Jahn—Teller Effects in Electron Paramagnetic Resonance Spectra

Ham, Frank S.

doi:10.1007/978-1-4899-5310-0_1

Cited by 135 publications

(189 citation statements)

References 142 publications

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“…The potential energy surface shows such a barrier for any real-valued |Ψ , and its direction is determined by the angle ϕ in Eq. (24). Similar to what was found for diatomic molecules [55][56][57][58][59] and a two-mode vibronic model, 54 the barrier in E(R) corresponds to nuclear configurations where |χ(R)| 2 drops close to zero.…”

Section: Potential Energy Surfacesupporting

confidence: 77%

“…spectroscopy of triatomic molecules 26,29,33 and dynamical Jahn-Teller defects in bulk crystals [23][24][25] . The identification of such topological phases has always been based on the Born-Oppenheimer approximation, leaving open the possibility that their topological character is an artifact of that approximation which would not survive in an exact calculation.…”

Section: Discussionmentioning

confidence: 99%

“…In this case as well, the geometric phase can be tuned by forming superpositions of degenerate states analogously to Eq. (24). Nevertheless, the geometric phase of such a state, γ BO = π cos θ, is still a topological quantity, which can only take the values nγ BO with integer n. For θ = π/2, |Ψ is real and the current and geometric phase vanish for any value of ϕ, since it is always possible to choose a gauge such that A is identically zero.…”

Section: Molecular Geometric Phasementioning

confidence: 99%

“…Recent work found a case in which the Longuet-Higgins phase of π becomes zero in the exact factorization. 14 However, the model studied does not have the degeneracy of the classic Jahn-Teller models 15 of pseudorotating molecules 3,5,[15][16][17][18] and transition metal ions in bulk crystals [18][19][20][21][22][23][24][25] and therefore leaves room for further investigation.…”

Section: Introductionmentioning

confidence: 99%

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Molecular geometric phase from the exact electron-nuclear factorization

2016

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The Born-Oppenheimer electronic wavefunction Φ BO R (r) picks up a topological phase factor ±1, a special case of Berry phase, when it is transported around a conical intersection of two adiabatic potential energy surfaces in R-space. We show that this topological quantity reverts to a geometric quantity e iγ if the geometric phase γ = Im ΦR|∇µΦR · dRµ is evaluated with the conditional electronic wavefunction ΦR(r) from the exact electron-nuclear factorization ΦR(r)χ(R) instead of the adiabatic function Φ BO R (r). A model of a pseudorotating molecule, also applicable to dynamical Jahn-Teller ions in bulk crystals, provides the first examples of induced vector potentials and molecular geometric phase from the exact factorization. The induced vector potential gives a contribution to the circulating nuclear current which cannot be removed by a gauge transformation. The exact potential energy surface is calculated and found to contain a term depending on the Fubini-Study metric for the conditional electronic wavefunction.

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Section: Potential Energy Surfacesupporting

confidence: 77%

Section: Discussionmentioning

confidence: 99%

Section: Molecular Geometric Phasementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Molecular geometric phase from the exact electron-nuclear factorization

2016

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“…A possibility for such a splitting could come from the following : the previous treatment, where we took account of the coupling between the two vanadium ions is in fact more complex than appears at first sight : since we are dealing with a non-linear molecule (which consists here of the two vanadium ions and the surrounding ligands) in an orbitally degenerate unperturbed level (1), the electron and nuclear motions cannot be separated (breakdown of the adiabatic approximation) [14,15] We use a Slater wave function for the radial part R(r) of the atomic orbital dXY(i) of ion i : R(r) = (2 P)7/2 r2 -fJr [19] where -Zef f wlth Z 5 [20] ( 6 ! )1/2 r e , were 3 a o with Zeff = 5 [20].…”

mentioning

confidence: 99%

Low frequency transition between vibronic levels of V9+2 in crystalline V2O5 from electron spin-lattice relaxation measurements

Gaillard¹,

Blanchard²,

Deville³

et al. 1983

J. Phys. France

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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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Jahn—Teller Effects in Electron Paramagnetic Resonance Spectra

Cited by 135 publications

References 142 publications

Molecular geometric phase from the exact electron-nuclear factorization

Molecular geometric phase from the exact electron-nuclear factorization

Low frequency transition between vibronic levels of V9+2 in crystalline V2O5 from electron spin-lattice relaxation measurements

Complex States of Simple Molecular Systems

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