types of nodes representing chemical species and reactions, respectively. The condition for diffusiondriven instability is related to the existence of a structure in the graph known as a critical fragment. The technique is illustrated using a substrateinhibited bifunctional enzyme mechanism which involves seven chemical species.

Atomic contributions to bond dissociation energies in aliphatic hydrocarbons
View Description Hide DescriptionThis paper explores the atomic contributions to the electronic vibrationless bonddissociationenthalpy (BDE) at of the central C–C bond in straightchain alkanes and transalkenes with an even number of carbon atoms, where , 4, 6, 8. This is achieved using the partitioning of the total molecular energy according to the quantum theory of atoms in molecules by comparing the atomic energies in the intact molecule and its dissociation products. The study is conducted at the level of theory. It is found that the bulk of the electronic energy necessary to sever a single C–C bond is not supplied by these two carbon atoms (the carbons) but instead by the atoms directly bonded to them. Thus, the burden of the electronic part of the BDE is primarily carried by the two hydrogens attached to each of the carbons and by the carbons. The effect drops off rapidly with distance along the hydrocarbon chain. The situation is more complex in the case of the double bond in alkenes, since here the burden is shared between the carbons as well as the atoms directly bonded to them, namely, again the hydrogens and the carbons. These observations may lead to a better understanding of the bonddissociation process and should be taken into account when locally dense basis sets are introduced to improve the accuracy of BDE calculations.

Reduction and solution of the chemical master equation using time scale separation and finite state projection
View Description Hide DescriptionThe dynamics of chemical reactionnetworks often takes place on widely differing time scales—from the order of nanoseconds to the order of several days. This is particularly true for gene regulatory networks, which are modeled by chemical kinetics. Multiple time scales in mathematical models often lead to serious computational difficulties, such as numerical stiffness in the case of differential equations or excessively redundant Monte Carlo simulations in the case of stochastic processes. We present a model reduction method for study of stochastic chemical kinetic systems that takes advantage of multiple time scales. The method applies to finite projections of the chemical master equation and allows for effective time scale separation of the system dynamics. We implement this method in a novel numerical algorithm that exploits the time scale separation to achieve model order reductions while enabling error checking and control. We illustrate the efficiency of our method in several examples motivated by recent developments in gene regulatory networks.

Addition by subtraction in coupledcluster theory: A reconsideration of the CC and CI interface and the hierarchy
View Description Hide DescriptionThe hierarchy of coupledcluster approximations, where guarantees exactness for electrons and all products of electrons are derived and applied to several illustrative problems. The condition of exactness for defines , with and being exact for three and four electrons. To achieve this, the minimum number of diagrams is evaluated, which is less than in the corresponding CC model. For all practical purposes, is also the proper definition of a sizeextensive CI. 2CC is also an orbitally invariant coupled electron pair approximation. The numerical results of are close to those for the full CC variant, and in some cases are closer to the full CI reference result. As 2CC is exact for separated electron pairs, it is the natural zerothorder approximation for the correlation problem in molecules with other effects introduced as these units start to interact. The hierarchy of approximations has all the attractive features of CC including its size extensivity, orbital invariance, and orbital insensitivity, but in a conceptually appealing form suited to bond breaking, while being computationally less demanding. Excited states from the equation of motion (EOM2CC) are also reported, which show results frequently approaching those of EOMCCSDT.

Secondorder MøllerPlesset perturbation energy obtained from divideandconquer HartreeFock density matrix
View Description Hide DescriptionThe density matrix (DM) obtained from Yang’s [Phys. Rev. Lett.66, 1438 (1991)] divideandconquer (DC) HartreeFock (HF) calculation is applied to the explicit secondorder MøllerPlesset perturbation (MP2) energy functional of the HF DM, which was firstly mentioned by Ayala and Scuseria [J. Chem. Phys.110, 3660 (1999)] and was improved by Surján [Chem. Phys. Lett.406, 318 (2005)] as DMLaplace MP2. This procedure, termed DCDM MP2, requires the HF DM of holes, for which we propose two evaluation schemes in DC manner. Numerical studies reveal that the DCDM MP2 energy deviation from canonical MP2 is the same order of magnitude as DCHF energy deviation from conventional HF whichever type of hole DM is adopted. It is also confirmed that the central processing unit time of DCDM MP2 is less than that of DMLaplace MP2 because the DCHF DM is sparser than conventional DM.

