Length Gauge Research Articles

Efficient exact exchange using Wannier functions and other related developments in planewave-pseudopotential implementation of RT-TDDFT.

The plane-wave pseudopotential (PW-PP) formalism is widely used for the first-principles electronic structure calculation of extended periodic systems. The PW-PP approach has also been adapted for real-time time-dependent density functional theory (RT-TDDFT) to investigate time-dependent electronic dynamical phenomena. In this work, we detail recent advances in the PW-PP formalism for RT-TDDFT, particularly how maximally localized Wannier functions (MLWFs) are used to accelerate simulations using the exact exchange. We also discuss several related developments, including an anti-Hermitian correction for the time-dependent MLWFs (TD-MLWFs) when a time-dependent electric field is applied, the refinement procedure for TD-MLWFs, comparison of the velocity and length gauge approaches for applying an electric field, and elimination of long-range electrostatic interaction, as well as usage of a complex absorbing potential for modeling isolated systems when using the PW-PP formalism.

First-principle study of two-photon absorption in Fe3O4.

Utilizing the length gauge and the electron density operator, we calculate the two-photon absorption (2PA) coefficient of Fe3O4 based on a full ab initio band structure. The pure two-photon interband transitions and those modulated by intraband transitions have been separated explicitly to determine their impact on the 2PA spectrum. A single main absorption peak instead of two will present in the spectrum by including the hybridization of inter- and intra-band transitions, which can be identified easily in future experimental studies. In addition, we find that in almost the whole 2PA-active spectral range, circularly polarized light can be absorbed with a much lower threshold power than the linearly polarized one. But the linearly polarized light is more easily to be manipulated. One can control the magnitude and resonance frequency of the 2PA coefficient by simply adjusting the polarization angle of the incident light. Our findings will deepen the understanding of the 2PA phenomenon in Fe3O4 nanoparticles.

Quantifying compound flood event uncertainties in a wave and tidally dominated coastal region: The impacts of copula selection, sampling, record length, and precipitation gauge selection

AbstractCoastal flooding is a growing hazard. Compound event characterization and uncertainty quantification are critical to accurate flood risk assessment. This study presents univariate, conditional, and joint probabilities for observed water levels, precipitation, and waves. Design events for 10‐ and 100‐year marine water level and precipitation events are developed. A total water level formulation explicitly accounting for wave impacts is presented. Uncertainties associated with sampling method, copula selection, data record length, and utilized rainfall gauge are determined. Eight copulas are used to quantify multivariate uncertainty. Generally, copulas present similar results, except the BB5. Sampling method uncertainty was quantified using four sampling types; annual maximum, annual coinciding, wet season monthly maximum, and wet season monthly coinciding sampling. Annual coinciding sampling typically produced the lowest event magnitude estimates. Uncertainty associated with record length was explored by partitioning a 100‐year record into various subsets. Withholding 30 years of observations (i.e., records of less than 70 years) resulted in substantial variability of both the 10‐ and 100‐year return period estimates. Approximately equidistant rainfall gauges led to large event estimate differences, suggesting microclimatology and gauge selection play a key role in characterizing compound events. Generally, event estimate uncertainty was dominated by sampling method and rainfall gauge selection.

High harmonic generation in graphene quantum dots

We study theoretically the generation of high harmonics in disk graphene quantum dots placed in linearly polarized short pulse. The quantum dots (QD) are described within an effective model of the Dirac type and the length gauge was used to describe the interaction of quantum dots with an optical pulse. The generated radiation spectra of graphene quantum dots can be controlled by varying the quantum dot size, i.e. its radius. With increasing the quantum dot radius, the intensities of low harmonics mainly decrease, while the cutoff frequency increases. The sensitivity of the cutoff frequency to the QD size increases with the intensity of the pulse.

