Time-dependent Formulation Research Articles

Rational design by DFT calculations of new metal complexes for photodynamic therapy based on an H2O2-Responsive Ir(III) photosensitizer activatable in physiological environment

A series of complexes based on the structure of an H2O2-responsive Ir(III) phenylpyridine(ppy)-containing complex were designed. The effect of changing the conjugation in the ppy ligands as well as of replacing the Ir(III) metal centre with the isoelectronic Os(II) were evaluated by means of DFT and its time-dependent formulation. The computational exploration of the photophysical properties of all the designed complexes suggest that the character of the low-lying singlet state represent the main factor affecting the region of absorption. In particular, for some of the Ir(III)-based complexes the change of the band character from mixed MLCT/LLCT to almost exclusively LLCT is essential for red-shifting the maximum absorption wavelength together with the destabilization of HOMO thus reducing the HOMO-LUMO energy gap; similarly, the replacement of Ir(III) with Os(II) converts the character of the band to mainly MLCT. The computed spin–orbit coupling constants and the triplet states’ energy confirm that all the designed complexes could, in principle, be able to generate the cytotoxic singlet oxygen under one-photon excitation by energy transfer from the triplet state of the photosensitizer to molecular oxygen, while the production of other types of ROS is precluded, similarly to the reference complex.

Analysis of the Medication Persistence Rate for and Adherence to Oral 5-Aminosalicylic Acid Preparations in Japanese Patients with Ulcerative Colitis: Study Using a Nationwide Claims Database

Introduction: 5-aminosalicylic acid (5-ASA) is the first-line drug for the treatment of mild-to-moderate ulcerative colitis (UC). Three oral sustained-release formulations are often used. However, no unified view of their actual use in routine medical practice has been presented to date. Methods: Using a health insurance claims database, we extracted patients with an initial diagnosis of mild-to-moderate UC during the period from December 1, 2017, to March 31, 2022. For the three types of oral 5-ASA formulation, we calculated and compared descriptive statistics of medication persistence rates (MPR), proportions of days covered (PDC), and adherence proportion (PDC ≥80%) in the extracted population. Results: An oral 5-ASA formulation was used in combination with a topical preparation (cohort 1) in 899 patients, and oral 5-ASA was used alone (cohort 2) in 1,829 patients. In cohort 1, MPR at days 151–180 with concomitant use of topical formulation was significantly higher for the Multi Matrix System™ (MMX) formulation (65.2%) compared with that for pH-dependent formulation (51.7%, p < 0.025), while MPR tended to be higher for MMX than for the time-dependent formulation (56.4%, not significant). During days 151–180 after starting the oral formulation, MPR for MMX (66.7% and 65.8%) was higher than for pH-dependent (55.9% and 55.3%) and time-dependent (57.6% and 55.9%) formulations in cohorts 1 + 2 and 2, respectively. In cohort 1, there was a significant difference between MMX (68.3%) and pH-dependent (57.1%) formulations, but no significant difference was seen with time-dependent formulations (61.8%). In terms of the proportion of adherence until day 180, MMX was significantly better than the other formulations. Conclusion: The analyses of the three oral 5-ASA formulations suggested that both MPR and medication adherence were better for the MMX formulation than for time-dependent or pH-dependent formulations.

Chalcogen atom effect on the intersystem crossing kinetic constant of oxygen- and sulfur disubstituted heteroporphyrins.

The modulation of the photophysical properties of di-substituted porphyrin rings upon the oxygen and sulfur-for-nitrogen replacement has been investigated at density functional theory (DFT) and its time-dependent formulation (TDDFT). The considered properties range from structural behaviors and excitation energies to spin-orbit coupling (SOC) and nonradiative intersystem kinetic constants. Results show that the SOC strongly increase upon chalcogen substitution and, accordingly, the computed nonradiative kinetic constant also indicate an efficient singlet-triplet intersystem crossing in the sulfur containing macrocycle. The presented results indicate an alternative way to properly modulate the porphyrin's crucial properties for their use in photodynamic therapy, without resorting to the use of heavy atoms.

