Theoretical investigation on the excited state intramolecular proton transfer in Me_(2)N substituted flavonoid by the time-dependent density functional theory method

Time-dependent density functional theory(TDDFT)method is used to investigate the details of the excited state intramolecular proton transfer(ESIPT)process and the mechanism for temperature effect on the Enol^(*)/Keto^(*)emission ratio for the Me_(2)N-substited flavonoid(MNF)compound.The geometric structures of the S_(0) and S_(1) states are denoted as the Enol,Enol^(*),and Keto*.In addition,the absorption and fluorescence peaks are also calculated.It is noted that the calculated large Stokes shift is in good agreement with the experimental result.Furthermore,our results confirm that the ESIPT process happens upon photoexcitation,which is distinctly monitored by the formation and disappearance of the characteristic peaks of infrared(IR)spectra involved in the proton transfer and in the potential energy curves.Besides,the calculations of highest occupied molecular orbital(HOMO)and lowest unoccupied molecular orbital(LUMO)reveal that the electronegativity change of proton acceptor due to the intramolecular charge redistribution in the S_(1) state induces the ESIPT.Moreover,the thermodynamic calculation for the MNF shows that the Enol^(*)/Keto^(*)emission ratio decreasing with temperature increasing arises from the barrier lowering of ESIPT.

Time-dependent Diffusion Coefficient and Conventional Diffusion Constant of Nanoparticles in Polymer Melts by Mode-coupling Theory

Time-dependent diffusion coefficient and conventional diffusion constant are calculated and analyzed to study diffusion of nanoparticles in polymer melts. A generalized Langevin equa- tion is adopted to describe the diffusion dynamics. Mode-coupling theory is employed to calculate the memory kernel of friction. For simplicity, only microscopic terms arising from binary collision and coupling to the solvent density fluctuation are included in the formalism. The equilibrium structural information functions of the polymer nanocomposites required by mode-coupling theory are calculated on the basis of polymer reference interaction site model with Percus-Yevick closure. The effect of nanoparticle size and that of the polymer size are clarified explicitly. The structural functions, the friction kernel, as well as the diffusion coefficient show a rich variety with varying nanoparticle radius and polymer chain length. We find that for small nanoparticles or short chain polymers, the characteristic short time non-Markov diffusion dynamics becomes more prominent, and the diffusion coefficient takes longer time to approach asymptotically the conventional diffusion constant. This constant due to the microscopic contributions will decrease with the increase of nanoparticle size, while increase with polymer size. Furthermore, our result of diffusion constant from mode- coupling theory is compared with the value predicted from the Stokes-Einstein relation. It shows that the microscopic contributions to the diffusion constant are dominant for small nanoparticles or long chain polymers. Inversely, when nanonparticle is big, or polymer chain is short, the hydrodynamic contribution might play a significant role.

A time-dependent density functional theory investigation of plasmon resonances of linear Au atomic chains

We report theoretical studies on the plasmon resonances in linear Au atomic chains by using ab initio time- dependent density functional theory. The dipole responses are investigated each as a function of chain length. They converge into a single resonance in the longitudinal mode but split into two transverse modes. As the chain length increases, the longitudinal plasmon mode is redshifted in energy while the transverse modes shift in the opposite direction （blueshifts）. In addition, the energy gap between the two transverse modes reduces with chain length increasing. We find that there are unique characteristics, different from those of other metallic chains. These characteristics are crucial to atomic-scale engineering of single-molecule sensing, optical spectroscopy, and so on.

A three-dimensional time-dependent theory for helix traveling wave tubes in beam-wave interaction

This paper presents a three-dimensional time-dependent nonlinear theory of helix traveling wave tubes for beam- wave interaction. The radio frequency electromagnetic fields are represented as the superposition of azimuthally sym- metric waves in a vacuum sheath helix. Coupling impedance is introduced to the electromagnetic field equations＇ stimulating sources, which makes the theory easier and more flexible to realize. The space charge fields are calculated by electron beam space-charge waves expressed as the superposition solutions of Helmholtz equations. The focusing forces due to either a solenoidal field or a periodic permanent magnetic field is also included. The dynamical equations of electrons are Lorentz equations associating with electromagnetic fields, focusing fields and space-charge fields. The numerically simulated results of a tube are presented.

