Nonadiabatic Radial Coupling Research Articles

К вопросу о методе перепроекцирования для неупругих процессов в атомных столкновениях в рамках подхода Борна — Оппенгеймера

The paper provides a detailed description of the reprojection method for the exact solution of the nonadiabatic nuclear dynamics within the Born–Oppenheimer formalism. In particular, it discusses the asymptotic behaviour of a state-to-state transition probability when a nonadiabatic radial coupling for this transition has a nonzero asymptotic value—a fundamental feature of the Born–Oppenheimer approach. It is known that the conventional Born–Oppenheimer approach leads to divergency of inelastic cross sections and inelastic rate coefficients, while the reprojection method provides convergences. The article describes physical background of the reprojection method.

Ab initio Calculations of the Lowest $$^{1}\Sigma _{g}^{ + }$$ States of the Na2 Dimer

The ground and 10 lowest excited $$^{1}\Sigma _{g}^{ + }$$ adiabatic electronic states of the Na2 dimer are calculated using the pseudopotential method. The use of the basis [7s6p5d4f] of atomic orbitals makes it possible to extend the range of available internuclear distances up to 1.7–50 A. It is found that the theoretical values of the Te and De constants are in a good agreement with the experimental ones. Herein you will find the sample calculations of the radial non-adiabatic coupling matrix elements enable to transform the basis of the adiabatic states to quasidiabatic one. It is found also that the Le Roy modified radius scales down the left boundary of an asymptotic range for the electronic state with the (3s + 5p) dissociation limit and for the higher states.

Ab Initio Calculation of the Lowest Singlet and Triplet Excited States of the N2 Molecule

Ab initio calculations of the adiabatic potential curves and matrix elements of radial nonadiabatic coupling of the N2 molecule for the states related to dissociation limits I–V were performed. The most important spectral characteristics of the adiabatic states agreed well with the available experimental and theoretical data. The diabatic states were constructed. The diabatic quantum defects and radial matrix elements of the configuration interaction of the dissociative and Rydberg configurations whose states converge to the ground state \(X^{2}\Sigma{_g^+}\) and the first electronically excited state A2Πu of the \(\rm{N_2^+}\) ion were calculated. The possibility of using the results for calculating the cross sections and rate constants of dissociative recombination and associative ionization within the framework of the multichannel quantum defect theory was discussed.

Excitation and charge transfer in low-energy hydrogen-atom collisions with neutral atoms: Theory, comparisons, and application to Ca

A theoretical method for the estimation of cross sections and rates for excitation and charge transfer processes in low-energy hydrogen atom collisions with neutral atoms, based on an asymptotic two-electron model of ionic-covalent interactions in the neutral atom-hydrogen atom system, is presented. The calculation of potentials and non-adiabatic radial couplings using the method is demonstrated. The potentials are used together with the multi-channel Landau-Zener model to calculate cross sections and rate coefficients. The main feature of the method is that it employs asymptotically exact atomic wavefunctions, which can be determined from known atomic parameters. The method is applied to Li+H, Na+H, and Mg+H collisions, and the results compare well with existing detailed full-quantum calculations. The method is applied to the astrophysically important problem of Ca+H collisions, and rate coefficients are calculated for temperatures in the range 1000-20000 K.

Excitation cross sections in low-energy hydrogen-helium collisions

Quantum chemical results for the lowest four potentials of the HeH molecule and the corresponding rotational and radial nonadiabatic coupling matrix elements are reported. Close-coupling calculations of the integral cross sections for the excitation processes $\mathrm{H}(1s)+\text{He}\ensuremath{\rightarrow}\phantom{\rule{4pt}{0ex}}\mathrm{H}(2s,2p)+\text{He}$ are performed on this basis. The calculated cross sections are in a reasonable agreement with the experimental data.

Quantum dynamics of the charge transfer in C+ + S at low collision energies

Following a recent semiclassical investigation by Bacchus-Montabonel and Talbi (2008 Chem. Phys. Lett. 467 28), the C+(2s22p)2P + S(3s23p4)3P charge transfer process involved in the modellization of the interstellar medium chemistry and its reverse reaction are revisited by combining a wave packet approach and semiclassical dynamics in a quasimolecular approach for doublet and quartet states. New radial non-adiabatic coupling matrix elements have been calculated and the mixed treatment gives access to new precise values of the rate coefficients for the direct and reverse charge transfer processes. For this system, quantum and semiclassical results are in good agreement even at low collision kinetic energies. The dominance of the quartet states in the process is confirmed. In the quantum treatment, the collision matrix elements are extracted from wave packets by the flux method with an absorbing potential. The formation of resonances due to a centrifugal barrier is illustrated.