DELFI: a computer oracle for recommending density functionals for excited states calculations.

Density functional theory (DFT) is the workhorse of computational quantum chemistry. One of its main limitations is that choosing the right functional is a non-trivial task left for human experts. The choice is particularly hard for excited state calculations when using its time-dependent formulation (TD-DFT). This is due to the approximations of the method, but also because the photophysical properties of a molecule are defined by a manifold of states that all need to be properly described. This includes not only the relative energy of the states, but also capturing the correct character, order, and intensity of the transitions. In this work, we developed a neural network to recommend functionals to be used on molecules for TD-DFT calculations, by simultaneously considering all these properties for a manifold of states. This was possible by developing a scoring system to define the accuracy of an excited state's calculation against a higher-accuracy reference. The scoring system is generalizable to any level of theory; we here applied it to evaluate the performance of common functionals of different rungs against a higher accuracy method on a large set of organic molecules. The results are collected in a database that we released and made open, providing four million data points to the community for future applications. The scoring system assigns a value between zero and one hundred to each functional for each molecule, transforming the complicated task of learning photophysical properties into a simpler regression task. We used the dataset to train a graph attention neural network to predict the scores for unseen molecules. We call this oracle DELFI (Data-driven EvaLuation of Functionals by Inference), which can be used to quickly screen and predict the ranking of functionals to calculate the optical properties of organic molecules. We validated DELFI in two in silico experiments: choosing a common functional for a series of spiropyran-merocyanine isomers and a unique functional to screen a large dataset of over 50 000 organic photovoltaic molecules, for which an extensive benchmark would be unfeasible. A corresponding web application allows DELFI to be easily run and the results to be analyzed, alleviating the hurdle of choosing the right functional for TD-DFT calculations.

Excited state properties of an A-D-A non-fullerene electron acceptor: a LC-TD-DFTB study.

Understanding charge transfer processes is essential to estimate the performance of organic photovoltaic technologies. Although experimental production is on the rise, predictability strongly relies on theoretical modeling, which is limited to the size of semiconductors. As a computationally favorable approach, we benchmarked the long-range corrected (LC) time-dependent (TD) formulation of the semi-empirical density functional-based tight-binding method (DFTB) for three polycyclic aromatic hydrocarbons (PAHs) and studied the DTP-IC-4Ph molecule, a PAH-based non-fullerene electron acceptor (NFA) with an A-D-A backbone structure. After a thorough investigation into the long-range parameter (ω) tuning for naphthalene, anthracene and pyrene, the excitation energies, oscillator strengths and Natural Transition Orbitals (NTOs) were compared with the standard ωB97X-D/6-31G(d,p) level of theory and the ADC2/6-31G(d,p) multiconfigurational method. We estimated mobility-related properties of the NFA and considered 1000 thermally accessible configurations to qualitatively reproduce the experimental absorption profile and investigate the energetic disorder. Finally, we conducted a fragment-based analysis using the one-electron transition density matrix (1TDM) to determine the character of the excited states and investigate the effect of side chains on exciton formation. Our results are sensitive to the level of theory and highly dependent on the long-range parameter but suggest that the presence of alkyl chains promotes a higher average charge delocalization and allows for additional hopping mechanisms, favoring the charge transfer dynamics.

