Erratum: On the determination of Born–Oppenheimer nuclear motion wave functions including complications due to conical intersections and identical nuclei [J. Chem. Phys. <b>70</b>, 2284 (1979)]

Mead, C. A.; Truhlar, Donald G.

doi:10.1063/1.445492

Cited by 201 publications

(348 citation statements)

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“…9 When conical intersections are present, nuclear motion on the adiabatic surfaces also involves geometric phases. 10,11 Although great progress has been made in the quantum mechanical treatment of nuclear motion on coupled potential energy surfaces, the practical treatment of systems with a large number of nuclear degrees of freedom is greatly facilitated by using classical mechanics. Since the light mass and antisymmetry requirements of the electrons preclude a classical treatment, one then requires a semiclassical treatment that combines quantum mechanics for the electron motion with classical mechanics for the nuclear motion.…”

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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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confidence: 99%

Introductory lecture: Nonadiabatic effects in chemical dynamics

et al. 2004

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“…Such crossings are closely related to the JT effect, and Herzberg and Longuet-Higgins [14] demonstrated that the degeneracy leads to anomalous statistics: to make the electronic wave function single valued, the orbital angular momentum must be quantized in halfintegral multiples ofh. An alternative approach is to introduce a pseudo magnetic field, so that single-valuedness of the electron is guaranteed by associating a quantized vortex of pseudoflux at the molecular site [15].…”

Section: Diabolical Points Of Energy Bandsmentioning

confidence: 99%

Van Hove exciton-cageons and high-Tc superconductivity XA. Role of spin-orbit coupling in generating a diabolical point

Markiewicz

1994

Physica C: Superconductivity

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Spin-orbit coupling plays a large role in stabilizing the low-temperature orthorhombic phase of La 2−x Sr x CuO 4 . It splits the degeneracy of the van Hove singularities (thereby stabilizing the distorted phase) and completely changes the shape of the Fermi surfaces, potentially introducing diabolical points into the band structure. The present paper gives a detailed account of the resulting electronic structure.A slave boson calculation shows how these results are modified in the presence of strong correlation effects. A scaling regime, found very close to the metal-insulator transition, allows an analytical determination of the crossover, in the limit of zero oxygen-oxygen hopping, t OO → 0. Extreme care must exercised in chosing the parameters of the three-band model. In particular, t OO is renormalized from its LDA value. Furthermore, it is suggested that the slave boson model be spin-corrected, in which case the system is close to a metal-insulator transition at half filling.

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“…It was pointed out by Longuet-Higgins and Herzberg [5,6] that each real adiabatic electronic state changes sign when transported continuously along a closed path encircling the point of a CI. Mead and Truhlar associated this topological phase effect with the single electronic state problem [7] and Berry generalized the theory [8], hence the name Berry phase. Ensuring that the electronic wave function remains single valued one has to multiply it by a phase factor and, as a consequence of it, this new electronic eigenfunction, instead of being real, becomes complex.…”

Section: Introductionmentioning

confidence: 99%

Nuclear-wave-packet quantum interference in the intense laser dissociation of the D2+molecule

et al. 2013

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Recently it has been recognized that electronic conical intersections in molecular systems can be induced by laser light even in diatomics. As is known a direct consequence of these accidental degeneracies is the appearance of nonadiabatic effects which has a strong impact on the nuclear quantum dynamics. Studying the photodissociation process of the D 2 + molecule, we report here some observable quantum interference phenomena that arise from the topological singularity induced by a strong laser field.

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Erratum: On the determination of Born–Oppenheimer nuclear motion wave functions including complications due to conical intersections and identical nuclei [J. Chem. Phys. 70, 2284 (1979)]

Cited by 201 publications

References 6 publications

Introductory lecture: Nonadiabatic effects in chemical dynamics

Introductory lecture: Nonadiabatic effects in chemical dynamics

Van Hove exciton-cageons and high-Tc superconductivity XA. Role of spin-orbit coupling in generating a diabolical point

Nuclear-wave-packet quantum interference in the intense laser dissociation of the D2+molecule

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