Dynamical Theory of Crystal Lattices

Born, Max; Huang, Kun; Lax, M.

doi:10.1119/1.1934059

Cited by 3,613 publications

(3,134 citation statements)

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“…(8) and (9). This choice for the electronic basis is called the adiabatic 18 electronic basis. Another choice for the electronic basis that is often useful is called the diabatic electronic basis.…”

Section: General Theoretical Considerations and Definitionsmentioning

confidence: 99%

Introductory lecture: Nonadiabatic effects in chemical dynamics

et al. 2004

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Recent progress in the theoretical treatment of electronically nonadiabatic processes is discussed. First we discuss the generalized Born-Oppenheimer approximation, which identifies a subset of strongly coupled states, and the relative advantages and disadvantages of adiabatic and diabatic representations of the coupled surfaces and their interactions are considered. Ab initio diabatic representations that do not require tracking geometric phases or calculating singular nonadiabatic nuclear momentum coupling will be presented as one promising approach for characterizing the coupled electronic states of polyatomic photochemical systems. Such representations can be accomplished by methods based on functionals of the adiabatic electronic density matrix and the identification of reference orbitals for use in an overlap criterion. Next, four approaches to calculating or modeling electronically nonadiabatic dynamics are discussed: (1) accurate quantum mechanical scattering calculations, (2) approximate wave packet methods, (3) surface hopping, and (4) self-consistent-potential semiclassical approaches. The last two of these are particularly useful for polyatomic photochemistry, and recent refinements of these approaches will be discussed. For example, considerable progress has been achieved in making the surface hopping method more applicable to the study of systems with weakly coupled electronic states. This includes introducing uncertainty principle considerations to alleviate the problem of classically forbidden surface hops and the development of an efficient sampling algorithm for low-probability events. A topic whose central importance in a number of quantum mechanical fields is becoming more widely appreciated is the introduction of decoherence into the quantal degrees of freedom to account for the effect of the classical treatment on the other degrees of freedom, and we discuss how the introduction of such decoherence into a self-consistent-potential approximation leads to a reasonably accurate but very practical trajectory method for electronically nonadiabatic processes. Finally, the performances of several dynamical methods for Landau-Zener-type and Rosen-Zener-Demkov-type reactive scattering problems are compared.

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Section: General Theoretical Considerations and Definitionsmentioning

confidence: 99%

Introductory lecture: Nonadiabatic effects in chemical dynamics

et al. 2004

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“…The stretching potential of each bond corresponds with the stretching of the corresponding truss element. Traditionally, atoms in a lattice have been viewed as masses that are held in place with atomic forces that resemble elastic springs [25]. Therefore, bending of truss elements is not needed to simulate the chemical bonds, and it is assumed that each truss joint is pinned, not fixed.…”

Section: Truss Modelmentioning

confidence: 99%

“…Values of the force constant, K ω , have been determined using computational chemistry data from several studies [36,[43][44][45][46] and equation (25). Even though the computational chemistry data was obtained for the specific case of bending of graphene sheets to form complete nanotubes or nanotube-like structures, the concepts of structural mechanics can be implemented such that these values could apply to any bending mode of graphene sheets.…”

Section: Molecular Mechanics Modelmentioning

confidence: 99%

Equivalent-continuum modeling of nano-structured materials

Odegard

2002

Composites Science and Technology

572

302

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A method has been proposed for developing structure-property relationships of nano-structured materials. This method serves as a link between computational chemistry and solid mechanics by substituting discrete molecular structures with equivalent-continuum models. It has been shown that this substitution may be accomplished by equating the molecular potential energy of a nano-structured material with the strain energy of representative truss and continuum models. As important examples with direct application to the development and characterization of singlewalled carbon nanotubes and the design of nanotube-based structural devices, the modeling technique has been applied to two independent examples: the determination of the effectivecontinuum geometry and bending rigidity of a graphene sheet. A representative volume element of the chemical structure of graphene has been substituted with equivalent-truss and equivalentcontinuum models. As a result, an effective thickness of the continuum model has been determined. The determined effective thickness is significantly larger than the inter-planar spacing of graphite. The effective bending rigidity of the equivalent-continuum model of a graphene sheet was determined by equating the molecular potential energy of the molecular model of a graphene sheet subjected to cylindrical bending (to form a nanotube) with the strain energy of an equivalent-continuum plate subjected to cylindrical bending.

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“…77 The shell polarisable interatomic forcefield we have used to treat the MM region is a modification of a forcefield model previously derived to treat SrTiO 3 , 12,16 which was based on the Born model of ionic solids. 78 The model is designed to reproduce the high frequency dielectric properties of TiO 2 , meaning that it has been employed to relax electronic degrees of freedom only. We simulate ion-ion interactions as two-body interactions using a Coulomb sum:…”

Section: Regionmentioning

confidence: 99%

“…9 In the context of ionic solids, a key descriptor is the Madelung potential of each crystallographic site, which is determined by a summation to infinity over the ionic charges of the surrounding ions. 10 Knowledge of the variations in the local electrostatic potential proved key to the development of theories of work functions, 11 defect chemistry including ionic conductivity, 12 and even, for example, to the understanding of the nature of hole pairing in high-temperature superconductors. 13 Since the discovery in 1972 by Fujishima and Honda 14 of the ability of TiO 2 to split water using sunlight, there has been extensive research into improving the efficiency of this process.…”

Section: Introductionmentioning

confidence: 99%

Polymorph Engineering of TiO₂: Demonstrating How Absolute Reference Potentials Are Determined by Local Coordination

et al. 2015

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We report that the valence and conduction band energies of TiO 2 can be tuned over a 4 eV range by varying the local coordination environments of Ti and O. We examine the electronic structure of eight known polymorphs and align their ionization potential and electron affinity relative to an absolute energy reference, using an accurate multi-scale quantum-chemical approach. For applications in photocatalysis, we identify the optimal combination of phases to enhance activity in the visible spectrum. The results provide a coherent explanation for a wide range of phenomena, including the performance of TiO 2 as an anode material for Li-ion batteries, allow us to pinpoint hollandite TiO 2 as a new candidate transparent conducting oxide, and serve as a guide to improving the efficiency of photoelectrochemical water splitting through polymorph engineering of TiO 2 .

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Dynamical Theory of Crystal Lattices

Cited by 3,613 publications

References 0 publications

Introductory lecture: Nonadiabatic effects in chemical dynamics

Introductory lecture: Nonadiabatic effects in chemical dynamics

Equivalent-continuum modeling of nano-structured materials

Polymorph Engineering of TiO₂: Demonstrating How Absolute Reference Potentials Are Determined by Local Coordination

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Dynamical Theory of Crystal Lattices

Cited by 3,613 publications

References 0 publications

Introductory lecture: Nonadiabatic effects in chemical dynamics

Introductory lecture: Nonadiabatic effects in chemical dynamics

Equivalent-continuum modeling of nano-structured materials

Polymorph Engineering of TiO2: Demonstrating How Absolute Reference Potentials Are Determined by Local Coordination

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Product

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Polymorph Engineering of TiO₂: Demonstrating How Absolute Reference Potentials Are Determined by Local Coordination