Semiclassical Conservation of Spin and Large Transverse Spin Current in Dirac Systems.

In Dirac materials, the low-energy excitations obey the relativistic Dirac equation. This dependence implies that electrons are exposed to strong spin-orbit coupling. Hence, real spin conservation is believed to be violated in Dirac materials. We show that this point of view needs to be refined in the semiclassical picture which applies to the case of doped Dirac materials (away from the nodal point in the spectrum). We derive a novel type of Boltzmann equation for these systems if they are brought slightly out of equilibrium. Remarkably, spin-momentum locking is softened and a generalized spin conservation law can be formulated. The most striking observable consequence of our theory is a large transverse spin current in a nearly ballistic transport regime.

Syntheses, crystal structures, photophysical and theoretical studies of 1,3,2-benzodiazaborolyl-functionalized diphenylacetylenes.

A series of diphenylacetylenes with one 1,3,2-benzodiazaborolyl end group (BDB) and a second end group X (X = H, OMe, NMe(2), SMe, CN and BDB) were synthesized using established 1,3,2-benzodiazaborole methodologies. The 1,3,2-benzodiazaborolyldiphenylacetylenes with X = p-H (4), p-OMe (5), p-NMe(2) (6), p-SMe (7) and p-CN (8) end groups are functionalized with cyano groups at the central ring in an ortho-position to the triple bond. Molecular structures of 2, 3, 5, 6 and 7 were determined by X-ray diffraction. These borylated systems show intense blue luminescence in cyclohexane, toluene, chloroform, dichloromethane and tetrahydrofuran, whereas green luminescence was observed in acetonitrile solutions. Thereby Stokes shifts in the range 1700-8600 cm(-1) and quantum yields of 0.60-1.00 were observed in cyclohexane solutions. The absorption maxima (308-380 nm) are well reproduced by TD-DFT computations (B3LYP/G-311G(d,p)) and arise from strong HOMO-LUMO transitions. The LUMOs in all the molecules under study are mainly located on the diphenylacetylene bridge, while with the exception of the dimethylamino derivative 6, the HOMO is largely benzodiazaborolyl in character. Thus, the S1←S0 absorption bands are assigned to π(diazaborolyl)-π*(diphenylacetylene) transitions. In contrast to this, in compound 6 the HOMO is mainly represented by the terminal dimethylaminophenyl unit. While calculated ground state dipole moments µ(g) are small (1.1-7.5 D), experimentally determined changes of the dipole moments upon excitation are large (14.8-19.7 D) and reflect a significant charge transfer upon excitation. NLO activities of the rod-structured compounds 2, 4, 6 and 8 are indicated by calculated static first-order hyperpolarizabilities ß up to 76.8 × 10(-30) esu.

Synthetic, structural, photophysical and computational studies of pi-conjugated bis- and tris-1,3,2-benzodiazaboroles and related bis(boryl) dithiophenes.

A series of pi-conjugated systems with two and three 1,3-diethyl-1,3,2-benzodiazaborolyl end-groups was synthesised in 58-91% yields using established 1,3,2-diazaborole methodologies. The bis(diazaborolyl) compounds contain thiophene -2,5-C4H2S- (2a), dithiophene -5,5'-(2,2'-C4H2S)2- (2b), phenylene -1,4-C6H4- (2c), biphenylene -4,4'-(1,1'-(C6H4)2)- (2d) and dioctylfluorene -2,7-(9,9-(C8H7)2C11H6)- (2e) bridges. The three-way linkers in the tris(diazaborolyl) assemblies contain a central phenylene unit -1,3,5-C6H3- linked to the borolyl end groups via thiophene -2,5-C4H2S- (3a), directly bonded (3b) or via phenylene -1,4-C6H4- (3c) units. Molecular structures of 2a, 2b, 2c, 3a, 3b and 3c were determined by X-ray crystallographic studies. These borolylated systems show intense blue/violet luminescence with Stokes shifts of 6200-9500 cm(-1) and quantum yields of 0.33 to 0.98. The absorption maxima (296-351 nm) of these assemblies are reproduced well by TD-DFT computations (B3LYP/6-31G*), and arise from strong, low energy HOMO-LUMO transitions. From molecular orbital computations on optimised geometries of these diazaborolyl systems, the LUMO is located mainly on the thiophene/benzene bridge (66-92%) while the HOMO is largely benzodiazaborolyl in character (53-83%). The S1 <-- S0 absorption bands are thus assigned to pi(diazaborolyl)-pi*(thiophene/ benzene) transitions. Computations on related bis(boryl) dithiophenes [with diarylboryl e.g. Ph2B, Mes2B, (C6F5)2B and FMes2B (Mes = 2,4,6-Me3C6H2; FMes = 2,4,6-(CF3)3C6H2), dioxaborolyl and other diazaborolyl groups] reveal strong, low energy UV-visible absorption bands arising from pi(thiophene)-pi*(thiophene) transitions, with increasing boron participation in the LUMO of the diarylboryl and especially the highly fluorinated systems.

