The perfect revival time of localized wave packet consisting of superposition of bound states with an arbitrary energy spectrum

A study is made of the long-term evolution of the wave packet, which is initially well localized in a one-dimensional confined potential. The wave packet consists of a linear superposition of bound states with an arbitrary energy spectrum. An exact analytical expression is derived, which predicts all revival times in any time scale. The perfect revival time is also calculated. The Pöschl–Teller oscillator has been considered as a simple example.     

Quantum stochastic resonance in parity violating chiral molecules

In order to explore parity violating effects in chiral molecules, of interest in some models of evolution towards homochirality, quantum stochastic resonance (QSR) is studied for the population difference between the two enantiomers of a chiral molecule (hence for the optical activity of the sample), under low viscous friction and in the deep quantum regime. The molecule is described by a two-state model in an asymmetric double well potential where the asymmetry is given by the known predicted parity violating energy difference (PVED) between enantiomers. In the linear response to an external driving field that lowers and rises alternatively each one of the minima of the well, a signal of QSR is predicted only in the case that the PVED is different from zero, the resonance condition being independent on tunneling between the two enantiomers. It is shown that, at resonance, the fluctuations of the first order contribution to the internal energy are zero. Due to the small value of the PVED, the resonance would occur in the ultracold regime. Some proposals concerning the external driving field are suggested.     

Study of the one-channel resonance states. Method without a stabilization procedure in the framework of the optical potential model

The resonances of some one-dimensional systems are studied in the framework of the optical potential model. Analysis of the discrepancies between the observed and exact resonance energy values shows that these differences come from the partial waves reflected upon the optical potential wall. When these disturbing waves have a small amplitude, an autocorrective procedure enables one to accurately determine the resonance energy if one only knows two approximate values of it deduced from a finite representation and the corresponding complex incoming and outgoing wave amplitudes.     

Single-electron tunneling spectroscopy of single C60 in double-barrier tunnel junction

The single-electron tunneling (SET) spectroscopy of C(60) molecule in a double-barrier tunnel junction is investigated by combining the scanning tunneling spectroscopy experiment and the theoretical simulation using the modified orthodox theory. The interplay between the SET effect and the discrete energy levels of C(60) molecule is studied. Three types of SET spectroscopies with different characters are obtained, corresponding to different tunneling processes and consistent with the previous theoretical prediction. Both the charging mode and resonance mode can arouse the current increase in the SET spectroscopy. The resonance mode is realized mainly by two mechanisms, including the resonance when the electron spans the second junction after already spanning the first junction. Some previous confused results have been clarified. Our results show that three types of SET spectroscopies can be together examined to quantitatively determine the frontier orbitals of the nanostructure by identifying the modes of various current increases.     

Formally exact quantization condition for nonrelativistic quantum systems

Based on the standard transfer matrix, a formally exact quantization condition for arbitrary potentials, which outflanks and unifies the historical approaches, is derived. It can be used to find the exact bound-state energy eigenvalues of the quantum system without solving an equation of motion for the system wave functions.     

A practical solution to the “unknown normalization” problem

We analyze the theoretical basis of a procedure to determine an unknown normalization factor in discretized wave functions, which we have successfully used in a series of calculations of resonance widths for atomic and molecular systems. By reducing this determination to that of a suitable interpolation function for the energy eigenvalues, the problem is easily solved when atomic basis sets are chosen according to simple rules. Illustrations of our procedure are presented for atomic, molecular, and model systems; renormalized wave functions are compared with the exact ones for these model systems. The resulting method of renormalized continuum wave functions has a wide range of application in the study of long-lived quasibound states (predissociation, autoionization, photoionization, unimolecular reactions, etc.).     

Overlap integrals for atom–metal surface interactions

Atom–metal surface overlap integrals are of utmost importance in surface energy calculations. Direct numerical evaluation of these triple integrals can be very time-consuming. However, we have developed an exact algebraic expression, where formulas for the coefficients are given for both the general case and the special case where the parallel wave vector is zero. Some numerical examples of the overlap for H on Al are given.     

Transmission and trapping of cold electrons in water ice

Experiments are reported which show that currents of low energy ("cold") electrons pass unattenuated through crystalline ice at 135 K for energies between zero and 650 meV, up to the maximum studied film thickness of 430 bilayers, indicating negligible apparent trapping. By contrast, both porous amorphous ice and compact crystalline ice at 40 K show efficient electron trapping. Ice at intermediate temperatures reveals metastable trapping that decays within a few hundred seconds at 110 K. Our results are the first to demonstrate full transmission of cold electrons in high temperature water ice and the phenomenon of temperature-dependent trapping.     

