Configurational Averaging Research Articles

Conservation laws in disordered electron systems: Thermodynamic limit and configurational averaging

AbstractWe discuss conservation of probability in noninteracting disordered electron systems. We argue that although the norm of the electron wave function is conserved in individual realizations of the random potential, we cannot extend this conservation law easily to configurationally averaged systems in the thermodynamic limit. A direct generalization of the norm conservation to averaged functions is hindered by the existence of localized states breaking translational invariance. Such states are elusive to the description with periodic Bloch waves. Mathematically this difficulty manifests itself via the diffusion pole in the electron–hole irreducible vertex. The pole leads to a clash with analyticity of the self‐energy, reflecting causality of the theory, when norm conservation is enforced by a Ward identity. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modelling Properties of Molecules with open d- or f-Shells Using Density Functional Theory

A new, non-empirical, Density Functional Theory (DFT) based Ligand Field (LF) model is proposed. The calculation involves two steps: (i) an Average Of Configuration (AOC), with equal occupation of the d- or f-orbitals is carried out, (ii) with these orbitals kept frozen, the energies of all Single Determinants (SD) within the whole LF manifold is performed. These energies are then used to estimate all the Racah- and LF-parameters needed in a conventional LF calculation. The results of this first-principle prediction are in very good agreement with the experimental values. Sample calculations of tetrahedral and octahedral Cr-complexes, hexa-acquo Ni(II)-and octaacquo Gd(III)-complexes are used to validate the new model and to analyse the calculated parameters.

Equilibrium atomic compositions of Mo xRe 1− x(0 0 1) and Mo xW 1− x(0 0 1) disordered alloys

The cluster expansion model for the internal energy in terms of effective cluster interactions is employed to study the thermodynamic properties of two semi-infinite binary alloy systems: MoRe and MoW. A realistic tight-binding Hamiltonian is used with configurational averages computed by the direct method. This framework is applied to calculate the equilibrium atomic compositions of the (0 0 1) surface of Mo x Re 1− x and Mo x W 1− x systems for different bulk concentrations. In all cases it is found that the Mo component segregates strongly to the surface plane, followed by a Mo depletion in the second plane. The major role played in the segregation process by the relevant quantities, namely, point energies and pair interactions, is emphasized. These results are in good agreement with available experimental data.

Triploid Property of Senno (Lychnis senno Siebold et Zucc., Caryophyllaceae), a Traditional Ornamental Plant Conserved in Japan

‘Senno’ (Lychnis senno Siebold et Zucc., Caryophyllaceae), is a traditional and endangered ornamental plant species and presently only eleven strains have been confirmed to be under cultivation in nine localities in Chugoku and Kyushu districts of Japan. Analyses on chromosome number and nuclear DNA contents using flow cytometry revealed that all of the strains are triploid (2n = 36). The average of meiotic chromosome configuration (10.1III + 1.9II + 1.9I) observed in one strain indicated that ‘Senno’ is an autotriploid. Chromosome bridges, lagging chromosomes and micronuclei were observed in microsporogenesis. Although about 70 % of pollen showed stainability with cotton blue solution, ‘Senno’ plants conserved in Japan did not produce any viable seeds by self-pollination. The origin of the ‘Senno’ conserved in Japan is discussed.

Crack path in an elastic material with a random array of small defects

This paper is devoted to the problem of interaction of a semi-infinite crack (propagating in elastic material) with a random array of small defects (e.g. inclusions, voids). This interaction manifests itself in changes of the crack orientation and, overall in randomly varying curvilinear crack trajectories. Making use of the asymptotic results proposed in (Movchan, 1991, 1995) the procedure for configurational averaging is presented which yields the mean crack path and the standard deviation from the mean. The general formulae for the mean crack path can serve as a basis for effective quantitative analysis for specific situations of practical interest. The illustrative examples elaborated in the paper show dependence of the shape of crack trajectory on the probabilistic characteristics of random locations of inclusions and on their elastic parameters. The analysis performed in the paper can be directly used in prediction of failure mechanisms of brittle materials containing small randomly distributed inclusions/voids.

