Nonadiabatic Coupling Matrix Elements Research Articles

Ab initio study of nonadiabatic coupling matrix elements between excited [formula omitted] and [formula omitted] electronic states of C 2H

The conical intersection (CI) between the 2 2 A ′ and 3 2 A ′ electronic states of C 2H occurring at the C 2v-symmetric geometry has been characterized by line integral calculations using ab initio nonadiabatic matrix coupling elements. The calculations confirmed that when a path surrounds this CI and does not approach, too closely, CIs formed by adjacent states, the line integral produces for the topological phase, the expected π-value. Increasing the radius of the circle was accompanied by a decrease in the topological phase indicating on the existence of other CIs in the vicinity of the present one.

Ab-initio-based model for the charge transfer mechanisms in Ar + + H 2O collisions

The mechanism of the charge-transfer reaction between water molecules and argon ions is analysed using a two-dimensional model with the reaction and HOH bending coordinates, which maintains the C 2v symmetry of the reaction system. Potential energy surfaces and nonadiabatic coupling matrix elements are computed using ab initio Möller-Plesset perturbation theory with multiple partitioning of the full Hamiltonian. Both ab initio calculations and semiclassical simulations of the vibrational distributions of the product H 2O +(Ã) ion indicate two possible charge-transfer mechanisms. The first involves a nonadiabatic transition induced by radial coupling, whereas the second is governed by the curve crossing along the bending coordinate. The coexistence of two mechanisms agrees qualitatively with that inferred from the experimental measurements.

Probing the nature of surface intersection by ab initio calculations of the nonadiabatic coupling matrix elements: A conical intersection due to bending motion in C2H

Nonadiabatic coupling matrix elements between the 1 2A′, 2 2A′, and 1 2A″ electronic states of the C2H radical are computed using ab initio full valence active space CASSCF method. The line-integral technique is then applied to study possible geometric phase effects. The results indicate the existence of a unique conical intersection due to CCH bending between the 1 2A′ and 2 2A′ states at the linear configuration in the vicinity of rCC=1.35 Å and rCH=1.60 Å. The line-integral calculations with ab initio nonadiabatic coupling terms confirm that when a path encircles the conical intersection, the line integral always produces the value π for the topological (Berry) phase and when a path encircles the two (symmetrical) conical interactions or none of them, the line integral produces the value of zero for the topological phase.

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.

Nonadiabatic coupling using a corrected Born-Oppenheimer basis: The vibronic spectrum ofHD+

We apply a method suggested by Delos [Rev. Mod. Phys. 53, 287 (1981)] to correct the Born-Oppenheimer basis by incorporation of proper boundary conditions for bound states of molecular systems. We calculate the correct nonadiabatic coupling matrix elements for ${\mathrm{H}}_{2}^{+}$ and its isotopic variants and use them to determine the ${\mathrm{HD}}^{+}$ vibronic spectrum.

Analytic derivative methods for evaluating nonadiabatic coupling matrix elements within the SC-QDPT method

The recently developed self-consistent variant of quasidegenerate perturbation theory (the SC-QDPT method) is shown to allow one to use analytic derivative methods for evaluating both first derivative nonadiabatic couplings and first derivatives of the adiabatic state energies with respect to nuclear perturbations. The expressions obtained for the couplings prove to deviate from the analogous expressions for CI wavefunctions by an additional term arising for inaccuracies in describing the primary–external interactions by perturbation theory. It is shown, however, that this `error-term' may be expected to be small in practice and it may be evaluated using reference space wavefunctions (e.g., MCSCF).

First-order nonadiabatic coupling matrix elements using coupled cluster methods. I. Theory

It is shown how first-order nonadiabatic coupling matrix elements can be calculated using coupled cluster electronic structure methods. The formalism is consistent with the coupled cluster response theory approach for calculation of excitation energies and adiabatic transition properties. Expressions are derived that are in the limit of a complete coupled cluster expansion give results equivalent to the full configuration interaction results. Computational tractable expressions are given for the first-order nonadiabatic coupling matrix in coupled cluster theory. The final expressions are quite similar to those employed in the implementation of the analytical calculation of molecular gradients.

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.

