Gaussian wavepacket dynamics and the Landau—Zener model for non-adiabatic transitions

The beam scattering method was used to investigate non-dissociative single-electron charge transfer between the molecular dication CO22+ and Ar or Ne at several collision energies between 3-10 eV (centre-of-mass, c.m.). Relative translational energy distributions of the product ions showed that in the reaction with Ar the CO2+ product was mainly formed in reactions of the ground state of the dication, CO22+(X3Σg-), leading to the excited states of the product CO2+(A2Πu) and CO2+(B2Σu+). In the reaction with Ne, the largest probability had the process from the reactant dication excited state CO22+(1Σg+) leading to the product ion ground state CO2+(X2Πg). Less probable were processes between the other excited states of the dication CO22+, (1∆g), (1Σu-), (3∆u), also leading to the product ion ground state CO2+(X2Πg). Using the Landau-Zener model of the reaction window, relative populations of the ground and excited states of the dication CO22+ in the reactant beam were roughly estimated as (X3Σg):(1∆g):(1Σg+):(1Σu-):(3∆u) = 1.0:0.6:0.5:0.25:0.25.

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Nearly perfectly matched layer absorber for viscoelastic wave equations

Geophysics ◽

10.1190/geo2018-0732.1 ◽

2019 ◽

Vol 84 (5) ◽

pp. T335-T345

Author(s):

Enjiang Wang ◽

José M. Carcione ◽

Jing Ba ◽

Mamdoh Alajmi ◽

Ayman N. Qadrouh

Keyword(s):

Wave Equations ◽

Pseudospectral Method ◽

Perfectly Matched Layer ◽

Zener Model ◽

Fourier Pseudospectral Method ◽

Time Stepping ◽

First Case ◽

Stress Strain Relation ◽

Viscoelastic Wave ◽

Spatial Derivatives

We have applied the nearly perfectly matched layer (N-PML) absorber to the viscoelastic wave equation based on the Kelvin-Voigt and Zener constitutive equations. In the first case, the stress-strain relation has the advantage of not requiring additional physical field (memory) variables, whereas the Zener model is more adapted to describe the behavior of rocks subject to wave propagation in the whole frequency range. In both cases, eight N-PML artificial memory variables are required in the absorbing strips. The modeling simulates 2D waves by using two different approaches to compute the spatial derivatives, generating different artifacts from the boundaries, namely, 16th-order finite differences, where reflections from the boundaries are expected, and the staggered Fourier pseudospectral method, where wraparound occurs. The time stepping in both cases is a staggered second-order finite-difference scheme. Numerical experiments demonstrate that the N-PML has a similar performance as in the lossless case. Comparisons with other approaches (S-PML and C-PML) are carried out for several models, which indicate the advantages and drawbacks of the N-PML absorber in the anelastic case.

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Wave propagation dynamics in a fractional Zener model with stochastic excitation

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2020-0079 ◽

2020 ◽

Vol 23 (6) ◽

pp. 1570-1604

Author(s):

Teodor Atanacković ◽

Stevan Pilipović ◽

Dora Seleši

Keyword(s):

Wave Propagation ◽

Constitutive Equation ◽

Equations Of Motion ◽

Weak Form ◽

Stochastic Excitation ◽

Expansion Theorem ◽

Zener Model ◽

Dissipation Inequality ◽

Regularity Properties ◽

Fractional Zener Model

Abstract Equations of motion for a Zener model describing a viscoelastic rod are investigated and conditions ensuring the existence, uniqueness and regularity properties of solutions are obtained. Restrictions on the coefficients in the constitutive equation are determined by a weak form of the dissipation inequality. Various stochastic processes related to the Karhunen-Loéve expansion theorem are presented as a model for random perturbances. Results show that displacement disturbances propagate with an infinite speed. Some corrections of already published results for a non-stochastic model are also provided.

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Comparison of the Performances of Different Computational Methods to Calculate the Electrochemical Stability of Selected Ionic Liquids

Materials ◽

10.3390/ma14123221 ◽

2021 ◽

Vol 14 (12) ◽

pp. 3221

Author(s):

Annalisa Paolone ◽

Sergio Brutti

Keyword(s):

Ionic Liquids ◽

Density Functional ◽

Quantitative Agreement ◽

Electrochemical Stability ◽

Functional Theory ◽

Molecular Systems ◽

Reduction Potentials ◽

Adiabatic Transitions ◽

Alkyl Ammonium ◽

Transition Scheme

The electrochemical stability windows (ESW) of selected ionic liquids have been calculated by comparing different computational approaches previously suggested in the literature. The molecular systems under study are based on di-alkyl imidazolium and tetra-alkyl ammonium cations coupled with two different imide anions (namely, bis-fluorosulfonyl imide and bis-trifluoromethyl sulfonyl imide), for which an experimental investigation of the ESW is available. Thermodynamic oxidation and reduction potentials have here been estimated by different models based on calculations either on single ions or on ionic couples. Various Density Functional Theory (DFT) functionals (MP2, B3LYP, B3LYP including a polarizable medium and empirical dispersion forces) were exploited. Both vertical and adiabatic transitions between the starting states and the oxidized or reduced states were considered. The approach based on calculations on ionic couples is not able to reproduce the experimental data, whatever the used DFT functional. The best quantitative agreement is obtained by calculations on single ions when the MP2 functional in vacuum is considered and the transitions between differently charged states are vertical (purely electronic without the relaxation of the structure). The B3LYP functional underestimates the ESW. The inclusion of a polar medium excessively widens the ESW, while a large shrinkage of the ESW is obtained by adopting an adiabatic transition scheme instead of a vertical transition one.

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