A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. I. General formalism and application to open-shell states

The solution of the time-dependent Schrodinger equation for systems of interacting electrons is generally a prohibitive task, for which approximate methods are necessary. Popular approaches, such as the time-dependent Hartree-Fock (TDHF) approximation and time-dependent density functional theory (TDDFT), are essentially single-configurational schemes. TDHF is by construction incapable of fully accounting for the excited character of the electronic states involved in many physical processes of interest; TDDFT, although exact in principle, is limited by the currently available exchange-correlation functionals. On the other hand, multiconfigurational methods, such as the multiconfigurational time-dependent Hartree-Fock (MCTDHF) approach, provide an accurate description of the excited states and can be systematically improved. However, the computational cost becomes prohibitive as the number of degrees of freedom increases, and thus, at present, the MCTDHF method is only practical for few-electron systems. In this work, we propose an alternative approach which effectively establishes a compromise between efficiency and accuracy, by retaining the smallest possible number of configurations that catches the essential features of the electronic wavefunction. Based on a time-dependent variational principle, we derive the MCTDHF working equation for a multiconfigurational expansion with fixed coefficients and specialise to the case of general open-shell states, which are relevant for many physical processes of interest. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3600397]

A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. II. Coulomb interaction effects in single conjugated polymer chains

Conjugated polymers have attracted considerable attention in the last few decades due to their potential for optoelectronic applications. A key step that needs optimisation is charge carrier separation following photoexcitation. To understand better the dynamics of the exciton prior to charge separation, we have performed simulations of the formation and dynamics of localised excitations in single conjugated polymer strands. We use a nonadiabatic molecular dynamics method which allows for the coupled evolution of the nuclear degrees of freedom and of multiconfigurational electronic wavefunctions. We show the relaxation of electron-hole pairs to form excitons and oppositely charged polaron pairs and discuss the modifications to the relaxation process predicted by the inclusion of the Coulomb interaction between the carriers. The issue of charge photogeneration in conjugated polymers in dilute solution is also addressed. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3600404]

Unrestricted Skyrme-tensor time-dependent Hartree-Fock model and its application to the nuclear response from spherical to triaxial nuclei

The nuclear time-dependent Hartree-Fock model formulated in three-dimensional space, based on the full standard Skyrme energy density functional complemented with the tensor force, is presented. Full self-consistency is achieved by the model. The application to the isovector giant dipole resonance is discussed in the linear limit, ranging from spherical nuclei (16O and 120Sn) to systems displaying axial or triaxial deformation (24Mg, 28Si, 178Os, 190W and 238U). Particular attention is paid to the spin-dependent terms from the central sector of the functional, recently included together with the tensor. They turn out to be capable of producing a qualitative change on the strength distribution in this channel. The effect on the deformation properties is also discussed. The quantitative effects on the linear response are small and, overall, the giant dipole energy remains unaffected. Calculations are compared to predictions from the (quasi)-particle random-phase approximation and experimental data where available, finding good agreement

Time-Dependent Density Functional Molecular Orbital and Excited State Calculations on Bis(porphyrinyl)butadiynes in the Monocationic, Neutral, Monoanionic, and Dianionic Oxidation States

We report a theoretical study of the multiple oxidation states (1+, 0, 1−, and 2−) of a meso,meso-linked diporphyrin, namely bis[10,15,20-triphenylporphyrinatozinc(II)-5-yl]butadiyne (4), using Time-Dependent Density Functional Theory (TDDFT). The origin of electronic transitions of singlet excited states is discussed in comparison to experimental spectra for the corresponding oxidation states of the close analogue bis{10,15,20-tris[3‘,5‘-di-tert-butylphenyl]porphyrinatozinc(II)-5-yl}butadiyne (3). The latter were measured in previous work under in situ spectroelectrochemical conditions. Excitation energies and orbital compositions of the excited states were obtained for these large delocalized aromatic radicals, which are unique examples of organic mixed-valence systems. The radical cations and anions of butadiyne-bridged diporphyrins such as 3 display characteristic electronic absorption bands in the near-IR region, which have been successfully predicted with use of these computational methods. The radicals are clearly of the “fully delocalized” or Class III type. The key spectral features of the neutral and dianionic states were also reproduced, although due to the large size of these molecules, quantitative agreement of energies with observations is not as good in the blue end of the visible region. The TDDFT calculations are largely in accord with a previous empirical model for the spectra, which was based simplistically on one-electron transitions among the eight key frontier orbitals of the C4 (1,4-butadiyne) linked diporphyrins.