Contribution of Discrete and Continuum Wave Functions in the Ground State Polarizability of Hydrogen

We analytically derive a discrete radial Green function for a hydrogenic system in terms of associated Leguerre polynomials. We investigate the polarizability of the ground-state hydrogen using the so-called length gauge approximation of electrodynamics. The polarizability is the sum of the polarization matrix elements for the negative and the positive frequency values. We estimate the contribution of discrete wavefunctions to the static ground state polarizability. We found that the contribution of continuum states dominates over that of discrete states to the polarizability by an order of magnitude.

Field and Laboratory Research of the Rut Development Process on Forest Roads

The main tasks of this research are an extended analysis of the technological rut formation process’s geometric, force, and energy characteristics as a result of repeated passage of a forest machine on the soil surface. Existing experimental studies of the rutting process are associated with significant material costs and disruption of the forest ecosystem. The purpose of this study is to obtain similar experimental data in laboratory conditions, as well as establishing the correspondence of these experimental results to the results of field studies. The experiments were carried out on the specialized “soil channel” stand of Technical University in Zvolen (Slovakia), as well as in natural conditions in Brody Forestry of the Lviv Region (Ukraine). Geometric track characteristics were determined by length gauges. Power and energy characteristics of the track development process were determined using dynamometers, ammeters, and voltmeters. The physical and mechanical characteristics of the soil with which the mover interacted were determined by a dynamic hardness tester, a penetrometer, and a moisture meter. The characteristics of rut development processes in natural and laboratory conditions are similar to each other. This makes it possible to carry out a wide range of studies of a wheel with soil on a specialized stand and save considerable money during the implementation of full-scale experiments. So, the process of track development can be analyzed with the help of the geometric, force, and energy characteristics of the “wheel-soil” system obtained on laboratory equipment.

Shift Current with Gaussian Basis Sets and General Prescription for Maximally Symmetric Summations in the Irreducible Brillouin Zone.

The bulk photovoltaic effect is an experimentally verified phenomenon by which a direct charge current is induced within a non-centrosymmetric material by light illumination. Calculations of its intrinsic contribution, the shift current, are nowadays amenable from first-principles employing plane-wave bases. In this work, we present a general method for evaluating the shift conductivity in the framework of localized Gaussian basis sets that can be employed in both the length and velocity gauges, carrying the idiosyncrasies of the quantum-chemistry approach. The (possibly magnetic) symmetry of the system is exploited in order to fold the reciprocal space summations to the representation domain, allowing us to reduce computation time and unveiling the complete symmetry properties of the conductivity tensor under general light polarization.

Computation of the complex energy shift of decaying states in intense laser fields

We present a specific calculation concerning laser-assisted decaying systems with non-Hermitian spectral calculations merged with the (t,t’)-formalism to estimate the possible intense laser-field-induced corrections to the lifetime of quasi-stationary states. The perturbed complex energy shift caused by the external vector potential which represents the linearly and circularly polarized laser field is calculated in details. This wavefunction-centered method implies the unsuitability of the radiation gauge and length gauge when quasi-stationary states are considered and described within the framework of non-hermitian quantum mechanics since in this case the A2 term cannot be transformed out.

