Calculating initial-state-selected reaction probabilities from thermal flux eigenstates: a transition-state-based approach

An approach for the calculation of initial-state-selected reaction probabilities utilizing a transition-state view and the multiconfigurational time-dependent Hartree approach is presented. Using flux correlation functions, wave packets located in the transition-state region are constructed and propagated into the asymptotic region to obtain initial-state-selected reaction probabilities. A complete set of reaction probabilities is obtained from a single set of thermal flux eigenstates. Concepts previously applied with success to the calculation of k(T) or N(E) are transferred to the calculation of state-selected probabilities. The benchmark H+H(2) (J=0) reaction on the LSTH potential-energy surface is used to test the reliability of this approach.     

Semiclassical nonadiabatic dynamics based on quantum trajectories for the O(3P,1D) + H2 system

The O(3P,1D) + H2 --> OH + H reaction is studied using trajectory dynamics within the approximate quantum potential approach. Calculations of the wave-packet reaction probabilities are performed for four coupled electronic states for total angular momentum J = 0 using a mixed coordinate/polar representation of the wave function. Semiclassical dynamics is based on a single set of trajectories evolving on an effective potential-energy surface and in the presence of the approximate quantum potential. Population functions associated with each trajectory are computed for each electronic state. The effective surface is a linear combination of the electronic states with the contributions of individual components defined by their time-dependent average populations. The wave-packet reaction probabilities are in good agreement with the quantum-mechanical results. Intersystem crossing is found to have negligible effect on reaction probabilities summed over final electronic states.     

Natural molecular shells as open subsystems of small molecules

We compare the first few natural molecular shells of several small molecules to the corresponding “restricted Hartree‐Fock,” “second‐order Møller‐Plesset,” and “local density approximation” molecular shells. Occupation probabilities of each molecular shell are computed ab initio, especially the single‐occupation and double‐occupation probabilities, that is, the probabilities that the molecular shell is occupied by exactly one electron or by exactly two electrons. We observe that among corresponding molecular shells, the natural molecular shell has the least single‐occupation probability and the greatest double‐occupation probability. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Generalized Landau-Zener formula for non-adiabatic transitions between degenerate states

Non-adiabatic transitions between degenerate states are considered in a model system of parallel degenerate levels intersected by a single degenerate level. Sublevel populations in the final state are found to be determined by transition matrices between degenerate levels and by phases of ψ-functions of the initial state. Expressions for transition probabilities are obtained, averaged over random phases of the initial state.     

隧道结电场辅助下叔丁胺分子在Cu(111)表面跳跃(英文)

采用扫描隧道显微镜(STM)于78 K研究了单个叔丁胺分子在Cu(111)表面的横向跃迁现象.研究发现叔丁胺分子的跳跃几率随隧道电流的增加而线性增加,这表明该过程是单电子激发过程;在不同极性的隧道结电场作用下,叔丁基胺分子跳跃行为发生的几率不同,这种现象可以用电场辅助的扩散过程解释.在不同极性电场作用下叔丁胺分子在Cu(111)表面的吸附能和扩散势垒不同,从而表现出不同的跳跃几率.     

Computer analysis of the cracking patterns of deuterated hydrocarbons

A generalized, statistical model for calculating the mass spectral fragmentation patterns of deuterated hydrocarbons of low molecular weight is presented. Isotopic differences in bond energies and probabilities of the bond breakage of hydrogen and deuterium are included. Only a single fitting parameter is used. This parameter seems to be consistent for similar species of hydrocarbons. Small statistical deviations from observed spectra for deuterated methanes, acetylenes, ethylenes, and ethanes are obtained when this model is used.     

Probing vibrational wave packets in molecular excited states

A time-dependent theoretical method is used to describe a UV pump?CUV probe strategy to trace, at a femtosecond time scale, the motion of vibrational wave packets created in excited states of the hydrogen molecule by measuring single ionization probabilities. We use a spectral method to solve the time-dependent Schr?dinger equation in full dimensionality, including correlation and all electronic and vibrational degrees of freedom. A pump pulse initially creates a vibrational wave packet in the intermediate electronic excited states of $\hbox{H}_2$ . The frequency of the probe is chosen to ionize the target leaving the ion in a bound vibrational state. By varying the time delay between pulses, non-dissociative single ionization is enhanced or suppressed. Energy differential ionization probabilities are reported and compared with a model based on the Franck?CCondon approximation.     

