Volume 129, Issue 9, 07 September 2008
 COMMUNICATIONS


On the Crooks fluctuation theorem and the Jarzynski equality
View Description Hide DescriptionThe Jarzynski equality (JE) and the undergirding Crooks fluctuation theorem (CFT) have generated intense interest recently among researchers in physical and biological sciences. It has been held that the CFT has wider applicability than the JE. This note shows that the two are equally applicable and that their applicability is possibly limited to nearequilibrium processes, where the linear fluctuationdissipation theorem holds.

Optical absorption spectra and monomer interaction in polymers: Investigation of exciton coupling in DNA hairpins
View Description Hide DescriptionWe investigate the effect of exciton coupling on the optical absorptionspectra of polymer molecules under conditions of strong inhomogeneous broadening. It is shown that the dependence of the maximum in the rescaled absorptionspectrum on the number of monomers is determined by their resonant exciton coupling and is insensitive to inhomogeneous broadening. Thus the absorptionspectrum can be used to determine optical interactions between monomers. Using our theory and semiempirical calculations we determine exciton coupling between adjacent AT pairs in DNA to be 0.04 eV and discuss exciton localization in DNA hairpins composed of AT pairs.
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 ARTICLES

 Theoretical Methods and Algorithms

Electronic stress tensor description of chemical bonds using nonclassical bond order concept
View Description Hide DescriptionThe stress tensors are used widely for description of internal forces of matter. For some time it is also applied in quantum theory in studies of molecular properties in chemical systems. Electronic stress tensors measure effects caused by internal forces acting on electrons in molecules and particularly those between bonded atoms. Utilized here stress tensor originated bond orders express bond strengths in terms of these internal forces. The unique concept of energy density and electronic chemical potential based bond orders gives natural evaluation of interaction strength compared with classical definition, considering delocalized nature of electrons. In addition to other causes, the relation to electronic energy may be used to predict relative stabilities of geometrical isomers or even conformers.

Spectral and entropic characterizations of Wigner functions: Applications to model vibrational systems
View Description Hide DescriptionThe Wigner function for the pure quantum states is used as an integral kernel of the nonHermitian operator , to which the standard singular value decomposition (SVD) is applied. It provides a set of the squared singular values treated as probabilities of the individual phasespace processes, the latter being described by eigenfunctions of (for coordinate variables) and (for momentum variables). Such a SVD representation is employed to obviate the wellknown difficulties in the definition of the phasespace entropymeasures in terms of the Wigner function that usually allows negative values. In particular, the new measures of nonclassicality are constructed in the form that automatically satisfies additivity for systems composed of noninteracting parts. Furthermore, the emphasis is given on the geometrical interpretation of the full entropymeasure as the effective phasespace volume in the Wigner picture of quantum mechanics. The approach is exemplified by considering some generic vibrational systems. Specifically, for eigenstates of the harmonic oscillator and a superposition of coherent states, the singular value spectrum is evaluated analytically. Numerical computations are given for the nonlinear problems (the Morse and double well oscillators, and the Henon–Heiles system). We also discuss the difficulties in implementation of a similar technique for electronic problems.

Exploring the origin of the internal rotational barrier for molecules with one rotatable dihedral angle
View Description Hide DescriptionContinuing our recent endeavor, we systematically investigate in this work the origin of internal rotational barriers for small molecules using the new energy partition scheme proposed recently by one of the authors [S. B. Liu, J. Chem. Phys.126, 244103 (2007)], where the total electronic energy is decomposed into three independent components, steric, electrostatic, and fermionic quantum. Specifically, we focus in this work on six carbon, nitrogen, and oxygen containing hydrides, , , , , , and , with only one rotatable dihedral angle . The relative contributions of the different energy components to the total energy difference as a function of the internal dihedral rotation will be considered. Both optimizedgeometry (adiabatic) and fixedgeometry (vertical) differences are examined, as are the results from the conventional energy partition and natural bond orbital analysis. A wealth of strong linear relationships among the total energy difference and energy component differences for different systems have been observed but no universal relationship applicable to all systems for both cases has been discovered, indicating that even for simple systems such as these, there exists no omnipresent, unique interpretation on the nature and origin of the internal rotation barrier. Different energy components can be employed for different systems in the rationalization of the barrier height. Confirming that the two differences, adiabatic and vertical, are disparate in nature, we find that for the vertical case there is a unique linear relationship applicable to all the six molecules between the total energy difference and the sum of the kinetic and electrostaticenergy differences. For the adiabatic case, it is the total potential energy difference that has been found to correlate well with the total energy difference except for ethane whose rotation barrier is dominated by the quantum effect.

