Diabatic Curves Research Articles

Time-dependent observables and diabatic curve crossing: a model study

We study the diabatic crossing of two electronic surfaces from the time-dependent point of view, looking at the time and frequency-resolved spontaneous emission spectra and to the total population of the excited state, which for a pump and-probe experiment with two δ-like pulses, is proportional to the total emission. The results of some computations on a model case are presented and discussed.

Doubly-excited states for the Na2 molecule: application to the dynamics of the associative ionization reaction

In a recent paper, we have performed accurate model potential calculations for the adiabatic excited states of the Na2 molecule. In view of dynamical calculations we propose a method to extract doubly excited potential curves, singly excited Rydberg series, and electronic couplings. In contrast to the previous work, the diabatic curves are correctly matching the adiabatic curves at large internuclear distances, and the electronic interactions do vanish in the asymptotic region. The adequacy of scaling laws to extract reduced parameters relevant to MQDT treatment of molecular autoionization is discussed. These parameters are used to calculate cross-sections for the associative ionization reaction at thermal collision energies when fine structure splitting can be neglected. In the framework of a simple model for the treatment of the long range dynamical couplings, we show the strong influence of the initial preparation of the atoms, and of long range population transfers. In contrast to the usual interpretation of experimental data, we predict that at least four doubly excited states may contribute efficiently to the process. Nevertheless, we may reproduce the marked variation of the observed ion signal as a function of the polarization of the exciting light. This work is a step towards a full treatment of the associative ionization between two cold atoms.

Photoinduced intermolecular electron transfer reaction between N,N-dimethylaniline and anthracene in acetonitrile solution: A theoretical study

The photoinduced intermolecular electron transfer (ET) reaction between N,N-dimethylaniline and excited state anthracene in acetonitrile solution is studied theoretically. A solvation coordinate s which represents stochastic one-dimensional dynamics of the solution phase reaction is defined and a Hamiltonian in terms of s and perpendicular bath modes is derived from the spin-boson Hamiltonian. This has an advantage that the dynamics of the transferring electron is influenced by the bath only through coupling with the coordinate s. Intra- and intermolecular potentials are constructed by using ab initio molecular orbital methods, and a series of molecular dynamics simulation analysis is performed. Mean force potentials as a function of the donor–acceptor distance R are computed and the bimolecular encounter dynamics is investigated. Diabatic free energy curves for the coordinate s are computed and shown to be well approximated by parabolas, indicating that the dielectric saturation effect is negligible. The dependence of the free energy relationships on R is examined. It is shown that the present system corresponds to the increasing region of the rate constant, in contrast with the conventional picture. The electronic coupling of the ET is evaluated by the method of corresponding orbitals. The R dependence of the ET rate is evaluated and the reaction adiabaticity and mechanism are discussed. Dynamical solvent effects are taken into consideration in terms of the generalized Langevin equation formalism.

Theoretical analysis of the effect of Lewis acid catalysts on reactivity in the Diels-Alder reaction of 2-azabutadiene with ethylene

The catalytic effect of a Lewis acid on the reaction of 2-azabutadiene with ethylene has been analyzed theoretically. It is found that catalytic action favors the electronic transference from ethylene to the diene through the iminic carbon atom leading to an increase in the asynchronicity and a stronger interaction between the diabatic curves corresponding to the transferred configuration and the zero configuration causing a decrease in the activation energy, and an earlier character of the transition structure for the process.

Molecular dynamics of adiabatic and nonadiabatic electron transfer at the metal–water interface

A molecular model for an electron transfer reaction at a solution–electrode interface is developed. The solvent diabatic free energy curves for the reaction Fe+3+e−→Fe+2 are calculated using an umbrella sampling procedure. These are used to calculate the rate of electron transfer as a function of the electrode–solution potential difference in the electronically nonadiabatic region. A model Hamiltonian for the adiabatic case is also developed and used to calculate the adiabatic free energy surface. Reactive flux correlation functions are used to determine the solvent dynamical corrections to the rate. A comparison between the molecular dynamics and the Kramers and Grote–Hynes theories is made.

