Incompletely symmetric non-bloch electron states in perfect cubic crystals. III. Density of dynamical observables in the FCC lattice

The operators of dynamical observables of the crystal electron (velocity vector components. reciprocal mass tensor components and their functions) commute with the energy operator; hence, the averages of these observables can be adequately approximated by the eigenfunctions for the energy operator. Calculations of the averages were based on the LCAO eigenfunctions classified according to incompletely symmetric irreducible representations of the point group of the cubic crystal, and a similar classification was made for the averages.     

Bifurcations on potential energy surfaces of organic reactions

A single transition state may lead to multiple intermediates or products if there is a post-transition-state reaction pathway bifurcation. These bifurcations arise when there are sequential transition states with no intervening energy minimum. For such systems, the shape of the potential energy surface and dynamic effects, rather than transition-state energetics, control selectivity. This Minireview covers recent investigations of organic reactions exhibiting reaction pathway bifurcations. Such phenomena are surprisingly general and affect experimental observables such as kinetic isotope effects and product distributions.     

Photodesorption of diatomic molecules from surfaces: A theoretical approach based on first principles

Photodesorption of small molecules from surfaces is one of the most fundamental processes in surface photochemistry. Despite its apparent simplicity, a microscopic understanding beyond a qualitative picture still poses a true challenge for theory. While the dynamics of nuclear motion can be treated on various levels of sophistication, all approaches suffer from the lack of sufficiently accurate potential energy surfaces, in particular for electronically excited states involved in the desorption scenario.In the last decade, a systematic and accurate methodology has been developed which allows a reliable calculation of accurate ground and excited state potential energy surfaces (PES) for different adsorbate–substrate systems. These potential energy surfaces serve as a prerequisite for subsequent quantum dynamical wave packet calculations, which allow for a direct simulation of experimentally observable quantities such as quantum state resolved velocity distributions.In the first part of this review, we will focus on scalar properties of desorbing diatomic molecules from insulating surfaces, where we also present a recently developed strategy of obtaining accurate potential energy surfaces using quantum chemical approaches. In general, diatomic molecules on large band gap materials such as oxide surfaces are studied which allows the use of sufficiently large cluster models and accurate ab initio methods beyond density functional theory (DFT). In the second part, we will focus on the vectorial aspects of the dynamics of nuclear motion and present simulations of experimentally accessible observables such as velocity distributions, Doppler profiles and alignment parameters. For each system, the microscopic mechanism of photodesorption is elucidated. We will demonstrate that the driving force of surface photochemistry is strongly dependent on details of the electronic structure of the adsorbate–substrate systems. This implies that great caution is advisable if experimental results are interpreted using empirical or semi-empirical models.     

Interaction between a rodlike inclusion and a supported bilayer membrane

The interactions between a rodlike inclusion and a supported copolymer bilayer membrane are investigated by using the self-consistent field theory. For different system parameters, physical observables, such as the interaction free energy, entropy, and translocation energy barrier, are obtained. Particular emphasis is put on the closely energetic and entropic analyses of the interaction. It shows that the interfacial energy provides a qualitative trend and dominates the basic shape of the interaction free energy curve; the combination of chemical potential energy and total entropy contribution is responsible for the translocation energy barrier and the weak attraction in the vicinity of upper monolayer surface. We also specify the nature, height, and shape of the energy barrier to translocation. Particularly, the height is roughly proportional to the rod radius.     

Quantized Hamilton Dynamics

The paper describes the quantized Hamilton dynamics (QHD) approach that extends classical Hamiltonian dynamics and captures quantum effects, such as zero point energy, tunneling, decoherence, branching, and state-specific dynamics. The approximations are made by closures of the hierarchy of Heisenberg equations for quantum observables with the higher order observables decomposed into products of the lower order ones. The technique is applied to the vibrational energy exchange in a water molecule, the tunneling escape from a metastable state, the double-slit interference, the population transfer, dephasing and vibrational coherence transfer in a two-level system coupled to a phonon, and the scattering of a light particle off a surface phonon, where QHD is coupled to quantum mechanics in the Schrödinger representation. Generation of thermal ensembles in the extended space of QHD variables is discussed. QHD reduces to classical mechanics at the first order, closely resembles classical mechanics at the higher orders, and requires little computational effort, providing an efficient tool for treatment of the quantum effects in large systems.     