Twocomponent relativistic hybrid density functional computations of nuclear spinspin coupling tensors using Slatertype basis sets and densityfitting techniques
View Description Hide DescriptionComputations of indirect nuclear spinspin coupling constants using twocomponent relativistic density functional theory with a hybrid functional are reported. The program implementation makes use of a Slatertype orbital expansion of the molecular orbitals and the zerothorder regular approximation for the treatment of relativistic effects. Exact exchange terms in the Kohn–Sham response kernel were computed using a fitting procedure. Computations with the PBE0 hybrid functional were carried out for heavyatomligandonebond couplings in , , , three platinum complexes, the interhalogen diatomics such as ClF, ClBr, ClI, BrF, BrI, IF, and the series with , Cl, Br, I. The hybrid functional computations performed very well. In particular, for the isotropic coupling and the coupling anisotropy of , the PBE0 hybrid functional yielded considerably improved agreement with experiment.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

The geometric, optical, and magnetic properties of the endohedral stannaspherenes (, V, Cr, Mn, Fe, Co, Ni)
View Description Hide DescriptionThe geometric, optical, and magnetic properties of the clusters (, V, Cr, Mn, Fe, Co, Ni) are studied using the relativistic densityfunctional method. The geometric optimization shows that the ground states of these clusters are probably very close to the structure. Our calculations demonstrate that the optical gaps of the can be tuned from infrared to green, and the magnetic moments of them vary from to by doping d transition metal atoms into cage, suggesting that could be a new class of potential nanomaterials with tunable magnetic and optical properties.

Exploring remnants of invariants buried in a deep potential well in chemical reactions
View Description Hide DescriptionWe revisit the concept of “remnant of invariant manifolds” originally discussed by Shirts and Reinhardt in a two degrees of freedom Hénon–Heiles system [J. Chem. Phys.77, 5204 (1982)]. This is regarded as the remnants of a destroyed invariant manifold that can dominate the transport in phase space even at high energy regions where most of all tori vanish. We present a novel technique to extract such remnants of invariants from a sea of chaos in highly nonlinear coupled molecular systems in terms of the canonical perturbation theory based on Lie transforms. As an illustrative example we demonstrate in HCN isomerizationreaction that the conventional procedure based on a finite order truncation of the coordinate transformation prevent us from detecting remnants of invariants. However, our technique correctly captures the underlying remnants of invariants that shed light on the energetics of chemical reaction, that is, how the reactive mode acquires (releases) energy from (to) the other vibrational mode in order to overcome the potential barrier (to be trapped in the potential well). We also found the qualitative difference between the two potential wells, HCN and CNH, which coincides with the nearest neighbor level spacing distribution of the vibrational quantum states within the wells.

Isolating the spectra of cluster ion isomers using Ar“tag” mediated IRIR double resonance within the vibrational manifolds: Application to
View Description Hide DescriptionWe demonstrate a method for isolating the vibrational predissociationspectra of different structural isomers of massselected cluster ions based on a populationlabeling double resonance scheme. This involves a variation on the “ion dip” approach and is carried out with three stages of mass selection in order to separate the fragment ion signals arising from a fixedfrequency populationmonitoring laser and those generated by a scanned laser that removes population of species resonant in the course of the scan. We demonstrate the method on the Artagged cluster, where we identify the spectral patterns arising from two isomers. One of these structures features accommodation of the water molecule in a double Hbond arrangement, while in the other, attaches in a single ionic Hbond motif where the nominally free OH group is oriented toward the N atom of . Transitions derived from both the and constituents are observed for both isomers, allowing us to gauge the distortions suffered by both the ion and solvent molecules in the different hydration arrangements.