QPC-TDSE: A parallel TDSE solver for atoms and small molecules in strong lasers

The QPC-TDSE program serves as a general tool to study laser-driven dynamics of electrons in ideal isolated atoms and molecules by solving the full-dimensional non-relativistic time-dependent Schrödinger equation (TDSE) within single-active-electron approximation. It expands the full-dimensional electronic wavefunction in spherical coordinates by spherical harmonics and B-spline functions and employs a set of parallel Crank-Nicolson propagators combined with split-operator techniques to evolve the wavefunction in time, which support centrifugal and multi-polar static potentials to treat atomic and molecular scenarios and accepts arbitrary combinations of linearly or elliptically polarized lasers within the dipole approximation. The program is capable of extracting the photo-electron momentum distribution via t-SURFF approach or projection onto either the exact scattering states or the planewaves. Its applications in different scenarios are given as examples, e.g., above threshold ionization, attosecond clock, higher-order harmonic generation. Program summaryProgram Title: QPC-TDSECPC Library link to program files:https://doi.org/10.17632/xjm3kfgv75.1Licensing provisions: GPLv3Programming language: C++External libraries: HDF5, GSL, MKLNature of problem: Numerical solution of TDSE and extraction of various types of electron spectrum.Solution method: The electronic wavefunction is expanded by B-spline functions and spherical harmonics whose range is chosen elaborately to reduce the total number of partial waves for non-linearly polarized lasers. The Crank-Nicolson approach combined with an operator-splitting scheme is used to propagate the wavefunction in time, either in velocity gauge or length gauge. Matrix inversions are solved via either dense or sparse linear algebra solvers according to their structures. The t-SURFF method and projections onto either the scattering states or planewaves are provided for the accurate extraction of the momentum distributions.Additional comments including restrictions and unusual features: Only lasers within dipole approximation are supported. For the multi-polar potentials, only pure Coulombic ones are supported. Routines for solving exact scattering states have only been implemented for centrifugal potentials. The codes are written in C++17 and can only be compiled on the platforms that support the avx instruction sets. An extension for the propagation algorithm using the avx-512 intrinsics is provided as optional.

On the choice of coordinate origin in length gauge optical rotation calculations.

In this work, we explore the issue of origin dependence in optical rotation (OR) calculations in the length dipole gauge (LG) using standard approximate methods belonging to density functional theory (DFT) and coupled cluster (CC) theory. We use the origin-invariant LG approach, LG(OI), that we recently proposed as reference for the calculations, and we study whether a proper choice of coordinate origin and molecular orientation can be made such that diagonal elements of the LG-OR tensor match those of the LG(OI) tensor. Using a numerical search algorithm, we show that multiple spatial orientations can be found where the LG and LG(OI) results match. However, a simple analytical procedure provides a spatial orientation where the origin of the coordinate system is close to the center of mass of the molecule. At the same time, we also show that putting the origin at the center of mass is not an ideal choice for every molecule (relative errors in the OR up to 70% can be obtained in out test set). Finally, we show that the choice of coordinate origin based on the analytical procedure is transferable across different methods and it is superior to putting the origin in the center of mass or center of nuclear charge. This is important because the LG(OI) approach is trivial to implement for DFT, but not necessarily for nonvariational methods in the CC family. Therefore, one can determine an optimal coordinate origin at DFT level and use it for standard LG-CC response calculations.

PO-02-206 A MECHANISM FOR PACING-INDUCED REGIONAL CONTRACTILE DYSFUNCTION MEDIATED BY RELEASED CATECHOLAMINES

We have previously shown that non-excitatory epicardial stimulation (NES) increases measures of cardiac function mediated by local release of norepinephrine. In this further investigation we focused on the effects of NES on the local myocardial contractile pattern. Farm pigs were anesthetized and instrumented with a LV high-fidelity pressure/volume conductance transducer, thoracic aortic pressure transducer, left atrial (LA)/ LV epicardial electrodes, and sonomicrometer segment length (SL) gauges placed proximal (lateral base) and distal (posterior mid LV) to the LV stimulation site. During constant LA pacing, LV pulses (0.8ms, 2-3x threshold volts) were applied during the absolute refractory period before and after β-receptor blockade (BB, metoprolol). Regional contractile function was analyzed by constructing LVP vs. SL loops in a beat-by-beat fashion thus allowing characterization of local cardiac function in relation to LV pressure over the entire cardiac cycle. NES resulted in a local contractile dysfunction characterized by an early shortening, subsequent lengthening, and re-shortening pattern during the cardiac cycle in the SL gauge proximal (middle tracing), but not remote to the stimulation site (bottom tracing). The onset of early lengthening in the proximal SL coincided with peak pressure generation, followed by re-shortening as LV pressure fell. The LVP vs. SL loop was markedly altered. This contractile effect rapidly waned within 10-15 seconds after cessation of electrical stimulation and was abolished by BB. The NES induced dysfunction developed within an average of 5-10 seconds of stimulation onset and was accompanied by increases in several global indices of cardiac function (dP/dt, peak LVP, early aortic valve opening) which were also abrogated by B-blockade. These findings demonstrate that pacing elicits local catecholamine release that may cause dyssynergy and mimic the regional pacing-induced contractile dysfunction seen at pacing sites in man.