Dynamics of randomly branched polymers: configuration averages and solvable models.

Treating the relaxation dynamics of an ensemble of random hyperbranched macromolecules in dilute solution represents a challenge even in the framework of Rouse-type approaches, which focus on generalized Gaussian structures (GGSs). The problem is that one has to average over a large class of realizations of molecular structures, and that each molecule undergoes its own dynamics. We show that a replica formalism allows to develop analytically, based on an integral equation, a systematic way to determine the ensemble averaged eigenvalue spectrum. Interestingly, for a specific probability distribution of the spring strengths of the GGSs, the integral equation takes a particularly simple form. Given that several dynamical observables, such as the mechanical moduli G'(omega) and G"(omega), as well as the averaged monomer displacement <Y(t)> are relatively simple functions of the eigenvalues, we can use the obtained spectra to compute the corresponding averaged dynamical forms. Comparing the results obtained from this approach and from extensive diagonalizations of hyperbranched GGSs we find a very good agreement.

A constrained maximum entropy method in polymer statistics

A modified version of the maximum entropy principle, called “constrained maximum entropy” method (MEC), is revisited to combine the information obtained in computer simulations of polymers with external information in the form of configurational averages. A random-temperature molecular dynamics trajectory is being proposed as a biased random walk in configurational space to be reweighted by using the given average information. This random walk, generating a “meta” configurational probability, has been found to contain relevant information on the system. The method is compared with other computational techniques, like the generalized-ensemble and configurational-biased Monte Carlo, for simple models in the field of polymers and biopolymers. The main features of polymer configurational distribution functions of interest in polymer physics are consistent among the different methods in a wide range of temperatures and especially at room conditions. The advantage of the MEC approach is in taking into account all the degrees of freedom in the model, thus allowing applications in complicated biopolymers in the explicit solvent.

Ultrafast singlet excited-state polarization in electronically asymmetric ethyne-bridged bis[(porphinato)zinc(II)] complexes.

The excited-state dynamics of two conjugated bis[(porphinato)zinc(II)] (bis[PZn]) species, bis[(5,5'-10,20-bis[3,5-bis(3,3-dimethyl-1-butyloxy)phenyl]porphinato)zinc(II)]ethyne (DD) and [(5,-10,20-bis[3,5-bis(3,3-dimethyl-1-butyloxy)phenyl]porphinato)zinc(II)]-[(5',-15'-ethynyl-10',20'-bis(heptafluoropropyl)porphinato)zinc(II)]ethyne (DA), were studied by pump-probe transient absorption spectroscopy and hole burning techniques. Both of these meso-to-meso ethyne-bridged bis[PZn] compounds display intense near-infrared (NIR) transient S(1)-->S(n) absorptions and fast relaxation of their initially prepared, electronically excited Q states. Solvational and conformational relaxation play key roles in both DD and DA ground- and excited-state dynamics; in addition to these processes that drive spectral diffusion, electronically excited DA manifests a 3-fold diminution of S(1)-->S(0) oscillator strength on a 2-20 ps time scale. Both DD and DA display ground-state and time-dependent excited-state conformational heterogeneity; hole burning experiments show that this conformational heterogeneity is reflected largely by the extent of porphyrin-porphyrin conjugation, which varies as a function of the pigment-pigment dihedral angle distribution. While spectral diffusion can be seen for both compounds, rotational dynamics driving configurational averaging (tau approximately 30 ps), along with a small solvational contribution, account for essentially all of the spectral changes observed for electronically excited DD. For DA, supplementary relaxation processes play key roles in the excited-state dynamics. Two fast solvational components (0.27 and 1.7 ps) increase the DA excited-state dipole moment and reduce concomitantly the corresponding S(1)-->S(0) transition oscillator strength; these data show that these effects derive from a time-dependent change of the degree of DA S(1)-state polarization, which is stimulated by solvation and enhanced excited-state inner-sphere structural relaxation.