Statistical thermodynamics of polymer solutions. VIII. Effect of intermolecular correlations on rayleigh scattering

The effect of intermolecular correlations on the angular dependence of the intensity of Rayleigh scattering from a dilute solution of a flexible-chain polymer in a good solvent is studied for an approximate model that retains the random-flight intramolecular segment-pair correlation while probabilities of multiple intermolecular contacts are simplified as products of probabilities of single contacts, all conditional on a common “initial” contact. This model, unlike one in which a polymer chain is represented as a spherically symmetrical cloud of segments, gives very little deviation from Zimm's “single-contact” approximation in light scattering: i.e., the initial concentration dependence of the concentration/intensity ratio is almost the same at all scattering angles. This behavior, which appears to underestimate the intermolecular correlations, can be accounted for by the symmetry of the bimolecular cluster as represented by the model.     

On the use of a single kinetic parameter in stochastic descriptions of relaxation

Model stochastic processes involving one particle per step transitions (evaluated by Monte-Carlo or theoretically) are often used to describe relaxation. We propose that, lacking further data, the transition probabilities should be defined uniformly with the help of a single kinetic parameter.     

Basic calculations about the limit of detection and its optimal determination

The limit of detection (LOD) is based strictly on an accepted probability for a false positive decision (type 1 error). For the needed standard deviation of the blank, a basic value for the calculation, three experimental different methods are described, which should be applicable in every case. Table values for simple but exact calculation, not only for single, but also for mean values, and with probabilities for the type 1 error of 1% and 5% are presented. Demands for an acceptable uncertainty of the LOD and for the validation of the result are specified.     

Exact quantum calculations on the collinear hydrogen atom transfer reaction I. Study on oscillations of the reaction probabilities of Cl + HCl

1-D quantum calculations of reaction probabilities have been carried out for the collinear reaction Cl + HCl (v≤3)→ClH (v′≤3) + Cl using hyperspherical coordinates. An LEPS potential energy surface with a shallow well depth of ?3.22 KJ/mol has been used in the calculations. The state-to-state reaction probabilities have been calculated. According to the results obtained we found that the diagonal (v=v′) reaction probabilities dominate over the off-diagonal (v≠v′) reaction probabilities and the largest off-diagonal reaction probabilities are smaller than 0.1. The reaction probabilities show oscillation as a function of energy. Dynamic resonances strengthen for the potential energy surface with a well.     

Transition probabilities in Sm II via optical nutation

We have measured the transition probabilities for three lines in Sm II. The measurements are made by studying optical nutation with a fast Doppler switching technique in collinear laser spectroscopy on ion beams. The recorded nutation curves are fitted to a quantum-optical theoretical model, and the transition probabilities are extracted. For all three lines, the measured transition probabilities are more accurate than those of earlier published measurements.     

Full-dimensional time-dependent wave packet dynamics of H2 + D2 reaction

Collision induced dissociation (CID), four center reaction (4C), and single exchange reaction (SE) in H(2) (v(1) = high) + D(2) (v(2) = low) were studied by means of time-dependent wave packet approach within a full-dimensional model. Initial state-selected total reaction probabilities for the three competitive processes have been computed on two realistic global potential energy surfaces of Aguado-Suárez-Paniagua and Boothroyd-Martin-Keogh-Peterson (BMKP) with the total angular momentum J = 0. The role of both vibrationally excited and rotationally excited reagents was examined by varying the initial vibrational and rotational states. The vibrational excitation of the hot diatom gives an enhancement effect on the CID process, while the vibrational excitation of the cold diatom gives an inhibition effect. The rotational excitation of both reagents has a significant effect on the reaction process. The 4C and SE probabilities are at least one order of magnitude smaller than the CID probabilities over the energy range considered. Isotope substitution effects were also studied by substituting the collider D(2) by H(2) and HD on the BMKP potential energy surfaces. The CID process is most efficient for the H(2) + D(2) combination and least efficient for the H(2) + H(2) combination and is different for the 4C and SE processes.     

