Geometric phase effect at <i>N</i>‐fold electronic degeneracies in Jahn–Teller systems

Varandas, A. J. C.; Xu, Z. R.

doi:10.1002/qua.20036

Cited by 7 publications

(19 citation statements)

References 32 publications

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“…Note that e θ [Q] is fixed, but e φ [Q] has its direction inverted when (θ, φ) → (π − θ, π + φ). Similar verifications may be performed for the SO(4) and SO(5) icosahedral JT models [44,50]. In every case, only the normal vector corresponding to the ground-state and one of the spherical basis vectors of S ⊥ 0 (Q) acquire a non-trivial phase when Q traverses a loop on O.…”

Section: Now Consider An Adiabatic Loop Starting At Arbitrarymentioning

confidence: 82%

Vibronic Ground-State Degeneracies and the Berry Phase: A Continuous Symmetry Perspective

Ribeiro

Yuen-Zhou

2017

J. Phys. Chem. Lett.

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We develop a geometric construction to prove the inevitability of the electronic ground-state (adiabatic) Berry phase for a class of Jahn-Teller models with maximal continuous symmetries and N > 2 intersecting electronic states. Given that vibronic ground-state degeneracy in JT models may be seen as a consequence of the electronic Berry phase, and that any JT problem may be obtained from the subset we investigate in this letter by symmetry-breaking, our arguments reveal the fundamental origin of the vibronic ground-state degeneracy of JT models.The Jahn-Teller (JT) theorem [1, 2] is a cornerstone of condensed matter and chemical physics; it enunciates that adiabatic electronically degenerate states of symmetric nonlinear molecules are unstable with respect to symmetry-breaking distortions of the molecular geometry (unless the degeneracy is protected by time-reversal symmetry). Given this statement, one might be tempted to loosely extrapolate that molecular quantum state degeneracies are generally unstable. This is, however, an incorrect conclusion: It is interesting that a large class of JT models exhibit robust vibronic ground-state degeneracies [3][4][5][6][7][8][9][10][11][12][13]. Thus, there is a counterintuitive flavor to the JT theorem: vibronic degeneracies can be born at the expense of the breakdown of their electronic counterparts [10,11]. These degeneracies leave distinctive signatures in the chemical dynamics of JT systems which are sometimes immune to degeneracy-breaking perturbations [13,14]. The goal of this letter is to explain the fundamental reason for the emergence of degenerate vibronic ground-states in JT models.Vibronic ground-state degeneracy (VGSD) in JT models appears frequently when linear vibronic couplings dominate [10,11] (for a recent proposal of direct noninterferometric experimental verification of VGSD, see e.g., [15,16]), although there are exceptions [17][18][19][20]. More specifically, there exists a particular class of JT models for which VGSD is guaranteed to exist whenever the adiabatic approximation with inclusion of Berry phase effects [22,23]) is valid [10,11,24]. These are the JT systems containing continuous symmetries and all possible couplings between JT active modes and a single electronically degenerate multiplet (at the reference geometry for a description of the JT effect, from now on denoted by JT center ) [3,4,[24][25][26][27][28][29], the simplest and most famous example being the linear E ⊗ e model (we use the standard convention where the electronic irreducible representation (irrep) is given by a capital letter and the vibrational irrep is given by a lowercase) which displays an exotic SO(2) (circular) symmetry in its potential energy surface [3,11]. The most complex spinless example is the SO(5)-invariant model of the icosahedral JT problem H ⊗ (g ⊕ 2h), which contains all possible JT active modes associated with the electronic H quintuplet [9,10,29,30]. On the other hand, the linearized H ⊗ h model has SO(3) symmetry [31], but it does not include the cou...

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Section: Now Consider An Adiabatic Loop Starting At Arbitrarymentioning

confidence: 82%

Vibronic Ground-State Degeneracies and the Berry Phase: A Continuous Symmetry Perspective

Ribeiro

Yuen-Zhou

2017

J. Phys. Chem. Lett.

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“…Thus, they possess simultaneous eigenfunctions that depend on (N −1) angular variables [128]. As above, this may explain why only (N − 1) angles are required to characterize unambiguously the corresponding adiabatic electronic wave vector [19,45,48].…”

Section: Configuration Vs Function Space and Conservation Lawsmentioning

confidence: 99%

“…The title JT problem has been much studied, and hence will serve here the purpose of comparing the two different formalisms discussed in the previous sections. Let the BO electronic wave vectors be {ψ 1 , ψ 2 } = {|E x , |E y } [19,45].…”

Section: 6mentioning

confidence: 99%

“…Compared with the vast amount of research on twofold degeneracies [17,24,26,[34][35][36][37][38][39][40][41][42] (the list is by no means exhaustive), the number of studies on the GP effect at higher electronic degeneracies is meager [19,28,[43][44][45]. Cullerne and O'Brien [46] have been the first to use both numerical and analytical methods to map the lowest adiabatic PESs of icosahedral molecular systems such as fullerenes with a view to understand the rich structure of their degenerate electronic and vibrational modes as well as the role of GP.…”

Section: Introductionmentioning

confidence: 99%

“…and to Baer [44] that focused on the topological features and existence of pure diabatic states. In a recent series of papers, we have instead advocated [19,45,48] the use of Lie group symmetries to study such N -fold degeneracies in JT systems.…”

Section: Introductionmentioning

confidence: 99%

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Adiabatic approximation and related issues including topological implications

Varandas¹

2011

Quantal Aspects in Chemistry and Physics: A Tribute to the Memory of Professor Couceiro Da Costa

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A study of the geometrical phase effect on scattering processes: Validity of the extended-Longuet–Higgins formalism for a four-fold Jahn–Teller type model system

Sarkar

Varandas

2011

Chemical Physics

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Geometric phase effect at N‐fold electronic degeneracies in Jahn–Teller systems

Cited by 7 publications

References 32 publications

Vibronic Ground-State Degeneracies and the Berry Phase: A Continuous Symmetry Perspective

Vibronic Ground-State Degeneracies and the Berry Phase: A Continuous Symmetry Perspective

Adiabatic approximation and related issues including topological implications

A study of the geometrical phase effect on scattering processes: Validity of the extended-Longuet–Higgins formalism for a four-fold Jahn–Teller type model system

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