A lower bound on the loss of graphite by atomic oxygen attack at asymptotic energy

A method is devised to find a lower bound on the loss function of graphite in the oxygen high energy range where that function is expected to assume constant value. It requires obtaining a small ensemble of classical trajectories of oxygen on graphite and making static measurements of an oxygen on ethylene potential energy surface. An oxygen atom is assumed to be bonded to the graphite surface by diabatic curve crossing from its initial repulsive potential. Subsequently, it is assumed to be ejected as part of a carbon monoxide molecule due to surface impact of another incident oxygen atom. A dynamical calculation is suggested to improve on the approximate method of this work. Once an excited state cross channel coupling constant is known, the ratio of the loss function of that excited state to the loss function of the ground state may be estimated at asymptotic oxygen energies.

Role of potential structure in nonadiabatic collisions with applications to He++Ne(2p6)-->He++Ne(2p53s) and Na+I-->Na++I-

The first-order functional-sensitivity densities \ensuremath{\delta}${\mathrm{\ensuremath{\sigma}}}_{12}$(E)/\ensuremath{\delta}${\mathit{V}}_{\mathit{i}\mathit{j}}$(R) from close-coupling calculations are used for a quantitative probe of the role of structure in crossing diabatic curves used to model nonadiabatic collisions. Application to the excitation of Ne by ${\mathrm{He}}^{+}$ shows a region of significance for \ensuremath{\delta}${\mathrm{\ensuremath{\sigma}}}_{12}$(E)/\ensuremath{\delta}${\mathit{V}}_{12}$(R) as a prominent Gaussian-like profile around the crossing point (${\mathit{R}}^{\mathrm{*}}$) in accord with the \ensuremath{\delta}(R-${\mathit{R}}^{\mathrm{*}}$) idealization of the Landau-Zener-Stueckelberg (LZS) theory. Similarly, the densities \ensuremath{\delta}${\mathrm{\ensuremath{\sigma}}}_{12}$(E)/\ensuremath{\delta}${\mathit{V}}_{11}$(R) and \ensuremath{\delta}${\mathrm{\ensuremath{\sigma}}}_{12}$(E)/\ensuremath{\delta}${\mathit{V}}_{22}$(R) mimic d\ensuremath{\delta}(R-${\mathit{R}}^{\mathrm{*}}$)/dR-type behavior with one being the negative of the other in the neighborhood of ${\mathit{R}}^{\mathrm{*}}$, in qualitative agreement with the LZS theory. However, all three sensitivity profiles identify a much broader area of importance for the curves than the loosely defined avoided-crossing region. Also, although the sensitivities themselves decrease with increasing energy, the domain of importance of the curves increases. Examination of the functional-sensitivity densities \ensuremath{\delta}${\mathrm{\ensuremath{\sigma}}}_{12}$(E)/\ensuremath{\delta}${\mathit{V}}_{\mathit{i}\mathit{j}}$(R) for the chemi-ionization collision Na+I\ensuremath{\rightarrow}${\mathrm{Na}}^{+}$+${\mathrm{I}}^{\mathrm{\ensuremath{-}}}$ reveals regions of potential-function importance very different from that predicted by the LZS theory.The chemi-ionization cross section is about ten times more sensitive to the ionic curve than the covalent curve. Also, the domain of sensitivity of the ionic curve is larger compared to that of the covalent curve. The density \ensuremath{\delta}${\mathrm{\ensuremath{\sigma}}}_{12}$(E)/\ensuremath{\delta}${\mathit{V}}_{12}$(R) for chemi-ionization shows that the area of maximum potential significance is not at the crossing point itself but the regions bracketing it on both sides. Also, the dominant sign dependence of the coupling sensitivity is unexpectedly negative. The results offer other observations about the domain of validity of the intuitive pictures rooted in the LZS theory. The significance of these results to the inversion of inelastic cross-section data is briefly discussed.

Computation and assignment of radial couplings using accurate diabatic data for the LiH molecule

The radial couplings between the 3,1 Sigma + adiabatic states dissociating into Li(2s, 2p, 3s, 3p, 3d, 4s and 4p)+H and Li++H- are determined from accurate diabatic data. The results are validated by a comparison with previous ab initio calculations. It is shown that the peaks of the radial coupling can be interpreted from the diabatic curves. An over-repulsiveness of the valence diabatic states as compared to the Rydberg diabatic states generates, at short internuclear distances, a series of crossings between neutral diabatic states which are associated with intense peaks of the radial coupling both for the singlet and triplet Sigma states.