Two-photon excitation for C_2Vmolecules based on the full relativistic theory

The present work explores a new phenomenon that not all the transition probability of two photon processes is negligible at low irradiance. The irreducible representation 2B2 of C2v is unexpected, for there is no much deviation in oscillator strength for two-photon and single-photon process A1 to 2B2. This new phenomenon is only possible to be explored by the symmetrical consideration: the necessary and sufficient condition is molecular plane coincident with yz plane or the operation σ ’v(yz) for group C2v. It is only possible to be evaluated out by use of the full relativistic quantum mechanical theory.

Theoretical Study on the Optical Properties for 2,7- and 3,6-Linked Carbazole Trimers by Time-dependent Density Functional Theory

Electronic properties, such as HOMO and LUMO energies, band gaps, ionization potential （IP） and electron affinity （EA） of 2,7- and 3,6-1inked carbazole trimers, two conjugated oligomcrs with different linkages of carbazole, were studicd by the density functional theory with Becke-Lee-Young-Parr composite exchange correlation functional （B3LYP）. The absorption spectra of these compounds were also investigated by time-dependent density functional theory （TD-DFT） with 6-3 IG＊ basis set. The calculated results indicated that the HOMO and LUMO of the 2,7- and 3,6-1inked carbazole trimers are both slightly destabilized on going from methyl substitution to sec-butyl substitution. Both IP and EA exhibit their good hole-transporting but poor electronaccepting ability. The presence of alkyl groups on the nitrogen atoms does not affect the intra-chain electronic delocalization along the molecular frame. Thus no significant effect on the band gap and absorption spectra of compounds has been found.

Theoretical Investigation on Triplet Excitation Energy Transfer in Fluorene Dimer

Triplet-triplet energy transfer in fluorene dimer with electronic structure calculations. The two is investigated by combining rate theories key parameters for the control of energy transfer, electronic coupling and reorganization energy, are calculated based on the diabatic states constructed by the constrained density functional theory. The fluctuation of the electronic coupling is further revealed by molecular dynamics simulation. Succeedingly, the diagonal and off-diagonal fluctuations of the Hamiltonian are mapped from the correlation functions of those parameters, and the rate is then estimated both from the perturbation theory and wavepacket diffusion method. The results manifest that both the static and dynamic fluctuations enhance the rate significantly, but the rate from the dynamic fluctuation is smaller than that from the static fluctuation.

Study of the excitation properties of the Si_3 O_2 cluster under an external electric field

The structure of the Si3Ox （x =2, 3） cluster is investigated; we find that the geometry of Si3O2 is similar to that of Si3O3 except for the oxygen-deficient defect structure （Si-Si band） which exists only in the Si3O2 cluster. It is known that oxygen-deficient defects are used to explain visible luminescence （especially blue, purple and ultraviolet light） from silicon-based materials, which are directly bound up with the excited states of the molecules. Therefore the excitation properties of the two clusters are also studied. Our results show that the absorption spectrum of Si3O2 is concentrated in the visible light region. In contrast, the absorption spectrum of Si3O3 is mainly located in the ultraviolet light region. The calculations are perfectly consistent with experimental data and also support the theory of oxygen-deficient defects.