Free energy partitioning analysis of the driving forces that determine ion density profiles near the water liquid-vapor interface

Free energy partitioning analysis is employed to explore the driving forces for ions interacting with the water liquid-vapor interface using recently optimized point charge models for the ions and SPC/E water. The Na(+) and I(-) ions are examined as an example kosmotrope/chaotrope pair. The absolute hydration free energy is partitioned into cavity formation, attractive van der Waals, local electrostatic, and far-field electrostatic contributions. We first compute the bulk hydration free energy of the ions, followed by the free energy to insert the ions at the center of a water slab. Shifts of the ion free energies occur in the slab geometry consistent with the SPC/E surface potential of the water liquid-vapor interface. Then the free energy profiles are examined for ion passage from the slab center to the dividing surface. The profiles show that, for the large chaotropic I(-) ion, the relatively flat total free energy profile results from the near cancellation of several large contributions. The far-field electrostatic part of the free energy, largely due to the water liquid-vapor interface potential, has an important effect on ion distributions near the surface in the classical model. We conclude, however, that the individual forms of the local and far-field electrostatic contributions are expected to be model dependent when comparing classical and quantum results. The substantial attractive cavity free energy contribution for the larger I(-) ion suggests that there is a hydrophobic component important for chaotropic ion interactions with the interface.     

Imaging the Reaction Dynamics of O(3P)+CH4→OH+CH3

The title reaction was studied in a crossed‐beam experiment, in which the ground‐state methyl products were probed using a time‐sliced velocity‐imaging technique. By taking images over the energy range of chemical significance, from the threshold to about 15 kcal mol^?1, the reactive excitation function as well as the dependences of product angular distributions and of the energy disposal on initial collision energies were determined. All experimental data are consistent with the picture that the ground‐state reaction of O(³P)+CH₄ proceeds via a direct abstraction rebound‐type mechanism with a narrow cone of acceptance. Deeper insights into the underlying mechanism and the key feature of the potential‐energy surface are elucidated by comparing the results with the corresponding observables in the analogous Cl+CH₄ reaction.     

Absorption linear dichroism measured directly on a single light-harvesting system: the role of disorder in chlorosomes of green photosynthetic bacteria

Chlorosomes are light-harvesting antennae of photosynthetic bacteria containing large numbers of self-aggregated bacteriochlorophyll (BChl) molecules. They have developed unique photophysical properties that enable them to absorb light and transfer the excitation energy with very high efficiency. However, the molecular-level organization, that produces the photophysical properties of BChl molecules in the aggregates, is still not fully understood. One of the reasons is heterogeneity in the chlorosome structure which gives rise to a hierarchy of structural and energy disorder. In this report, we for the first time directly measure absorption linear dichroism (LD) on individual, isolated chlorosomes. Together with fluorescence-detected three-dimensional LD, these experiments reveal a large amount of disorder on the single-chlorosome level in the form of distributions of LD observables in chlorosomes from wild-type bacterium Chlorobaculum tepidum . Fluorescence spectral parameters, such as peak wavelength and bandwidth, are measures of the aggregate excitonic properties. These parameters obtained on individual chlorosomes are uncorrelated with the observed LD distributions and indicate that the observed disorder is due to inner structural disorder along the chlorosome long axis. The excitonic disorder that is also present is not manifested in the LD distributions. Limiting values of the LD parameter distributions, which are relatively free of the effect of structural disorder, define a range of angles at which the excitonic dipole moment is oriented with respect to the surface of the two-dimensional aggregate of BChl molecules. Experiments on chlorosomes of a triple mutant of Chlorobaculum tepidum show that the mutant chlorosomes have significantly less inner structural disorder and higher symmetry, compatible with a model of well-ordered concentric cylinders. Different values of the transition dipole moment orientations are consistent with a different molecular level organization of BChl's in the mutant and wild-type chlorosomes.     

