Semiclassical analysis of resonance states induced by a conical intersection

Zhu, Chaoyuan; Nikitin, E. E.; Nakamura, Hiroki

doi:10.1063/1.471423

Cited by 16 publications

(5 citation statements)

References 24 publications

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“…Specifically, regions of non-analytic behavior are expected to be found in the upper half, which is the one that corresponds to negative temperatures, and analytic behavior is expected in the lower half plane, that corresponds to positive temperatures. The formal extension of the nuclear coordinate space onto a complex plane, as is done in [44,45], is an essentially equivalent procedure, since in the semi-classical formalism of these works the particle coordinates depend parametrically on time. Complex topological phases are considered in, e.g., [170,171], which can arise from a non-Hermitean Hamiltonian.…”

Section: Aspects Of Phase In Moleculesmentioning

confidence: 99%

“…It features in wave optics [28] for "complex analytic signals" (which is an electromagnetic field with only positive frequencies) and in non-demolition measurements performed on photons [41]. For transitions between adiabatic states (which is also discussed in this review), it was previously introduced in several works ( [42] - [45]).…”

Section: Introduction and Preview Of The Chaptermentioning

confidence: 99%

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Complex States of Simple Molecular Systems

Englman¹,

Yahalom²

2002

Advances in Chemical Physics

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A review is given of phase properties in molecular wave functions, composed of a number of (and, at least, two) electronic states that become degenerate at some nearby values of the nuclear configuration. Apart from discussing phases and interference in classical (non-quantal) systems, including light-waves, the review looks at the constructability of complex wave functions from observable quantities ("the phase problem"), at the controversy regarding quantum mechanical phase-operators, at the modes of observability of phase and at the role of phases in some non-demolition measurements. Advances in experimental and (especially) theoretical aspects of Aharonov-Bohm and topological (Berry) phases are described, including those involving two-electron and relativistic systems. Several works in the phase control and revivals of molecular wave-packets are cited as developments and applications of complex-function theory. Further topics that this review touches on are: coherent states, semiclassical approximations and the Maslov index. The interrelation between time and the complex state is noted in the contexts of time delays in scattering, of time-reversal invariance and of the existence of a molecular time-arrow.When the stationary Born-Oppenheimer description for nearly degenerate state is regarded as "embedded" in a broader dynamic formulation, namely through solution of the time dependent Schrödinger equation, the wave function becomes necessarily complex. The analytic behavior of this function in the complex time-plane can be exploited to gain information about the connection between phases and moduli of the componentamplitudes. One form of this connection are a pair of reciprocal (Kramers-Kronig type) relations in the complex time-domain. These show that certain phase changes in a component amplitude (such as, e.g., lead to a non-zero Berry-phase) require changes in the amplitude-moduli, too, and imply degeneracies of the electronic state.The subject of conical degeneracy, or intersection, of adjacent potential surface is extended to nonlinear nuclear-electronic coupling, which can then result in multiple conical degeneracies on a nuclear coordinate plane. We treat cases of double and fourfold intersections, the latter under trigonal symmetry, and employ an analytic-graphical phase tracing method to obtain the resulting Berry phases as the system circles around some or all of the degeneracy points. These phases can take up values that are all integral multiples of π, with integers that vary with the physical situation (or with the model postulated for it).A further type of invariance, with respect to gauge transformation, is also tied to the complex form of the wave function. For a many-component state this leads to a consideration of tensorial (Yang-Mills type) fields F for molecular systems. It is shown that it is the truncation of the Born-Oppenheimer electron-nuclear superposition that generates the molecular Yang-Mills fields.The equations of motion for the nuclear degrees of freedom are derived from a Lagr...

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Section: Aspects Of Phase In Moleculesmentioning

confidence: 99%

Section: Introduction and Preview Of The Chaptermentioning

confidence: 99%

Complex States of Simple Molecular Systems

Englman¹,

Yahalom²

2002

Advances in Chemical Physics

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“…Such potentials are always real (provided that the coupling P is real) because the matrix U + i cP is Hermitian. The post-adiabatic potentials in the sense of Zhu et al are just the usual adiabatic potentials. In a number of papers by Berry et al, − a hierarchy of corrections to the adiabatic approximation is studied in certain systems with classical slow variables and classical or quantum fast variables, and some of those corrections (e.g., the so-called geometric magnetism and deterministic friction) are sometimes referred to as post-adiabatic corrections. , However, such corrections have nothing in common with the post-adiabatic representations and potentials as introduced by Klar and Fano …”

Section: Post-adiabatic Iterative Proceduresmentioning

confidence: 99%

Long-Range Interaction in Some Simple Open-Shell Systems, Including Rare-Gas Sulfides: Features of Post-Adiabatic Potentials and Couplings

Sevryuk¹,

Rusin²,

Cavalli³

et al. 2004

J. Phys. Chem. A

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The first-order post-adiabatic representations in the sense of Klar and Fano (Klar, H.; Fano, U. Phys. Rev. Lett. 1976, 37, 1132−1134) are obtained for two-channel stationary Schrödinger equations describing the interaction of the fluorine and chlorine (in the 2P state) and oxygen and sulfur (in the 3P state) atoms with a number of closed-shell particles, in particular, with rare gases, hydrogen, deuterium, and methane. Information on the adiabatic potentials and the nonadiabatic coupling comes mostly from scattering experiments, although some input from ab initio quantum mechanical calculations is also exploited. Various trends in the behavior of the first-order post-adiabatic coupling are analyzed, and the optimal ways to estimate the smallness of this coupling are discussed. The best measure of the strength of the post-adiabatic coupling of order s is found to be the differences between the respective post-adiabatic potentials of orders s and s + 1. A rigorous proof is given of the fact that post-adiabatic representations exist only in the important case of a single “slow” degree of freedom.

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“…Thus the above replacement should be applied only to the LZ-case. complex crossing point, 20, 29, 31, 36, 92, 107, 108, 131, 133, 159, 194, 195, 197, 206, 16,145,147,149,179,183,185,252, 286 nonadiabatic tunneling (NT) type, 8, 9, 28, 62-65, 68, 78, 80, 84, 85, 125, 150-152, 154-157, 179, 180, 182, 183, 209, 224, 229, 231, 235, 236, …”

Section: Appendix B Time-dependentmentioning

confidence: 99%

Back Matter

2002

Nonadiabatic Transition

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Semiclassical analysis of resonance states induced by a conical intersection

Cited by 16 publications

References 24 publications

Complex States of Simple Molecular Systems

Complex States of Simple Molecular Systems

Long-Range Interaction in Some Simple Open-Shell Systems, Including Rare-Gas Sulfides: Features of Post-Adiabatic Potentials and Couplings

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