Computer simulations of enzyme catalysis: methods, progress, and insights.

Understanding the action of enzymes on an atomistic level is one of the important aims of modern biophysics. This review describes the state of the art in addressing this challenge by simulating enzymatic reactions. It considers different modeling methods including the empirical valence bond (EVB) and more standard molecular orbital quantum mechanics/molecular mechanics (QM/MM) methods. The importance of proper configurational averaging of QM/MM energies is emphasized, pointing out that at present such averages are performed most effectively by the EVB method. It is clarified that all properly conducted simulation studies have identified electrostatic preorganization effects as the source of enzyme catalysis. It is argued that the ability to simulate enzymatic reactions also provides the chance to examine the importance of nonelectrostatic contributions and the validity of the corresponding proposals. In fact, simulation studies have indicated that prominent proposals such as desolvation, steric strain, near attack conformation, entropy traps, and coherent dynamics do not account for a major part of the catalytic power of enzymes. Finally, it is pointed out that although some of the issues are likely to remain controversial for some time, computer modeling approaches can provide a powerful tool for understanding enzyme catalysis.

Effects of Configurational Fluctuation on Electronic Coupling for Charge Transfer Dynamics

We advance a theory for the effects of bridge configurational fluctuations on the electronic coupling for electron transfer reactions in donor-bridge-acceptor systems. The theory of radiationless transitions was applied for activationless electron transfer, where the nuclear Franck-Condon constraints are minimized, with the initial vibronic state interacting directly with the final vibronic manifold, without the need for thermal acti- vation. Invoking the assumption of energy-independent coupling, the time-dependent initial state population probability was analyzed in terms of a cumulant expansion. Two limiting situations were distinguished, i.e. the fast configurational fluctuation limit, where the electron transfer rate is given in terms of the configurational average of me squared electronic coupling, and the slow configurational fluctuation limit, where the dynamics is determined by a configurational averaging over a static distribution of electron transfer probability densities. The correlation times for configurational fluctuations of the electronic coupling will be obtained from the anal- ysis of molecular dynamics, in conjunction with quantum mechanical calculations of the electronic coupling, to establish the appropriate limit for electron transfer dynamics.

Bulk Magnetic Properties of the Fe0.5Mn0.1Al0.4Disordered Alloy: A Monte Carlo Study

In this work we present a simulational study of the bulk magnetic properties of the Fe0.5Mn0.1Al0.4 disordered system. The magnetization per site, specific heat and magnetic susceptibility were obtained using Monte Carlo simulation. Simulation results were performed in the framework of a random site-diluted 3D Ising model with nearest neighbor interactions, and using a single-spin-flip Metropolis dynamics for equilibration and energy minimization, from which canonical ensemble and configurational averages were computed. In the simulation, atoms were randomly distributed on a body-centered cubic lattice in order to simulate the disorder and crystalline structure as obtained in the arc-melted Fe0.5Mn0.1Al0.4 alloy treated at high temperatures for long periods of time and followed by fast quenching. Competitive Fe–Fe ferromagnetic and Fe–Mn and Mn–Mn antiferromagnetic interactions were taken into account, as well as the Al dilutor effect. We conclude that, accordingly with Mossbauer results, the Fe0.5Mn0.1Al0.4 system exhibits a reentrant spin-glass behavior below 30 K characterized by a sharp increase of the mean hyperfine field attributed to the magnetic ordering of the Mn sublattice at these temperatures. Additionally, a ferromagnetic to paramagnetic transition at around 300 K was also evidenced.