Determination of safe mud window considering time-dependent variations of temperature and pore pressure:Analytical and numerical approaches

Wellbore stability is a key to have a successful drilling operation.Induced stresses are the main factors affecting wellbore instability and associated problems in drilling operations.These stresses are significantly impacted by pore pressure variation and thermal stresses in the field.In order to address wellbore instability problems,it is important to investigate the mechanisms of rockefluid interaction with respect to thermal and mechanical aspects.In order to understand the induced stresses,different mathematical models have been developed.In this study,the field equations governing the problem have been derived based on the thermo-poroelastic theory and solved analytically in Laplace domain.The results are transferred to time domain using Fourier inverse method.Finite difference method is also utilized to validate the results.Pore pressure and temperature distributions around the wellbore have been focused and simulated.Next,induced radial and tangential stresses for different cases of cooling and heating of formation are compared.In addition,the differences between thermo-poroelastic and poroelastic models in situation of permeable and impermeable wellbores are described.It is observed that cooling and pore pressure distribution reinforce the induced radial stress.Whereas cooling can be a tool to control and reduce tangential stress induced due to invasion of drilling fluid.In the next step,safe mud window is obtained using Mohr-Coulomb,Mogi-Coulomb,and modified Lade failure criteria for different inclinations.Temperature and pore pressure distributions do not change the minimum allowable wellbore pressure significantly.However,upper limit of mud window is sensitive to induced stresses and it seems vital to consider changes in temperature and pore pressure to avoid any failures.The widest and narrowest mud windows are proposed by modified Lade and Mohr-Coulomb failure criteria,respectively.

Influence of Auxiliary Equation on Wave Functions for Time-Dependent Pauli Equation in Presence of Aharonov-Bohm Effect

Invariant operator method for discrete or continuous spectrum eigenvalue and unitary transformation approach are employed to study the two-dimensional time-dependent Pauli equation in presence of the Aharonov-Bohm effect （AB） and external scalar potential. For the spin particles the problem with the magnetic field is that it introduces a singularity into wave equation at the origin. A physical motivation is to replace the zero radius flux tube by one of radius R, with the additional condition that the magnetic field be confined to the surface of the tube, and then taking the limit R → 0 at the end of the computations. We point that the invariant operator must contain the step function θ（r - R）. Consequently, the problem becomes more complicated. In order to avoid this dimculty, we replace the radius R by ρ（t）R, where ρ（t） is a positive time-dependent function. Then at the end of calculations we take the limit R →0. The qualitative properties for the invariant operator spectrum are described separately for the different values of the parameter C appearing in the nonlinear auxiliary equation satisfied by p（t）, i.e., C 〉 0, C = 0, and C 〈0. Following the C＇s values the spectrum of quantum states is discrete （C 〉 0） or continuous （C ≤ 0）.

Time Evolution Caused by Hamiltonian Composed of Quadratic Combination of Canonical Operators and Time-Dependent Two-Mode Fresnel Operator

We show that the time-dependent two-mode Fresnel operator is just the time-evolutional unitary operator governed by the Hamiltonian composed of quadratic combination of canonical operators in the way of exhibiting SU（1,1） algebra. This is an approach for obtaining the time-dependent Hamiltonian from the preassigned time evolution in classical phase space, an approach which is in contrast to Lewis-Riesenfeld＇s invariant operator theory of treating timedependent harmonic oscillators.

Variational Calculation of the Doubly-Excited States Nsnp of He-Like Ions via the Modified Atomic Orbitals Theory

In this paper, we have declined the formalism of the method of the Modified Atomic Orbital Theory (MAOT) applied to the calculations of energies of doubly excited states 2snp, 3snp, and 4snp Helium-like systems. Then we also applied the variational procedure of the Modified Atomic Orbital Theory to the computations of total energies, excitation energies of doubly-excited states 2snp, 3snp, 4snp types of Helium-like systems. The results obtained in this work are in good agreement with the experimental and theoretical values available.

