Interaction of the Vibrational and Electronic Motions in Some Simple Conjugated Hydrocarbons

Part III A Semiempirical Formulation

Andrew D. Liehr 1
  • 1 Bell Telephone Laboratories, Inc. Murray Hill, New Jersey, U.S.A.

A semiempirical theory of vibrational and electronic reciprocation, in both degenerate and nondegenerate electronic states, is developed under the assumptions that (1) a molecule may be accurately described by the adiabatic approximation; (2) solutions of the electronic and vibrational SCHRÖ-DINGER equations for some fixed molecular conformation are available; (3) the electronic wave functions may be analytically continued to vicinal geometries; (4) the power series expansion of the electronic wave functions and HAMILTONian operator, in terms of nuclear displacements, may be truncated at degree two; and (5) first order perturbation theory is applicable.

The formulae derived for nondegenerate electronic distributions are employed to compute the intensities of the HERZBERG-TELLER (“vibronic”) type absorptions of normal benzene, the cyclopentadienide ion, and the tropylium ion. For convenience in numerically evaluating the requisite phenomenological vibronic constants, the LENNARD-JONES approximation is introduced. The resultant accord of experiment and theory is good.

To test the educed mathematical expressions for either essentially or fortuitously degenerate electronic dispositions, extremal energy calculations are performed for the cyclobutadiene and benzene molecules, the cyclopentadienyl radical, and the benzene plus one ion. It is found, in agreement with the JAHN-TELLER theorem, that all these systems are configurationally unstable with respect to some asymmetric nuclear displacement. The utilization of the LENNARD-JONES approximation again permits a numerical specification of the required vibronic parameters. Application is then made to the ultraviolet spectrum of benzene: the second singlet absorption system and the RYDBERG spectrum are theoretically interpreted in the light of the reckoned predictions. An attempt is made to answer the four cogent queries of WILKINSON concerning the nature of JAHN-TELLER interactions in the RYDBERG spectrum of benzene.

A mathematical and pictorial description of the nuclear dynamics of JAHN-TELLER and HERZBERG–TELLER molecules is also given, and the portraitures of the underlying potential surfaces are verbally and diagrammatically painted. In addition, a critical discussion of the reality of both the computational techniques and of the emergent algebraic forms is presented, and paths for future progress are indicated. A censorius discourse on the flagrant abuse of the phrase “JAHN-TELLER effect” is appended; it is recommended that its use be restricted to the dynamical manifestations of the theorem of JAHN and TELLER (e. g., forbidden asymmetric vibrational progressions and abnormal paramagnetic behavior). Statical demonstrations of the theorem are better ascribed to intrinsic JAHN-TELLER instability.

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