New insights into the effects of covalency on the ligand field parameters: a DFT study

A new, non-empirical, DFT based ligand field (LF) model is proposed. The calculation involves two steps: (i) an average of configuration (AOC), with equal occupation of the d-orbitals is carried out, (ii) with these Kohn–Sham orbitals kept frozen, the energies of all single determinants (SD) within the whole LF-manyfold is performed. These energies are then used to estimate all the Racah- and LF-parameters needed in a conventional LF-calculation. The results of this first-principle prediction are in very good agreement with the experimental values. Test calculation of tetrahedral Cr (IV) and Ni (II) complexes are used to validate the new model and to analyze the parameters of the LF.

Monte Carlo study of the magnetic properties of Fe0.9−qMn0.1Alq-disordered alloys

Within the framework of a random site-diluted Ising model with nearest-neighbor interactions, and using the Metropolis algorithm for equilibration and energy minimization, we have computed the ensemble and configurational averages for magnetization per site, magnetic susceptibility and specific heat of Fe 0.9− q Mn 0.1 Al q -disordered alloys with 0.1⩽ q ⩽0.55. In the model, atoms have been randomly distributed on a body-centered cubic lattice in order to simulate the disorder and structure as that obtained in arc-melted Fe 0.9− q Mn 0.1 Al q alloys treated at high temperatures during long periods of time and followed by fast quenching. Competitive interactions coming from Fe–Fe ferromagnetic bonds and Fe–Mn and Mn–Mn antiferromagnetic couplings, as well as the Al dilutor effect, have been taken into account in our study. Results allow us to conclude that, in agreement with previous Mössbauer data of the average hyperfine field, for which a comparison is also carried out, the Fe 0.9− q Mn 0.1 Al q -disordered alloys are well characterized by a critical concentration at room temperature at around 40 at% Al, for which the system undergoes a transition from a ferromagnetic state to a paramagnetic one. The finite size scaling analysis to obtain the critical Al concentration in the thermodynamic limit, as well as the critical exponents, is also presented and discussed.

Image forces on a collection of charged particles near conducting surfaces

In a recent study, Vauge (2002) showed that particles in a charged aerosol system confined to a conducting cavity do not experience image forces provided the aerosol is treated as a continuous distribution in space. However, in reality, since an aerosol is a collection of discrete charges and not a continuum, we propose that the collective image–particle interactions have to be analysed using statistical techniques based on configuration averaging. Two cases are considered: (i) charged particles confined to a conducting spherical cavity and (ii) those distributed outside a conducting sphere which is insulated from the ground. It is shown that in both the cases, a given charged particle experiences an average attractive electric field due to its image charge and the average field due to the images of other charged particles present in the aerosol vanishes. This arises because the position of the particle is delta correlated with the position of its image charge, whereas it is non-correlated with the positions of the image charges of other particles. The proposition of Vauge conforms to the case of an image field at an arbitrary point and not to that on a charged particle. The study also investigates, for the first time, the root mean square fluctuations in the electric fields arising due to particle–particle and image–particle interactions. However, for the charge densities normally encountered in aerosol systems, these contributions are found to be quite small.

SASSIM: a method for calculating small-angle X-ray and neutron scattering and the associated molecular envelope from explicit-atom models of solvated proteins.

A method is presented to calculate efficiently small-angle neutron and X-ray solution scattering intensities from explicit-atom models of macromolecules and the surrounding solvent. The method is based on a multipole expansion of the scattering amplitude. It is particularly appropriate for extensive configurational averaging, as is required for calculations based on computer-simulation results. In test calculations, excellent agreement with experiment is found between neutron and X-ray scattering profiles calculated from a molecular-dynamics simulation of lysozyme in water. The question of definition of the protein surface is also addressed. For comparison with the continuum model, an analytical envelope around the protein is defined in terms of spherical harmonics and is calculated using a Lebedev grid. The analytical surface thus defined is shown to reproduce well the scattering profile calculated from the explicit-atom model of the protein.