Error analysis of zirconium and zinc oxides/kerosene oil-based hybrid nanofluid flow between rotating disks: An innovative case study

Zinc oxide and zirconium oxide have huge applications in science and engineering. Zinc oxide and zirconium oxide nanoparticles can be utilized as lubricant additives in kerosene oil to enhance the oil's lubricating qualities. These nanoparticles also, reduce friction and wear between moving parts, and due to this enhance the efficiency and life span of machinery. Zinc oxide and zirconium oxide in kerosene oil also, improve the combustion properties, anti-corrosion coating in the metal surface, catalysis in the oil refining process, etc. Due to the above applications, this article predicts the hybrid nanofluid between two rotating, squeezing, and permeable discs. The current model's main purpose is to examine the effects of zirconium oxide and zinc oxide on a kerosene oil-based hybrid nanofluid that flows between two discs. Angular velocities are being used to rotate the two discs. A system of ordinary differential equations is formed by the time-dependent constitutive formulations of the mass, momentum, energy, and mass distribution equations. In this case, the system of the equation is solved analytically through by Homotopy analysis method (HAM), resulting in the fast convergence of the problem. The dimensionless temperature, concentration, and velocity characteristics of various essential factors are illustrated and explained. The thermal profile is improved by raising the thermophoresis, thermophoresis volume percentage, and Brownian motion parameters.

A combined VOF-RANS approach for studying the evolution of incipient two-dimensional wind-driven waves over a viscous liquid

Recent laboratory experiments have revealed that important insights into the physical processes involved in the wind-driven generation of surface waves may be obtained by varying the viscosity of the carrying liquid over several orders of magnitude. The present paper reports on the development of a companion approach aimed at studying similar phenomena through numerical simulation, a way expected to remove some of the experimental limitations, especially in the near-interface region, and to allow the relative influence of several physical processes to be assessed by disregarding or inactivating arbitrarily some of them. After reviewing available options, we select and approach based on the combination of a volume of fluid technique to track the evolution of the air–liquid interface, and a two-dimensional Reynolds-averaged version of the Navier–Stokes equations supplemented with a turbulence model to predict the velocity and pressure fields in both fluids. We examine the formal and physical frameworks in which such a time-dependent two-dimensional formulation is meaningful, and close the governing momentum equations with the one-equation Spalart–Allmaras model which directly solves a transport equation for the eddy viscosity. For this purpose, we assume the interface to behave as a rigid wall with respect to turbulent fluctuations in the air, and implement a versatile algorithm to compute the local distance to the interface whatever its shape. We first assess the performance of this model in unseparated and separated single-phase flows over a wavy rigid wall, which are of specific relevance with respect to wind-wave generation. Then, we discuss the initialization protocol used in two-phase simulations, which involves an impulse disturbance with a white noise distribution applied to the interface position. We finally present some examples of interface evolutions obtained at several wind speeds with liquids of various viscosities, and discuss the underlying physics revealed by the associated statistics of interface disturbances, streamline patterns and energy spectra.

Second-Law Considerations in Monte Carlo Ray-Trace and Discrete Green’s Function Analysis of Coupled Radiation and Conduction Heat Transfer

Abstract A generic Monte Carlo ray-trace (MCRT) engine for computing radiation distribution factors (RDFs), working in tandem with an efficient finite volume formulation based on discrete Green’s functions (DGFs), has been used to solve a massive (2636 nodes) coupled radiation/conduction problem. Distribution factors computed using the MCRT method are known to produce unconditionally stable solutions to pure radiation problems even though the RDFs themselves do not conform exactly to the reciprocity principle. However, when these same RFDs are introduced into time-dependent finite volume conduction formulations based on DGFs, the resulting model is found to be fundamentally unstable due to inherent violations of the second law of thermodynamics. A novel approach to addressing this instability is presented and demonstrated for the case of a telescope typical of those employed to monitor the planetary energy budget from low Earth orbit.

A Generalised Time-Dependent Mathematical Formulation for Magnetoelectrically Coupled Soft Solids at Finite Strains

To date, the mechanical models of magnetoelectric couplings at finite strains have mainly been limited to time-independent constitutive equations. This paper enhances the literature by developing a time-dependent electromagnetic constitutive equation to characterise the mechanical behaviour of soft solids at finite strains and take into account the full form of the Maxwell equations. Our formulation introduces a symmetrical total stress and uses recently developed spectral invariants in the amended energy function; as a result, the proposed constitutive equation is relatively simple and is amenable to a finite-element formulation.

