Competitive aryl-iodide vs aryl-aryl reductive elimination reactions in Pt(IV) complexes: experimental and theoretical studies

The platinum(IV) complex trans-(dmpe)Pt(IV)(Ar)2I2 (2, dmpe = 1,2-dimethylphosphinoethane, Ar = 4-FC6H4) rapidly reacts, upon moderate heating in solution under ambient light, via two distinct pathways: isomerization to the corresponding cis-isomer (3) and Ar-I reductive elimination to give (dmpe)Pt(II)(Ar)I (4). Complex 3 undergoes, upon prolonged heating at high temperatures, an exclusive Ar-Ar reductive elimination reaction to give (dmpe)Pt(II)I2. Experimental and DFT studies showed that the 2-to-3 isomerization proceeds via three pathways: photochemical or thermal phosphine chelate opening and a mechanism involving cleavage of the Pt-I bond. The isomerization reaction is significantly slowed down but not stopped in the absence of light or in the presence of an excess of tetra-n-butylammonium iodide. On the other hand, the Ar-I reductive elimination from 2 proceeds via the Pt(delta+)-I(delta-) ion pairlike transition state. Use of the rigid dmpe analogue 1,2-dimethylphosphinobenzene (dmpbz) as the ligand shuts down the chelate ring-opening isomerization pathway and enables faster Ar-I reductive elimination thus making the latter reaction the major reaction route for the dmpbz supported trans-diiodo Pt(IV) complex 8.     

Frequency-domain time-resolved four wave mixing spectroscopy of vibrational coherence transfer with single-color excitation

Triply vibrationally enhanced four-wave mixing spectroscopy is employed to observe vibrational coherence transfer between the asymmetric and symmetric CO-stretching modes of rhodium(I) dicarbonyl acetylacetonate (RDC). Coherence transfer is a nonradiative transition of a coherent superposition of quantum states to a different coherent superposition due to coupling of the vibrational modes through the bath. All three excitation pulses in the experiment are resonant with a single quantum coherence, but coherence transfer results in new coherences with different frequencies. The new output frequency is observed with a monochromator that resolves it from the stronger peak at the original excitation frequency. This technique spectrally resolves pathways that include coherence transfer, discriminates against spectral features created solely by radiative transitions, and temporally resolves modulations created by interference between different coherence transfer pathways. Redfield theory simulates the temporal modulations in the impulsive limit, but it is also clear that coherence transfer violates the secular approximation invoked in most Redfield theories. Instead, it requires non-Markovian and bath memory effects. RDC may provide a simple model for the development of theories that incorporate these effects.     

Effects of structural deformations on optical properties of tetrabenzoporphyrins: free-bases and Pd complexes

A recently developed method of synthesis of pi-extended porphyrins made it possible to prepare a series of tetrabenzoporphyrins (TBP) with different numbers of meso-aryl substituents. The photophysical parameters of free-bases and Pd complexes of meso-unsubstituted TBP's, 5,15-diaryl-TBP's (Ar2TBP's) and 5,10,15,20-tetraaryl-TBP's (Ar4TBP's) were measured. For comparison, similarly meso-arylsubstituted porphyrins fused with nonaromatic cyclohexeno-rings, i.e. Ar(n)-tetracyclohexenoporphyrins (Ar(n)TCHP's, n = 0, 2, 4), were also synthesized and studied. Structural information was obtained by ab initio (DFT) calculations and X-ray crystallography. It was found that: 1) Free-base Ar4TBP's are strongly distorted out-of-plane (saddled), possess broadened, red-shifted spectra, short excited-state lifetimes and low fluorescence quantum yields (tau(fl) = 2-3 ns, phi(fl) = 0.02-0.03). These features are characteristic of other nonplanar free-base porphyrins, including Ar4TCHP's. 2) Ar2TBP free-bases possess completely planar geometries, although with significant in-plane deformations. These deformations have practically no effect on the singlet excited-state properties of Ar2TBP's as compared to planar meso-unsubstituted TBP's. Both types of porphyrins retain strong fluorescence (tau(fl) = 10-12 ns, phi(fl) = 0.3-0.4), and their radiative rate constants (k(r)) are 3-4 times higher than those of planar H2TCHP's. 3) Nonplanar deformations dramatically enhance nonradiative decay of triplet states of regular Pd porphyrins. For example, planar PdTCHP phosphoresces with high quantum yield (phi(phos) = 0.45, tau(phos) = 1118 micros), while saddled PdPh4TCHP is practically nonemissive. In contrast, both ruffled and saddled PdAr(n)TBP's retain strong phosphorescence at ambient temperatures (PdPh2TBP: tau(phos) = 496 micros, phi(phos) = 0.15; PdPh4TBP: tau(phos) = 258 micros, phi(phos) = 0.08). It appears that pi-extension is capable of counterbalancing deleterious effects of nonplanar deformations on triplet emissivity of Pd porphyrins.     

Multiplicities of Points on Schubert Varieties in Grassmannians

We obtain an explicit determinantal formula for the multiplicity of any point on a classical Schubert variety.     

Approximating a solution set of nonlinear inequalities

In this paper we propose a method for solving systems of nonlinear inequalities with predefined accuracy based on nonuniform covering concept formerly adopted for global optimization. The method generates inner and outer approximations of the solution set. We describe the general concept and three ways of numerical implementation of the method. The first one is applicable only in a few cases when a minimum and a maximum of the constraints convolution function can be found analytically. The second implementation uses a global optimization method to find extrema of the constraints convolution function numerically. The third one is based on extrema approximation with Lipschitz under- and overestimations. We obtain theoretical bounds on the complexity and the accuracy of the generated approximations as well as compare proposed approaches theoretically and experimentally.     

Asymptotic velocity for fibered Hamiltonians

We show the existence of the asymptotic velocity for a large class of Hamiltonians with a fibered structure.