Dynamic evolution of Kohn-Sham electron density in the real-time domain with finite basis expansion.

We present a novel method for time-dependent density functional theory calculations on dynamic linear response and electron density evolution in the real-time domain with the finite basis expansion approach of conventional quantum chemistry. To demonstrate the validity and efficiency of this method, dynamic polarizabilities of a water chain and diphenylene molecules are computed by employing the Chebyshev interpolation algorithm, which was developed by Baer and co-workers. The calculated dynamic polarizabilities show good agreement with those obtained from conventional linear response calculations. The density evolution in the real-time domain with application of a long-duration electric field gives electronic conduction in molecules, where a dynamic process of charge transfer is observed with the snapshots of response density in real time. Charge transfer oscillating with the frequency of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) gap is shown in a diphenylene molecule while there is little change in time for a water chain.     

Multiscale quantum propagation using compact-support wavelets in space and time

Orthogonal compact-support Daubechies wavelets are employed as bases for both space and time variables in the solution of the time-dependent Schrodinger equation. Initial value conditions are enforced using special early-time wavelets analogous to edge wavelets used in boundary-value problems. It is shown that the quantum equations may be solved directly and accurately in the discrete wavelet representation, an important finding for the eventual goal of highly adaptive multiresolution Schrodinger equation solvers. While the temporal part of the basis is not sharp in either time or frequency, the Chebyshev method used for pure time-domain propagations is adapted to use in the mixed domain and is able to take advantage of Hamiltonian matrix sparseness. The orthogonal separation into different time scales is determined theoretically to persist throughout the evolution and is demonstrated numerically in a partially adaptive treatment of scattering from an asymmetric Eckart barrier.     

电磁波作用下化学反应体系极化特性表征

近年来,微波促进化学反应引起人们的广泛关注,但是热点和热失控等问题限制了微波化学工业的发展。为了解决这些问题,需要研究电磁波与化学反应体系的相互作用规律。其中,电磁波作用下化学反应体系极化特性的表征是研究电磁波与化学反应体系的相互作用的基础。本文通过改进的SmoluchowskiDebye方程,得到了极性分子反应体系的极化特性的表征。由于电磁波作用下化学反应体系的极化过程实际上是一个线性时变系统的响应,只在一定条件下是马尔可夫过程。本文进一步讨论了极化的时域表征与频域表征的关系以及频域表征的局限性。     

Analysis of the topological dependency of the characteristic polynomial in its chebyshev expansion

The structural dependency (effect of branching and cyclisation) of an alternative form, the Chebyshev expansion, for the characteristic polynomial were investigated systematically. Closed forms of the Chebyshev expansion for an arbitrary star graph and a bicentric tree graph were obtained in terms of the “structure factor” expressed as the linear combination of the “step-down operator”. Several theorems were also derived for non-tree graphs. Usefulness and effectiveness of the Chebyshev expansion are illustrated with a number of examples. Relation with the topological index (Z _G ) was discussed. Operated for the U.S. Department of Energy by ISU under contract no. W-ENG-7405-82. Supported in part by the Office of Director     

Density matrix based time-dependent density functional theory and the solution of its linear response in real time domain

A density matrix based time-dependent density functional theory is extended in the present work. Chebyshev expansion is introduced to propagate the linear response of the reduced single-electron density matrix upon the application of a time-domain delta-type external potential. The Chebyshev expansion method is more efficient and accurate than the previous fourth-order Runge-Kutta method and removes a numerical divergence problem. The discrete Fourier transformation and filter diagonalization of the first-order dipole moment are implemented to determine the excited state energies. It is found that the filter diagonalization leads to highly accurate values for the excited state energies. Finally, the density matrix based time-dependent density functional is generalized to calculate the energies of singlet-triplet excitations.     