A Galerkin formulation for the nonlinear analysis of a flexible beam in channel flow

In this paper we propose a Galerkin formulation for the 1-D model describing the nonlinear flow-structure interaction of a flexible beam in confined flow. In broad terms, the system of PDEs is converted into a set of time-dependent equations (ODEs and algebraic) by developing all variables in terms of series of space-dependent orthogonal functions. The beam motion is developed in terms of its mode shapes while the flow pressure and velocity fields in each channel are developed in terms of Chebyshev polynomials. Additionally, a tau-variant of the Galerkin approach enables the enforcement of the nonlinear time-dependent boundary conditions in a well-posed manner. Ultimately, the resulting system is a set of nonlinear differential–algebraic equations that can be truncated at any suitable numbers of terms, leading to exploitable reduced formulations. Compared to CFD methods, this type of formulations is not only more computationally efficient, but also provide an easy discernment of the relevant parameters and often a more intuitive interpretation of results. Convergence studies, in terms of both the truncation of Chebyshev polynomials and beam modes, are performed to access to what extent reduced formulations are viable in different scenarios, including linear stability analysis as well as the calculation of limit-cycle oscillations with or without intermittent impacts between the beam and the side-walls. The presented framework can serve as a basis for a comprehensive analysis of the nonlinear dynamics of flexible beams in confined flow. Namely, it is well adapted to the use of bifurcation analysis tools for the continuation of periodic solutions, which will contribute to a richer understanding of the underlying physics occurring in this type of FSI systems. Moreover, the generic methodology presented here can also be adapted to different systems in the field of fluid–structure interaction, providing compact time-dependent formulations for nonlinear analysis.

Density functionals for core excitations.

The core excitation energies and related principal ionization energies are obtained for selected molecules using several density functionals and compared with benchmark equation-of-motion coupled cluster (EOM-CC) results. Both time-dependent and time-independent formulations of excitation spectra in the time-dependent density functional theory and the EOM-CC are employed to obtain excited states that are not always easily accessible with the time-independent method. Among those functionals, we find that the QTP(00) functional, which is only parameterized to reproduce the five IPs of water, provides excellent core IPs and core excitation energies, consistently yielding better excitation and ionization energies. We show that orbital eigenvalues of KS density functional theory play an important role in determining the accuracy of the excitation and photoelectron spectra.

Comment on “Origin of symmetry-forbidden high-order harmonic generation in the time-dependent Kohn-Sham formulation”

In their recent paper [Phys. Rev. A 103, 043106 (2021)], Zang et al. theoretically investigated high harmonic generation (HHG) in benchmark two-electron systems that are inversion symmetric with time-dependent density functional theory (TDDFT) in the Kohn-Sham formulation. They found that the theory wrongly predicted the emission of symmetry-forbidden even harmonics and concluded that this error originates from an inherent problem of TDDFT that unphysically populates one- and two-electron excited states. They further claimed that this effect results in an incorrect HHG cutoff energy. We reproduced their main results, but found that the unphysical even harmonics that they observed originated from numerical errors introduced by the boundary conditions. We show that contrary to their claims, the HHG cutoff energy calculated within TDDFT agrees perfectly with the standard and well-established models of HHG.

Reply to “Comment on ‘Origin of symmetry-forbidden high-order harmonic generation in the time-dependent Kohn-Sham formulation’”

In reply to the Comment by O. Neufeld et al. [Phys. Rev. A 105, 047101 (2022)], we argue that the conclusions of Phys. Rev. A 103, 043106 (2021) remain valid. We disprove the claim that the unphysical even-order harmonics originate from convergence issues related to reflections at the boundary of the simulation box. By additional calculations, we show that such reflections perturb the high-order harmonic generation spectra by oscillations with periods much smaller than the distance between the harmonics. We also demonstrate that the convergence argument of the Comment, in contrast to our multielectron excitations argument, cannot explain why there are no unphysical even-order harmonics in one-electron systems. Moreover, we show that the argument put forward in the Comment to conclude that the time-dependent Kohn-Sham equations are superior to the time-dependent natural Kohn-Sham equations is not valid.

