Time-dependent Wave Packet Quantum Scattering Study of Reaction S（3p）＋H2→HS＋H on a New ab initio Potential Energy Surface 3A’

A new potential energy surface is presented for the triplet state 3At of the chemical reaction S（3P）＋H2 from a set of accurate ab initio data. The single point energies are computed using highly correlated complete active space self-consistent-field and multi-reference configuration interaction wave functions with a basis set of aug-cc-pV5Z. We have fitted the full set of energy values using many-body expansion method with an Aguado-Paniagua function. Based on the new potential energy surface, we carry out the time-dependent wave packet scattering calculations over the collision energy range of 0.8-2.2 eV. Both the centrifugalsudden approximation and Coriolis Coupling cross sections are obtained. In addition, the total reaction probabilities are calculated for the reactant H2 initially in the vibrational states v=0-3 （j=0）. It is found that initial vibrational excitation enhances the title reaction.

Dynamics of the Au+H2 reaction by time-dependent wave packet and quasi-classical trajectory methods

Dynamics of the Au + H2 reaction are studied using time-dependent wave packet(TDWP) and quasi-classical trajectory(QCT) methods based on a new potential energy surface [Int. J. Quantum Chem. 118 e25493(2018)]. The dynamic properties such as reaction probability, integral cross section, differential cross section and the distribution of product are studied at state-to-state level of theory. Furthermore, the present results are compared with the theoretical studies available.The results indicate that the complex-forming reaction mechanism is dominated in the reaction in the low collision energy region and the abstract reaction mechanism plays a dominant role at high collision energies. Different from previous theoretical calculations, the side-ways scattering signals are found in the present work and become more and more apparent with increasing collision energy.

Time-Dependent Quantum Wave Packet Calculation for Reaction S-(^(2)P)+H_(2)(^(1)∑_(g)^(+))→SH-(^(1)∑)+H(^(2)S) on Ab Initio Potential Energy Surface

The time-dependent wave packet propagation method was applied to investigate the dynamic behaviours of the reaction S-(^(2)P)+H_(2)(^(1)∑_(g)^(+))→SH-(^(1)∑)+H(^(2)S)based on the electronic ground state(^(2)A′)potential energy surface of the SH_(2)-ionic molecule.The collision energy dependent reaction probabilities and integral cross sections are obtained.The numerical results suggest that there are significant oscillation structures over all the studied range of the collision energies.The vibrational excitation and rotational excitation of the diatomic reagent H_(2) promote the reactivity significantly as suggested by the numerical total reaction probabilities with the initial rotational quantum number of j=0,2,4,6,8,10,and the vibrational quantum number v=0,1,2,3,4.The numerical integral cross sections are quite consistent with the experimental data reported in previous work.

Time-dependent wave packet approach to the pulse delay effect upon RbI photoelectron spectrum

The time-resolved photoelectron spectrum (TRPES) of Rbl molecule is simulatedusing the time-dependent wave-packet method. Both the normal three-photon ionization process andauto-ionization process are involved in the simulation. The calculated results show that the changeof delay time will influence the shape of the photoelectron spectrum (PES), and the influence issubstantially due to the existence of the crossing between excited states and the strong laser fieldwhich will change the position of relevant curves.

Three-dimensional quantum dynamics study of vibrational predissociation of HeI_2 van der Waals molecule for low vibrational excitation using the time-dependent wave packet method

Three-dimensional quantum mechanical calculations for vibrational predissociation of HeI2(B) van der Waals molecules are presented using the time-dependent wave packet technique within the golden rule approxima tion.The total and partial decay widths,lifetimes,rates and their dependence on initial vibrational states were obtained for HeI2 at low initial vibrational excited levels.Our calculations show that the calculated tota decay widths,lifetimes and rates agree well with those extrapolated from experimental data available The predicted total decay widths as a function of initial vibrational states exhibit highly nonlinear behavior.The very short propagation time (less.than 1 ps) required in the golden rule wave packet calculation is determined by the duration time of the final state inter-action between the fragments on the vibrationally deexcited adiabatic potential surface.The final state interaction between the fragments is shown to play an important role in determining the final rotational distribution This interpreta tion clearly explains the dynamical effect that the final rotational distribution shifts to the lower rotational energy levels as the initial vibrational quantum number v increases.

