Introduction to the theory of electronic non-adiabatic coupling terms in molecular systems

The Born–Oppenheimer treatment leads to the adiabatic framework where the non-adiabatic terms are the physical entities responsible for the coupling between adiabatic states. The main disadvantage of this treatment is in the fact that these coupling terms frequently become singular thus causing difficulties in solving the relevant Schroedinger equation for the motion of the nuclei that make up the molecular systems. In this review, we present the line integral approach which enables the formation of the adiabatic-to-diabatic transformation matrix that yields the friendlier diabatic framework. The review concentrates on the mathematical conditions that allow the rigorous derivation of the adiabatic-to-diabatic transformation matrix and its interesting physical properties. One of the findings of this study is that the non-adiabatic coupling terms have to be quantized in a certain manner in order to yield single-valued diabatic potentials. Another important feature revealed is the existence of the topological matrix, which contains all the topological features of a given molecular system related to a closed contour in configuration space. Finally, we present an approximation that results from the Born–Oppenheimer treatment which, in contrast to the original Born–Oppenheimer approximation, contains the effect of the non-adiabatic coupling terms. The various derivations are accompanied by examples which in many cases are interesting by themselves.     

The influence of phonon admixture and non-adiabatic effects in the even-even core on the coriolis mixing of odd nuclei states

Some generalizations of the model for odd nuclei suggested by Kerman are considered. The effects of phonon admixtures on matrix elements of Coriolis interaction are studied. Several schemes are considered for studying the role of non-adiabatic effects in the even-even core.One of the authors B. Ch. thanks L. A.Malov and V. O.Nesterenko for many discussions of some questions connected with the determination of the phonon-quasiparticle admixtures.     

Quantum dynamics studies on the non-adiabatic effects of H + LiD reaction

After the Big Bang, chemical reactions of hydrogen with LiH and its isotopic variants played an important role in the late stage of recombination. Moreover, these reactions have attracted the attention of experts in the field of molecular dynamics because of its simple structure. Electronically non-adiabatic effects play a key role in many chemical reactions, while the related studies in LiH₂ reactive system and its isotopic variants are not enough, so the microscopic mechanism of this system has not been fully explored. In this work, the microscopic mechanism of H + LiD reaction are performed by comparing both the adiabatic and non-adiabatic results to study the non-adiabatic effects. The reactivity of R1 (H + LiD → Li + HD) channel is inhibited, while that of R2 (H + LiD → D + LiH) channel is enhanced when the non-adiabatic couplings are considered. For R1 channel, a direct stripping process dominates this channel and the main reaction mechanism is not influenced by the non-adiabatic effects. For R2 channel, at relatively low collision energy, the dominance changes from a rebound process to the complex-forming mechanism when the non-adiabatic effects are considered, whereas the rebound collision approach still dominates the reaction at relatively high collision energy in both calculations. The presented results provide a basis for further detailed study on this importantly astrophysical reaction system.     

Quantum Invariant Theory and Non-Adiabatic Non-Abelian Phase Factor

An alternative formulation is proposed for the calculation of the non-adiabatic non-Abelian connection and phase factor by making use of the invariant theory and invariantrelated unitary transformation method. In order to illustrate the formulation, we study the non-adiabatic non-Abelian phase associated with the motion of a charged particle in a timedependent magnetic field (the time-dependent Landau level problem).     

Optical phonon self-energies in titanium phases: effects of electron–phonon interaction

Temperature-dependent Raman investigations of titanium in the α and pressure-quenched ω-phase have been carried out. The results obtained suggest the possible coexistence of both phases at ambient pressure and low temperatures. Comparison of the low-temperature E_2g phonon self-energies in both phases with simulations based on the calculated electronic structures for α- and ω-Ti implies significant contributions from non-adiabatic electron–phonon interactions.     

Adiabatic approach to non-radiative transitions: Exact transition rates of order Δ2

The static (SBA) and adiabatic base (ABA) approaches are analyzed for an electronic two-level system coupled to a single vibrational mode. In the ABA due account is taken of the non-adiabatic contribution to the oscillatory potential. This permits the introduction of a suitable model potential whose eigenfunctions can be exactly calculated. It is proven that the calculation of the non-adiabatic transition matrix elements by means of these model eigenfunctions yields the exact first order result in the promoting mode coupling constant Δ. The calculation evinces the importance of the diagonal non-adiabaticity operator, which has been neglected in earlier work. The transition matrix elements of the two approaches are compared. It is found that the absolute value of the SBA-result is always larger than that of the ABA-result and rises up to a factor 2 of the latter for higher Huang-Rhys factors. Our finding resolves an old controversy.     