Investigating the effect of fabric design on properties of different weft knit fabrics

Fabric structure exhibits a significant impact on the various properties of weft knitted fabric if processing variables such as yarn count, stitch length, machine diameter, and needle gauge are modified. In this study, weft knitted constructions such plain jersey, Lacoste, waffle, fleece, and rib are evaluated in relation to a number of attributes, including dimensional stability, fabric breadth, spirality and bursting strength. According to the study, lengthwise shrinkage reduces as tuck stitch and spirality grow, however widthwise shrinkage rises. The experiment also revealed that weft knit fabric's bursting strength is less affected by variations in fabric structure.

Hole diameter variation compensation by integrating computation geometry for helical milling of stacked aerostructure

The stack-ups of composite and metal are used in aircraft manufacturing to produce modern high-performance aircraft, which makes fastener-hole-making more difficult. Helical milling is an advanced machining process to improve the quality of hole-making. This paper seeks to control the hole diameter error and guarantee fastener-hole fitting performance. The setup of automated helical milling for assembling composite/metal aerostructures is first presented. Meanwhile, the helical milling procedure in aircraft wing manufacturing is discussed. Based on the designed helical milling end-effector, a length-gauge-based feedback control mechanism of the orbital eccentricity is designed to reduce the diameter error of an intended fastener hole. For accurate measurement, a least-squares method is used to find the calibration parameters of the length gauge. Then the mathematical model of hole diameter variation extraction based on B-spline curve construction is given for further variation compensation. After that, the feedback control system of the radial feed mechanism is established. Besides, the modeling and compensation system of the hole diameter variation is developed and used. In helical milling of CFRP/Ti stacks in an aircraft assembly, fastener holes tend to achieve the target diameter of 7.9400 mm without extending the range of hole entrance and exit diameters.

Theory for all-optical responses in topological materials: The velocity gauge picture

High Harmonic Generation (HHG), which has been widely used in atomic gas, has recently expanded to solids as a means to study highly nonlinear electronic response in condensed matter and produce coherent high frequency radiation with new properties. Most recently, attention has turned to Topological Materials (TMs) and the use of HHG to characterize topological bands and invariants. Theoretical interpretation of nonlinear electronic response in TMs, however, presents many challenges. In particular, the Bloch wavefunction phase of TMs has undefined points in the Brillouin Zone. This leads to singularities in calculating the inter-band and intra-band transition dipole matrix elements of Semiconductor Bloch Equations (SBEs). Here, we use the laser-electromagnetic velocity gauge ${\boldsymbol p}\cdot {\bf A}(t)$ to numerically integrate the SBEs and treat the singularity in the production of the electrical currents and HHG spectra. We use a prototype of Chern Insulators (CIs), the Haldane model, to demonstrate our approach. We find good qualitative agreement of the velocity gauge compared to the length gauge and the Time-Dependent Density Functional theory in the case of topologically trivial materials such as MoS$_2$. For velocity gauge and length gauge, our two-band Haldane model reproduces key HHG spectra features: ($\textit i$) The selection rules for linear and circular light drivers, ($\textit ii$) The linear cut-off law scaling and ($\textit iii$) The anomalous circular dichroism. We conclude that the velocity-gauge approach captures experimental observations and provides theoretical tools to investigate topological materials.