Quantum approaches for the insertion dynamics of the H+ + D2 and D+ + H2 reactive collisions

The H(+)+D(2) and D(+)+H(2) reactive collisions are studied using a recently proposed adiabatic potential energy surface of spectroscopic accuracy. The dynamics is studied using an exact wave packet method on the adiabatic surface at energies below the curve crossing occurring at approximately 1.5 eV above the threshold. It is found that the reaction is very well described by a statistical quantum method for a zero total angular momentum (J) as compared with the exact ones, while for higher J some discrepancies are found. For J >0 different centrifugal sudden approximations are proposed and compared with the exact and statistical quantum treatments. The usual centrifugal sudden approach fails by considering too high reaction barriers and too low reaction probabilities. A new statistically modified centrifugal sudden approach is considered which corrects these two failures to a rather good extent. It is also found that an adiabatic approximation for the helicities provides results in very good agreement with the statistical method, placing the reaction barrier properly. However, both statistical and adiabatic centrifugal treatments overestimate the reaction probabilities. The reaction cross sections thus obtained with the new approaches are in rather good agreement with the exact results. In spite of these deficiencies, the quantum statistical method is well adapted for describing the insertion dynamics, and it is then used to evaluate the differential cross sections.     

Fundamental importance of the Coulomb hole sum rule to the understanding of the Colle-Salvetti wave function functional

In this paper we consider the general form of the correlated-determinantal wave function functional of Colle and Salvetti (CS) for the He atom. The specific form employed by CS is the basis for the widely used CS correlation energy formula and the Lee-Yang-Parr correlation energy density functional of Kohn-Sham density functional theory. We show the following: (i) The key assumption of CS for the determination of this wave function functional, viz., that the resulting single-particle density matrix and the Hartree-Fock theory Dirac density matrix are the same, is equivalent to the satisfaction of the Coulomb hole sum rule for each electron position. The specific wave function functional derived by CS does not satisfy this sum rule for any electron position. (ii) Application of the theorem on the one-to-one correspondence between the Coulomb hole sum rule for each electron position and the constraint of normalization for approximate wave functions then proves that the wave function derived by CS violates charge conservation. (iii) Finally, employing the general form of the CS wave function functional, the exact satisfaction of the Coulomb hole sum rule at each electron position then leads to a wave function that is normalized. The structure of the resulting approximate Coulomb holes is reasonably accurate, reproducing both the short- and the long-range behavior of the hole for this atom. Thus, the satisfaction of the Coulomb hole sum rule by an approximate wave function is a necessary condition for constructing wave functions in which electron-electron repulsion is represented reasonably accurately.     

Construction of complex STO-NG basis sets by the method of least squares and their applications

The goals of electronic structure theory are to make quantitative predictions of molecular properties and to provide qualitative insight into bonding as well as features of potential energy surfaces. Oftentimes, the two goals are at odds as an accurate treatment requires a complicated wave function that obscures chemical insight. The multifacet graphically contracted function (MFGCF) method offers a new approach that allows both goals to be addressed simultaneously. The recursive product structure of the MFGCF wave function reduces the exponential scaling of the exact wave function and allows the computation of molecular properties with polynomial scaling with respect to system size. Additionally, the graph density concept provides an intuitive tool for visualizing and analyzing the qualitative features of the wave function. In this work, the graph densities for model systems are examined to demonstrate their utility in analyzing the changes in wave function character along potential energy surfaces and near avoided crossings. Finally, we demonstrate that the graph density exposes the structure of the exact wave function for a system of noninteracting molecules as a product of the fragment wave functions.     

Lewis-based valence bond scheme: application to the allyl cation

A method for expressing the wave function in terms of Lewis structures is proposed and tested on the allyl cation. This computational scheme is called valence bond BOND (VBB). The compact VBB wave function gives consistent results with the breathing orbital valence bond method (BOVB) for the resonance energy of the allyl cation (54 and 55 kcal/mol for VBB and BOVB, respectively). The optimization of the sigma orbitals, in such a way they adapt to each resonance structure, makes use of the breathing orbital effect. It is shown that this "breathing" of the sigma frame is more efficient in the resonant hybrid than in the localized state, so that a resonance energy of 63 kcal/mol is obtained at this level of computation.     

Exact ground state for a Herndon–Simpson model via resonance–theoretic cluster expansion

The Herndon–Simpson model for a particular catacondensed polyphene chain is considered as a nontrivial many-body Hamiltonian, defined on a space with a basis of orthonormal Kekulé structures. An Explicitly correlated cluster expanded resonance–theoretic wave function is described for this model, and its quality is judged by calculation of the standard deviation for the energy expectation. The quality is found to be high. Indeed, for a particular parameter ratio within the range of experimental interest, the wave function ansatz is found to be exact. This very accurate solution is then used to gauge the quality of the common ansatz with equally weighted Kekulé structures, and it is found to be reasonably good.     

