The noncrossing rule and spurious avoided crossings

Hatton, Gregory J.

doi:10.1103/physreva.14.901

Cited by 30 publications

(10 citation statements)

References 7 publications

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“…In particular, Ref. [34] correctly criticizes the standard proof of the no-crossing rule for being not precise and not general enough. In response to this and several related criticisms, (at least) two complete and general derivations appeared which settled the issue [35,36].…”

Section: Now We Usementioning

confidence: 99%

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Minimal work principle: Proof and counterexamples

2005

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The minimal work principle states that work done on a thermally isolated equilibrium system is minimal for adiabatically slow (reversible) realization of a given process. This principle, one of the formulations of the second law, is studied here for finite (possibly large) quantum systems interacting with macroscopic sources of work. It is shown to be valid as long as the adiabatic energy levels do not cross. If level crossing does occur, counter examples are discussed, showing that the minimal work principle can be violated and that optimal processes are neither adiabatically slow nor reversible. The results are corroborated by an exactly solvable model.

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Section: Now We Usementioning

confidence: 99%

“…(26,34) as applied to the full cyclic process (i.e., changing in them t f → t ′ f ), Eq. (70) implies:…”

Section: VImentioning

confidence: 99%

Minimal work principle: Proof and counterexamples

2005

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“…In this sense, symmetry other than spatial and spin may be present, as pointed out by Hatton [ 2 ] . If so, we say that the system, or more rigorously the Hamiltonian, has a special symmetry.…”

Section: Theorymentioning

confidence: 93%

“…For a pericyclic reaction with intermediate states in the form of odd.alternant hydrocarbons without any symmetry, no crossing can be present, because all pairing orbitals are separated by the self-pairing (nonbonding) one. The [2,4]-cycloaddition of allyl to butadiene has been found to have no crossing in the HMO correlation diagram. It can thus be predicted that either an allyl cation or an allyl anion is allowed to perform a [2,4]-cycloaddition to butadiene, and both the supra-supra and the supra-antara processes are allowed.…”

Section: B Alternancementioning

confidence: 99%

“…The [2,4]-cycloaddition of allyl to butadiene has been found to have no crossing in the HMO correlation diagram. It can thus be predicted that either an allyl cation or an allyl anion is allowed to perform a [2,4]-cycloaddition to butadiene, and both the supra-supra and the supra-antara processes are allowed. Such a prediction is beyond the Woodward-Hoffmann rule, and remains to be verified by experiments.…”

Section: B Alternancementioning

confidence: 99%

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Violations of the noncrossing rule due to special symmetry and alternance

Zhixing¹,

Ruiyu²,

Yala³

1983

Int J of Quantum Chemistry

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This paper reports a study on which behavior of the Hamiltonian gives rise to violation of the noncrossing rule. In principle, the noncrossing rule may be violated when a special symmetry other than spatial and spin symmetries is present or there exists the so-called alternance, which corresponds to a Hamiltonian in a real vector space anticommuting with a Hermitian operator. In the HMO models for pericyclic reactions, violations due to special symmetry or alternance have been found. The [ m , n ] supra-antara cycloadditions have no symmetry in the traditional sense, but have special symmetry leading to the existence of crossings in the correlation diagram. Alternance results in one crossing in the middle of the correlation diagram of a forbidden pericyclic reaction with intermediate states in the form of even alternant hydrocarbon. For the reactions with intermediate states in the form of odd alternant hydrocarbon such as [2,4]-cycloaddition of an allyl cation or an allyl anion to butadiene, there should be no crossing in the correlation diagrams, and both the supra-supra and the supra-antara processes are predicted to be allowed. Such a prediction is beyond the WoodwardHoffmann rule.

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