Electron capture in collisions of with H and with C

A comprehensive theoretical and experimental study of electron capture in collisions of with H and with C extending over the energy range to is presented. A variety of theoretical approaches were used including those based on quantal molecular-orbital close-coupling (MOCC), multielectron hidden crossings (MEHC), quantal decay and classical trajectory Monte Carlo techniques. Radiative charge transfer cross sections were computed using the optical potential/distorted wave (OPDW) and fully quantal (FQ) approaches. The MOCC, OPDW and FQ calculations incorporated ab initio potentials, nonadiabatic coupling matrix elements and transition moments computed at the configuration-interaction level. Ab initio potential surfaces in the plane of complex internuclear distance were obtained for the MEHC calculations. Merged-beam measurements were performed between and for the collision system. Diagnostics of the beam with a crossed electron beam could find no presence of a metastable component. The current results, in conjunction with previous measurements, are used to deduce a set of recommended cross sections.

Charge transfer in collisions ofC2+ions with H atoms at low-keV energies: A possible bound state ofCH2+

Electron capture in ${\mathrm{C}}^{2+}+\mathrm{H}$ collisions is studied theoretically by using a semiclassical molecular representation with nine molecular states for the doublet manifold at collision energies above 10 eV. The ab initio potential curves and nonadiabatic coupling matrix elements for the ${\mathrm{CH}}^{2+}$ system are obtained from the multireference single- and double-excitation configuration interaction method. The adiabatic potential curves show no bound state for the $1{}^{2}{\ensuremath{\Sigma}}^{+}$ state, but a very shallow well in the $2{}^{2}{\ensuremath{\Sigma}}^{+}$ potential, suggesting a possibility of a bound state of ${\mathrm{CH}}^{2+}.$ The corresponding total and partial cross sections for charge transfer are found to be in a reasonable agreement with experiment in shape, but the present magnitude is found to be larger by nearly a factor of 2 at the high-energy end.

Ab initio study of charge transfer in low energy collisions with atomic hydrogen

Charge transfer cross sections for collisions of ground state and excited state with atomic hydrogen are presented for energies less than . The cross sections are calculated in a diabatic representation using a fully quantum-mechanical, molecular-orbital, close-coupled method. Completely ab initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained with the spin-coupled valence-bond method are incorporated. Inclusion of the and closed-channels results in oscillations in the charge transfer cross section for collision energies above the separated-atom energy of the lowest closed-channel . Rate coefficients for temperatures between 500 and 100 000 K and cross sections for collisions with isotopic D are presented. Results for the reverse process, charge transfer ionization, are also given.

Collisions between multiply charged ions The He 2+C 3+ case

Total cross sections for single charge transfer in 3He 2+ 13C 3− collisions are calculated in the 2–200 keV centre of mass energy range within the molecular approximation. Model potential techniques are used to determine the adiabatic energies and the nonadiabatic coupling matrix elements. The collision dynamics are then treated by the semiclassical impact-parameter approximation with allowance for translation factors. The reliability of straight-line nuclear trajectories is asserted by fully quantum mechanical test calculations. Comparison is made with recent experimental results.

Electron capture in collisions of H^{+} ions with S atoms and its reverse process below kilo-electron-volt energies

Electron capture in ${\mathrm{H}}^{+}+\mathrm{S}{(}^{3}{P,}^{1}D)$ collisions is studied theoretically by using a semiclassical molecular representation with five molecular channels from the initial ground and excited states at collision energies above 10 eV. Electron capture in ${\mathrm{S}}^{+}$ ${(}^{4}S)+\mathrm{H}(1\mathrm{}\mathrm{s})$ collisions is also investigated by using three molecular channels in order to assess the earlier estimation which gave the rate constant of ${10}^{\ensuremath{-}15}{\mathrm{cm}}^{3}/\mathrm{s}$ at ${10}^{4}\mathrm{K}$ for the process. The ab initio potential curves and nonadiabatic coupling matrix elements for the ${\mathrm{HS}}^{+}$ system are obtained from multireference single- and double-excitation configuration-interaction calculations employing relatively large basis sets. Dominant capture channels corresponding to the $[{\mathrm{H}+\mathrm{S}}^{+}{(}^{2}P)]$ and $[{\mathrm{H}+\mathrm{S}}^{+}{(}^{2}D)]$ states lie lower by 0.2 and 1.4 eV, and 1.34 and 2.5 eV from the initial ground $[{\mathrm{H}}^{+}+\mathrm{S}{(}^{3}P)]$ and excited $[{\mathrm{H}}^{+}+\mathrm{S}{(}^{1}D)]$ states, respectively. The present results show that electron capture from the excited species is found to be rather weak at lower energies. But it rapidly becomes comparable to that from the ground state. Electron capture in ${\mathrm{S}}^{+}$ ${(}^{4}S)+\mathrm{H}$ collisions proceeds through the two-step mechanism at lower energies, and therefore, the cross section is found to be small with the value less than ${10}^{\ensuremath{-}17}{\mathrm{cm}}^{2}$ below 1 keV, thus supporting the earlier estimation.