Tolerance Analysis of Cylindrical Roller Bearing under Combined Radial and Axial Loads

In order to analyze the influence of tolerance values of key parameters for cylindrical roller bearings under combined axial and radial loads, a coupled model, incorporating a dynamic model of cylindrical roller bearings, contact model, and fatigue life model, is developed to investigate the effect of flange angle, roller-end radius, interval of roller length gauge, and roller profile on contact performance and fatigue life. The results show that the grouping design of flange angle and roller-end radius in the tolerance range was helpful for reducing contact ellipse truncation. The difference of the roller length would change the axial load distribution of the bearings. For the longest roller located in the bottom position, the bigger the difference, the bigger the roller tilt angle and carried-axial load. The (0, +2.5 μm) tolerance range of the crown drop can limit the difference of the fatigue life within 20% in the current analysis.

Abstract 12821: Progressive Improvement in Left Ventricular Performance Associated With Progressive Regional Dyssynchrony

Background : We have shown that non-excitatory epicardial stimulation (NES) increases measures of cardiac function mediated by local release of norepinephrine. In this further investigation we determined whether NES is accompanied by improved indices of left ventricular (LV) performance, reflected in PV loops and timing of aortic valve opening and closing. Methods : Anesthetized pigs (n=6) were instrumented with a LV high-fidelity pressure/volume conductance transducer, thoracic aortic pressure transducer, left atrial (LA)/ LV epicardial electrodes, and sonomicrometer segment length (SL) gauges placed proximal (lateral base) and distal (posterior mid LV) to the LV stimulation site. During constant LA pacing, LV pulses (0.8ms, 2-3x threshold volts) were applied during the absolute refractory period for 3 minutes (3x), before and after β-receptor blockade (BB, metoprolol). Data were analyzed at baseline, and at an estimated 30%, 60% and 100% of developed ventricular dyssynchrony (DVD) contraction pattern. Results: Consistent with earlier findings, NES resulted in an early shortening and relaxation pattern of the proximal SL manifest as an 80% decrease in the LVP vs. SL loop area in the absence of change in the remote segment. This was accompanied by an increase in peak systolic pressure and LV dP/dt max. Although NES did not change the area of the LVP vs. LV volume loop (stroke work) or alter the interval from LV electrical activation (R wave) to the onset of LV pressure increase, aortic valve opening occurred up to 14.1 ± 2.8 ms earlier (p <0.01) compared to baseline. The duration of an open aortic valve slightly increased (6.0 ± 3.9 ms) whereas ejection duration from valve opening to peak Pao decreased 18.2 ± 3.0 ms (p < 0.01). Conclusion : These findings demonstrate that NES elicits a local contractile dysynchrony resulting in an enhanced cardiac inotropic state characterized by more rapid global LV contraction with earlier aortic valve opening with no change in stroke work.

Two-photon absorption in semiconductors: A multiband length gauge analysis

The simplest approach to deal with light excitations in direct-gap semiconductors is to model them as a two-band system: one conduction and one valence band. For such models, particularly simple analytical expressions are known to exist for the optical response such as multi-photon absorption coefficients. Here we show that generic multi-band models do not require much more complicated expressions. Our length-gauge analysis is based on the semiconductors Bloch equations in the absence of all scattering processes. In the evaluation, we focus on two-photon excitation by a pump-probe scheme with possibly non-degenerate and arbitrarily polarized configurations. The theory is validated by application to graphene and its bilayer, described by a tight-binding model, as well as bulk Zincblende semiconductors described by k.p theory.