Influence of a transport current on a domain wall in an antiferromagnetic metal

We consider the influence of an electric current on the position of a domain wall in an antiferromagnetic metal. We first microscopically derive an equation of motion for the Néel vector in the presence of current by performing, in the transport steady state, a linear-response calculation in the deviation from collinearity of the antiferromagnet. This equation of motion is then solved variationally for an antiferromagnetic domain wall. We find that, in the absence of dissipative or non-adiabatic coupling between magnetization and current, the current displaces the domain wall by a finite amount and that the domain wall is then intrinsically pinned by the exchange interactions. In the presence of dissipative or non-adiabatic current-to-domain-wall coupling, the domain wall velocity is proportional to the current and is no longer pinned.     

Transformation of director configuration upon changing boundary conditions in droplets of nematic liquid crystal

The transformation of the director configuration upon changing boundary conditions from planar to homeotropic for bipolar nematic droplets dispersed in a polymeric matrix was studied. The characteristic textural patterns are presented for droplets with different concentrations of homeotropic surfactants, and their orientational structure is identified. The scenario predicted earlier by G.E. Volovik and O.D. Lavrentovich (ZhETF 85, 1997 (1983)) for the transformation of orientational structure of nematic droplets from bipolar to radial, without the formation of additional disclinations, is revealed. It is shown that, by using the computational method of minimization of the director elastic-strain energy in the droplet bulk and by introducing the inhomogeneous boundary conditions, one can obtain orientational structures that are analogous to the observed ones.     

Some realistic calculations on the migration process of hydrogen isotopes in bcc metals

By adopting the empirical interaction potential between hydrogen and metal atoms determined in our previous paper, calculations have been performed of the 2T configuration, in which two neighboring tetrahedral (T) sites are equally shared by a hydrogen (H) atom. The tunneling matrix element J and the activation energy are estimated by calculating the excitation energy of the H atom for the 2T state and the energy difference between the 2T and 1T state, respectively.From these calculations, it is suggested that H atoms in V and Fe migrate between the ground states of neighboring T sites by adiabatic transitions, whereas in the lower temperature region in Ta by non-adiabatic tunneling process.     

Dynamics of domain walls in magnetically multiaxial films in the thickness range corresponding to the Bloch-Néel transformations of the structure

The numerical minimization of the total energy functional and the solution of the nonlinear Landau-Lifshitz equation have been performed exactly taking into account the fundamental (including dipole-dipole) interactions in terms of the two-dimensional magnetization distribution. The equilibrium structure, energy, mobility, and scenario of the dynamic transformation of the domain walls (in their non- steady-state motion) have been determined as a function of the film thickness b and external magnetic field H for two different ((010) and (110)) orientations of the surfaces of magnetically triaxial films. The range of film thicknesses, including the thickness b = b _N, for which the Néel domain walls can be transformed into the Bloch domain walls, has been investigated. The phenomena of anisotropy of the domain-wall energy, the domain-wall mobility, and the period of dynamic transformations of the domain walls have been analyzed as a function of the film thickness b and external magnetic field H. The range of film thicknesses has been determined, in which the non-steady-state motion of the Néel domain walls is accompanied by the creation and annihilation of vortex-like structures despite the one-dimensional character of the magnetization distribution in these walls.     

混合量子-经典非绝热动力学理论与应用

Electronically non-adiabatic processes are essential parts of photochemical process, collisions of excited species, electron transfer processes, and quantum information processing. Various non-adiabatic dynamics methods and their numerical implementation have been developed in the last decades. This review summarizes the most significant development of mixed quantum-classical methods and their applications which mainly include the Liouville equation, Ehrenfest mean-field, trajectory surface hopping, and multiple spawning methods. The recently developed quantum trajectory mean-field method that accounts for the decoherence corrections in a parameter-free fashion is discussed in more detail.     

Comparison of coordinate-space techniques in nuclear mean-field calculations

We investigate three different numerical representations for nuclear mean-field calculations: finite differences, Fourier representation, and basis-splines. We compare these schemes with respect to precision and speed. It turns out that Fourier techniques and basis-splines are much superior in precision to finite differences. The Fourier representation in connection with the fast Fourier transformation is advantageous for large grids whereas matrix techniques, derived either from basis-splines or from Fourier representation, are preferable for smaller grids.     