Hyperspherical nuclear motion of H3 + and D3 + in the electronic triplet state, a 3Sigmau +

The potential energy surface of H(3) (+) in the lowest electronic triplet state, a (3)Sigma(u) (+), shows three equivalent minima at linear nuclear configurations. The vibrational levels of H(3) (+) and D(3) (+) on this surface can therefore be described as superimposed linear molecule states. Owing to such a superposition, each vibrational state characterized by quantum numbers of an isolated linear molecule obtains a one- and a two-dimensional component. The energy splittings between the two components have now been rationalized within a hyperspherical picture. It is shown that nuclear motion along the hyperangle phi mainly accounts for the splittings and provides upper bounds. This hyperspherical motion can be considered an extension of the antisymmetric stretching motion of the individual linear molecule.     

Embedding scaling relations in Padé approximants: Detours to tame divergent perturbation series

A divergent perturbation series is known to yield very unreliable results for observables even at moderate coupling strengths. One of the most popular techniques in handling such series is to express them as rational functions, but it is often faithful only for small coupling. We outline here how one can gain considerable advantages in the large‐coupling regime by properly embedding known asymptotic scaling relations for selected observables during construction of the aforesaid Padé approximants. Three new bypass routes are explored in this context. The first approach involves a weighted geometric mean of two neighboring PA. The second idea is to consider series for specific ratios of observables. The third strategy is to express observables as functionals of the total energy in the form of series expansions. Symanzik's scaling relation, and the virial and Hellmann–Feynman theorems, are used at appropriate places to aid each of the strategies. Pilot calculations on the ground‐state perturbation series of certain observables for the quartic anharmonic oscillator problem reveal readily the benefit and novelty. © 2012 Wiley Periodicals, Inc.     

A hierarchical construction scheme for accurate potential energy surface generation: an application to the F+H2 reaction

We present a hierarchical construction scheme for accurate ab initio potential energy surface generation. The scheme is based on the observation that when molecular configuration changes, the variation in the potential energy difference between different ab initio methods is much smaller than the variation for potential energy itself. This means that it is easier to numerically represent energy difference to achieve a desired accuracy. Because the computational cost for ab initio calculations increases very rapidly with the accuracy, one can gain substantial saving in computational time by constructing a high accurate potential energy surface as a sum of a low accurate surface based on extensive ab initio data points and an energy difference surface for high and low accuracy ab initio methods based on much fewer data points. The new scheme was applied to construct an accurate ground potential energy surface for the FH(2) system using the coupled-cluster method and a very large basis set. The constructed potential energy surface is found to be more accurate on describing the resonance states in the FH(2) and FHD systems than the existing surfaces.     

Effect of direct-current discharge treatment on the surface properties of chitosan-poly(L,L-lactide)-gelatin composite films

The surface of films made from a chitosan-poly(L,L-lactide)-gelatin mixture stabilized with a grafted-copolymer fraction has been modified by dc discharge treatment, as well as that of films made of the individual components. The surface properties of the films (wettability, surface energy), the chemical structure of surface layers, and their morphology have been examined by goniometric measurement of contact angles, X-ray photoelectron spectroscopy, and scanning electron microscopy.     

Proton—molecule collisional interactions. II. Model calculations for vibrational excitation of CO targets

A previously computed potential energy surface (PES) for CO(¹Σ) + H⁺ interaction is here employed to generate vibrational coupling matrix elements within a simplified model. The scattering equations are solved by means of a rigorous, close-coupling (CC) treatment of the vibrational degree of freedom while rotations are dealt with via the infinite order sudden approximation (IOSA). Comparisons are made with other calculations and the energy dependence, up to 50.0 eV of collisions energy, is examined for total, integral and differential cross section vis à vis the experimental findings from proton scattering in the forward direction. The oscillatory behaviour found in the measurements is also present in the computed observables and is here related to the strong, chemical interaction acting between these collisional partners.     

