Thermal reaction of [3,4]-benzo-8-substituted-3Z,5Z,7E-octatetraenes and quantum-chemical study of the (8π,6π)-electrocyclisation

The first example of thermal (8π,6π)-electrocyclisation of 1,3,5,7-octatetraene with one double bond embedded in an aromatic moiety is described. By this process, [3,4]-benzo-8-substituted octatetraene derivatives, the cis,trans-1-(o-vinylphenyl)-4-(R = Me, Ph, 2-furyl)buta-1,3-dienes were transformed to a new endo-7-(R = Me, Ph, 2-furyl) and exo-7-(R = Me)-2,3-benzobicyclo[4.2.0]octa-2,4-dienes. Mechanism of reaction was also studied by DFT quantum-chemical calculations. The M06/6-311+G(d,p)//M06/6-31+G(d,p) calculations indicate that formation of the single endo-isomer in the case of phenyl and 2-furyl substituents is determined by higher activation barriers for exo-6π-electrocyclisation than for 8π-cycloreversion.     

Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems

The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the linear response of the equilibrium distribution of the system, (ii) maximise the linear response of the expectation of a specified observable, and (iii) maximise the linear response of the rate of convergence of the system to the equilibrium distribution. We also consider the inhomogeneous, sequential, or time-dependent situation where the governing dynamics is not stationary and one wishes to select a sequence of small perturbations so as to maximise the overall linear response at some terminal time. We develop the theory for finite-state Markov chains, provide explicit solutions for some illustrative examples, and numerically apply our theory to stochastically perturbed dynamical systems, where the Markov chain is replaced by a matrix representation of an approximate annealed transfer operator for the random dynamical system.     

Population and deactivation of lowest lying barium levels by collisions with He,Ar, Xe and Ba ground state atoms

Excitation transfer between the barium low lying excited states 6s6p ³ P ₁ ⁰ , 6s5d ¹ D ₂ and 6s5d ³ D _J by collisions with He,Ar,Xe and Ba has been investigated. The population densities in all levels involved were probed by absorption or by fluorescence usingcw lasers. The depopulation cross sections of the Ba³ P ₁ ⁰ state by collisions with noble gases were found to be σ_He(³ P ₁ ⁰ )=5.5·10^?16 cm², σ_Ar(³ P ₁ ⁰ )=4.6·10^?16 cm², and σ_Xe(³ P ₁ ⁰ )=1.7·10^?16 cm². For Ar, the collisional depopulation of the³ P ₁ ⁰ level is exclusively due to the transition to the¹ D ₂ state. Under the assumption that the³ D _J metastable states are populated collisionally by¹ D ₂ →³ D _J transfer only, we have deduced the upper limit for the corresponding cross section σ ₁₃ ^Ar =1.5·10^?18 cm². From the Ba¹ D ₂ and Ba³ D _J steady-state diffusion distributions, collisional relaxation rates of the¹ D ₂ and³ D _J levels were evaluated. The collisional relaxation rates by Ar and Ba yielded total cross sections for the depopulation of metastable levels: σ_Ar(¹ D ₂)=1.5·10^?17 cm², σ_Ba(¹ D ₂)?1·10^?13 cm², σ_Ar(³ D _J)=7·10^?21 cm², and σ_Ba(³ D _J)=1·10^?15 cm². Furthermore, it was found that the main contribution of the collisional depopulation of the¹ D ₂ state by Ar is related to back transfer to the³ P _J ⁰ state, whereas the deactivation of the³ D _J metastable state is due to back transfer to the¹ D ₂ state. Taking into account other cross sections reported in literature we can conclude that collisional deactivation of both metastable levels by Ba ground state atoms can be attributed to their mutual collisional mixing.     

Structure of Diels-Alder adduct of phenylated germole and 1,4-epoxy-1,4-dihydronaphthalene revisited

High pressure synthesis of Diels-Alder adduct of 1,1-dimetyl-2,3,4,5-tetraphenylgermole and 6,7-dibromo-1,4-epoxy-1,4-dihydronaphthalene is described. The X-ray crystallography analysis of the so obtained adduct indicated that the adduct has exo,endo-structure in agreement with our earlier proposal for the stereochemistry of the structurally related germa analogue, 11,11-dimethyl-9,10-epoxy-1,4-germa-1,2,3,4-tetraphenyl-1,4,4a,9,9a,10-hexahydroanthracene based on NMR analysis.     

Collision cross sections for excitation energy transfer in Na* (3P 1/2)+K(4S 1/2)⇔Na*(3P 3/2)+K(4S 1/2) processes

The cross sections for the excitation energy transfer between the 3² P _J states of sodium atoms by collisions with ground-state potassium atoms have been measured by resonant Doppler-free two-photon spectroscopy, where the population densities of directly pumped and collisionally excited Na(3P _J )(J=1/2, 3/2) levels were probed by counter-propagating Na(3P _J ) → Na(4D _{3/2, 5/2}) excitation and detected with the thermionic diode. Cross sections of σ(3P _1/2 → 3P _3/2)=190 Ų±20% and σ(3P _3/2 → 3P _1/2)=100 Ų±20% were found. The theoretical calculations taking into account the long-range interaction termsR ^?6,R ^?8 andR ^?10 yield a value σ(3P _1/2 → 3P _3/2)=165 Ų. On the basis of these long-range interaction potentials the differential cross section has been calculated and compared with recently published experimental data. Very good agreement between the theoretical and experimental data was found.