Non-Condon Correction to Franck–Condon Values of Second-order Reduction Factors: The Cubic T Term

Al-Hazmi, Faten; Polinger, V. Z.; Dunn, J L; Bates, C A; Moujaes, Elie A.; Abou-Ghantous, M.

doi:10.1016/s0065-3276(03)44011-2

Cited by 2 publications

(5 citation statements)

References 16 publications

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“…and agree with those obtained previously by analytical methods [12]. It should be noted that all the contributions to the above soRF come from the identity operator when the Green operator is simplified with the closure relation [10,16].…”

Section: Application To Cubic T ⊗ T Jt Systemssupporting

confidence: 90%

“…Since the JT systems considered here all involve the orbital triplet terms only, the Green operator can be simplified by writing it in terms of the ground electronic well state |ψ p using the closure relation as in [16]. However, the orbital operators after the introduction of the non-Condon correction do not satisfy the closure relation and thus G p (T 1 ) must be replaced by the standard form of second-order perturbation theory namely: (16) where E p m is the appropriate energy denominator including the non-Condon element. The general expression for the soRF within the corrected FC approximation thus becomes…”

Section: The Non-condon Perturbative Methodsmentioning

confidence: 99%

“…(2) p Mµ,corr ( l ⊗ m ) is now calculated with the corrected Green operator in equation (16). In this final result, we have terms independent of q p (which are the standard FC results) together with the non-Condon correction containing terms which are of order q 2 p .…”

Section: The Non-condon Perturbative Methodsmentioning

confidence: 99%

“…The FC approximation is an accurate analytical technique in the strong coupling regime. As emphasized in [10,16] for the octahedral T ⊗ t 2 and icosahedral T ⊗ h JT systems, respectively, the underlying physics is clearly exposed.…”

Section: The Franck-condon Approximation In the Theory Of Sorfs In Or...mentioning

confidence: 99%

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Second-order vibronic reduction factors for orbital triplet Jahn–Teller systems in cubic and icosahedral symmetry

Bates

Abou-Ghantous

Dunn

et al. 2004

J. Phys.: Condens. Matter

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It is well-known that vibronic interactions can be modelled in terms of an effective Hamiltonian incorporating first and second-order reduction factors (RFs), particularly when analysing the spectroscopic properties. Measurements and calculations of the RFs as a function of the strength of vibronic coupling are therefore of much interest. In this paper, we develop a new general method for determining second-order RFs (soRFs) from the strength of the Jahn–Teller (JT) coupling for systems in which electron orbital degeneracy or pseudo-degeneracy exists. These include in particular the fullerene molecule C60, pseudo-Jahn–Teller molecules and impurity centres in crystals. In order to calculate the important soRFs for intermediate to strong coupling, it is necessary to determine non-Condon corrections to the strong coupling values obtained using the Franck–Condon (FC) approximation. This gives an additional contribution to the nuclear polarizability of the system, thus enabling the electrons to follow the nuclear vibrations. These non-Condon corrections are derived using perturbation theory and are found to be inversely proportional to the square of the JT energy. The validity of the approximation is first tested in the cubic JT system due to its relative simplicity. It is found that the results are closer to those obtained earlier by numerical methods than the analytical FC values alone. Results are then presented that are applicable to C60− anions.

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Section: Application To Cubic T ⊗ T Jt Systemssupporting

confidence: 90%

Section: The Non-condon Perturbative Methodsmentioning

confidence: 99%

Section: The Non-condon Perturbative Methodsmentioning

confidence: 99%

Section: The Franck-condon Approximation In the Theory Of Sorfs In Or...mentioning

confidence: 99%

See 2 more Smart Citations

Second-order vibronic reduction factors for orbital triplet Jahn–Teller systems in cubic and icosahedral symmetry

Bates

Abou-Ghantous

Dunn

et al. 2004

J. Phys.: Condens. Matter

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show abstract

“…Thus the FC approximation is an accurate analytical technique in the strong coupling regime. As emphasized in [5] and [11] for the octahedral T ⊗ t 2 and icosahedral T ⊗ h JT systems respectively, the underlying physics of soRFs is clearly exposed by the FC analysis.…”

Section: Second-order Perturbation Theory Generates a Second-order Ha...mentioning

confidence: 97%

Accurate calculations of second-order vibronic reduction factors for C₆₀ions

Al-Hazmi¹,

Moujaes²,

Abou-Ghantous³

et al. 2005

J. Phys.: Condens. Matter

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An effective Hamiltonian containing Jahn-Teller (JT) first-and secondorder vibronic reduction factors (RFs) is a convenient way of modelling the spectroscopic properties of solids and molecules in which vibronic interactions are important. It can act as a bridge between experimental data and basic theory. In particular, second-order RFs can give valuable information on many of the fundamental properties of strongly coupled systems. As interest in the icosahedral fullerene molecules and ions has grown over the last few years, it has become necessary to be able to calculate values for second-order RFs in icosahedral symmetry in terms of more fundamental vibronic coupling parameters. Following on from earlier work on the icosahedral T ⊗ h JT system, we present here results of such calculations of the second-order vibronic RFs for the icosahedral G ⊗ g, G ⊗ h, H ⊗ g and H ⊗ h JT systems. These systems are relevant for the ground and excited states of C 60 anions and cations. The calculations are based on the Franck-Condon approximation followed by additional non-Condon corrections. Previous work has demonstrated that such an approach can give values for the RFs close to those deduced from experiments.

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Non-Condon Correction to Franck–Condon Values of Second-order Reduction Factors: The Cubic T Term

Cited by 2 publications

References 16 publications

Second-order vibronic reduction factors for orbital triplet Jahn–Teller systems in cubic and icosahedral symmetry

Second-order vibronic reduction factors for orbital triplet Jahn–Teller systems in cubic and icosahedral symmetry

Accurate calculations of second-order vibronic reduction factors for C₆₀ions

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Non-Condon Correction to Franck–Condon Values of Second-order Reduction Factors: The Cubic T Term

Cited by 2 publications

References 16 publications

Second-order vibronic reduction factors for orbital triplet Jahn–Teller systems in cubic and icosahedral symmetry

Second-order vibronic reduction factors for orbital triplet Jahn–Teller systems in cubic and icosahedral symmetry

Accurate calculations of second-order vibronic reduction factors for C60ions

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Product

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Accurate calculations of second-order vibronic reduction factors for C₆₀ions