Implementation of a symplectic multipletimestep molecular dynamics algorithm, based on the unitedresidue mesoscopic potential energy function
View Description Hide DescriptionA symplectic multipletimestep (MTS) algorithm has been developed for the unitedresidue (UNRES) force field. In this algorithm, the slowvarying forces (which contain most of the longrange interactions and are, therefore, expensive to compute) are integrated with a larger time step, termed the basic time step, and the fastvarying forces are integrated with a shorter time step, which is an integral fraction of the basic time step. Based on the split operator formalism, the equations of motion were derived. Separation of the fast and slowvarying forces leads to stable molecular dynamics with longer time steps. The algorithms were tested with the polypeptide chain and two versions of the UNRES force field: the current one in which the energy components accounting for the energetics of sidechain rotamers can lead to numerically unstable forces and a modified one in which the the present was replaced by a numerically stable expression which, at present, is parametrized only for polyalanine chains. With the modified UNRES potential, stable trajectories were obtained even when extending the basic time step to and, with the original UNRES potentials, the basic time step is . An adaptive multipletimestep (AMTS) algorithm is proposed to handle instabilities in the forces; in this method, the number of substeps in the basic time step varies depending on the change of the magnitude of the acceleration. With this algorithm, the basic time step is but the number of substeps and, consequently, the computational cost are reduced with respect to the MTS algorithm. The use of the UNRES mesoscopic energy function and the algorithms derived in this work enables one to increase the simulation time period by several orders of magnitude compared to conventional atomicresolution molecular dynamics approaches and, consequently, such an approach appears applicable to simulating proteinfolding pathways, proteinfunctionaldynamics in a real molecular environment, and dynamical molecular recognition processes.

Spatially distributed stochastic systems: Equationfree and equationassisted preconditioned computations
View Description Hide DescriptionSpatially distributed problems are often approximately modeled in terms of partial differential equations(PDEs) for appropriate coarsegrained quantities (e.g., concentrations). The derivation of accurate such PDEs starting from finer scale, atomistic models, and using suitable averaging is often a challenging task; approximatePDEs are typically obtained through mathematical closure procedures (e.g., mean field approximations). In this paper, we show how such approximate macroscopic PDEs can be exploited in constructing preconditioners to accelerate stochastic computations for spatially distributed particlebased process models. We illustrate how such preconditioning can improve the convergence of equationfree coarsegrained methods based on coarse timesteppers. Our model problem is a stochastic reactiondiffusion model capable of exhibiting Turing instabilities.

BornOppenheimer expansion at constant energy
View Description Hide DescriptionThe wellknown BornOppenheimer procedure considers molecular properties in the limit of large values of the nuclear mass (in units of electronic mass), with quantum numbers held constant. It is shown that the lowestorder correction to the molecular wave function is proportional to . Here we consider the same expansion, but with energy held constant instead of quantum numbers. We show that, if the singular coupling term near a conical intersection is removed via a quasidiabatic transformation, the lowestorder remaining correction is proportional to .

Koopmans’ theorem in the ROHF method: Canonical form for the HartreeFock Hamiltonian
View Description Hide DescriptionSince the classic work of Roothaan [Rev. Mod. Phys.32, 179 (1960)], the oneelectron energies of a ROHF method are known as ambiguous quantities having no physical meaning. Together with this, it is often assumed in presentday computational studies that Koopmans’ theorem is valid in a ROHF method. In this work we analyze the specific dependence of orbital energies on the choice of the basic equations in a ROHF method which are the Euler equations and different forms of the generalized HartreeFock equation. We first prove that the oneelectron openshellenergies derived by the Euler equations can be related to the respective ionization potentials via the modified Koopmans’ formula where is an occupation number. As compared to this, neither the closedshell orbital energies nor the virtual ones derived by the Euler equations can be related to the respective ionization potentials and electron affinities via Koopmans’ theorem. Based on this analysis, we derive the new (canonical) form for the Hamiltonian of the HartreeFock equation, the eigenvalues of which obey Koopmans’ theorem for the whole energy spectrum. A discussion of new orbital energies is presented on the examples of a free N atom and an endohedral . The vertical ionization potentials and electron affinities estimated via Koopmans’ theorem are compared with the respective observed data and, for completeness, with the respective estimates derived via a method. The agreement between observed data and their estimates via Koopmans’ theorem is qualitative and, in general, appears to possess the same accuracy level as in the closedshell SCF.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Dissociative electron attachment to gas phase valine: A combined experimental and theoretical study
View Description Hide DescriptionUsing a crossed electron/molecule beam technique the dissociative electron attachment (DEA) to gas phase valine, , is studied by means of mass spectrometric detection of the product anions. Additionally, ab initio calculations of the structures and energies of the anions and neutral fragments have been carried out at G2MP2 and B3LYP levels. Valine and the previously studied aliphatic amino acids glycine and alanine exhibit several common features due to the fact that at low electron energies the formation of the precursor ion can be characterized by occupation of the orbital of the carboxyl group. The dominant negative ion is observed at electron energies of . This ion is the dominant reaction product at electron energies below . Additional fragment ions with , 72, 56, 45, 26, and 17 are observed both through the low lying and through higher lying resonances at about 5.5 and , which are characterized as core excited resonances. According to the threshold energies calculated here, rearrangements play a significant role in the formation of DEA fragments observed from valine at subexcitation energies.