Inelastic processes in collisions ofH+ions with C, N, O, and Si atoms below 1 keV

Electron capture in collisions of C, N, O, and Si atoms with H{sup +} ions is studied theoretically based on a molecular representation within a fully quantum framework by including six molecular channels both for the ground and excited states for the [H{sup +}+C] system, and four channels for the ground-state [H{sup +}+N] and [H{sup +}+O] systems. For the [H{sup +}+Si] system, we employed the molecular representation both in fully quantum and semiclassical frameworks to investigate electron capture at higher energy as well. The {ital ab initio} potential curves and nonadiabatic coupling matrix elements for all these systems are obtained from multireference single- and double-excitation configuration interaction calculations. For all systems, the effect of excited atoms on electron capture is examined in addition to that from the ground state. Because of a small asymptotic energy defect (near-resonant processes) between the initial and closest electron capture channels for almost all systems, electron capture cross sections from the ground-state atoms are large with values of approximately 10{sup {minus}16}{minus}10{sup {minus}15}cm{sup 2} for all systems at above 100 eV. Corresponding rate coefficients are found to be much smaller than those previously reported for the NH{sup +} and OH{sup +}, but, on the contrary, foundmore » to be larger by a few orders of magnitude than the previously estimated value for the SiH{sup +} system. Those from excited states are also found to be extremely efficient for all cases. {copyright} {ital 1997} {ital The American Physical Society}« less

Ab initio study of charge transfer in low-energy collisions ofSi4+with helium

We present state-dependent and total charge transfer cross sections for the process ${\mathrm{Si}}^{4+}$(${2\mathrm{p}}^{6}$)+He(${1\mathrm{s}}^{2}$)\ensuremath{\rightarrow}${\mathrm{Si}}^{3+}$(3l)+${\mathrm{He}}^{+}$(1s), where l=s,p, in the collision energy range 0.004--10 eV/amu. The cross sections are determined using a close-coupled quantal method. Fully ab initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained with the spin-coupled valence-bond method are incorporated. Rate coefficients for temperatures between 1000 and 50 000 K and results for isotopic $^{3}\mathrm{He}$ are also presented. Astrophysical applications are briefly discussed.

Charge Transfer Rate in Collisions of H+Ions with Si Atoms

Charge transfer in Si(3P, 1D) + H+ collisions is studied theoretically by using a semiclassical molecular representation with six molecular channels for the triplet manifold and four channels for the singlet manifold at collision energies above 30 eV, and by using a fully quantum mechanical approach with two molecular channels for both triplet and singlet manifolds below 30 eV. The ab initio potential curves and nonadiabatic coupling matrix elements for the HSi+ system are obtained from multireference single- and double-excitation configuration interaction (MRD-CI) calculations employing a relatively large basis set. The present rate coefficients for charge transfer to Si+(4P) formation resulting from H+ + Si(3P) collisions are found to be large with values from 1 × 10–10 cm3 s–1 at 1000 K to 1 × 10–8 cm3 s–1 at 100,000 K. The rate coefficient for Si+(2P) formation, resulting from H+ + Si(3P) collisions, is found to be much smaller because of a larger energy defect from the initial state. These calculated rates are much larger than those reported by Baliunas & Butler, who estimated a value of 10–11 cm3 s–1 in their coronal plasma study. The present result may be relevant to the description of the silicon ionization equilibrium.

An ab initio study of the internal conversion rate from the first singlet excited state to the ground state in formaldehyde

The nonradiative transition rates from the single vibronic levels of the first singlet excited state to the ground state were estimated using a time-dependent method based on Fermi’s golden rule. In the present method, the initial wave packet is constructed with the use of the nonadiabatic coupling matrix elements calculated by ab initio molecular orbital method. The wave packet dynamics calculation is carried out using the reaction path Hamiltonian. The vibrational relaxation on the ground state surface is treated by introducing the effective Hamiltonian. The parameters required to construct these Hamiltonians were obtained with the complete active space self-consistent field wave function and the electronic matrix elements of nonadiabatic coupling between the ground and first singlet excited states were calculated with the state-averaged complete active space self-consistent field wave function analytically. The calculated rate constants were in good agreement with the experimental ones. It is found that vibrational relaxation in the ground electronic state is an important factor in obtaining the nonradiative transition rate constants.