Potential energy surface for interactions between two hydrogen molecules
View Description Hide DescriptionNonrelativistic clampednuclei energies of interaction between two groundstate hydrogen molecules with intramolecular distances fixed at their average value in the lowest rovibrational state have been computed. The calculations applied the supermolecular coupledcluster method with single, double, and noniterative triple excitations [CCSD(T)] and very large orbital basis sets—up to augmented quintuple zeta size supplemented with bond functions. The same basis sets were used in symmetryadapted perturbation theory calculations performed mainly for larger separations to provide an independent check of the supermolecular approach. The contributions beyond CCSD(T) were computed using the full configuration interaction method and basis sets up to augmented triple zeta plus midbond size. All the calculations were followed by extrapolations to complete basis set limits. For two representative points, calculations were also performed using basis sets with the cardinal number increased by one or two. For the same two points, we have also solved the Schrödinger equation directly using fourelectron explicitly correlated Gaussian (ECG) functions. These additional calculations allowed us to estimate the uncertainty in the interaction energies used to fit the potential to be about 0.15 K or 0.3% at the minimum of the potential well. This accuracy is about an order of magnitude better than that achieved by earlier potentials for this system. For a nearminimum Tshaped configuration with the centerofmass distance , the ECG calculations give the interaction energy of , whereas the orbital calculations in the basis set used for all the points give . The computed points were fitted by an analytic fourdimensional potential function. The uncertainties in the fit relative to the ab initio energies are almost always smaller than the estimated uncertainty in the latter energies. The global minimum of the fit is for the Tshaped configuration at . The fit was applied to compute the second virial coefficient using a pathintegral Monte Carlo approach. The achieved agreement with experiment is substantially better than in any previous work.

A comparison of quantum and quasiclassical statistical models for reactions of electronically excited atoms with molecular hydrogen
View Description Hide DescriptionA detailed comparison of statistical models based on the quasiclassical trajectory (SQCT) and quantum mechanical (SQM) methods is presented in this work for the , , and insertion reactions.Reaction probabilities, integral (ICS) and differential (DCS) cross sections at different levels of product’s state resolution are shown and discussed for these reactions. The agreement is in most cases excellent and indicates that the effect of tunneling through the centrifugal barrier is negligible. However, if there exists a dynamical barrier, as in the case of the reaction, some of the SQM results can be slightly different than those calculated with the SQCT model. The rationale of the observed similarities and discrepancies can be traced back to the specific topologies of the potential energy surfaces for each of the reactions examined. The SQCT model is sensitive enough to show the relatively small inaccuracies resulting from the decoupling inherent to the centrifugal sudden approximation when used in the SQM calculations. In addition, the effect of ignoring the parity conservation is also examined. This effect is in general minor except in particular cases such as the DCS from initial rotational state , which requires, in order to reproduce the sharp forward and backward peaks, the explicit conservation of parity.

Infrared predissociation spectroscopy of cluster cations of protic molecules, , and ,
View Description Hide DescriptionInfrared predissociationspectroscopy is carried out for the structure investigation of unprotonated cluster cations of protic molecules such as ammonia and methanol, which are generated through vacuumultraviolet onephoton ionization of their jetcooled neutral clusters. The observed spectral features show that the cluster cations have the protontransferred type structures, where a pair of a protonated cation and a neutral radical, or , is formed. Theoretical calculations at the MP2 and B3LYP levels support the formation of the protontransferred type structures for the cluster cations, and indicate that they are formed by protontransfer following the photoionization of the neutral clusters.

