The centrifugally decoupled exponential distorted wave (CDEDW) approximation for the calculation of rotationally inelastic molecular collision cross se

A new approximate method is presented for the rapid calculation of rotationally inelastic molecular collision cross sections. The method is called the centrifugally decoupled exponential distorted wave (CDEDW) approximation and involves the combination of two well known approximations. The first approximation is the neglect of the off-diagonal coupling terms which arise from the orbital angular momentum operator in the coupled differential equations in the body-fixed axis system. The second approximation is to treat the remaining coupling terms, which arise from the interaction potential, using a unitary perturbation approximation. The CDEDW method is applied to the calculation of total and partial rotationally inelastic cross sections in the ArN₂ system, and detailed comparisons are made with exact and several other types of approximate calculations. Agreement with exact calculations is good and often comparable with the coupled states and p-helicity decoupled approximations. The CDEDW method requires a similar amount of computational effort to the infinite order sudden (IOS) approximation, and we show that for the present system the CDEDW method gives more reliable results.     

Classical rotational and centrifugal sudden approximations for atom—molecule collisional energy transfer

The application of centrifugal and rotational sudden approximations to classical trajectory studies of rotational energy transfer in atom—molecule collisions to examined. Two different types of approximations are considered: a centrifugal sudden (CS) approximation, in which the orbital angular momentum is assumed to be constant during collisions, and a classical infinite order sudden (CIOS) approximation, in which the CS treatment is combined with an energy sudden approximation to totally decouple translational and rotational equations of motion. The treatment of both atom plus linear and nonlinear molecule collisions is described, including the use of rotational action-angle variables for the rotor equations of motion. Applications of both CS and CIOS approaches to rotational energy transfer in He + I₂ collisions are presented. We find the calculated CS and CIOS rotationally inelastic cross sections are in generally good agreement [errors of (typically) 10–50%] with accurate quasiclassical (QC) ones, with the CS results slightly more accurate than CIOS. Both methods are less accurate for small |Δj| transitions than for large |Δj| transitions. Computational savings for the CS and CIOS applications is about a factor of 3 (per trajectory) compared to QC. We also present applications using the CS method to rotational energy transfer in He, Ar, Xe + O₃ collisions, making comparisons with analogous QC results of Stace and Murrell (SM). The agreement between exact and approximate results in these applications is generally excellent, both for the average energy transfer at fixed impact parameters, and for rotationally inelastic cross sections. Results are better for He + O₃ and Ar + O₃ than for Xe + O₃, and better at low temperatures than at high. Since SM's quasiclassical treatment considered only total internal energy transfer without attempting a partitioning between vibration and rotation, while our CS calculation considers only rotational energy transfer, the observed good agreement between our and SM's cross sections indicates that most internal energy transfer in He, Ar, Xe + O₃ is rotational. The relation of this result to models of the activation process in thermal unimolecular rate constant determination is discussed.     

Accuracy of the IOS approximation for highly inelastic R-T collisional energy transfer

Rate constants for rotational excitation of CO by collisions with He atoms computed within the infinite order sudden (IOS) approximation are compared with accurate quantum (coupled-states) and classical trajectory values. Taking the IOS energy as the initial kinetic energy for upward. 0 → J, transitions is found to overestimate the rates, especially for higher J (larger inelasticity). Taking the IOS energy as the initial energy for downward, J → 0, transitions underestimates the rates by a comparable amount. The geometric average of IOS rates computed in these two ways is found to provide accurate values.     

Energy extrapolation schemes for adaptive multi-scale molecular dynamics simulations

This paper evaluates simple schemes to extrapolate potential energy values using the set of energies and forces extracted from a molecular dynamics trajectory. In general, such a scheme affords the maximum amount of information about a molecular system at minimal computational cost. More specifically, schemes like this are very important in the field of adaptive multi-scale molecular dynamics simulations. In this field, often the computation of potential energy values at certain trajectory points is not required for the simulation itself, but solely for the a posteriori analysis of the simulation data. Extrapolating the values at these points from the available data can save considerable computational time. A set of extrapolation schemes are employed based on Taylor series and central finite difference approximations. The schemes are first tested on the trajectories of molecular systems of varying sizes, obtained at MM and QM level using velocity-Verlet integration with standard simulation time steps. Remarkably good accuracy was obtained with some of the approximations, while the failure of others can be explained in terms of the distinct features of a molecular dynamics trajectory. We have found that, for a Taylor expansion of the potential energy, both a first and a second order truncation exhibit errors that grow with system size. In contrast, the second order central finite difference approximation displays an accuracy that is independent of the size of the system, while giving a very good estimate of the energy, and costing as little as a first order truncation of the Taylor series. A fourth order central finite difference approximation requires more input data, which is not always available in adaptive multi-scale simulations. Furthermore, this approximation gives errors of similar magnitude or larger than its second order counterpart, at standard simulation time steps. This leads to the conclusion that a second order central finite difference approximation is the optimal choice for energy extrapolation from molecular dynamics trajectories. This finding is confirmed in a final application to the analysis of an adaptive multi-scale simulation.     