Moment expansion of the linear density‐density response function

We present a low rank moment expansion of the linear density‐density response function. The general interacting (fully nonlocal) density‐density response function is calculated by means of its spectral decomposition via an iterative Lanczos diagonalization technique within linear density functional perturbation theory. We derive a unitary transformation in the space of the eigenfunctions yielding subspaces with well‐defined moments. This transformation generates the irreducible representations of the density‐density response function with respect to rotations within SO(3). This allows to separate the contributions to the electronic response density from different multipole moments of the perturbation. Our representation maximally condenses the physically relevant information of the density‐density response function required for intermolecular interactions, yielding a considerable reduction in dimensionality. We illustrate the performance and accuracy of our scheme by computing the electronic response density of a water molecule to a complex interaction potential. © 2015 Wiley Periodicals, Inc.     

Time reversible and symplectic integrators for molecular dynamics simulations of rigid molecules

Molecular dynamics integrators are presented for translational and rotational motion of rigid molecules in microcanonical, canonical, and isothermal-isobaric ensembles. The integrators are all time reversible and are also, in some approaches, symplectic for the microcanonical ensembles. They are developed utilizing the quaternion representation on the basis of the Trotter factorization scheme using a Hamiltonian formalism. The structure is similar to that of the velocity Verlet algorithm. Comparison is made with standard integrators in terms of stability and it is found that a larger time step is stable with the new integrators. The canonical and isothermal-isobaric molecular dynamics simulations are defined by using a chain thermostat approach according to generalized Nosé-Hoover and Andersen methods.     

Efficient computation of root mean square deviations under rigid transformations

The computation of root mean square deviations (RMSD) is an important step in many bioinformatics applications. If approached naively, each RMSD computation takes time linear in the number of atoms. In addition, a careful implementation is required to achieve numerical stability, which further increases runtimes. In practice, the structural variations under consideration are often induced by rigid transformations of the protein, or are at least dominated by a rigid component. In this work, we show how RMSD values resulting from rigid transformations can be computed in constant time from the protein's covariance matrix, which can be precomputed in linear time. As a typical application scenario is protein clustering, we will also show how the Ward‐distance which is popular in this field can be reduced to RMSD evaluations, yielding a constant time approach for their computation. © 2014 Wiley Periodicals, Inc.     

Reduced eigensystem representation of the linear density-density response function

The linear density-density response function represents a formulation of the generalized density response of a molecular (or extended) system to arbitrary perturbing potentials. We have recently established an approach for reducing the dimension of the (in principle infinite) eigenspace representation (the moment expansion) and generalized it to arbitrary self-adjoint, positive-definite, and compact linear operators. Here, we present a modified representation—the reduced eigensystem representation—which allows to define a trivial criterion for the convergence of the approximation to the density response. By means of this novel eigensystem-like structure, the remarkable reduction of the dimensionality becomes apparent for the calculation of the density-density response function.     

Irreducible correlation functions of the S matrix in the coordinate representation: application in calculating Lorentzian half-widths and shifts

By introducing the coordinate representation, the derivation of the perturbation expansion of the Liouville S matrix is formulated in terms of classically behaved autocorrelation functions. Because these functions are characterized by a pair of irreducible tensors, their number is limited to a few. They represent how the overlaps of the potential components change with a time displacement, and under normal conditions, their magnitudes decrease by several orders of magnitude when the displacement reaches several picoseconds. The correlation functions contain all dynamical information of the collision processes necessary in calculating half-widths and shifts and can be easily derived with high accuracy. Their well-behaved profiles, especially the rapid decrease of the magnitude, enables one to transform easily the dynamical information contained in them from the time domain to the frequency domain. More specifically, because these correlation functions are well time limited, their continuous Fourier transforms should be band limited. Then, the latter can be accurately replaced by discrete Fourier transforms and calculated with a standard fast Fourier transform method. Besides, one can easily calculate their Cauchy principal integrations and derive all functions necessary in calculating half-widths and shifts. A great advantage resulting from introducing the coordinate representation and choosing the correlation functions as the starting point is that one is able to calculate the half-widths and shifts with high accuracy, no matter how complicated the potential models are and no matter what kind of trajectories are chosen. In any case, the convergence of the calculated results is always guaranteed. As a result, with this new method, one can remove some uncertainties incorporated in the current width and shift studies. As a test, we present calculated Raman Q linewidths for the N2-N2 pair based on several trajectories, including the more accurate "exact" ones. Finally, by using this new method as a benchmark, we have carried out convergence checks for calculated values based on usual methods and have found that some results in the literature are not converged.     