Catastrophe Model of Steam Flow Excitation Vibration in Steam Turbine Governing Stage

汽流激振是影响大型汽轮机组安全运行的主要故障之一。根据突变理论、非线性振动理论以及流体动力学，从机理分析的角度出发，对汽轮机调节级在部分进汽下导致的汽流激振突变性能进行了定量分析。建立了部分进汽情况下调节级气流激振力模型，以及考虑汽流激振力的调节级非线性动力学模型，通过基于突变理论的推导，得到了调节级汽流激振的尖点突变流形和分岔集，确定了系统汽流激振突变的影响因子，讨论了振幅突变与影响因子的相关性，划分了系统工作的突变区域。最后，利用数值计算方法对汽流激振的幅值响应进行了分析，分析结果验证了基于突变理论的汽流激振突变分析方法的正确性。研究成果为汽轮机汽流激振突变性能的研究提供了一条新的途径。

Effects of the Earth’s triaxiality on the polar motion excitations

This study aims to evaluate the significance of the Earth＇ s triaxiality to the polar motion theory. First of all, we compare the polar motion theories for both the triaxial and rotationally-symmetric Earth models, which is established on the basis of the EGM2008 global gravity model and the MHB2000 Earth model. Then, we use the atmospheric and oceanic data （the NCEP/NCAR reanalyses and the ECCO assimulation products） to quantify the triaxiality effect on polar motion excitations. Numerical results imply that triaxiality only cause a small correction （ about 0. 1 - 0. 2 mas） to the geophysical excitations for the rotationally-symmetric case. The triaxiality correction is much smaller than the errors in the atmospheric and oceanic data, and thus can be neglected for recent studies on polar motion excitations.

Resonance enhanced electron impact excitation for P-like Cu XV

Employing both the Dirac R-matrix and the relativistic distorted wave with independent process and isolated reso- nance approaches, we report resonance enhanced electron impact excitation data （specifically, effective collision strengths） among the lowest 41 levels from the n = 3 configurations of Cu XV. The results show that the latter approach can obtain resonance contributions reasonably well for most excitations of Cu XV, though a comparison between the two approaches shows that the close-coupling effects are truly significant for rather weak excitations, especially for two-electron excitations from the 3s3p4 to 3s23p23d configuration. Resonance contributions are significant （more than two orders of magnitude） for many excitations and dramatically influence the line intensity ratios associated with density diagnostics.

Time-dependent Density Functional-based Tight-bind Method Efficiently Implemented with OpenMP Parallel and GPU Acceleration

The time-dependent density functional-based tight-bind （TD-DFTB） method is implemented on the multi-core and the graphical processing unit （GPU） system for excited state calcu-lations of large system with hundreds or thousands of atoms. Sparse matrix and OpenMP multithreaded are used for building the Hamiltonian matrix. The diagonal of the eigenvalue problem in the ground state is implemented on the GPUs with double precision. The GPU- based acceleration fully preserves all the properties, and a considerable total speedup of 8.73 can be achieved. A Krylov-space-based algorithm with the OpenMP parallel and CPU acceleration is used for finding the lowest eigenvalue and eigenvector of the large TDDFT matrix, which greatly reduces the iterations taken and the time spent on the excited states eigenvalue problem. The Krylov solver with the GPU acceleration of matrix-vector product can converge quickly to obtain the final result and a notable speed-up of 206 times can be observed for system size of 812 atoms. The calculations on serials of small and large systems show that the fast TD-DFTB code can obtain reasonable result with a much cheaper computational requirement compared with the first-principle results of CIS and full TDDFT calculation.

Testing the validity of the Ehrenfest theorem beyond simple static systems: Caldirola–Kanai oscillator driven by a time-dependent force

The relationship between quantum mechanics and classical mechanics is investigated by taking a Gaussian-type wave packet as a solution of the Schr o¨dinger equation for the Caldirola–Kanai oscillator driven by a sinusoidal force. For this time-dependent system, quantum properties are studied by using the invariant theory of Lewis and Riesenfeld. In particular,we analyze time behaviors of quantum expectation values of position and momentum variables and compare them to those of the counterpart classical ones. Based on this, we check whether the Ehrenfest theorem which was originally developed in static quantum systems can be extended to such time-varying systems without problems.