Anisotropic interactions from double rainbows in Na atom—molecule collisions

Crossed molecular beam experiments have been performed measuring differential cross sections for Na scattered from CH₃I, (CH₃)₃CCl, (CH₃)₃CBr and (CH₃)₃CI at collision energies of 0.170 to 0.220 eV. The angular distributions show pronounced double rainbow structure which is attributed to the anisotropy of the interaction potential. The origin and the conditions for this structure are investigated by calculations in the infinite order sudden approximation. The effect is used to determine the anisotropic interaction potentials for the measured systems which all exhibit minima in the linear configuration of the collision complex ranging from 30 to 60 meV.     

Calculation of the binary diffusion coefficient and interaction viscosity of the H–H2 system

It has been argued that the Mason–Monchick approximation (MMA) and infinite order sudden approximation (IOSA) are not suitable for the calculation of the transport property coefficients of light polyatomic systems. It is proposed, on physical grounds, that a new approximation, the hybrid-MMA, is more appropriate. Although the hybrid-MMA belongs to the MMA/IOSA type methods, its accuracy is expected to decrease with increasing temperature.     

A classical reactive study within the infinite order sudden approximation: integral cross sections for the reactions F + H2vi = 0) → HF(vf = 0,1,2,3) + H

Integral reactive classical cross sections and product vibrational distributions are presented for the F+H₂ system. The calculations were made within the infinite order sudden approximation (IOSA) and the results compared with recent quantum-mechanical IOSA and exact classical results.     

Exchange reactions of hydrogen halides with hydrogenic atoms

Calculations on the D + HBr → DBr + H and D + HI → DI + H reactions are reported. A three-dimensional, quantum-dynamical approximation is used which involves applying the energy sudden approximation to the entrance channel hamiltonian and the centrifugal sudden approximation to the exit channel hamiltonian. Results of integral and differential cross sections, rate coefficients and rotational distributions are presented. Diatomics-in-molecules potential-energy surfaces have been used in the computations. The HBrH potential has been optimesed so that the calculated room-temperature rate coefficient agrees with experiment. This potential has a barrier height of 0.237 eV. Rate coefficient computations for the four reactions H′ + H″ Cl → - H′Cl + H″ (H′, H″ = H or D) are also reported. These results, for a LEPS surface, agree well with those obtained in quasiclassical trajectory and variational transition state theory calculations.     

Simple bond length dependence: a correspondence between reactive fluid theories

Two elementary models of reactive fluids are examined, the first being a standard construction assuming molecular dissociation at infinite separation; the second is an open mixture of nondissociative molecules and free atoms in which the densities of free atoms and molecules are coupled. An approximation to the density of molecules, to low order in site density, is derived in terms of the classical associating fluid theory variously described by Wertheim [J. Chem. Phys. 87, 7323 (1987)] and Stell [Physica A 231, 1 (1996)]. The results are derived for a fluid of dimerizing hard spheres, and predict dependence of the molecular density on the total site density, the hard sphere diameter, and the bond length of the dimer. The results for the two reactive models are shown to be qualitatively similar, and lead to equivalent predictions of the molecular density for the infinitely short and infinitely long bond lengths.     

EMP as a similarity measure: a geometric point of view

Soft Coulomb potentials constructed by multiplying the classical potential by a Gaussian function (or a linear combination of them) permit to consider a wide family of distributions which limit with the classical potential when the exponent becomes infinite. Soft Coulomb potentials can be employed as potential operators with first order density functions in order to compute families of soft electrostatic molecular potentials (EMP) for any quantum object. The soft EMP family possesses two interesting computational features: being not only formally equivalent to classical EMP, but finite everywhere, even at the atomic nuclei. The structure of the soft Coulomb operator family yielding soft EMP can be easily related with a quantum similarity integral feature.     

On the classical mechanical reactive infinite order sudden approximation

The classical mechanical formulation of the reactive infinite order sudden approximation (RIOSA) is reconsidered. It is shown that the classical RIOSA conserves the total energy of the system not only in each arrangement channel, but also on the borderline separating the different arrangement channel configuration spaces. A unique interchannel transformation rule for the RIOSA angular momenta parameters is derived, which is valid for any masses of the interacting atoms and which explicitly incorporates the specificity of the RIOSA approach.     

First-principles T-matrix calculations of double-ionization energy spectra of atoms and molecules

Strong electron correlation plays an important role in the determination of double ionization energy, which is required for removing or adding two electrons, particularly in small-sized systems. Starting from the state-of-the-art GW approximation, we evaluate the particle-particle ladder diagrams up to the infinite order by solving the Bethe-Salpeter equation of the T-matrix theory to calculate the double-ionization energy spectra of atoms and molecules (Be, Mg, Ca, Ne, Ar, Kr, CO, C(2)H(2), Li(2), Na(2), and K(2)) from first principles. The ladder diagrams up to the infinite order are significant to calculations of double-ionization energy spectra. The present results are in good agreement with available experimental data as well as the previous calculations using, e.g., the configuration-interaction method.     

