Symmetry Rule for Predicting Bond Distortions in Conjugated Hydrocarbons

Nakajima, Takeshi; Toyota, Azumao; Fujii, Sadao

doi:10.1246/bcsj.45.1022

Cited by 50 publications

(20 citation statements)

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“…6) shows the same tracking of the extremal eigenvector by the unique Heilbronner mode, although in this case the maximum eigenvalue bl p lies below the critical threshold, and indeed at equilibrium the molecule retains its C 2v symmetry. 5…”

Section: (Iv) Limitationsmentioning

confidence: 99%

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Symmetry and distortive π-electrons in two- and three-dimensional conjugated systems

Fowler

Rassat

2002

Phys. Chem. Chem. Phys.

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The distortive effect of p electrons in conjugated systems in two and three dimensions is modelled, following Heilbronner, by varying Hu ¨ckel bond parameters subject to retention of a constant sum around each graph vertex. For this simplified model a symmetry theorem gives the numbers and types of distortion modes that lead away from the s optimal geometry. General results are given for linear and cyclic polyenes, linear and cyclic acenes, and carbon prisms. Connections between Heilbronner modes, eigenvectors of the bond polarisability matrix and the frontier-orbital rule for symmetry lowering are established. An application to the C 60 fullerene shows that the seven most distortive of its 24 symmetry-distinct p modes are well modelled by the set of seven non-totally symmetric Heilbronner modes, and confirms that this system lies below the threshold for spontaneous distortion to non-icosahedral symmetry.

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Section: (Iv) Limitationsmentioning

confidence: 99%

“…2,3 Criteria for predicting whether s or p electrons will win the energy-geometry competition have been developed. 4,5 The history of the evolution, defence, computational exploration and experimental verification of the p distortivity concept is recounted in comprehensive review articles 6,7 and will not be discussed in detail here.…”

Section: Introductionmentioning

confidence: 99%

Symmetry and distortive π-electrons in two- and three-dimensional conjugated systems

Fowler

Rassat

2002

Phys. Chem. Chem. Phys.

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“…Changes in bond distances would be more difficult. For example, Nakajima has examined bond distortions in planar, polycyclic conjugated hydrocarbons (32). It is found that the first excited state must lie within 1.2 eV of the ground state to produce distortions of 0.1 A, or less.…”

Section: El + -] )mentioning

confidence: 99%

Concerning Jahn-Teller Effects

Pearson

1975

Proc. Natl. Acad. Sci. U.S.A.

145

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Jahn-Teller effects are grouped into two categories. The first arises from incomplete shells of degenerate orbitals. It includes the first-order Jahn-Teller effect, and the pseudo Jahn-Teller effect. The second arises from filled and empty molecular orbitals that are close in energy, and is the second-order Jahn-Teller effect. The two categories have quite different physical bases. As a result, geometric distortions produced by the first are quite small and normally lead to dynamic effects only. In favorable cases, the second-order Jahn-Teller effect produces very large distortions, including complete dissociation of a molecule. This can occur even when the relevant molecular orbitals are separated in energy by as much as 4 eV.An examination of the recent literature shows a rapidly increasing number of phenomena that are explained by invoking a Jahn-Teller effect. The examples come from many areas of physics and chemistry, including biochemistry.The effects invoked are those arising from orbitally degenerate states (Jahn-Teller effect proper), and from states which are nondegenerate but close in energy (pseudo, or secondorder Jahn-Teller effect).One attitude has been to lump these several effects together and to blur any distinction between them (1, 2). Another has been a reasonable belief that nondegenerate states must be very close in energy, less than 1 eV separation, before any distortion of molecular shape could be expected, and that second-order effects are very small (3-5). The purpose of this note is to point out that the nature of the first-order effect (FOJT) is such that distortions are inevitably very small, leading to the dynamic Jahn-Teller situation as a rule. Paradoxically, the second-order effect (SOJT) has a physical basis that can lead to very large distortions of molecular geometry, or even to complete dissociation.Following Jahn and Teller and Bader (6, 7), the potential energy, in terms of small displacements, Q, from an initial nuclear configuration, is given byEo -Ek The FOJT proper comes from the term linear in Q. For small displacements there is a complex mixing of electronic and vibrational states. This mixing is not under discussion here, but rather the possibility of a large distortion, which permanently affects the geometry of the molecule (static effect). Eq.[I] will not be valid for large distortions, but it still can be used to derive the symmetry constraints on the nuclear motions. The SOJT effect comes from the terms in [1] that are quadratic in Q. The Renner-Teller effect is a special second-order distortion which is important for linear molecules, but which will not be discussed further (8).Eq [1] is written in terms of state wave functions. It is necessary to interpret these in terms of molecular orbital (MO) theory to proceed further. The FOJT effect arises from incompletely filled shells. These shells are doubly and triply degenerate MO's which by their nature are not only of the same symmetry, but of the same kind. Examples are d orbitals in inorganic chemistry an...

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“…2). The lattice instability thus predicted for the heptafulvalene trianion radical is closely related with the pseudo-Jahn-Teller effect [20][21][22][23] as follows: in the RHF approximation, the ground state is of Big symmetry and the lowest excited doublet state is of Au symmetry, and both the states are nearly degenerate, the energy difference being calculated to be 0.050 eV. Thus, it is predicted that the Dah nuclear arrangement does not represent a minimum of the potential energy and a nuclear configuration with a lower symmetry (C2~) is more stable.…”

Section: Lattice Instabilitymentioning

confidence: 99%

The electronic structure of the heptafulvalene trianion radical—The doublet instability of the Hartree-Fock solution and related phenomena

Toyota

Nakajima

1982

Theoret. Chim. Acta

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The restricted Hartree-Fock (RHF) solution for the trianion radical of heptafulvalene, obtained using the open-shell SCF formalism of the Pariser-Parr-Pople method, is found to be doublet unstable at the conventional D2h nuclear arrangement. We calculate the broken-symmetry charge-density wave (CDW) solution and examine its properties. It is shown that the proton hyperfine splittings for the trianion radical calculated from the CDW solution are in good agreement with the experimental values. Further, we briefly refer to the possibility of the lattice instability of the trianion radical from the fully-symmetrical D2h to the C2~ nuclear arrangement.

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Symmetry Rule for Predicting Bond Distortions in Conjugated Hydrocarbons

Cited by 50 publications

References 50 publications

Symmetry and distortive π-electrons in two- and three-dimensional conjugated systems

Symmetry and distortive π-electrons in two- and three-dimensional conjugated systems

Concerning Jahn-Teller Effects

The electronic structure of the heptafulvalene trianion radical—The doublet instability of the Hartree-Fock solution and related phenomena

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