Volume 16, Issue 7

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.

The expansion of the potential energy function of a molecule in powers of the distances R α of the nuclei from the united atom (UA) is discussed in detail. It is shown to be valid for all states of diatomic and linear polyatomic molecules and for all those molecular states, which can be derived from UA-S-states, when the expressions given earlier for the coefficients E 2,α and E 3,α in terms of the electron density of the corresponding UA-state u are used. It is further shown that the same expansion can also be used for nonlinear polyatomic molecules with orbitally degenerate UA-states, if linear combinations of the correct symmetry are used in the evaluation of E 2,α and E 3,α . Finally, it is proved that for diatomic and linear polyatomic molecules the quadratic terms E 2,α ·R α 2 are independent of the position of the united atom on the molecular axis.

In einem Massenspektrographen wurde die Schwärzung von Ilford Q 2-Platten als Funktion der aufgetroffenen Teilchenzahl für die verschieden schweren Kohlenstoffmolekülionen C 1 + , C 2 + , . . . C n + ... C 26 + untersucht und dabei festgestellt, daß die von diesen Ionenarten hervorgerufenen Schwärzungen durch eine gemeinsame „reduzierte Schwärzungsfunktion“ S = f (log ν*) dargestellt werden kann. Dabei ist S = log θ = Schwärzung; θ =Φ 0 /Φ = Opazität, Φ 0 = ungeschwächte Beleuchtungsstärke der Photozelle beim Photometrieren, Φ = durch geschwärzte Körner geschwächte Beleuchtungsstärke und ν* die der wirklichen Flächendichte der aufgetroffenen Teilchen proportionale „reduzierte Teilchendichte“ ν* = ν n * = β n ν n β n ist ein von der Atomzahl n der Molekülionen abhängiger Faktor, für den der Ansatz β n = const/n α (α = 1,25 ± 0,25) versucht wird. Damit von C 4 + -, C 8 + -, C 12 + -, C 20 + - bzw. von C 28 + -Ionen einer Energie von 14 keV auf einer Ilford Q2-Platte eine erkennbare Schwärzung entsteht, müssen 4 · 10 4 , 1 · 10 5 , 2 · 10 5 , 4 · 10 5 bzw. 6 · 10 5 Ionen pro mm 2 auf die Photoplatte auftreffen.

Für die Beweglichkeiten b + - isotoper Kationen der Massen m + wurden in fünf Salzen die Masseneffekte μ + = Δb + m + /b + - Δm + bestimmt: MgCl 2 (790°C): μ + = -0,102 ± 0,01, CaCl 2 (850°C): μ + = -0,0051 ± 0,003, CaBr 2 (850°C): μ + = - 0,063 ± 0,003, SrCl 2 (1000°C): μ + = -0,036 ± 0,002, BaCl 2 (1080°C): μ + = -0,019 ± 0,002. Es zeigt sich, daß unter den 2-1-wertigen Salzen diejenigen einen besonders großen Masseneffekt der Kationenbeweglichkeiten besitzen, welche wie MgCl 2 , ZnCl 2 , ZnBr 2 und CdCl 2 beim Erstarren ein Schichtengitter bilden. Für die Anreicherung von 46 Ca werden Kostenberechnungen mitgeteilt.

8,7 mm-Wellen werden mittels Hornantennen durch ein Entladungsgefäß geschickt und ihre Amplituden- und Phasenänderung bei Variation der plasmaerzeugenden Hochfrequenzleistung gemessen. Aus den Meßergebnissen werden die Elektronendichte und die geometrischen Abmessungen des Plasmas ermittelt.

The method of normal mode analysis of KRUSKAL and SCHWARZSCHILD is applied in an investigation of the instabilities of the tubular pinch. The dispersion formula is derived and discussed for the limits of very large and very small wave numbers k. The cases m=0 and m = 1 are evaluated numerically. One special case (m=0, k=0) is not included in the other-wise general dispersion formula and is therefore discussed separately.