<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">H</mml:mi><mml:mo>⊗</mml:mo><mml:mi /><mml:mi mathvariant="italic">h</mml:mi></mml:math>: A Jahn-Teller Coupling That Really Does Reduce the Degeneracy of the Ground State

Moate, C P; O’Brien, Mary Claire; Dunn, J L; Bates, C A; Liu, Y. M.; Polinger, V. Z.

doi:10.1103/physrevlett.77.4362

Cited by 64 publications

(49 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They showed that, contrary to what had been widely thought before, the ground state may be either a vibronic doublet or a singlet, depending on the distance (which is a function of the parameters in the vibronic Hamiltonian) of these trigonal ci's from the centre. (A similar instance of "quantum phase transition" was noted for a threefold degenerate system in [275] and, earlier, for an icosahedral system, in [276]). …”

Section: Non-linearities That Lead To Multiple Degeneraciesmentioning

confidence: 89%

Complex States of Simple Molecular Systems

Englman¹,

Yahalom²

2002

Advances in Chemical Physics

View full text Add to dashboard Cite

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...

show abstract

Section: Non-linearities That Lead To Multiple Degeneraciesmentioning

confidence: 89%

Complex States of Simple Molecular Systems

Englman¹,

Yahalom²

2002

Advances in Chemical Physics

View full text Add to dashboard Cite

show abstract

“…If one wants to consider a distortion of C m+ 60 or C n− 60 [18,19,20,21,22], the computed energy levels and their eigenvectors can be used as a starting point for the description of the Jahn-Teller effect in these systems. Indeed, the electron-phonon (or vibronic) coupling occurs if [Γ el ] 2 contains Γ vib [23,24].…”

Section: Introductionmentioning

confidence: 99%

Molecular terms, magnetic moments, and optical transitions of molecular ions C60m±

Николаев

Michel

2002

The Journal of Chemical Physics

View full text Add to dashboard Cite

Starting from a multipole expansion of intra-molecular Coulomb interactions, we present configuration interaction calculations of the molecular energy terms of the hole configurations (h + u ) m , m = 2 − 5, of C m+ 60 cations, of the electron configurations t n 1u , n = 2 − 4, of the C n− 60 anions, and of the exciton configurations (h + u t − 1u ), (h + u t − 1g ) of the neutral C60 molecule. The ground state of C 2− 60 is either 3 T1g or 1 Ag, depending on the energy separation between t1g and t1u levels. There are three close (∼0.03 eV) low lying triplets 3 T1g, 3 Gg, 3 T2g for C 2+ 60 , and three quartets 4 T1u, 4 Gu, 4 T2u for C 3+ 60 , which can be subjected to the Jahn-Teller effect. The number of low lying nearly degenerate states in largest for m = 3 holes. We have calculated the magnetic moments of the hole and electron configurations and found that they are independent of molecular orientation in respect to an external magnetic field. The coupling of spin and orbital momenta differs from the atomic case. We analyze the electronic dipolar transitions (t1u) 2 → t1ut1g and (t1u) 3 → (t1u) 2 t1g for C 2− 60 and C 3− 60 . Three optical absorption lines ( 3 T1g → 3 Hu, 3 T1u, 3 Au) are found for the ground level of C 2− 60 and only one line ( 4 Au → 4 T1g) for the ground state of C 3− 60 . We compare our results with the experimental data for C n− 60 in solutions and with earlier theoretical studies.

show abstract

“…Our results are an example of where the high symmetry produces features not seen in systems of lower symmetry. Other cases where the high symmetry produces unexpected results includes the H ⊗ h JT system, where non-simple reducibility of the product H ⊗ H can result in a singlet ground state rather than the expected five-fold state [32,33].…”

Section: Resultsmentioning

confidence: 99%

The effect of cooperative Jahn–Teller interactions on C₆₀⁻anions

Moujaes

Dunn²

2010

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

Abstract. Singly-charged buckminster fullerene anions, C ions in a solid through a co-operative JT effect, they will be subject to an additional interaction. There are a number of different mechanisms that can cause this interaction. However, in the molecular field approximation, all can be modelled phenomenologically in terms of a symmetry-lowering interaction written in terms of a linear combination of electronic operators for the h modes involved in the intramolecular JT effect. We will consider the combined effect of this distortion and the intramolecular JT effect. We will analyse the lowest adiabatic potential energy surface, and calculate the energies of the resultant vibronic states. The results are shown to have a complicated dependence on the particular combination of h modes chosen, and the energies of the resultant vibronic states can not easily be deduced from the form of the potential alone.

show abstract

H⊗h: A Jahn-Teller Coupling That Really Does Reduce the Degeneracy of the Ground State

Cited by 64 publications

References 12 publications

Complex States of Simple Molecular Systems

Complex States of Simple Molecular Systems

Molecular terms, magnetic moments, and optical transitions of molecular ions C60m±

The effect of cooperative Jahn–Teller interactions on C₆₀⁻anions

Contact Info

Product

Resources

About

H⊗h: A Jahn-Teller Coupling That Really Does Reduce the Degeneracy of the Ground State

Cited by 64 publications

References 12 publications

Complex States of Simple Molecular Systems

Complex States of Simple Molecular Systems

Molecular terms, magnetic moments, and optical transitions of molecular ions C60m±

The effect of cooperative Jahn–Teller interactions on C60−anions

Contact Info

Product

Resources

About

The effect of cooperative Jahn–Teller interactions on C₆₀⁻anions