On boundary conditions to the diffusion equation

The boundary conditions to the diffusion equation are obtained in the case of a diffusing particle which, in a single collision, may either recoil from or stick to the boundary wall with a priori known probabilities q and p. It is shown that the value p may be determined from diffusion penetration measurements in a circular tube.     

氢原子共线交换反应的动力学计算I.Cl与HCl反应几率的振荡现象研究

我们利用超球坐标对共线Cl+HCl(V-3)→ClH(V'≤3)+Cl作了一维精确量子计算,计算所用势能面是LEPS型,Et=-3.23KJ/mol, 得到了态态反应几率等动力学信息, 通过分析结果发现, 反应是振动绝热的, 即以对角(V'-V')反应几率为主,非对角(V' V')反应几率小于0.1, 反应几率随总能量表现出强裂地振荡, 在有阱的势能面上动力学共振增强。     

Transition probabilities for a time-dependent bilinear Hamiltonian with two harmonic limits

A method is developed for calculating transition probabilities for a time-dependent bilinear Hamiltonian that yields two different Harmonic oscillators at initial and final times. The procedure is based on the equations of motion for the creation and annihilation operators and the transition probabilities are obtained from recurrence relations that are most suitable for computational purposes.     

Correlations in single molecule photon statistics: renewal indicator

Multiple time scales are the intrinsic nature of complex systems and can be revealed through single molecule photon statistical analysis. The standard Poisson indicator defined by the time-averaged initial condition measures photon bunching and antibunching but cannot be directly related to multiple time scales. A new indicator defined by the event-averaged initial condition is proposed to detect the deviation from the renewal behavior and to directly probe the effects of conformational fluctuations. Detailed calculations of modulated two-level systems are carried out using the transfer matrix method to demonstrate the difference between the two indicators. The relationship between ensemble-averaged survival probabilities and photon statistics is also explored in the context of single molecule measurements.     

A transition state view on reactive scattering: initial state-selected reaction probabilities for the H + CH4 → H2 + CH3 reaction studied in full dimensionality

Initial state-selected reaction probabilities for the H+CH(4)→H(2)+CH(3) reaction are computed for vanishing total angular momentum by full-dimensional calculations employing the multiconfigurational time-dependent Hartree approach. An ensemble of wave packets completely describing reactivity for total energies up to 0.58 eV is constructed in the transition state region by diagonalization of the thermal flux operator. These wave packets are then propagated into the reactant asymptotic region to obtain the initial state-selected reaction probabilities. Reaction probabilities for reactants in all rotational states of the vibrational 1A(1), 1F(2), and 1E levels of methane are presented. Vibrational excitation is found to decrease reactivity when reaction probabilities at equivalent total energies are compared but to increase reaction probabilities when the comparison is done at the basis of equivalent collision energies. Only a fraction of the initial vibrational energy can be utilized to promote the reaction. The effect of rotational excitation on the reactivity differs depending on the initial vibrational state of methane. For the 1A(1) and 1F(2) vibrational states of methane, rotational excitation decreases the reaction probability even when comparing reaction probabilities at equivalent collision energies. In contrast, rotational energy is even more efficient than translational energy in increasing the reaction probability when the reaction starts from the 1E vibrational state of methane. All findings can be explained employing a transition state based interpretation of the reaction process.     

Exact quantum,quasiclassical forward and reverse reaction probabilities for a colldmear asymmetric model reaction

Detailed quasiclassical and time-independent quantum reaction probabilities are given for a surface on which large discrepancies between quasiclassical and wavepacket results have previously been found. The quasiclassical results are shown to agree relatively reasonably with the oscillation-averaged time-independent quantum ones if the quasiclassical reverse probabilities are chosen in the threshold region.