Ab initio calculation of two-photon absorption in semiconductors

A theoretical derivation of two-photon absorption (2PA) from semiconductors, based on the length gauge analysis and the electron density operator, is formulated; the intraband ${\mathbit{r}}_{i}$ part and the interband ${\mathbit{r}}_{e}$ part of the position operator $\mathbit{r}$ are properly accounted for. Within the independent-particle approximation, the nonlinear third-order susceptibility tensor ${\ensuremath{\chi}}^{\mathrm{a}\mathrm{b}\mathrm{c}\mathrm{d}}(\ensuremath{-}\ensuremath{\omega};\ensuremath{-}\ensuremath{\omega},\ensuremath{-}\ensuremath{\omega},\ensuremath{\omega})$ and the two-photon absorption coefficient are calculated, including the scissors correction needed to correct the well-known underestimation of the local-density-approximation band gap. Using time-reversal symmetry, it is shown that the expression for ${\ensuremath{\chi}}^{\mathrm{a}\mathrm{b}\mathrm{c}\mathrm{d}}(\ensuremath{-}\ensuremath{\omega};\ensuremath{-}\ensuremath{\omega},\ensuremath{-}\ensuremath{\omega},\ensuremath{\omega})$ is finite at $\ensuremath{\omega}=0$, avoiding nonphysical divergences presented in previous calculations when $\ensuremath{\omega}\ensuremath{\rightarrow}0$. Ab initio band structure calculations using different pseudopotential schemes that include spin-orbit coupling are used to calculate the 2PA for several semiconductors, and the calculations are compared with available experimental results for photon energies that are below the optical band gap.

Comparison of Length, Velocity, and Symmetric Gauges for the Calculation of Absorption and Electric Circular Dichroism Spectra with Real-Time Time-Dependent Density Functional Theory.

A velocity and symmetric gauge implementation for real-time time-dependent density functional theory (RT-TDDFT) in the CP2K package using a Gaussian and plane wave approach is presented, including the explicit gauge-transformed contributions due to the nonlocal part of pseudopotentials. Absorption spectra of gas-phase α-pinene are calculated in length and velocity gauges in the long-wavelength approximation for the application of a δ pulse in linear and full order. The velocity gauge implementation is also applied to a solvated uracil molecule to showcase its use within periodic boundary conditions (PBC). For the calculation of the expectation value of the electric dipole moment in PBC, both the velocity representation and the modern theory of polarization give equivalent absorption spectra if a distributed reference point is used for the nonlocal term of the velocity operator. The discussion of linear response theory takes place in a unified framework in terms of linear response functions in propagator notation, distinguishing the parts of the linear response functions associated with perturbation and response. To further investigate gauge dependence, electric circular dichroism (ECD) spectra of α-pinene were calculated either as magnetic response to an electric field perturbation, in length or velocity gauge, or as electric response to a magnetic field perturbation in the symmetric gauge. Both approaches, electric and magnetic perturbations, have been found to yield equivalent ECD spectra.

Cavity-induced non-adiabatic dynamics and spectroscopy of molecular rovibrational polaritons studied by multi-mode quantum models

We study theoretically the quantum dynamics and spectroscopy of rovibrational polaritons formed in a model system composed of a single rovibrating diatomic molecule, which interacts with two degenerate, orthogonally polarized modes of an optical Fabry-Pérot cavity. We employ an effective rovibrational Pauli-Fierz Hamiltonian in length gauge representation and identify three-state vibro-polaritonic conical intersections (VPCIs) between singly excited vibro-polaritonic states in a two-dimensional angular coordinate branching space. The lower and upper vibrational polaritons are of mixed light-matter hybrid character, whereas the intermediate state is purely photonic in nature. The VPCIs provide effective population transfer channels between singly excited vibrational polaritons, which manifest in rich interference patterns in rotational densities. Spectroscopically, three bright singly excited states are identified when an external infrared laser field couples to both a molecular and a cavity mode. The non-trivial VPCI topology manifests as pronounced multi-peak progression in the spectral region of the upper vibrational polariton, which is traced back to the emergence of rovibro-polaritonic light-matter hybrid states. Experimentally, ubiquitous spontaneous emission from cavity modes induces a dissipative reduction of intensity and peak broadening, which mainly influences the purely photonic intermediate state peak as well as the rovibro-polaritonic progression.