Surface chemistry of hot electron and metal-oxide interfaces

Fundamental mechanisms for energy conversion and dissipation on surfaces and at interfaces have been significant issues in the community of surface science. Electronic excitation in exothermic chemical reactions or photon absorption involves the generation of energetic or hot electrons that are not in thermal equilibrium via non-adiabatic electronic excitation. A number of experimental and theoretical studies have demonstrated the influence of excited hot electrons on atomic and molecular processes, and it is a key moderator in the surface energy conversion process. The charge transfer through the metal-oxide interfaces has a significant impact on catalytic performance in mixed metal-oxide catalysts. In order to understand the influence of hot electrons and metal-oxide interfaces on the surface reactions, various detection schemes of exoelectron detection, including metal-insulator-metal and metal-semiconductor Schottky diodes, have been developed. Catalysts coupled with surface plasmons exhibit peculiar catalytic performance related to hot electron flow. In this review, we outline recent research efforts to relate hot electron flow with surface reactions occurring at metal-oxide interfaces. We report recent studies on the observation of hot electrons and the correlation between hot electrons and catalytic activity and selectivity on metallic surfaces. We show recent results from studies of surface reactions on nanocatalysts coupled with surface plasmons, where hot electron transport is the key process in energy dissipation and conversion processes.     

Relativistic corrections for the vibration-rotation levels of the ground electronic state of the hydrogen molecular cation H+ 2

Previous work [Moss, R. E., and Valenzano, L., 2002, Molec. Phys., 100, 649 and 1527] on the non-adiabatic properties of the vibration-rotation levels of the ground electronic state of the hydrogen molecular cation is extended to the calculation of relativistic corrections. Unlike the earlier calculations, in which all matrix elements were evaluated analytically, numerical methods are needed for some of the integrals.     

Optimal low-dispersion low-dissipation LBM schemes for computational aeroacoustics

Lattice Boltmzann Methods (LBM) have been proved to be very effective methods for computational aeroacoustics (CAA), which have been used to capture the dynamics of weak acoustic fluctuations. In this paper, we propose a strategy to reduce the dispersive and disspative errors of the two-dimensional (2D) multi-relaxation-time lattice Boltzmann method (MRT-LBM). By presenting an effective algorithm, we obtain a uniform form of the linearized Navier–Stokes equations corresponding to the MRT-LBM in wave-number space. Using the matrix perturbation theory and the equivalent modified equation approach for finite difference methods, we propose a class of minimization problems to optimize the free-parameters in the MRT-LBM. We obtain this way a dispersion-relation-preserving LBM (DRP-LBM) to circumvent the minimized dispersion error of the MRT-LBM. The dissipation relation precision is also improved. And the stability of the MRT-LBM with the small bulk viscosity is guaranteed. Von Neuman analysis of the linearized MRT-LBM is performed to validate the optimized dispersion/dissipation relations considering monochromatic wave solutions. Meanwhile, dispersion and dissipation errors of the optimized MRT-LBM are quantitatively compared with the original MRT-LBM. Finally, some numerical simulations are carried out to assess the new optimized MRT-LBM schemes.     

Van der Waals interactions in DFT made easy by Wannier functions

Ubiquitous van der Waals interactions between atoms and molecules are important for many molecular and solid structures. These systems are often studied from first principles using the density functional theory (DFT). However, the commonly used DFT functionals fail to capture the essence of van der Waals effects. Most attempts to correct for this problem have a basic semiempirical character, although computationally more expensive first principles schemes have been recently developed. We here describe a novel approach, based on the use of the maximally localized Wannier functions, that appears to be promising, being simple, efficient, accurate, and transferable (charge polarization effects are naturally included). The results of test applications to small molecules and bulk graphite are presented.     

Born-Oppenheimer breakdown and non-adiabatic lifetimes of rovibrational levels of D2 lying near the n = 2 dissociation limit: Experiment and theory

The singlet gerade states of the hydrogen molecule are strongly affected by the breakdown of the Born-Oppenheimer approximation. This leads to strong non-adiabatic coupling resulting in large changes of the energies and lifetimes of the quantum levels compared to the values obtained in the Born-Oppenheimer or even the adiabatic levels of approximation. The non-adiabatic calculations of Quadrelli, Dressler, and Wolniewicz (1990) [7] (hereinafter QDW) for the three highest vibrational levels (υ = 44, 45, and 46) of the EF ¹Σ_g⁺ state of D₂ predicted an enormous increase of the lifetimes upon excitation of just one quantum of rotational motion. However, although our experimental results for these levels just below the n = 2 dissociation limit do show a strong increase in lifetime, the non-adiabatic lifetimes calculated by QDW are longer than experiment by as much as three orders of magnitude. In their work on isotopomers of hydrogen QDW and Yu and Dressler (1994) [5] published extensive summary tables of ab initio non-adiabatic coupling data. We present a technique which allows us to use their summary data to calculate approximate non-adiabatic ab initio lifetimes. The results reconcile our observed lifetimes with the non-adiabatic coupling from those previous ab initio calculations and also provide a detailed quantitative and qualitative understanding of the unusual rotational dependence of the lifetimes of these very highly excited levels. We also test the current technique by calculating the lifetimes of other levels involved in interactions with these EF levels and by calculating the lifetimes of the EF υ = 33 level of H₂, for which no corresponding level exists in the Born-Oppenheimer or adiabatic approximations.