Charge transfer in collisions of B2+(2S,2P) and B3+(1S) ions with He atoms below 200 keV.

Charge transfer in ${\mathrm{B}}^{2+}$${(}^{2}$S${,}^{2}$P)+He and in ${\mathrm{B}}^{3+}$${(}^{1}$S)+He collisions is studied theoretically by using a semiclassical molecular representation with 8 and 12 molecular channels for ${\mathrm{B}}^{2+}$ and ${\mathrm{B}}^{3+}$ on He systems, respectively, at collision energies between 200 eV and 200 keV for the former and between 600 eV and 50 keV for the latter. The ab initio potential curves and nonadiabatic coupling matrix elements are obtained from the multireference single- and double-excitation configuration-interaction (MRD-CI) calculations for the ${\mathrm{B}}^{2+}$-He system and a pseudopotential-modified configuration-interaction method for the ${\mathrm{B}}^{3+}$-He system. The present cross sections for charge transfer by the ground state ${\mathrm{B}}^{2+}$ ions are found to have a broad maximum with a magnitude as large as 2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ ${\mathrm{cm}}^{2}$ at 100 keV and those by an excited ${\mathrm{B}}^{2+}$${(}^{2}$P) state are found to be larger by a factor of 6 than those by the ground state in the same energy regime. ${\mathrm{B}}^{2+}$-excitation cross sections are smaller than those for charge transfer below 1 keV, while they increasingly dominate above this energy. The present total charge-transfer cross section for ${\mathrm{B}}^{3+}$ in collisions with He is similar to that obtained in earlier work by Gargaud et al. [J. Phys. B 27, 3985 (1994)] both in magnitude and energy dependence, but is found to show slightly different ${\mathrm{B}}^{2+}$(2s) and ${\mathrm{B}}^{2+}$(2p) production ratio. \textcopyright{} 1996 The American Physical Society.

Electron capture in collisions of O2+(3P) ions with He atoms at energies below 10 keV: The effect of metastable O2+(1D) ions.

Electron capture in ${\mathrm{O}}^{2+}$${(}^{3}$P${,}^{1}$D)+He collisions is studied theoretically by using a semiclassical molecular representation with six molecular channels at collision energies above 50 eV and by using a fully quantum-mechanical molecular representation with three \ensuremath{\Pi} channels below these energies. The ab initio potential curves and nonadiabatic coupling matrix elements for the ${\mathrm{HeO}}^{2+}$ system are obtained from multireference single- and double-excitation configuration-interaction calculations employing a relatively large basis set. The present total cross sections for electron capture by the ground-state ${\mathrm{O}}^{2+}$ ions are found to be in reasonable accord with those calculated by Gargaud, Bacchus-Montabonel, and McCarroll [J. Chem. Phys. 99, 4495 (1993)] below 30 eV/u but are slightly larger above this energy. Partial cross sections for the l distribution are also slightly different. Cross sections for electron capture by the metastable ${\mathrm{O}}^{2+}$ ions decrease much more sharply than those for the ground-state ion as the energy is lowered, reaching a difference between them approximately as large as one to two orders of magnitude below 100 eV. The present rate coefficient for the reaction is approximately ${10}^{\mathrm{\ensuremath{-}}9}$ ${\mathrm{cm}}^{3}$/s above 10 000 K, suggesting that the small rate coefficient of about ${10}^{\mathrm{\ensuremath{-}}12}$ ${\mathrm{cm}}^{3}$/s at 20 000 K observed by Kwang and Fang [Phys. Rev. Lett. 71, 4127 (1993)] for electron capture by the ground-state ion might be caused, in part, by a mixture of ground and metastable ions in their experiment. \textcopyright{} 1996 The American Physical Society.

Electron capture and target excitation in collisions of Bq+ and Beq+ ions with H and He atoms at energies below 10 keV/u

Electron capture and target excitation in Beq+ (q = 2–4) and Bq+ (q = 2–3) + H and He collisions are studied theoretically by using a semiclassical molecular representation with six to 22 molecular channels at collision energies above 50 eV/u and by using a fully quantum mechanical molecular representation with three to five channels below 50 eV/u. The ab initio potential curves and nonadiabatic coupling matrix elements for the HeBeq+ and HeBq+ systems are obtained from either a pseudopotential-modified configuration interaction method or multireference single- and double-excitation configuration interaction (MRD-CI) calculations. Cross sections for electron capture are summarized in numerical tables. Target-excitation processes are also examined for some systems and significant effects of these channels on capture channels are discussed.