Theoretical spectroscopic study of van der Waals systems

In this paper we discuss the application of three dimensional quantum models, in order to study the dynamics of vibrational predissociation of van der Waals molecules. In the first model the vibrations are described in the distorted-wave diabatic approximation while rotations are treated in the sudden approximation. The second model is related to the “Infinite order sudden approximation” and after a close coupling formalism for the vibrations, the bending motion is considered in an approximate way. We present the 3D quasibound levels and the rates for vibrational predissociation in a test case, the HeI₂.     

Π态双原子分子Λ分裂引起的量子干涉

To interpret theoretically the abnormal phenomenon in the experiment of collision-induced rotational energy transfer of CO（A1Π,v=3）with He by Sun et al.,the time dependent first order Born approximation,and the long-range interaction potentials and“straight-line”trajectory approximation are taken into account. A theoretical model of quantum interference of Π-state diatomic molecules,which originates from the difference between the two "Λ-related collision potential energy surface,is presented. The abnormal phenomenon of σε→ε'ΔJ=0<σε→ε'ΔJ=±1 for He is also interpreted successfully. At first the theoretical development of collision-induced quantum interference on rotational energy transfer is reported;then a theoretical model of quantum interference of Π-state diatomic molecules,which originates from the difference between the two "Λ-related collision potential energy surfaces,is presented;in the end the results have been discussed and concluded.     

Integral and differential cross sections for the heavy-light-heavy cihci reaction. A quantum mechanical study within the infinite order sudden approximation

In this communication we present quantum mechanical integral and differential cross sections for the reaction HCl(ν_i = 0) + Cl′ → HCl′ + Cl. The calculations employed the the infinite order sudden approximation. The characteristic oscillations encountered in collinear calculations were still apparent in three dimensions.     

Trajectory-based solution of the nonadiabatic quantum dynamics equations: an on-the-fly approach for molecular dynamics simulations

The non-relativistic quantum dynamics of nuclei and electrons is solved within the framework of quantum hydrodynamics using the adiabatic representation of the electronic states. An on-the-fly trajectory-based nonadiabatic molecular dynamics algorithm is derived, which is also able to capture nuclear quantum effects that are missing in the traditional trajectory surface hopping approach based on the independent trajectory approximation. The use of correlated trajectories produces quantum dynamics, which is in principle exact and computationally very efficient. The method is first tested on a series of model potentials and then applied to study the molecular collision of H with H(2) using on-the-fly TDDFT potential energy surfaces and nonadiabatic coupling vectors.     

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.     

Spin-orbit effects on a gold-based superatom: a relativistic Jellium model

The inclusion of relativistic effects always brings to the scientific community great and stimulating surprises. To consider the spin-orbit term, which accounts for the interaction between the spatial and spin coordinates, requires the use of double point groups of symmetry in order to solve the Dirac equation or the two component approximation to it, leading to total angular momenta (j) functions, atomic or molecular spinors, instead of pure orbital angular momenta (l), atomic or molecular orbitals. Large and small components, derived from the Dirac treatment, depict wavefunctions corresponding to fermions, electrons, which are described for the first time for a superatom case. In addition, their behavior is revisited in order to clarify the effects of the inclusion of the spin-orbit coupling into the electronic structure calculations, which can be extended to other superatoms, clusters, molecules and atoms.     

Stringent test of the statistical quasiclassical trajectory model for the H+3 exchange reaction: a comparison with rigorous statistical quantum mechanical results

A complete formulation of a statistical quasiclassical trajectory (SQCT) model is presented in this work along with a detailed comparison with results obtained with the statistical quantum mechanical (SQM) model for the H+ +D2 and H+ +H2 reactions. The basic difference between the SQCT and the SQM models lies in the fact that trajectories instead of wave functions are propagated in the entrance and exit channels. Other than this the two formulations are entirely similar and both comply with the principle of detailed balance and conservation of parity. Reaction probabilities, and integral and differential cross sections (DCS's) for these reactions at different levels of product's state resolution and from various initial states are shown and discussed. The agreement is in most cases excellent and indicates that the effect of tunneling through the centrifugal barrier is negligible. Some differences are found, however, between state resolved observables calculated by the SQCT and the SQM methods which makes use of the centrifugal sudden (coupled states) approximation (SQM-CS). When this approximation is removed and the full close coupling treatment is used in the SQM model (SQM-CC), an almost perfect agreement is achieved. This shows that the SQCT is sensitive enough to show the relatively small inaccuracies resulting from the decoupling inherent to the CS approximation. In addition, the effect of ignoring the parity conservation is thoroughly examined. This effect is in general minor except in particular cases such as the DCS from initial rotational state j=0. It is shown, however, that in order to reproduce the sharp forward and backward peaks the conservation of parity has to be taken into account.