On non-adiabatic potential energy surfaces

The concept of a Born–Oppenheimer (BO) potential energy surface (PES) has been extended to non-adiabatic wavefunctions by Hunter and by Wilson. A Hunter non-adiabatic PES corresponding to an excited vibrational state has a set of spikes superimposed on a BO-like PES. It was believed that Wilson PESs were spike-free. We show that it is not the case and that the Wilson PES value at a given nuclear configuration is not the expectation value of a quantum observable but a quotient of such expectation values. Consequently, BO PESs have the quantum interpretation of quotients of approximate expectation values of observables.     

Benzene-pyridine interactions predicted by the effective fragment potential method

The accurate representation of nitrogen-containing heterocycles is essential for modeling biological systems. In this study, the general effective fragment potential (EFP2) method is used to model dimers of benzene and pyridine, complexes for which high-level theoretical data -including large basis spin-component-scaled second-order perturbation theory (SCS-MP2), symmetry-adapted perturbation theory (SAPT), and coupled cluster with singles, doubles, and perturbative triples (CCSD(T))-are available. An extensive comparison of potential energy curves and components of the interaction energy is presented for sandwich, T-shaped, parallel displaced, and hydrogen-bonded structures of these dimers. EFP2 and CCSD(T) potential energy curves for the sandwich, T-shaped, and hydrogen-bonded dimers have an average root-mean-square deviation (RMSD) of 0.49 kcal/mol; EFP2 and SCS-MP2 curves for the parallel displaced dimers have an average RMSD of 0.52 kcal/mol. Additionally, results are presented from an EFP2 Monte Carlo/simulated annealing (MC/SA) computation to sample the potential energy surface of the benzene-pyridine and pyridine dimers.     

Coordinate measurements and operators

Relativistic quantum-field theory provides the machinery for calculating wave functions or probability amplitudes depending upon space-time coordinates. The currently accepted theory, however, fails to provide position operators and a means of measuring particle coordinates that are consistent with Dirac's properties of physical observables. This is because it calls for a space position probability distribution at a specified time. This paper shows, however, that space-time event coordinate operators, together with a corresponding measurement procedure, can be found that are consistent with Dirac's requirements. This is done through a reinterpretation of the amplitudes computed by field theory and does not involve any change in that mathematical formalism. The measurement of the space-time coordinates of an event is accomplished by detecting the absorption of a photon by a particle from each of two light pulses designed to overlap at a given point at a given time. If a final emitted photon has an energy whose sum with the final particle energy approximately equals the sum of the mean energies of the pulses, then the absorption of the two pulse photons must certainly have taken place within a distance the order of a Compton wavelength of the small space-time region of overlapping pulses. This is clear from the fact that the high energy required to confine the pulses to very small volumes must throw a particle absorbing them far off the mass shell. Thus the absorption of the two photons throws the particle into a narrowly confined spatial wave function that must decay extremely rapidly—to within a Compton wavelength, a delta function in space-time. This delta function is the eigenfunction of space-time coordinate operators X^μ and is the scalar product of vectors in a Hilbert space spanned by spin–space-time kets large enough to contain the operators of the Poincaré group. These event operators transform properly under the action of Poincaré operators but do not commute with the mass. If the Compton wavelength is not negligible compared to the accuracy desired in the coordinate measurements, individual coordinate measurements are no longer possible. Nevertheless, a large number of repeated coordinate measurements can be carried out to produce a coordinate probability distribution. This distribution can be unfolded to find a true coordinate probability distribution if the charge form factor is known from basic theory. An analysis of laboratory particle detection techniques shows that they actually determine space coordinates and energy rather than spatial coordinates at a given time. When this fact is included, the Klein–Nishina formula can be derived using the electromagnetic four-vector potential as the photon probability amplitude wave. To clarify the meaning of the observables, a mass-momentum measurement is described.     