Theoretical Insights into Intermolecular Hydrogen-Bonding Strengthening in Fluorenone-Methanol Complexes Induced by Electronic Excitation and Bulk Solvent Effect

This work presents a theoretical insight into the variation of the site-specific intermolecular hydrogen-bonding （HB）, formed between C=O group of fluorenone （FN） and O-H groups of methanol （MeOL） molecules, induced by both the electronic excitation and the bulk solvent effect. Through the calculation of molecular ground- and excited-state properties, we not only demonstrate the characters of HB strengthening induced by electronic excitation and the bulk solvent effect but also reveal the underlying physical mechanism which leads to the HB variation. The strengthening of the intermolecular HB in electronically excited states and in liquid solution is characterized by the reduced HB bond-lengths and the red-shift IR spectra accompanied by the increasing intensities of IR absorption corresponding to the characteristic vibrational modes of the O-H and C--O stretching. The HB strengthening in the excited electronic states and in solution mainly arises from the charge redistribution of the FN molecule induced by the electronic excitation and bulk solvent instead of the intermolecular charge transfer. The charge redistribution of the solute molecule increases the partial dipole moment of FN molecule and the FN-MeOL intermolecular interaction, which subsequently leads to the HB strengthening. With the bulk solvent effect getting involved, the theoretical IR spectra of HBed FN-MeOL complexes agree much better with the experiments than those of gas-phase FN-MeOL dimer. All the calculations are carried out based on our developed analytical approaches for the first and second energy derivatives of excited electronic state within the time-dependent density functional theory.

Photodetachment dynamics of H^- ion in a harmonic potential plus a time-dependent oscillating electric field

The photodetachment dynamics of H^- ion in a harmonic potential plus an oscillating electric field is studied using the time-dependent closed orbit theory. An analytical formula for calculating the photodetachment cross section of this system is put forward. It is found that the photodetachment cross section of this system is nearly unaffected for the weak oscillating electric field strength, but oscillates complicatedly when the oscillating electric field strength turns strong. In addition, the frequency of the harmonic potential and the oscillating electric field （the frequency of the harmonic potential and the frequency of the oscillating electric field are the same in the paper, unless otherwise stated.） can also affect the photodetachment dynamics of this system. With the increase of the frequency in the harmonic potential and the oscillating electric field, the number of the closed orbits for the detached electrons increased, which makes the oscillatory structure in the photodetachment cross section much more complex. Our study presents an intuitive understanding of the photodetachment dynamics driven by a harmonic potential plus an oscillating electric field from a space and time dependent viewpoint. This study is very useful in guiding the future experimental research for the photodetachment dynamics in the electric field both changing with space and time.

Redshift of Excitation Wavelength Caused by the Concentration of L-Tryptophan in Water: A Theoretical and Experimental Study

A redshift in the wavelength of excitation spectra is experimentally measured as a function of the concentration parameter for tryptophan solutions in water. To understand the microscopic causes of this behavior, theoretical calculations obtained from four model clusters are carried out: (Trp)1 - (H2O)9, (Trp)2 - (H2O)18, (Trp)3 - (H2O)27 and (Trp)4 - (H2O)36, where there are interactions among 1, 2, 3 and 4 molecules of tryptophan. According to the literature, each interaction occurred with nine molecules of water to stabilize its expected zwitterionic form. In these models, the molecules of tryptophan appear at an adjacent distance among them to generate an analogous behavior when there is an experimental increase in the concentration. It is evident that the distance between adjacent molecules of tryptophan decreases as their concentration increases. The optical properties of these clusters are obtained by studying the corresponding excited states and the molecular orbitals involved, showing charge transfers by using time-dependent density functional theory (TD-DFT) methods. The experimental spectroscopic data are obtained by using the clusters proposed, and good agreement is found by drawing a comparison with the theoretical data.