The phosphorescence of benzene: Zeeman effect and microwave induced emission

Results are given of Zeeman and microwave induced delayed phosphorescence experiments which determine the relative activities of the three zero-field spin components in the phosphorescence of benzene. The results allow one to decide which of the mechanisms proposed by Albrecht are responsible for the intensity of some of the most prominent bands in the phosphorescence spectrum. It is confirmed that vibronic coupling in the triplet manifold plays the dominant role for the phosphorescence bands that involve e _2g vibrations and it follows that the phosphorescence in these bands is almost purely out-of-plane polarized. Our results indicate that spin-orbit coupling occurs via the same mechanism as in other aromatic hydrocarbons.     

Vibronic interaction in the lower electronic states of benzene

Results of further calculations on the dynamic coupling between the lower B _1u and E _1u electronic states of benzene via a single e _2g mode are presented. In part I we gave the ‘pseudo-cylindrical’ solutions that result when the leading coupling term, linear in the nuclear displacements, is considered (cylindrical Born-Oppenheimer potential). Here we investigate the effect of

1. (1) the next higher terms in the expansion of the coupling hamiltonian for the free molecule (hexagonal Born-Oppenheimer potential);

2. (2) a crystal field anisotropy.

From the scanty data on the coupling constants available a priori it would follow that the refinement introduced by (1) is small for benzene. On the contrary, the effect of even a small crystal field anisotropy is predicted to be appreciable.

The results of the calculations are analysed by comparison with experimental data on the benzene crystal at low temperature. A consistent interpretation of both magnetic resonance results and the triplet ← singlet absorption spectrum is obtained.     

Sulfide determination in hydrothermal seawater samples using a vibrating gold micro-wire electrode in conjunction with stripping chronopotentiometry

A rapid electrochemical stripping chronopotentiometric procedure to determined sulfide in unaltered hydrothermal seawater samples is presented. Sulfide is deposited at −0.25 V (vs Ag/AgCl, KCl 3 M) at a vibrating gold microwire and then stripped through the application of a reductive constant current (typically −2 μA). The hydrodynamic conditions are modulated by vibration allowing a short deposition step, which is shown here to be necessary to minimize H₂S volatilization. The limit of detection (LOD) is 30 nM after a deposition step of 7 s. This LOD is in the same range as the most sensitive cathodic voltammetric technique using a mercury drop electrode and is well below those reported previously for other electrodes capable of being implemented in situ.     

On the efficiency of VBSCF algorithms,a comment on “An efficient algorithm for energy gradients and orbital optimization in valence bond theory”

We comment on the paper [Song et al., J. Comput. Chem. 2009, 30, 399]. and discuss the efficiency of the orbital optimization and gradient evaluation in the Valence Bond Self Consistent Field (VBSCF) method. We note that Song et al. neglect to properly reference Broer et al., who published an algorithm [Broer and Nieuwpoort, Theor. Chim. Acta 1988, 73, 405] to use a Fock matrix to compute a matrix element between two different determinants, which can be used for an orbital optimization. Further, Song et al. publish a misleading comparison with our VBSCF algorithm [Dijkstra and van Lenthe, J. Chem. Phys. 2000, 113, 2100; van Lenthe et al., Mol. Phys. 1991, 73, 1159] to enable them to favorably compare their algorithm with ours. We give detail timings in terms of different orbital types in the calculation and actual timings for the example cases. © 2012 Wiley Periodicals, Inc.     

The transient EPR spectra and spin dynamics of coupled three-spin systems in photosynthetic reaction centres

The concept of introducing an additional, stable paramagnetic species into photosynthetic reaction centres to increase the information content of their spin polarized transient EPR spectra is investigated theoretically. The light-induced electron transfer in such systems generates a series of coupled three-spin states consisting of sequential photoinduced radical pairs coupled to the stable spin which acts as an “observer”. The spin polarized transient EPR spectra are investigated using the coupled three-spin system P⁺I⁻Q⁻ _A in pre-reduced bacterial reaction centres as a specific example which has been studied experimentally. The evolution of the spin system and the spin polarized EPR spectra of P⁺I⁻Q⁻ _A and Q⁻ _A following recombination of the radical pair (P = primary donor, I = primary acceptor, Q_A = quinone acceptor) are calculated numerically by solving the equations of motion for the density matrix. The net polarization of the observer spin is also calculated analytically by perturbation theory for the case of a single, short-lived, charge-separated state. The result bears a close resemblance to the chemically induced nuclear polarization (CIDNP) generated in photolysis reactions in which a nuclear spin plays the role of the observer interacting with the radical pair intermediates. However, because the Zeeman frequencies of the three electron spins involved are usually quite similar, the polarization of the electron observer spin in strong magnetic fields can reflect features of the CIDNP effect in both, high and low magnetic fields. The dependence of the quinone spin polarization on the exchange couplings in the three-spin system is investigated by numerical simulations, and it is shown that the observed emissive polarization pattern is compatible with either sign, positive or negative, for a range of exchange couplings, J_PI, in the primary pair. The microwave frequency and orientation dependence of the spectra are discussed as two of several possible criteria for determining the sign of J_PI.     

Homoclinic Solutions for Swift-Hohenberg and Suspension Bridge Type Equations

We establish the existence of homoclinic solutions for a class of fourth-order equations which includes the Swift-Hohenberg model and the suspension bridge equation. In the first case, the nonlinearity has three zeros, corresponding to a double-well potential, while in the second case the nonlinearity is asymptotically constant on one side. The Swift-Hohenberg model is a higher-order extension of the classical Fisher-Kolmogorov model. Its more complicated dynamics give rise to further possibilities of pattern formation. The suspension bridge equation was studied by Chen and McKenna (J. Differential Equations136 (1997), 325-355); we give a positive answer to an open question raised by the authors.     

Topological equivalence of discontinuous norms

We show that for everyp>0 there is an autohomeomorphismh of the countable infinite product of linesR ^Nsuch that for everyr>0,h maps the Hilbert cube [−r, r] ^N precisely onto the “elliptic cube” . This means that the supremum norm and, for instance, the Hilbert norm (p=2) are topologically indistinguishable as functions onR ^N.The result is obtained by means of the Bing Shrinking Criterion. Research supported in part by a grant from NSF-EPSCoR Alabama.     

Polar decompositions and related classes of operators in spaces ∏κ

Polar decompositions with respect to an indefinite inner product are studied for bounded linear operators acting on a space. Criteria are given for existence of various forms of the polar decompositions, under the conditions that the range of a given operatorX is closed and that zero is not an irregular critical point of the selfadjoint operatorX ^[*]X. Both real and complex spaces are considered. Relevant classes of operators having a selfadjoint (in the sense of the indefinite inner product) square root, or a selfadjoint logarithm, are characterized.The work of this author was partially supported by INdAM-GNCS and MURSTThe work of this author was partially supported by NSF grant DMS-9988579.