Ab initiocalculation ofH+He+charge-transfer cross sections for plasma physics

The charge-transfer in low-energy ($0.25$ to $150$ eV/amu) $\mathrm{H}(\mathit{nl})+{\mathrm{He}}^{+}(1s)$ collisions is investigated using a quasimolecular approach for the $n=2,3$ as well as the first two $n=4$ singlet states. The diabatic potential energy curves of the HeH${}^{+}$ molecular ion are obtained from the adiabatic potential energy curves and the nonadiabatic radial coupling matrix elements using a two-by-two diabatization method, and a time-dependent wave-packet approach is used to calculate the state-to-state cross sections. We find a strong dependence of the charge-transfer cross section on the principal and orbital quantum numbers $n$ and $l$ of the initial or final state. We estimate the effect of the nonadiabatic rotational couplings, which is found to be important even at energies below $1$ eV/amu. However, the effect is small on the total cross sections at energies below $10$ eV/amu. We observe that to calculate charge-transfer cross sections in an $n$ manifold, it is only necessary to include states with ${n}^{\ensuremath{'}}\ensuremath{\leqslant}n$, and we discuss the limitations of our approach as the number of states increases.

Nonadiabatic couplings in the collisional removal of O2(b Σ1g+,v) by O2

The effect of nonadiabatic couplings on the collisional removal of O(2)(b (1)Sigma(g) (+),v) by O(2)(X (3)Sigma(g) (-), v=0) is investigated. Two-dimensional adiabatic and quasidiabatic potential energy surfaces for the excited dimer states and the corresponding nonadiabatic radial couplings have been computed by means of ab initio calculations. Alternately, a two-state theoretical model, based on the Landau-Zener and Rosen-Zener-Demkov assumptions, has been employed to derive analytical forms for the nonadiabatic couplings and an adiabatic-to-diabatic transformation only depending on a reduced set of adiabatic energy terms. Compared to the ab initio results, the predictions of the model are found to be highly accurate. Quantum dynamics calculations for the removal of the first ten vibrational states of O(2)(b (1)Sigma(g) (+),v) indicate a clear dominant contribution of the vibration-electronic relaxation mechanism relative to the vibration-translation energy transfer. Although the present reduced-dimensionality model precludes any quantitative comparison with experiments, it is found that the removal probabilities for v=1-3 are qualitatively consistent with the experimental observations, once the vibrational structure of the fragments is corrected with spectroscopical terms. Besides, the model served to show how the computation of the adiabatic PESs just at the crossing seam was sufficient to describe the nonadiabatic dynamics related to a given geometrical arrangement. This implies considerable savings in the calculations which will eventually allow for larger accuracy in the ab initio calculations as well as higher dimensional treatments.

Accurate ab initio potential energy curves for the classic Li–F ionic-covalent interaction by extrapolation to the complete basis set limit and modeling of the radial nonadiabatic coupling

Multireference configuration interaction calculations using large correlation consistent basis sets and full configuration interaction calculations with the smallest of such basis are utilized to describe the ionic-neutral curve crossing for the title system. The results of the former calculations have then been extrapolated to the complete basis set limit using the uniform singlet- and triplet-pair extrapolation scheme. A recent suggestion for locating the nonadiabatic matrix terms at the point where the dynamical correlation split vanishes has also been tested. Additionally, a consistent formalism is suggested to model the radial dependence of the nonadiabatic matrix terms that warrants an overlap dependence away from the crossing. When applied to LiF, the overall approach yields results in excellent agreement with the commonly accepted values for the geometric and energetic attributes at both the equilibrium and diabatic crossing regions.

Mutual neutralization in low-energyH++H−collisions: A quantumab initiostudy

The mutual neutralization of ${\mathrm{H}}^{+}$ and ${\mathrm{H}}^{\ensuremath{-}}$ at low collision energies is studied by means of a molecular close-coupling approach. All degrees of freedom are treated at the full quantum level also taking into account the identity of the nuclei. The relevant $^{1}\ensuremath{\Sigma}_{g}^{+}$ and $^{1}\ensuremath{\Sigma}_{u}^{+}$ electronic states as well as the associated nonadiabatic radial couplings are calculated for internuclear distances between 0.5 and $50{a}_{0}$. Following a transformation into a strictly diabatic basis, these quantities enter into a set of coupled equations for the motion of the nuclei. Numerical solution of these equations allows the cross sections for neutralization into the $\mathrm{H}(1)+\mathrm{H}(n)$, $n=1,2,3$ final states to be calculated. In the present paper, results are reported for the collision energy region $0.001--100\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, with special emphasis on the important energy region below $10\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The low temperature rate coefficient is obtained from a parametrization of the calculated cross section and is estimated to be valid over the range $10--10\phantom{\rule{0.2em}{0ex}}000\phantom{\rule{0.3em}{0ex}}\mathrm{K}$.