Valence‐bond calculations on ZNO and HGO using integrals computed through the semiempirical AM1 method

AbstractValence‐bond calculations have been carried out on ZnO and HgO using a basis set of Slatertype atomic orbitals and the one‐ and two‐electron integrals as computed in the semiempirical AM1 molecular orbital method. The zero differential overlap approximation has been used to calculate integrals between atomic orbital Slater determinants using the rules for matrix elements between determinants formed by orthogonal orbitals. Diabatic and adiabatic curves have been analyzed for the two systems, and results compared with molecular orbital AM1 results. © 1992 John Wiley & Sons, Inc.

Monte Carlo simulation of the diabatic free energy curves for a dissociative electron transfer reaction in a polar solvent

AbstractIn the present work we have carried out a Monte Carlo simulation of a dissociative electron transfer reaction in a polar solvent. In particular, we have chosen as a very simple model the electrochemical reduction of hydrogen fluoride to give a hydrogen atom and a fluoride anion in a dipolar solvent. From a classical point of view, the electron transfer occurs at the intersection region S* of the diabatic potential hypersurfaces Hpp and Hss, corresponding to the precursor and successor complexes, respectively. We have evaluated both diabatic surfaces using potential functions that have been built up with ab initio methods by us. For each of the obtained configurations the parameter ΔE = Hss – Hpp has been calculated. This parameter is then used as the reaction coordinate for obtaining the diabatic free energy curves of the reaction. Because the activation energy is high, a suitable mapping potential along with the statistical perturbation theory is employed to force the system to evolve toward the intersection region S*. A total of 68,340,000 configurations have been generated. The main conclusion of this article is that Marcus' relationship seems to fail for this kind of inner‐sphere processes. © 1992 by John Wiley & Sons, Inc.

Single-channel quantum-defect theory for the description of doubly excited states of helium.

A single-channel quantum-defect theory for the doubly excited states of helium is formulated in hyperspherical coordinates. For doubly excited states associated with each excited ${\mathrm{He}}^{+}$(N) threshold, the outer electron experiences asymptotically a combined Coulomb and dipole potential, -1/R+\ensuremath{\alpha}/${\mathit{R}}^{2}$. The two independent solutions in the asymptotic region for energies below and above the threshold are explicitly given for both the attractive and the repulsive dipole potentials. Quantum defects for $^{1}$P\ifmmode^\circ\else\textdegree\fi{} doubly excited states of five channels in the N=3 manifold and of the dominant channels below the N=2, 3, and 4 thresholds of ${\mathrm{He}}^{+}$ are calculated in a single-channel hyperspherical potential, and the results are compared with quantum defects extracted from other theoretical calculations and recent experimental results. Procedures for obtaining diabatic curves from the adiabatic potentials are also discussed.

On the role of medium electrons in the outer-sphere electron transfer reactions

We consider the nonlinear Schrödinger equation arising when an explicit separation of the medium electron polarization is performed in the Hamiltonian describing the outer-sphere electron transfer (ET) reaction. The corresponding classical activation energy is determined by the point of intersection of two diabatic energy curves rather than by the stationary saddle point of the free energy functional, in agreement with the earlier treatment of Kim and Hynes. Analytical expressions for the free energy terms as functions of the ET coordinate are derived. The relative energy of this cross point is the same as the traditional activation energy of the Et process as given by the Marcus formula. In order to find the interaction matrix elements which promote the nonadiabatic transition and avoided crossing, an alternative quantum-mechanical description of the two-level ET model is given in terms of the wavefunction which allows independent reorganization of electrons belonging to the medium and to the chemical substrate. Explicit expression for matrix elements are presented and different kinetic regimes generated by this refined model are discussed.

Ab initio adiabatic and diabatic potential-energy curves of the LiH molecule

For nearly all states below the ionic limit [i.e., Li(2s, 2p, 3s, 3p, 3d, 4s, and 4p)+H] we perform the first adiabatic and diabatic studies. This treatment involves a nonempirical pseudopotential for Li and a full configuration-interaction treatment of the valence-electron system. Core–valence correlation is taken into account according to a core-polarization-potential method. We present an analysis of the diabatic curves and introduce appropriate small corrections accounting for basis-set limitations. For the low-lying states, our vibrational level spacings and spectroscopic constants are in excellent agreement with the available experimental data and with the best all-electron results. Experimental suggestions are given for the higher states.