The lowest excited state of the waterhydroxyl complex
View Description Hide DescriptionVertical and adiabatic excitation energies of the lowest excited state in the waterhydroxyl complex have been determined using coupled cluster, multireference configuration interaction, multireference perturbation theory, and densityfunctional methods. A significant redshift of about in the vertical excitation energy of the complex compared to that of the hydroxyl radical monomer is found with the coupled cluster calculations validating previous results. Electronic excitation leads to a structure with nearequal sharing of the hydroxyl hydrogen by both oxygen atoms and a concomitantly large redshift of the adiabatic excitation energy of approximately relative to the vertical excitation energy. The combination of redshifts ensures that the electronic transition in the complex lies well outside the equivalent excitation in the hydroxyl radical monomer. The complex is approximately five times more strongly bound in the excited state than in the ground state.

Combined experimentaltheoretical study of the lower excited singlet states of paravinyl phenol, an analog of the paracoumaric acid chromophore
View Description Hide DescriptionThe lowlying excited singlet states of paravinyl phenol (pVP) are investigated experimentally and theoretically paying attention to their similarity to excited states of paracoumaric acid, the chromophore of the photoactive yellow protein (PYP). Resonance enhanced multiphoton ionization and laser induced fluorescence spectroscopic techniques are employed to obtain supersonically cooled, vibrationally resolved excitation and emission spectra related to the lowest excited state of pVP. Comprehensive analyses of the spectral structures are carried out by means of the equationofmotion coupled cluster singles and doubles and time dependent density functional theory methods in combination with the linear vibronic coupling model and FranckCondon calculations. The assignments of the spectral patterns are given, mostly in terms of excitations of totally symmetric modes. Weak activity of the nontotallysymmetric modes indicates low probability of photochemical processes in the FranckCondon region of the state. The second and third excited states of pVP are characterized with regard to their electronic structure, properties, and effects of geometry relaxations. The lengthening of the double bond relevant to the transcis isomerization of the PYP chromophore is found for the state. A possibility of photochemical processes and strong vibronic interactions in this state can be expected. The theoretical results for the state predict that dissociation with respect to the O–H bond is possible.

Electron affinity of
View Description Hide DescriptionVariationally optimized exponentially correlated Gaussian functions are employed to obtain nonrelativistic wave functions of the lithium atom and its negative ion. The energy levels are computed by means of the expansion in powers of the finestructure constant . The first term of this expansion corresponds to the nonrelativistic energy. The higher order terms represent the relativistic and radiative corrections and are determined by some effective Hamiltonians. Highly accurate expectation values of singular operators entering these Hamiltonians are computed using a set of expectation value identities. The resulting electron affinity of lithium atom agrees very well with of the latest measurements.

Ionization and double ionization of small water clusters
View Description Hide DescriptionThe valence ionization and double ionizationspectra of the water molecule, of the water dimer, and the cyclic waterclusters and are calculated by ab initioGreen’s function methods and discussed in some detail. Particular attention is paid to the analysis of the development of the spectra with increasing cluster size. Electronic decay following inner valence ionization is addressed and a crude estimate for the kinetic energyspectrum of the secondary electrons is given for the clusters.

A rigorous fulldimensional quantum dynamics calculation of the vibrational energies of
View Description Hide DescriptionThe vibrational energy levels of the anion have been calculated using a rigorous quantum dynamics method based on an accurate ab initiopotential energy surface. The eigenvalue problem is solved using the twolayer Lanczos iterative diagonalization algorithm in a mixed grid/nondirect product basis set, where the system Hamiltonian is expressed in a set of orthogonal polyspherical coordinates. The lowest 312 vibrational energy levels in each inversion symmetry, together with a comparison of fundamental frequencies with previous quantum dynamics calculations, are reported. Finally, a statistical analysis of nearest level spacing distribution is carried out, revealing a strongly chaotic nature.