Ab initio potential energy surfaces and nonadiabatic collision dynamics in H++O2 system

The adiabatic potential energy surfaces for the lowest five electronic states of (3)A" symmetry for the H(+)+O(2) collision system have been obtained at the multireference configuration interaction level of accuracy using Dunning's correlation consistent polarized valence triple zeta basis set. The radial nonadiabatic coupling terms and the mixing angle between the lowest two electronic states (1 (3)A" and 2 (3)A"), which adiabatically correlate in the asymptotic limit to H((2)S)+O(2) (+)(X (2)Pi(g)) and H(+)+O(2)(X (3)Sigma(g)(-)), respectively, have been computed using ab initio procedures at the same level of accuracy to yield the corresponding quasidiabatic potential energy matrix. The computed strengths of the vibrational coupling matrix elements reflect the trend observed for inelastic vibrational excitations of O(2) in the experiments at collision energy of 9.5 eV. The quantum dynamics has been preformed on the newly obtained coupled quasidiabatic potential energy surfaces under the vibrational close-coupling rotational infinite-order sudden framework at the experimental collision energy of 9.5 eV. The present theoretical results for vibrational elastic/inelastic excitations of O(2) are in overall good agreement with the available experimental data obtained from the proton energy-loss spectra in molecular beam experiments [F. A. Gianturco et al., J. Phys. B 14, 667 (1981)]. The results for the complementary charge transfer processes are also presented at this collision energy.

Computed lifetimes of metastable states of the NO2+ dication

Based on the ab initio potential energy, spin-orbit coupling, electronic transition dipole moment, and radial nonadiabatic coupling functions, the energy level positions, lifetimes, and radiative transition probabilities (Einstein A coefficients) have been determined for the lowest electronic states of NO2+ using the log-amplitude-phase, stabilization, and complex-scaling methods. The calculated characteristics are in reasonable agreement to the available experimental data, thus, evidencing the reliability of the theoretical predictions for the characteristics unobserved to date. With the exception of the v<or=2 vibrational states of the B 2Sigma+ electronic state, the calculated radiative lifetimes of the excited electronic states are longer than their predissociation lifetimes, hence, accounting for the failure of the attempts which have been made so far to observe any emission from the latter states.

Nonadiabatic coupling in cold collisions of spin-polarized metastable hydrogen atoms

Previous calculations of low-temperature cross sections for collisions between spin-polarized metastable hydrogen atoms are improved to include nonadiabatic radial and angular coupling at large interatomic separations. The electrostatic dipole-quadrupole interaction produces nonadiabatic radial coupling between (2s,2p) and (2p,2p) states, while the Coriolis interaction produces nonadiabatic angular coupling. Both of these long-range contributions are handled in a space-fixed atomic gauge that is particularly convenient for a spin-polarized system. The improved theoretical results are compared with an existing experiment.

Charge transfer and ionization in collisions ofSi3+with H from low to high energy

Charge transfer processes due to collisions of ground state ${\mathrm{Si}}^{3+}(3s\phantom{\rule{0.3em}{0ex}}^{1}S)$ ions with atomic hydrogen are investigated using the quantum-mechanical molecular-orbital close-coupling (MOCC) and classical-trajectory Monte Carlo (CTMC) methods. The MOCC calculations utilize ab initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained from Herrero et al. [J. Phys. B 29, 5583 (1996)] which were calculated with a full configuration-interaction method. Total and state-selective single-electron capture cross sections are obtained for collision energies from $0.01\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\mathrm{u}$ to $1\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}∕\mathrm{u}$. Total and state-selective rate coefficients are also presented for temperatures from $2\ifmmode\times\else\texttimes\fi{}{10}^{3}\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ to ${10}^{7}\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Comparison with existing data reveals that the total CTMC cross sections are in good agreement with the experimental measurements at the higher considered energies and that previous Landau-Zener calculations underestimate the total rate coefficients by a factor of up to two. The CTMC calculations of target ionization are presented for high energies.

Two center shell model with Woods–Saxon potentials: Adiabatic and diabatic states in fusion

A realistic two-center shell model for fusion is proposed, which is based on two spherical Woods–Saxon potentials and the potential separable expansion method. This model describes the single-particle motion in a fusing system. A technique for calculating stationary diabatic states is suggested which makes use of the formal definition of those states, i.e., they minimize the radial nonadiabatic coupling between the adiabatic states. As an example the system 16O + 40Ca → 56Ni is discussed.