Magnetism of Fe–Al disordered alloys: An Ising–Monte Carlo approach

Using a model of atoms randomly distributed on a cubic lattice, we have simulated the atomic disorder induced in quenched binary alloys. Our study has been developed within the framework of a random site-diluted Ising model with nearest-neighbor interactions and used a Monte Carlo algorithm implemented with Metropolis kinetics for sampling states. After equilibration, ensemble and configurational averages for magnetization, magnetic susceptibility, and heat capacity were computed. We conclude that, in agreement with previous experimental Mössbauer data for which a comparison is carried out, Fe–Al disordered alloys exhibit room-temperature ferromagnetic behavior up to around 43 at. % Al, beyond which the system becomes paramagnetic. This result contrasts with that for alloys with atomic order, which exhibit ferromagnetism only up to 30 at. % Al.

Instantaneous normal mode analysis of hydrated electron solvation dynamics

The instantaneous normal mode (INM) method is implemented in the context of mixed quantum-classical molecular dynamics (MD) simulations and applied to the analysis of the short-time solvation dynamics of the hydrated electron. Numerically suitable equations for computing the solvent dynamical matrix (Hessian) for both ground and excited adiabatic electronic states are derived using analytical derivative methods of quantum chemistry. Standard diagonalization of the Hessian leads to the sets of eigenfrequencies and eigenvectors that underlie the INM theory. Comparison of the hydrated electron and pure water INM spectra and the corresponding mode participation ratios shows that the quantum solute enhances the participation of collective low-frequency unstable modes (imaginary frequencies) at the expenses of stable ones. Distinct differential INM spectra, involving distinct solvent configurational averages, are introduced to describe the changes experienced by the solvent INMs upon the vertical excitation of the electron. The overall picture is that the INMs associated with lower frequency translational and rotational motions, as well as fast librational reorientations are markedly affected by the photoexcitation, as opposed to the localized internal vibrations of the individual water molecules. The INM solvation response for the upward transition calculated from the real modes agrees with the response obtained directly from the energy gap time correlation up to approximately 100 fs. The agreement extends over much longer times for downward transitions. The INM analysis of the solvation responses following vertical upward and downward transitions reveals that diffusive translational and librational motions are both important mechanisms for the early stages (≲50 fs) of the solvent response, with the latter dominating the first half of this time period. It is also shown that the short-time solvent relaxation involves the combined motion of molecules from the first and second hydration shells. In addition, the linearized INM solvation response calculated for D2O indicates a significant (∼36%) solvent isotope effect in the first 25 fs of the response, where the decay is Gaussian. These results are compared with previous studies of the hydrated electron solvation dynamics.

Mathematical Problems of Nuclear Configuration Averaging

The concept of the average of a family of related nuclear configurations, for example, the average of those configurations which are slightly distorted versions of a given stable conformer of a molecule, has a role as both interpretative tool and also as a reference configuration in practical, computational use. However, depending on the actual coordinates used along which the average is defined, the average of nuclear configurations is not necessarily a physically viable arrangement, a fact that has to be taken into account when generating the corresponding electron density averages. Some of the associated mathematical and computational problems are described and the validity of a macroscopically motivated approach to conformation averaging is discussed.

Rare events by constrained molecular dynamics

Abstract We present a computationally efficient molecular dynamics method, based on holonomic constraints, devised to estimate the rate constants of rare activated events of short duration. We assume that the process is described by a reaction coordinate ξ(r), a well-defined function in configuration space, and we constrain the system at the “bottleneck” region by prescribing the value of ξ(r). MD trajectories sample phase space according to a biased configurational distribution and averages can be taken form such a new Blue Moon ensemble, with suitable reweighting, to study rare events.

Stochastic resonance effects in the scattering of neutrons by modulated two-state systems

Recent work indicates that the stochastic resonance phenomenon (SR) can have a strong signature in the neutron scattering cross section. Here we consider neutron scattering by a sample containing a random distribution of bistable scattering centres. The robustness of the stochastic resonance signal is tested by performing suitable configurational averages over the potential parameters. By showing that the resonant line is not significantly weakened by the randomness, our results suggest that SR should be observable in a real glass.