Excited 2Σ +u states of He +2 and the formation of explosive He 2+2

Reliable MRD-Cl calculations have been carried out on the He + 2 2Σ + u ground and first six excited states. The adiabatic potential energy curves and the non-adiabatic matrix elements at the numerous avoided crossings have been obtained; from these, approximate diabatic curves have been constructed. The results point to the possibility of producing vibrationally excited (ν=1) He 2+ 2 1Σ + g through He ++H * collisions. The computed tunneling lifetime of this level is ≈ 10 −2s. A recent observation of He 2+ 2 via its Coulomb explosion, determined that its lifetime was longer than μs.

Dominant photodetachment channels in H-

Adiabatic hyperspherical potential curves are calculated for very highly excited states of H{sup {minus}} converging to H({ital n}{le}12). These potential curves reveal surprisingly weak channel interactions, manifested as extremely diabatic multiple curve crossings. We demonstrate that only resonances associated with the {ital lowest} +'' diabatic channel within each {ital n} manifold are observed in the recent experiments at Los Alamos (Harris {ital et} {ital al}.). A simple Rydberg-dipole formula gives the positions of all dominant resonances, permitting extrapolation to arbitrarily high quantum numbers.

Crossings of potential-energy surfaces in a magnetic field.

We investigate the interaction of molecular electronic states through nuclear motion in the presence of a homogeneous magnetic field. The different possibilities and effects of this interaction are classified according to the symmetries and the qualitative behavior of the diabatic energy curves. As a central result we show that conical intersections of electronic energy potential surfaces, which are in the field-free case common for polyatomic molecules, appear in the presence of a magnetic field already on the level of a diatomic molecule.

Influence of collision gas on doubly charged ion mass spectra

AbstractThe influence of the collision gas on doubly charged ion mass spectra of a selected number of hydrocarbons has been examined. Relative abundances of various product ions in 2E spectra, resulting from charge exchange collisions of doubly charged hydrocarbon ions, do not vary drastically as the collision gas is varied. However, the absolute intensities of these doubly charged ion mass spectra increase significantly when the collision gas is changed from argon to methane to isobutane. Tbese observations are rationalized in terms of a multichannel diabatic curve crossing model.

Ion-surface interactions and electronically stimulated desorption of physisorbed atoms.

Diabatic potential-energy curves for ${\mathrm{Ar}}^{+}$ and ${\mathrm{Kr}}^{+}$ interacting with a metal surface are reported. At intermediate distances, the attractive force is considerably smaller than the classical result for an ion attracted to its image charge. This has a substantial impact on the dynamics of electronically stimulated desorption, and on the Franck-Condon broadening of photoemission lines. Quantum effects on ion motion are considered, and the validity of a classical treatment is discussed.

Simple models for describing the fragmentation behavior of multiply charged cations

The potential energy curve describing the fragmentation of a diatomic dication AB2+ is considered as arising from an avoided crossing between an attractive diabatic curve (correlating with A2+ + B) and a repulsive diabatic curve (correlating with A+ + B+). The simplest avoided-crossing (AC) model neglects diabatic coupling and polarization and leads to useful predictions of the transition structure bond length (rTS) and the kinetic energy released (T) in fragmentations of dicationic systems in which the difference (Δ1) between the ionization energies of A+ and B is small. When Δ1 is not small, it is necessary to include diabatic coupling and polarization in the treatment. The resultant ACDCP (avoided crossing with diabatic coupling and polarization) model provides very satisfactory estimates of rTS and T for both small and large Δ1. Its implementation requires only atomic ionization energy and polarizability data and comes at virtually no computational cost. Both the AC and ACDCP models are readily generalized to fragmentations of more highly charged cations.

Adiabatic calculations of the 2Σ +g excited states of He +2

The first six 2Σ + g adiabatic potential energy curves of He + 2 are calculated with the MRD CI method employing configuration selection ( T = 10 μ hartree) and perturbative energy corrections and using two basis sets differing in the number of diffuse functions. The non-adiabatic matrix elements at the numerous avoided crossings are also calculated and approximate diabatic curves are constructed. Various aspects of the results are discussed.