Vibrationally resolved charge transfer ofO3+with molecular hydrogen

Charge transfer due to collisions of ground state ${\mathrm{O}}^{3+}(2{s}^{2}2p{\phantom{\rule{0.2em}{0ex}}}^{2}{P}^{o})$ ions with molecular hydrogen are investigated using the quantum-mechanical molecular-orbital (QMO) coupled-channel method. The QMO calculations utilize $ab$ initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained with the spin-coupled valence-bond approach for a representative range of orientation angles and diatom internuclear separations. Vibrationally resolved cross sections for nondissociative single electron capture are obtained for energies between 0.1 eV∕u and 10 keV∕u for ${\mathrm{H}}_{2}$ in its ground vibrational level using the infinite order sudden approximation (IOSA). Two further approximations are considered in which the electronic radial couplings are assumed to be independent of the diatom stretching. In the first case, vibrational motion is taken into account by multiplying the electronic radial couplings by Franck-Condon (FC) ionization factors while in the second, vibrational motion is completely neglected. We refer to these two approaches as the vibrational sudden approximation (VSA) and the electronic approximation (EA), respectively. In the latter, the resulting cross sections for electronic transitions are multiplied by FC factors to obtain relative vibrationally resolved cross sections which are independent of the collision energy (the centroid approximation). Comparison with existing experimental data for total and electronic state-selective cross sections shows best agreement with IOSA and VSA, but discrepancies for EA. The triplet-singlet electronic cross section ratio reveals a departure at low collision energies from the statistical value.

Electron capture in collisions of S4+ with helium

Charge transfer due to collisions of ground-stateS4+(3s2 1S) ions with helium is investigated for energiesbetween 0.1 meV u-1 and 10 MeV u-1. Total and state-selective singleelectron capture (SEC) cross sections and rate coefficients areobtained utilizing the quantum mechanical molecular-orbitalclose-coupling (MOCC), atomic-orbital close-coupling (AOCC),classical trajectory Monte Carlo (CTMC) and continuum distorted wavemethods. The MOCC calculations utilize ab initio adiabaticpotentials and nonadiabatic radial coupling matrix elements obtainedwith the spin-coupled valence-bond approach. Previous data arelimited to a calculation of the total SEC rate coefficient using theLandau-Zener model that is, in comparison to the results presentedhere, three orders of magnitude smaller. The MOCC SEC cross sectionsat low energy reveal a multichannel interference effect. True doublecapture is also investigated with the AOCC and CTMC approaches whileautoionizing double capture and transfer ionization (TI) is exploredwith CTMC. SEC is found to be the dominant process except forE>200 keV u-1 when TI becomes the primary capture channel.Astrophysical implications are briefly discussed.

On the independence of nonadiabatic coupling elements on the choice of origin of the coordinate system

A finite-difference approach is employed to demonstrate the manner in which the values of nonadiabatic radial coupling matrix elements vary with the choice of origin of the nuclear coordinate system. Configuration interaction (CI) calculations for a series of excited states of the HCl molecule verify that such results do not depend on the location of the center of mass XCM as long as it is held fixed during the differentiation process. The reason that radial coupling matrix elements are found to vary with the choice of origin of the coordinate system in standard scattering formulations is that the corresponding motion is not purely internal but rather has a definite translational component, namely a linear dependence of XCM on the bond distance R is assumed. An identity which relates variations of such (mixed internal-translational motion) nonadiabatic coupling elements to the value of the electric dipole transition moment when the latter prescription is employed for choosing the origin of the nuclear coordinate system is also verified by the present CI calculations.

Ab initio study of charge transfer in low-energy collisions with helium

Charge transfer cross sections for collisions of ground state and excited state ) with atomic helium are presented for energies less than 250 eV . Using a fully quantum mechanical, molecular-orbital, close-coupling approach, the cross sections are calculated in a diabatic representation. Completely ab initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained with the spin-coupled valence-bond method are utilized. Rate coefficients for temperatures between 100 and 100 000 K and cross sections for collisions with isotopic are presented. Results for the reverse process, , are also given.

Charge Transfer in Collisions of C+with H and H+with C

Charge transfer rate coefficients for collisions of C+ with H and H+ with C are presented for temperatures from 30,000 to 107 K and from 10 to 107 K, respectively. The rate coefficients were calculated from recommended cross sections deduced in a recent theoretical and experimental investigation that took into account previous measurements. Nonadiabatic radial coupling is the dominant mechanism for both reactions above ~50,000 K, but for lower temperatures the reaction of H+ with C proceeds primarily by radiative charge transfer. Implications, due to the magnitude of the rate coefficients, for various astrophysical environments are discussed.