Tangent hyperbolic nanofluid: Significance of Lorentz and buoyancy forces on dynamics of bioconvection flow of rotating sphere via finite element simulation

Enhanced thermal transportation for bio convection and mixed convection of Tangent hyperbolic nano fluid flow in stagnation region of rotating sphere is scrutinized in the existence of magnetic field. The nano-sized tiny particles are incorporated due to their unusual qualities like enhanced the thermal transport in the base fluid, which play significance role in modern nanotechnology. Further, improve the stability of nano-sized particles for long time period and avoid possible sedimentation, also incorporated auto-motile and gyrotactic microorganisms. The bioconvection of nano fluid transportation across spherical surface is considered important for heat storage and thermal balancing in technological processes. In this communication, time dependent partial differential formulation is transmuted to a set of dimensionless partial differential equation via similarity transformation. A numerical solution is sought through Galerkin based finite element discretization while it is coded and run on Matlab platform. The role of variables for the dependent quantities is monitored through computational procedure. The parameters of rotating sphere and Casson fluid speeded up the fluid flow in x-direction, but it recedes the flow in y-direction. The larger inputs of Brownian motion and thermophoresis parameters raised the nano fluid temperature.

Bioconvection: Significance of mixed convection and mhd on dynamics of Casson nanofluid in the stagnation point of rotating sphere via finite element simulation

Enhanced thermal transportation for bio convection and mixed convection of Casson nano fluid flow in stagnation region of rotating sphere is scrutinized in the existence of magnetic field. The bioconvection of nano fluid transportation across spherical surface is considered important for heat storage and thermal balancing in technological processes. To enhanced heat transportation, the gyrotactic microorganisms are used with nano sized particles to improve stability. In this communication, time dependent partial differential formulation is transmuted to a set of dimensionless partial differential equation via similarity transformation. A numerical solution is sought through Galerkin based finite element discretization while it is coded and run on Matlab platform. The role of variables for the dependent quantities is monitored through computational procedure. The parameters of rotating sphere and Casson fluid speeded up the fluid flow in x-direction, but it recedes the flow in y-direction. The larger inputs of Brownian motion and thermophoresis parameters raised the nano fluid temperature. The absolute value of Nusselt number is up-surged with enhanced buoyancy and rotation but diminishes against parameters of Brownian motion, bio convection, and Rayleigh number.

Normal ordered exponential approach to thermal properties and time-correlation functions: general theory and simple examples

A normal ordered exponential parametrisation is used to obtain equations for thermal one-and two-particle reduced density matrices, as well as free energies, partition functions and entropy for both Fermionic (electronic) and Bosonic (vibrational) Hamiltonians. A first principles derivation of the equations, relying only on a simple Wick's theorem and starting from the differential equation , is presented that yields a differential equation for the amplitudes representing density cumulants, as well as the grand potential. In contrast to other approaches reported in the literature, the theory does not use the interaction picture and an integral formulation as a starting point but rather requires a propagation of the resulting differential equation for the amplitudes in the Schrödinger representation. While the theory is applicable to general classes of many-body problems in principle, here, the theory is illustrated using simple model systems. As an application of the related time-dependent formulation numerically exact time-autocorrelation functions and absorption spectra are obtained for harmonic Franck–Condon problems. These examples illustrate the basic soundness of the scheme and are used for pedagogical purposes. Other approaches in the literature are only discussed briefly and no detailed comparative discussion is attempted.