Quantum dynamics of dissociative adsorption of H_2 and D_2:The time-dependent wave packet method

A time dependent quantum wave packet method was used to study the dynamics of dissociative adsorption of H 2 and D 2 on a flat and static surface. The molecule surface interaction is described using a modified London Eyring Polanyi Sato (LEPS) type potential for the H 2/Ni(100) system. The three dimensional (3 D) dissociation probabilities were calculated for different initial rovibrational states as a function of initial incident energies. Our results show that the dissociation of the diatomic rotational states whose quantum numbers satisfy j+m =odd is forbidden at low energies for the homonuclear H 2 and D 2 due to the selection rule. The effect of the rotational orientation of diatoms on adsorption predicts that the in plane rotation (m=j) is more favorable for dissociation than the out of plane rotation (m=0) . Enhanced dissociation for vibrationally excited molecules and the significant enhancement of the dissociation probability of H 2 when compared to D 2 were explained reasonably in terms of quantum mechanical zero point energies, the tunneling effect and the reflection from an activation barrier.

High-Accurate Transparent Boundary Conditions for Time-Dependent Quantum Wave Packet Method

Complex absorbing potential is usually required in a time-dependent wave packet method to accomplish the calculation in a truncated region.Usually it works effectively but becomes inefficient when the wave function involves translational energy of broad range,particularly involving ultra-low energy.In this work,a new transparent boundary condition(TBC)is proposed for the time-dependent wave packet method.It in principle is of spectral accuracy when typical discrete variable representations are applied.The prominent merit of the new TBC is that its accuracy is insensitive to the translational energy distribution of the wave function,in contrast with the complex absorbing potential.Application of the new TBC is given to one-dimensional particle wave packet scatterings from a barrier with a potential well,which supports resonances states.

Exact Wave Function of a Quantum Oscillator with Time-Dependent Frequency and Driving

The harmonic oscillator with time? dependent frequency and driving is studied by means of a new, simple method. By means of simple transformations of variables, the time dependent Schrdinger equation is first transformed into the time independent one. And then exact wave function is found in terms of solutions of the classical equation of motion of the oscillator.

Quantum Mechanics: Harmonic Wave-Packets, Localized by Resonant Response in Dispersion Dynamics

From a combination of Maxwell’s electromagnetism with Planck’s law and the de Broglie hypothesis, we arrive at quantized photonic wave groups whose constant phase velocity is equal to the speed of light c = ω/k and to their group velocity dω/dk. When we include special relativity expressed in simplest units, we find that, for particulate matter, the square of rest mass , i.e., angular frequency squared minus wave vector squared. This equation separates into a conservative part and a uniform responsive part. A wave function is derived in manifold rank 4, and from it are derived uncertainties and internal motion. The function solves four anomalies in quantum physics: the point particle with prescribed uncertainties;spooky action at a distance;time dependence that is consistent with the uncertainties;and resonant reduction of the wave packet by localization during measurement. A comparison between contradictory mathematical and physical theories leads to similar empirical conclusions because probability amplitudes express hidden variables. The comparison supplies orthodox postulates that are compared to physical principles that formalize the difference. The method is verified by dual harmonics found in quantized quasi-Bloch waves, where the quantum is physical;not axiomatic.

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.

Variable Coefficient KdV Equation for Amplitude of Nonlinear Solitary Rossby Waves in a Sort of Time-Dependent Zonal Flow

On the basis of the quasi-geostrophic vorticity equation,theoretical research has been down upon the evolution of the amplitude of solitary Rossby waves employing the perturbation method,and come to the conclusion that the evolution of the amplitude satisfies the variable coefficient Korteweg-de Vries(KdV) equation.