势阱中粒子能级与波函数微扰计算的代数递推公式

利用超位力定理(HVT)和Hellmann-Feynman 定理(HFT),导出了由有精确解的势阱的能级值用微扰法直接计算一维势阱的各级近似能级的普遍代数公式,并导出了由能级近似值计算定态波函数近似表达式的代数公式.给出了代数公式具体应用的几个典型一维势阱实例.此法可推广到二维势阱与三维势阱的情形.     

Scattered wave packet formalism for the energy-resolved reaction probability

The scattered wave packet formalism developed for a quantum subsystem interacting with reservoirs through open boundaries is utilized to calculate the energy-resolved transmission probability. The total wave function is split into incident and scattered components. Markovian outgoing wave boundary conditions are imposed on the scattered or total wave function by the polynomial method. The wave packet correlation function approach is employed to compute the energy-resolved transmission probability for a one-dimensional potential barrier and a one-dimensional model chemical reaction exhibiting a quantum resonance. Accurate results demonstrate that this formalism can significantly reduce the number of grid points required in a dynamical calculation for the reaction probability.     

Light trapping and guidance in plasmonic nanocrystals

We illustrate the possibility of light trapping and funneling in periodic arrays of metallic nanoparticles. A controllable minimum in the transmission spectra of such constructs arises from a collective plasmon resonance phenomenon, where an incident plane wave sharply localizes in the vertical direction, remaining delocalized in the direction parallel to the crystal plane. Using hybrid arrays of different structures or different materials, we apply the trapping effect to structure the eigenmode spectrum, introduce overlapping resonances, and hence direct the light in space in a wavelength-sensitive fashion.     

A resonance mechanism of efficient energy transfer mediated by Fenna-Matthews-Olson complex

The Wigner-Weisskopf-type model developed by Alicki and Giraldi [J. Phys. B 44, 154020 (2011)] is applied to the biological process of energy transfer from a large peripheral light harvesting antenna to the reaction center. This process is mediated by the Fenna-Matthews-Olson (FMO) photosynthetic complex with a remarkably high efficiency. The proposed model provides a simple resonance mechanism of this phenomenon employing exciton coherent motion and is described by analytical formulas. A coupling to the vibrational environment is a necessary component of this mechanism as well as a fine-tuning of the FMO complex Hamiltonian. The role of the relatively strong coupling to the energy sink in achieving the resonance condition and the absence of heating of the vibrational environment are emphasized.     

Scattering properties,stability analysis,and phase separation of polyelectrolyte mixtures

The conditions of stability for weakly charged polyelectrolyte mixtures are analyzed from a scattering theory developed previously. In the thermodynamic limit of zero wave vector q = 0, it is found that electrostatic interaction induces a compatibility enhancement which is discussed for various cases of charge distributions. The condition of microphase separation transition at the wave vector for which the scattering is a maximum is also discussed. © 1993 John Wiley & Sons, Inc.     

General method to simulate molecular processes involving complex interactions between combining subsystems

We consider the transformation process of one molecular subsystem into another (for example, structural isomer-isomer transformation) under the condition of a group of close levels in the first subsystem that have the energy on average coincident with the mean energy of the second subsystem (quasi-degeneration). It is shown that, similar to the previously discussed resonance between two levels of two subsystems, it is also possible in this case to compose an oscillating wave packet leading to a resonant transition from one subsystem to another. The calculation procedure is described that can be applied to atomic ensembles of any complexity with any number of quasi-resonant levels.     

Extended quantization condition for constructive and destructive interferences and trajectories dominating molecular vibrational eigenstates

The role of destructive quantum interference in semiclassical quantization of molecular vibrational states is studied. This aspect is crucial for correct quantization, since failure in the appropriate treatment of destructive interference quite often results in many spurious peaks and broad background to hide the true peaks. We first study the time-Fourier transform of the autocorrelation function without performing summation over the trajectories. The resultant quantity, the prespectrum which is a function of individual classical trajectories, provides a clear view about how destructive interference among the trajectories should function. It turns out that the prespectrum is oscillatory but never a random noise. On the contrary, it bears a systematic and regular structure, which is sometimes characterized in terms of very sharp and high peaks in the energy space of the sampled classical trajectories. We have found an extended quantization condition that is responsible for generating these peaks in the prespectrum, which we call the prior quantization condition. Integration of the prespectrum over the trajectory space is supposed to give "zero" (practically a small value of the order of the Planck constant) at a noneigenvalue energy, which is actually a materialization of the destructive interference. Besides, certain finite peaks in the prespectrum survive after the integration to form the true spikes (eigenvalues) in the final spectrum, if they satisfy an additional resonance condition. For these resonance components, the prior quantization condition is reduced to the Einstein-Brillouin-Keller quantization condition. Based on these analyses, we propose a rather conventional filtering technique to efficiently handle tedious computation for destructive interference, and numerically verify that it works well even for multidimensional chaotic systems. This filtering technique is further utilized to extract a few trajectories that dominate an eigenstate of molecular vibration.