Minimum-error method for scattering problems in quantum mechanics: Two stable and efficient implementations

We examine here, by using a simple example, two implementations of the minimum error method (MEM), a least-squares minimization for scattering problems in quantum mechanics, and show that they provide an efficient, numerically stable alternative to Kohn variational principle. MEM defines an error-functional consisting of the sum of the values of (HPsi - EPsi)2 at a set of grid points. The wave function Psi, is forced to satisfy the scattering boundary conditions and is determined by minimizing the least-squares error. We study two implementations of this idea. In one, we represent the wave function as a linear combination of Chebyshev polynomials and minimize the error by varying the coefficients of the expansion and the R-matrix (present in the asymptotic form of Psi). This leads to a linear equation for the coefficients and the R-matrix, which we solve by matrix inversion. In the other implementation, we use a conjugate-gradient procedure to minimize the error with respect to the values of Psi at the grid points and the R-matrix. The use of the Chebyshev polynomials allows an efficient and accurate calculation of the derivative of the wave function, by using Fast Chebyshev Transforms. We find that, unlike KVP, MEM is numerically stable when we use the R-matrix asymptotic condition and gives accurate wave functions in the interaction region.     

Support vector regression with digital band pass filtering for the quantitative analysis of near‐infrared spectra

This paper proposes a novel calibration technique based on combining support vector regression with a digital band pass (DBP) filter for the quantitative analysis of near‐infrared spectra. The efficacy of the proposed method is investigated and validated in the determination of glucose from near‐infrared spectra of a mixture composed of urea, triacetin and glucose. In this paper, the DBP filtering was implemented as a pre‐processing technique in the frequency domain as a Gaussian band pass filter and in the time domain as a Chebyshev filter. The grid‐search optimization method was used to optimize the filter parameters. The results demonstrate that utilization of the optimized DBP filters as a pre‐processing technique improved the performance of the predictive models. Copyright © 2013 John Wiley & Sons, Ltd.     

Dérivées de fonctionnelles intégrales dans des perturbations de fissures exprimées par intégrales de frontière

This note presents, in the framework of three-dimensional linear elastodynamics in the time domain, a method for evaluating sensitivities of integral functionals to crack shapes, based on the adjoint state approach and resulting in a sensitivity formula expressed in terms of surface integrals (on the external boundary and the crack surface) and contour integrals (involving the direct and adjoint stress intensity factor distributions on the crack front). This method is well-suited to boundary element treatments of e.g. crack reconstruction inverse problems.     

Discrete version of Wiener-Khinchin theorem for Chebyshev’s spectrum of electrochemical noise

A discrete version of Wiener-Khinchin theorem for Chebyshev’s spectrum of electrochemical noise is developed. Based on the discrete version of Wiener-Khinchin theorem, the theoretical discrete Chebyshev spectrum for the Markov random process is calculated. It is characterized by two parameters: the dispersion and the relaxation frequency (or relaxation time). The noise of corrosion process and the noise of recording equipment are measured. Using the theoretical Chebyshev spectrum, the Markov parameters were found both for the noise of the corrosion process and for the noise of the measuring equipment.     

Hyper-aging dynamics of nanoclay suspension

Aqueous suspension of nanoclay Laponite undergoes structural evolution as a function of time, which enhances its elasticity and relaxation time. In this work, we employ an effective time approach to investigate long-term relaxation dynamics by carrying out creep experiments. Typically, we observe that the monotonic evolution of elastic modulus shifts to lower aging times, while maxima in viscous moduli get progressively broader for experiments carried out on a later date after preparation (idle time) of the nanoclay suspension. Application of effective time theory produces a superposition of all the creep curves irrespective of their initial state. The resulting dependence of the relaxation time on aging time shows very strong hyper-aging dynamics at short idle times, which progressively weakens to demonstrate a linear dependence in the limit of very long idle times. Remarkably, this behavior of nanoclay suspensions is akin to that observed for polymeric glasses. Consideration of aging as a first-order process suggests that continued hyper-aging dynamics causes cessation of aging. The dependence of relaxation time on aging time, therefore, must attenuate eventually producing linear or weaker dependence on time in order to approach a progressively low-energy state in the limit of very long times as observed experimentally. We also develop a simple scaling model based on a concept of aging of an energy well, which qualitatively captures various experimental observations very well, leading to profound insight into the hyper-aging dynamics of nanoclay suspensions.     