Nonlinear time-dependent simulation of helix traveling wave tubes

A one-dimensional nonlinear time-dependent theory for helix traveling wave tubes is studied. A generalized electromagnetic field is applied to the expression of the radio frequency field. To simulate the variations of the high frequency structure, such as the pitch taper and the effect of harmonics, the spatial average over a wavelength is substituted by a time average over a wave period in the equation of the radio frequency field. Under this assumption, the space charge field of the electron beam can be treated by a space charge wave model along with the space charge coefficient. The effects of the radio frequency and the space charge fields on the electrons are presented by the equations of the electron energy and the electron phase. The time-dependent simulation is compared with the frequency-domain simulation for a helix TWT, which validates the availability of this theory.

Dynamics of Periodic Waves in Bose-Einstein Condensate with Time-Dependent Atomic Scattering Length

Evolution of periodic waves and solitary waves in Bose-Einstein condensates （BECs） with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the mapping deformation method, we successfully obtain periodic wave solutions and solitary wave solutions, including the bright and dark soliton solutions.The results in this paper include some in the literatures [Phys. Rev. Lett. 94 （2005） 050402 and Chin. Phys. Left. 22 （2005） 1855].

Lax pair and vector semi-rational nonautonomous rogue waves for a coupled time-dependent coefficient fourth-order nonlinear Schrodinger system in an inhomogeneous optical fiber

Optical fibers are seen in the optical sensing and optical fiber communication. Simultaneous propagation of optical pulses in an inhomogeneous optical fiber is described by a coupled time-dependent coefficient fourth-order nonlinear Schr?dinger system, which is discussed in this paper. For such a system, we work out the Lax pair, Darboux transformation, and corresponding vector semi-rational nonautonomous rogue wave solutions. When the group velocity dispersion(GVD) and fourth-order dispersion(FOD) coefficients are the constants, we exhibit the first-and second-order vector semirational rogue waves which are composed of the four-petalled rogue waves and eye-shaped breathers. Both the width of the rogue wave along the time axis and temporal separation between the adjacent peaks of the breather decrease with the GVD coefficient or FOD coefficient. With the GVD and FOD coefficients as the linear, cosine, and exponential functions, we respectively present the first-and second-order periodic vector semi-rational rogue waves, first-and second-order asymmetry vector semi-rational rogue waves, and interactions between the eye-shaped breathers and the composite rogue waves.

Theoretical study of the influence of intense femtosecond laser field on the evolution of the wave packet and the population of NaRb molecule

Employing the two-state model and the time-dependent wave packet method, we have investigated the influences of the parameters of the intense femtosecond laser field on the evolution of the wave packet, as well as the population of ground and double-minimum electronic states of the NaRb molecule. For the different laser wavelengths, the evolution of the wave packet of 6{ }^1／Sigma ^ ＋ state with time and internuclear distance is different, and the different laser intensity brings different influences on the population of the electronic states of the NaRb molecule. One can control the evolutions of wave packet and the population in each state by varying the laser parameters appropriately, which will be a benefit for the light manipulation of atomic and molecular processes.

Influence of laser fields on the vibrational population of molecules and its wave-packet dynamical investigation

The time-dependent wave packet method is used to investigate the influence of laser-fields on the vibrational population of molecules. For a two-state system in laser fields, the populations on different vibrational levels of the upper and lower electronic states are given by wavefunctions obtained by solving the Schrbdinger equation with the split- operator method. The calculation shows that the field parameters, such as intensity, wavelength, duration, and delay time etc. can have different influences on the vibrational population. By varying the laser parameters appropriately one can control the evolution of wave packet and so the vibrational population in each state, which will benefit the light manipulation of atomic and molecular processes.