Incidental walking activity is sufficient to induce time-dependent conditioning of the Achilles tendon

The Achilles tendon has been seen to exhibit time-dependent conditioning when isometric muscle actions were of a prolonged duration, compared to those involved in dynamic activities, such as walking. Since, the effect of short duration muscle activation associated with dynamic activities is yet to be established, the present study aimed to investigate the effect of incidental walking activity on Achilles tendon diametral strain. Eleven healthy male participants refrained from physical activity in excess of the walking required to carry out necessary daily tasks and wore an activity monitor during the 24 h study period. Achilles tendon diametral strain, 2 cm proximal to the calcaneal insertion, was determined from sagittal sonograms. Baseline sonographic examinations were conducted at ∼08:00 h followed by replicate examinations at 12 and 24 h. Walking activity was measured as either present (1) or absent (0) and a linear weighting function was applied to account for the proximity of walking activity to tendon examination time. Over the course of the day the median (min, max) Achilles tendon diametral strain was −11.4 (4.5, −25.4)%. A statistically significant relationship was evident between walking activity and diametral strain (P < 0.01) and this relationship improved when walking activity was temporally weighted (AIC 131 to 126). The results demonstrate that the short yet repetitive loads generated during activities of daily living, such as walking, are sufficient to induce appreciable time-dependant conditioning of the Achilles tendon. Implications arise for the in vivo measurement of Achilles tendon properties and the rehabilitation of tendinopathy.

Time-dependent analysis of length of stay and mortality due urinary tract infections in ten developing countries : INICC findings

Catheter associated urinary tract infections (CAUTI) are a worldwide problem that may lead to increased patient morbidity, cost and mortality.1e3 The literature is divided on whether there are real effects from CAUTI on length of stay or mortality. Platt4 found the costs and mortality risks to be largeyetGraves et al found the opposite.5 A reviewof the published estimates of the extra length of stay showed results between zero and 30 days.6 The differences in estimates may have been caused by the different epidemiological methods applied. Accurately estimating the effects of CAUTI is difficult because it is a time-dependent exposure. This means that standard statistical techniques, such asmatched case-control studies, tend to overestimate the increased hospital stay and mortality risk due to infection. The aim of the study was to estimate excess length of stay andmortality in an intensive care unit (ICU) due to a CAUTI, using a statistical model that accounts for the timing of infection. Data collected from ICU units in lower and middle income countries were used for this analysis.7,8 There has been little research for these settings, hence the need for this paper.

Time-dependent fractional advection–diffusion equations by an implicit MLS meshless method

Recently, many new applications in engineering and science are governed by a series of fractional partial differential equations (FPDEs). Unlike the normal partial differential equations (PDEs), the differential order in a FPDE is with a fractional order, which will lead to new challenges for numerical simulation, because most existing numerical simulation techniques are developed for the PDE with an integer differential order. The current dominant numerical method for FPDEs is Finite Difference Method (FDM), which is usually difficult to handle a complex problem domain, and also hard to use irregular nodal distribution. This paper aims to develop an implicit meshless approach based on the moving least squares (MLS) approximation for numerical simulation of fractional advection-diffusion equations (FADE), which is a typical FPDE. The discrete system of equations is obtained by using the MLS meshless shape functions and the meshless strong-forms. The stability and convergence related to the time discretization of this approach are then discussed and theoretically proven. Several numerical examples with different problem domains and different nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the FADE.