Real-time propagation of the reduced one-electron density matrix in atom-centered Gaussian orbitals: application to absorption spectra of silicon clusters

We solve the time-dependent density functional theory equation by propagating the reduced one-electron density matrix in real-time domain. The efficiency of several standard solvers such as the short-iterative Krylov-subspace propagator, the low-order Magnus integration method with the matrix polynomial (MP) or Chebyshev matrix polynomial (CMP) expansion of the evolution operator, and Runge-Kutta algorithm are assessed. Fast methods for summing MP and CMP are implemented to speed the calculation of the matrix exponential. It is found that the exponential propagators can tolerate large time step size and retain the computational accuracy whereas the Krylov-subspace algorithm is a little inferior for a larger time step size compared with the second-order Magnus integration method with the MP/CMP expansion of the evolution operator in both weak and intense fields. As an application, we calculate the absorption spectra of hydrogen-passivated silicon nanoparticles Si(29)H(x). The popular hybrid and generalized gradient approximation exchange-correlation functionals are applied. We find that the experimental spectra can be reproduced by using B3LYP and that the silicon particles with sizes of 1 nm and the optical excitations at 3.7, 4.0, and 4.6 eV may consist of 29 Si atoms surrounded by 24 hydrogen atoms.     

Multiphonon decay of excited states of rare earth ions in crystals

Although the relaxation of excited electronic states through radiationless multiphonon processes has been well established by experiment, there are several serious problems concerning the current theoretical model in which the electron-phonon interaction is treated as a small perturbation, and the multiphonon transitions are attributed to high order expansion terms of perturbation theory. Here, we approach the problem in the framework of the adiabatic approximation. The rate of the multiphonon process is expressed in the form of the linear response time correlation function which is then evaluated by means of the saddle point approximation. The resulting expression predicts an approximately exponential dependence of the rate on the transition gap and a temperature dependence that agrees quantitatively with experiment.     

Wavelet-Based Method for Time-Domain Noise Analysis and Reduction in a Frequency-Scan Ion Trap Mass Spectrometer

We adopt an orthogonal wavelet packet decomposition (OWPD) filtering approach to cancel harmonic interference noises arising from an AC power source in time domain and remove the resulting rf voltage interference noise from the mass spectra acquired by using a charge detection frequency-scan quadrupole ion trap mass spectrometer. With the use of a phase lock resampling technique, the transform coefficients of the rf interference in signals become a constant, exhibiting a shift of the baseline in different rf phases. The rf interference is therefore removable by shifting the baselines back to zero in OWPD coefficients. The approach successfully reduces the time-domain background noise from 1367 electrons (rms) to 408 electrons (rms) (an improvement of 70?%) and removes the high frequency noise components in the charge detection ion trap mass spectrometry. Unlike other smoothing or averaging methods commonly used in the mass-to-charge (m/Ze) domain, our approach does not cause any distortion of original signals.     

An Eigenfunction Expansion for the Schrödinger Equation with Arbitrary Non-Central Potentials

An eigenfunction expansion for the Schrödinger equation for a particle moving in an arbitrary non-central potential in the cylindrical polar coordinates is introduced, which reduces the partial differential equation to a system of coupled differential equations in the radial variable r. It is proved that such an orthogonal expansion of the wavefunction into the complete set of Chebyshev polynomials is uniformly convergent on any domain of (r,). As a benchmark application, the bound states calculations of the quartic oscillator show that both analytical and numerical implementations of the present method are quite satisfactory.