Highly delocalized orbiting resonances
View Description Hide DescriptionThe intermolecular resonances embedded in the continuum of the vibrational manifold have been characterized. The nature of these states as longlived, strongly overlapping orbitingresonances supported by centrifugal barriers originated in rotational excitation of within the complex has been confirmed. The orbitingresonances are found to be highly delocalized in space, both in the radial and angular coordinates, giving rise to longlived, largesized complexes.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Study of secondary relaxation in disordered plastic crystals of isocyanocyclohexane, cyanocyclohexane, and 1cyanoadamantane
View Description Hide DescriptionIn the present communication, dielectric relaxation investigations on three interesting supercooled plastic crystalline substances, i.e., isocyanocyclohexane (ICNCH), cyanocyclohexane (CNCH), and 1cyanoadamantane (CNADM) are reported. All of these have the main dipole moment situated in their side group– or– . Differential scanning calorimetry(DSC) was also employed as a supporting technique. Glassy crystal were easily formed in the first two samples by slowly cooling the plastic phase, but in CNADM it was formed by rapidly quenching the room temperature plastic phase. In addition to the so called process that can reasonably be described by a Havriliak–Negami (HN) shape function, a secondary (or ) relaxation process is found in all the materials. The process in CNADM has an activation energy of about , and is present even in the corresponding ordered crystalline phase, i.e., in its monoclinic phase. On the other hand, the magnitude of in both the isomers of cyanocyclohexane, i.e., ICNCH and CNCH, is similar and is about 21.1 and , respectively. Unlike CNADM, the cyclohexane derivatives are capable of exhibiting additional intramolecular process due to chairchair conversion (i.e., in addition to the rotational motion of the side group– or– ). Therefore, the secondary process of these systems is compared to that occuring in the binary liquidglass formed by dispersing a small quantity of these dipolar liquids in nearly nonpolar orthoterphenyl (OTP). Measurements were also made in the supercooled binary mixures of other cyclohexyl derivatives like cyclohexylchloride and cyclohexylbromide with OTP which lack a flexible side group. The subrelaxation process exhibited in all these cases have almost similar activation energy as in case of pure ICNCH and CNCH. These observations together with the fact that the activation energy for this process is much below that of chairchair conversion which is about leads us to the conclusion that subrelaxation process in the binary mixtures is JG type, and perhaps relaxation process in phase I of ICNCH and CNCH is also similar. With the help of semiemperical calculations of the dipolemoments for the axial and equitorial confirmers, it is concluded that the process associated with the chairchair may not be dielectrically very active and, hence, should be relatively weaker in magnitude. The process in CNADM has an activation energy of about , and is present even in the corresponding ordered crystalline phase indicating that it may not be characteristic of the glass formation of phase I. The molecular structure of CNADM is such that it does not possess other intramolecular degrees of freedom of the type equitorial to axial (or chairchair) transformation. Our experimental finding that JG relaxation for CNADM dispersed in glassy OTP matrix is about , indicating that the well resolved sub process in CNADM is due to the small side group, i.e., and JG relaxation in phase I of CNADM is perhaps not resolvable or too small to be detected.

Molecular representation of molar domain (volume), evolution equations, and linear constitutive relations for volume transport
View Description Hide DescriptionIn the traditional theories of irreversible thermodynamics and fluid mechanics, the specific volume and molar volume have been interchangeably used for pure fluids, but in this work we show that they should be distinguished from each other and given distinctive statistical mechanical representations. In this paper, we present a general formula for the statistical mechanical representation of molecular domain (volume or space) by using the Voronoi volume and its mean value that may be regarded as molar domain (volume) and also the statistical mechanical representation of volume flux. By using their statistical mechanical formulas, the evolution equations of volume transport are derived from the generalized Boltzmann equation of fluids. Approximate solutions of the evolution equations of volume transport provides kinetic theory formulas for the molecular domain, the constitutive equations for molar domain (volume) and volume flux, and the dissipation of energy associated with volume transport. Together with the constitutive equation for the mean velocity of the fluid obtained in a previous paper, the evolution equations for volume transport not only shed a fresh light on, and insight into, irreversible phenomena in fluids but also can be applied to study fluid flow problems in a manner hitherto unavailable in fluid dynamics and irreversible thermodynamics. Their roles in the generalized hydrodynamics will be considered in the sequel.