Cycloaddition reactions of acrylonitrile on the Si(100)-2 x 1 surface

Multi-reference as well as single-reference quantum mechanical methods were adopted to study the potential energy surface along three possible surface reaction mechanisms of acrylonitrile on the Si(100)-2 x 1 surface. All three reactions occur via stepwise radical mechanisms. According to the computed potential energy surfaces, both [4+2] and [2+2](CN) cycloaddition products resulting from the reactions of surface dimers with the C[triple bond]N of acrylonitrile are expected, due to the negligible activation barriers at the surface. Another possible surface product, [2+2](CC), requires a 16.7 kcal/mol activation energy barrier. The large barrier makes this route much less favorable kinetically, even though this route produces the thermodynamically most stable products. Isomerization reactions among the surface products are very unlikely due to the predicted large activation barriers preventing thermal redistributions of the surface products. As a result, the distribution of the final surface products is kinetically controlled leading to a reinterpretation of recent experiments. An intermediate Lewis acid-base type complex appears in both the [4+2] and [2+2](CN) cycloadditions entrance channels, indicating that the surface may act as an electrophile/Lewis acid toward a strong Lewis base substrate.     

The molecular-level relationship between the properties of liquid water molecules and orientational order

The relationship between the orientational (tetrahedral) order (q) of an individual liquid water molecule and its various properties such as Voronoi volume, potential energy, kinetic energy, and nearest neighbors was thoroughly examined using molecular dynamics simulations of TIP5P model at 278, 298, and 318 K. By constructing Voronoi polyhedra (VP), we found that the average volume of water molecules classified according to q decreased monotonically as q increased, while the surface of VP increased in the range of high q. Kinetic energy was almost invariant but potential energy decreased monotonously as q increased. The volumes of molecules having a very large q increased as temperature decreased, implying a possible density maximum phenomena. Using time correlation functions, it was shown that total energy rather than potential energy was a more significant factor in the determination of the orientational order. With varying temperature, the relation between the properties of central molecules and those of nearest neighbor molecules were investigated. It required a very systematic cooperative motion to obtain LDL (low-density liquid) formed by ordering. It was supposed that density maximum phenomena should be accomplished by the growth of LDL and HDL (high-density liquid) of low quality with a consistent population of HDL and a drop of LDL of high quality as temperature lowered.     

Regarding the validity of the time-dependent Kohn-Sham approach for electron-nuclear dynamics via trajectory surface hopping

The implementation of fewest-switches surface-hopping (FSSH) within time-dependent Kohn-Sham (TDKS) theory [Phys. Rev. Lett. 95, 163001 (2005)] has allowed us to study successfully excited state dynamics involving many electronic states in a variety of molecular and nanoscale systems, including chromophore-semiconductor interfaces, semiconductor and metallic quantum dots, carbon nanotubes and graphene nanoribbons, etc. At the same time, a concern has been raised that the KS orbital basis used in the calculation provides only approximate potential energy surfaces [J. Chem. Phys. 125, 014110 (2006)]. While this approximation does exist in our method, we show here that FSSH-TDKS is a viable option for computationally efficient calculations in large systems with straightforward excited state dynamics. We demonstrate that the potential energy surfaces and nonadiabatic transition probabilities obtained within the TDKS and linear response (LR) time-dependent density functional theories (TDDFT) agree semiquantitatively for three different systems, including an organic chromophore ligating a transition metal, a quantum dot, and a small molecule. Further, in the latter case the FSSH-TDKS procedure generates results that are in line with FSSH implemented within LR-TDDFT. The FSSH-TDKS approach is successful for several reasons. First, single-particle KS excitations often give a good representation of LR excitations. In this regard, DFT compares favorably with the Hartree-Fock theory, for which LR excitations are typically combinations of multiple single-particle excitations. Second, the majority of the FSSH-TDKS applications have been performed with large systems involving simple excitations types. Excitation of a single electron in such systems creates a relatively small perturbation to the total electron density summed over all electrons, and it has a small effect on the nuclear dynamics compared, for instance, with thermal nuclear fluctuations. In such cases an additional, classical-path approximation can be made. Third, typical observables measured in time-resolved experiments involve averaging over many initial conditions. Such averaging tends to cancel out random errors that may be encountered in individual simulated trajectories. Finally, if the flow of energy between electronic and nuclear subsystems is insignificant, the ad hoc FSSH procedure is not required, and a straightforward mean-field, Ehrenfest approach is sufficient. Then, the KS representation provides rigorously a convenient and efficient basis for numerically solving the TDDFT equations of motion.