Time-dependent rates of molecular evolution

For over half a century, it has been known that the rate of morphological evolution appears to vary with the time frame of measurement. Rates of microevolutionary change, measured between successive generations, were found to be far higher than rates of macroevolutionary change inferred from the fossil record. More recently, it has been suggested that rates of molecular evolution are also time dependent, with the estimated rate depending on the timescale of measurement. This followed surprising observations that estimates of mutation rates, obtained in studies of pedigrees and laboratory mutation-accumulation lines, exceeded long-term substitution rates by an order of magnitude or more. Although a range of studies have provided evidence for such a pattern, the hypothesis remains relatively contentious. Furthermore, there is ongoing discussion about the factors that can cause molecular rate estimates to be dependent on time. Here we present an overview of our current understanding of time-dependent rates. We provide a summary of the evidence for time-dependent rates in animals, bacteria and viruses. We review the various biological and methodological factors that can cause rates to be time dependent, including the effects of natural selection, calibration errors, model misspecification and other artefacts. We also describe the challenges in calibrating estimates of molecular rates, particularly on the intermediate timescales that are critical for an accurate characterization of time-dependent rates. This has important consequences for the use of molecular-clock methods to estimate timescales of recent evolutionary events.

Optical data encryption using time-dependent dynamics of refractive index changes in LiNbO3

We present a method for optical encryption of information, based on the time-dependent dynamics of writing and erasure of refractive index changes in a bulk lithium niobate medium. Information is written into the photorefractive crystal with a spatially amplitude modulated laser beam which when overexposed significantly degrades the stored data making it unrecognizable. We show that the degradation can be reversed and that a one-to-one relationship exists between the degradation and recovery rates. It is shown that this simple relationship can be used to determine the erasure time required for decrypting the scrambled index patterns. In addition, this method could be used as a straightforward general technique for determining characteristic writing and erasure rates in photorefractive media.

Shrinkage empirical likelihood estimator in longitudinal analysis with time-dependent covariates-application to modeling the health of Filipino children

The method of generalized estimating equations (GEE) is a popular tool for analysing longitudinal (panel) data. Often, the covariates collected are time-dependent in nature, for example, age, relapse status, monthly income. When using GEE to analyse longitudinal data with time-dependent covariates, crucial assumptions about the covariates are necessary for valid inferences to be drawn. When those assumptions do not hold or cannot be verified, Pepe and Anderson (1994, Communications in Statistics, Simulations and Computation 23, 939–951) advocated using an independence working correlation assumption in the GEE model as a robust approach. However, using GEE with the independence correlation assumption may lead to significant efficiency loss (Fitzmaurice, 1995, Biometrics 51, 309–317). In this article, we propose a method that extracts additional information from the estimating equations that are excluded by the independence assumption. The method always includes the estimating equations under the independence assumption and the contribution from the remaining estimating equations is weighted according to the likelihood of each equation being a consistent estimating equation and the information it carries. We apply the method to a longitudinal study of the health of a group of Filipino children.

Critical review of time-dependent shortest path algorithms: A multimodal trip planner perspective

A multimodal trip planner that produces optimal journeys involving both public transport and private vehicle legs has to solve a number of shortest path problems, both on the road network and the public transport network. The algorithms that are used to solve these shortest path problems have been researched since the late 1950s. However, in order to provide accurate journey plans that can be trusted by the user, the variability of travel times caused by traffic congestion must be taken into consideration. This requires the use of more sophisticated time-dependent shortest path algorithms, which have only been researched in depth over the last two decades, from the mid-1990s. This paper will review and compare nine algorithms that have been proposed in the literature, discussing the advantages and disadvantages of each algorithm on the basis of five important criteria that must be considered when choosing one or more of them to implement in a multimodal trip planner.

High temperature time-dependent low cycle fatigue behaviour of a type 316L(N) stainless steel

Total strain controlled low cycle fatigue tests on 316L(N) stainless steel have been conducted in air at various strain rates in the temperature range of 773-873 K to identify the operative time-dependent mechanisms and to understand their influence on the cyclic deformation and fracture behaviour of the alloy. The cyclic stress response at all the testing conditions was marked by an initial hardening followed by stress saturation. A negative strain rate stress response is observed under specific testing conditions which is attributed to dynamic strain ageing (DSA). Transmission electron microscopy studies reveal that there is an increase in the dislocation density and enhanced slip planarity in the DSA regime. Fatigue life is found to decrease with a decrease in strain rate. The degradation in fatigue resistance is attributed to the detrimental effects associated with DSA and oxidation. Quantitative measurement of secondary cracks indicate that both transgranular and intergranular cracking are accelerated predominantly under conditions conducive to DSA.