Force autocorrelation function in linear response theory and the origin of friction
View Description Hide DescriptionVanishing of the equilibrium fluctuation expression for the friction coefficient of a massive particle in a finitevolumeliquid has been well documented and discussed in literature. This paper investigates the decay of the friction force in the corresponding nonequilibrium situation, when the massive particle moves through a finite volume at a constant velocity. The friction force ultimately vanishes (with the decay form as predicted by the equilibrium integral) because of the finite mass of the rest of the system, which allows it to be dragged by the moving particle. However, it is sufficient to have two infinite masses moving relative to each other in a finite liquid volume for the friction force to be finite at all times.

Femtosecond midinfrared study of the photoinduced Wolff rearrangement of diazonaphthoquinone
View Description Hide DescriptionTimeresolved vibrational femtosecond spectroscopy is employed to investigate the photoinduced Wolff rearrangement reaction of diazonaphthoquinone (DNQ) dissolved in different solvents (methanol and water). DNQ is an important compound in commercial Novolak photoresists. Upon photoexcitation the ketene intermediate appears within 300 fs, indicating that the ketene is formed in a very fast concerted process involving loss and rearrangement. The strong shift of the vibrational band, assigned to the ketene by density functional theory calculations and experimental infrared spectra, toward higher wavenumbers is attributed to vibrational cooling. The relaxation time depends on the solvent (10 ps in methanol and 3 ps in water). However, the spectroscopic data show that the indirect ketene formation via a carbene intermediate might also be involved in the reaction process contributing to the ketene formation on the 10 ps time scale.

Columnar mesophases of hexabenzocoronene derivatives. I. Phase transitions
View Description Hide DescriptionUsing atomistic molecular dynamic simulations we study the transitions between solid herringbone and liquid crystalline hexagonal mesophases of discotic liquid crystals formed by hexabenzocoronene derivatives. Combining a united atom representation for the side chains with the fully atomistic description of the core, we study the effect of side chain substitution on the transition temperatures as well as molecular ordering in the mesophases. Our study rationalizes the differences in charge carriermobilities in the herringbone and hexagonal mesophases, which is predominantly due to the better rotational register of the neighboring molecules.

Columnar mesophases of hexabenzocoronene derivatives. II. Charge carrier mobility
View Description Hide DescriptionCombining atomistic molecular dynamic simulations, Marcus–Hush theory description of chargetransport rates, and master equation description of charge dynamics, we correlate the temperaturedriven change of the mesophase structure with the change of charge carriermobilities in columnar phases of hexabenzocoronene derivatives. The time dependence of fluctuations in transfer integrals shows that static disorder is predominant in determining chargetransport characteristics. Both site energies and transfer integrals are distributed because of disorder in the molecular arrangement. It is shown that the contributions to the site energies from polarization and electrostatic effects are of opposite sign for positive charges. We look at three mesophases of hexabenzocoronene: herringbone, discotic, and columnar disordered. All results are compared to time resolved microwave conductivity data and show excellent agreement with no fitting parameters.

Femtosecond spectral interferometry of optical activity: Theory
View Description Hide DescriptionOptical activities such as circular dichroism (CD) and optical rotatory dispersion (ORD) are manifested by almost all natural products. However, the CD is an extremely weak effect so that timeresolved CD spectroscopy has been found to be experimentally difficult and even impossible for vibrational CD with current technology. Here, we show that the weaksignal and nonzero background problems can be overcome by heterodyned spectralinterferometric detection of the phase and amplitude of optical activity freeinductiondecay (OA FID) field. A detailed theoretical description and a crosspolarization scheme for selectively measuring the OA FID are presented and discussed. It is shown that the parallel and perpendicular electric fields when the solution sample contains chiral molecules are coupled to each other. Therefore, simultaneous spectral interferometric measurements of the parallel and perpendicular FID fields can provide the complex susceptibility, which is associated with the circular dichroism and optical rotatory dispersion as its imaginary and real parts, respectively. On the basis of the theoretical results, to examine its experimental possibility, we present numerical simulations for a model system. We anticipate the method discussed here to be a valuable tool for detecting electronic or vibrational optical activity in femtosecond time scale.