Nonlinear IGABEM formulations for the mechanical modelling of 3D reinforced structures

The adequate coupling of dissimilar materials and structural element types provides effective engineering designs. Particularly, it enables high stiffness and low weight mechanical components, which are largely desired in numerous applications. Besides, Isogeometric Analysis (IGA) has recently stood out as a robust and accurate approach for the mechanical modelling of complex 3D engineering designs directly from Computer-Aided Design (CAD) tools. In this context, this study presents nonlinear Isogeometric Boundary Element Method (IGABEM) formulations for the effective mechanical modelling of nonhomogeneous 3D structural systems reinforced by embedded fibres. The IGABEM based on NURBS surfaces represents the solid whereas the 1D approach of BEM models the reinforcements, which characterises a 1DBEM/IGABEM coupling technique. The sub-region technique enables the nonhomogeneous system modelling whereas connection 1DBEM elements allow for crossing reinforcements along boundary interfaces without the need for surfaces remeshing. Thus, the CAD model information can be straightforwardly used in the mechanical model. Nonlinear time independent formulations are presented accounting for both elastoplastic and bond-slip behaviours. Besides, linear and nonlinear time dependent formulations are presented herein applying the Kelvin-Voigt and Boltzmann viscoelastic rheological models. Five applications illustrate the accuracy and robustness of the proposed formulations. The IGABEM formulations lead to accurate and stable results, in addition to efficient modelling. Besides, it demonstrates excellent performance considering the computational time consuming and the total number of degrees of freedom in each application.

The Contribution of Density Functional Theory to the Atomistic Knowledge of Electrochromic Processes.

In this review, we provide a brief overview of the contribution that computational studies can offer to the elucidation of the electronic mechanisms responsible for the electrochromism phenomenon, through the use of the density functional theory (DFT) and its time-dependent formulation (TDDFT). Although computational studies on electrochromic systems are not as numerous as those for other physico-chemical processes, we will show their reliability and ability to predict structures, excitation energies, and redox potentials. The results confirm that these methods not only help in the interpretation of experimental data but can also be used for the rational design of molecules with interesting electrochromic properties to be initiated for synthesis and experimental characterization.

An efficient boundary-type meshfree method for analysis of two-dimensional laser heating problems

The purpose of this study is to formulate a truly and effective boundary-type meshfree method for analysis of 2D transient heat conduction problems including moving laser heat sources. Being based on the method of fundamental solutions (MFS), the present work formulates new time-dependent formulations to solve the problem directly in the time-domain. The motion path and the intensity of the laser heat source over a moving area can be arbitrary functions of time and space. In the proposed formulations, the particular solution associated to the heat source function is evaluated using a simple approach without using any internal points or cells. By solving two example problems, the efficiency and accuracy of the proposed method are demonstrated. The analyses show that the presented boundary-type meshfree method is relatively more efficient than other domain-type techniques. From the analyses, it is also observed that very accurate results can be obtained by the proposed method employing large time-step size and small number of collocation points.

Variable polarization states in free-electron lasers

Free-electron lasers (FELs) can emit light with different optical polarizations including linear, elliptic and circular polarizations corresponding to the characteristics of the undulators used. X-ray FELs depend upon long undulator lines consisting of a sequence of short undulators. Linearly polarized undulators are most commonly used; hence the optical output is linearly polarized. Alternately, APPLE-II, Delta undulator designs, or a sequence of linearly polarized undulators with alternating orientations can be used to produce undulating magnetic fields with arbitrary polarizations. We present a three-dimensional, time-dependent formulation that self-consistently includes two optical orientations and, therefore, treats any given sequence or combination of undulator including undulator imperfections and degradation There are two principal characteristics of the formulation that underpin this capability. First, particles are tracked using the full Newton–Lorentz force equations with analytic models of the undulators fields. This permits an accurate model of the interaction of the electrons with a large variety of undulator fields and orientations. Second, the electrons can couple simultaneously to two independent electromagnetic polarizations and, therefore, the optical polarization evolves self-consistently along the undulator line. We present the numerical model and give some examples using prevailing undulator configurations.