Synthetic, structural, photophysical and computational studies on 2-arylethynyl-1,3,2-diazaboroles.

New 2-arylalkynyl benzo-1,3,2-diazaboroles, 2-(4'-XC(6)H(4)C[triple bond, length as m-dash]C)-1,3-Et(2)-1,3,2-N(2)BC(6)H(4) (X =Me ; MeO ; MeS ; Me(2)N ), were prepared from B-bromodiazaborole, 2-Br-1,3-Et(2)-1,3,2-N(2)BC(6)H(4), with the appropriate lithiated arylacetylene, ArC[triple bond, length as m-dash]CLi. Molecular structures of , and were determined by X-ray diffraction studies. UV-vis and luminescence spectroscopic studies on these diazaboroles reveal intense blue/violet fluorescence with very large quantum yields of 0.89-0.99 for . The experimental findings were complemented by DFT and TD-DFT calculations. The Stokes shift of only 2600 cm(-1) for , compared to Stokes shifts in the range of 5900-7300 cm(-1) for , is partly explained by the different electronic structures found in compared to (X = H). The HOMO is mainly located on the aryl group in and on the diazaborolyl group in whereas the LUMOs are largely aryl in character for all compounds. Thus, in contrast to other conjugated systems containing three-coordinate boron centers such as B(Mes)(2), (Mes = 2,4,6-Me(3)C(6)H(2)), in which the boron serves as a pi-acceptor, the 10-pi electron benzodiazaborole moiety appears to function as a pi-donor moiety.

1,3,2-Diazaborolyl-functionalized thiophenes and dithiophenes: synthesis, structure, electrochemistry and luminescence.

Reaction of 2-bromo-1,3-diethyl-1,3,2-benzodiazaborole (1) with equimolar amounts of thienyl lithium or 2,2-dithienyl lithium led to the generation of benzodiazaboroles 2 and 3 which are functionalized at the boron atom by a 2-thienyl or a 5-(2,2-dithienyl) unit. Similarly 2-bromo-1,3-diethyl-1,3,2-naphthodiazaborole (4) and thienyl lithium or 2,2-dithienyl lithium afforded the naphthoborolyl-substituted thiophene 5 or dithiophene 6. Treatment of 2,5-bis(dibromoboryl)-thiophene 7 with 2 eq. of tBuN=CH-CH=NtBu in n-hexane followed by sodium amalgam reduction of the obtained bis(diazaborolium) salt 8 gave the 2,5-bis(diazaborolyl)thiophene 9. The 2,5-bis(diazaborolidinyl)-thiophene 10 resulted from the cyclocondensation of 7 with 2 eq. of N,N-di-tert-butylethylenediamine in the presence of NEt3. Analogously, cyclocondensation of 7 with N,N-diethylphenylenediamine gave the bis(benzodiazaborolyl) functionalized thiophene 11. The novel compounds were characterized by elemental analysis and spectroscopy (1H-, 11B-, 13C-NMR, MS and UV-VIS). The molecular structure of 3 was elucidated by X-ray diffraction. Cyclovoltammograms show an irreversible oxidation wave at 298-598 vs. Fc/Fc+. The borolylated thiophenes and dithienyls show intense blue luminescence with Stokes shifts of 30-107 nm.