Berry’s geometrical phase and the sequence of states in the Jahn-Teller effect

Ham, Frank S.

doi:10.1103/physrevlett.58.725

Cited by 185 publications

(115 citation statements)

References 28 publications

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“…Spectroscopic signatures of the Berry phase have been observed in Jahn-Teller systems since the 1960's [9][10][11]. Although the BO approximation breaks down at conical intersections in these systems, the effects of the Berry phase are nevertheless observable because they influence the global behavior of the conditional electronic wave function far from the point of conical intersection.…”

Section: Discussionmentioning

confidence: 99%

“…The electronic wave function chosen this way is therefore a double-valued function of the nuclear coordinates. The sign change, known as the Longuet-Higgins phase [1,2], is a special case of the Berry phase [3,4], and its effects are observable in the vibrational spectroscopy of pseudorotating molecules [5,6] and electron paramagnetic resonance [7][8][9][10][11] and optical [12,13] spectroscopy of transition metal impurities in bulk crystals. Evidence for the dynamical Jahn-Teller effect in the excited states of the nitrogen-vacancy center in diamond has been reported [14][15][16][17][18], making the Longuet-Higgins phase rele- * Electronic address: rrequist@mpi-halle.mpg.de vant to its optical properties.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic analysis of the Berry curvature in theE⊗eJahn-Teller model

2017

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The effective Hamiltonian for the linear E ⊗ e Jahn-Teller model describes the coupling between two electronic states and two vibrational modes in molecules or bulk crystal impurities. While in the Born-Oppenheimer approximation the Berry curvature has a delta function singularity at the conical intersection of the potential energy surfaces, the exact Berry curvature is a smooth peaked function. Numerical calculations revealed that the characteristic width of the peak is K 1/2 /gM 1/2 , where M is the mass associated with the relevant nuclear coordinates, K is the effective internuclear spring constant and g is the electronic-vibrational coupling. This result is confirmed here by an asymptotic analysis of the M → ∞ limit, an interesting outcome of which is the emergence of a separation of length scales. Being based on the exact electron-nuclear factorization, our analysis does not make any reference to adiabatic potential energy surfaces or nonadiabatic couplings. It is also shown that the Ham reduction factors for the model can be derived from the exact geometric phase.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Asymptotic analysis of the Berry curvature in theE⊗eJahn-Teller model

2017

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“…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%

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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“…It is well known that the electronic and vibrational parts of a vibronic wave function both change sign after a circuit in coordinate space returns to the same geometry and encloses a conical intersection. 15 This is a molecular manifestation of Berry's geometric phase 16 and is required for the total vibronic wave function to remain single valued.…”

Section: The Vibronic Wavefunctionsmentioning

confidence: 99%

Coupling of a Jahn–Teller pseudorotation with a hindered internal rotation in an isolated molecule: 9-hydroxytriptycene

Furlan

Leutwyler

Riley

1998

The Journal of Chemical Physics

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Experimental investigation of the Jahn-Teller effect in the ground and excited electronic states of the tropyl radical. Part II. Vibrational analysis of the A ̃ E 3 ″ 2 -X ̃ E 2 ″ 2 electronic transition J. Chem. Phys. 128, 084311 (2008) The Jahn-Teller effect in the lower electronic states of benzene cation. III. The ground-state vibrations of C 6 H 6 + and C 6 D 6 + J. Chem. Phys. 120, 8587 (2004) The irregular vibronic structure in the S 1 ←S 0 resonant two-photon ionization ͑R2PI͒ spectrum of supersonically cooled triptycene is a result of a classic E e Jahn-Teller effect ͓A. Furlan et al., J. Chem. Phys. 96, 7306 ͑1992͔͒. This is well characterized and can be used as an effective probe of intramolecular perturbations. Here we examine the S 1 ←S 0 R2PI spectrum of 9-hydroxytriptycene and the fluorescence from various excited state vibronic levels. In this system the pseudorotation of the Jahn-Teller vibration is strongly coupled to the torsional motion of the bridgehead hydroxy group. This torsional motion results in a tunneling splitting in both the ground and excited states. The population of the upper level in the ground electronic state results in additional vibronic transitions becoming symmetry allowed in the R2PI spectrum that are forbidden in the bare triptycene molecule. The assignment of the R2PI and fluorescence spectra allows the potential energy surfaces of these vibrational modes to be accurately quantified. The full C 3v vibronic point group must be used to interpret the spectra. The time scale of the internal rotation of the-OH group and the butterfly flapping of the Jahn-Teller pseudorotation are of similar magnitude. The tunneling between the nine minima on the three dimensional potential energy surface is such that the JahnTeller pseudorotation occurs in concert with the-OH internal rotation. The Berry phase that is acquired during this motion is discussed. The simple physical picture emerges of the angle between two of the three benzene moieties opening in three equivalent ways in the S 1 electronic state. This geometry follows the position of the hydroxy group, which preferentially orients itself to point between these two rings.

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Berry’s geometrical phase and the sequence of states in the Jahn-Teller effect

Cited by 185 publications

References 28 publications

Asymptotic analysis of the Berry curvature in theE⊗eJahn-Teller model

Asymptotic analysis of the Berry curvature in theE⊗eJahn-Teller model

Molecular geometric phase from the exact electron-nuclear factorization

Coupling of a Jahn–Teller pseudorotation with a hindered internal rotation in an isolated molecule: 9-hydroxytriptycene

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