Time-dependent approach to the double-channel dissociation of the NaCs molecule induced by pulsed lasers

The dynamics of the double-channel dissociation of the NaCs molecule is investigated by using the time-dependent wave packet （TDWP） method with the ＂split operator-Fourier transform＂ scheme. At a given wavelength and intensity of laser pulse, the population of each state changing with time is obtained. The photo-absorption spectra and kinetic- energy distribution of the dissociation fragments, which exhibit vibration-level structure and dispersion of the wave packet, respectively, are also obtained. The results show that by increasing the laser intensity, one can find not only the band center shift of the photo-absorption spectrum, but also the change of the fragment energy. The appearance of the diffusive band in the photo-absorption spectrum and the multiple peaks in the kinetic-energy spectrum can be attributed to the effects of the predissoeiation limit and the external field.

Study on wave packet dynamics of E^1Σ_g^+ state of Li_2 with femtosecond-resolved photoelectron spectra

Wave packet dynamics of the Li2 molecule are investigated by using the time-dependent quantum wave packet method, and the time-resolved photoelectron spectra of the Li2 molecule are calculated. The time-resolved wave packet theory is used to reasonably interpret the phenomena of the photoelectron spectra for different parameters. Our calculation shows that the loss of the wave packets in the shelf state area of E1∑g＋ plays a prominent role in the process of photoionization with the increase of the delay time. Moreover, the oscillation of the wave packet on the E1∑g＋ curve symbolizes a decreasing process of energy.

Wave packet solutions in a bounded equatorial ocean and its interannual and decadal variabilities

Linearized shallow water perturbation equations with approximation in an equatorial β plane are used to obtain the analytical solution of wave packet anomalies in the upper bounded equatorial ocean. The main results are as follows. The wave packet is a superposition of eastward travelling Kelvin waves and westward travelling Rossby waves with the slowest speed, and satisfies the boundary conditions of eastern and western coasts, respectively.The decay coefficient of this solution to the north and south sides of the equator is inversely proportional only to the phase velocity of Kelvin waves in the upper water. The oscillation frequency of the wave packet, which is also the natural frequency of the ocean, is proportional to its mode number and the phase velocity of Kelvin waves and is inversely proportional to the length of the equatorial ocean in the east-west direction. The flow anomalies of the wave packet of Mode 1 most of the time appear as zonal flows with the same direction. They reach the maximum at the center of the equatorial ocean and decay rapidly away from the equator, manifested as equatorially trapped waves. The flow anomalies of the wave packet of Mode 2 appear as the zonal flows with the same direction most of the time in half of the ocean, and are always 0 at the center of the entire ocean which indicates stagnation, while decaying away from the equator with the same speed as that of Mode 1. The spatial structure and oscillation period of the wave packet solution of Mode 1 and Mode 2 are consistent with the changing periods of the surface spatial field and time coefficient of the first and second modes of complex empirical orthogonal function(EOF)analysis of flow anomalies in the actual equatorial ocean. This indicates that the solution does exist in the real ocean, and that El Ni?o-Southern Oscillation(ENSO) and Indian Ocean dipole(IOD) are both related to Mode 2.After considering the Indonesian throughflow, we can obtain the length of bounded equatorial ocean by taking the sum of that of the tropical Indian Ocean and the tropical Pacific Ocean, thus this wave packet can also explain the decadal variability(about 20 a) of the equatorial Pacific and Indian Oceans.

The Propagation of Wave Packets and Its Relationship with the Subtropical Jet over Southern China in January 2008

The propagation of wave packets and its relationship with the subtropical jet was investigated for the period 26 29 January 2008 over southern China using ECMWF Interim re-analysis data. Wave packets propagated from the north to the south side of an upper front with eastward development along the upper front during this period. Due to the eastward development of propagation, the acceleration of geostrophic westerly winds shifted eastward along the front. There were two primary sources of the propagation of wave packets at around 30°N. The first was the temperature inversion layer below 500 hPa, and the second was baroclinic zones located along the polarward flank of the subtropical jet in the middle and upper troposphere. Most wave packets propagated horizontally from the baroclinic zones and then converged on the zero meridional gradients of zonal winds.