Synthesis and solid-state structures of dimethyl 2,2'-bithiophenedicarboxylates

The syntheses of dimethyl 2,2'-bithiophene-4,4'-dicarboxylate (3), dimethyl 2,2'-bithiophene-3,4'-dicarboxylate (4), and dimethyl 2,2'-bithiophene-3,3'-dicarboxylate (5) are described. Single-crystal X-ray structural analysis of these compounds shows that the thiophene rings in 3 and 4 are nearly coplanar (dihedral angle close to 0 degrees ) and they adopt the anti sulfur conformation in the solid state. Further, the structure of 4 is in agreement with our previous suggestion that there is an electrostatic stabilization of the planar structure due to attraction of the 3-carbonyl oxygen to the sulfur of the distal ring. In 5, however, the thiophene rings are nearly perpendicular (dihedral angle 75 degrees ), indicating considerable steric hindrance between the two large ester groups at the 3- and 3'-positions. Unlike compounds 3 and 4, where the thiophene rings have the sulfur atoms anti, the sulfur atoms in 5 are completely syn. This is the first instance where a bithiophene has been shown to adopt a conformation where the sulfur atoms are completely syn. The solid-state conformations of 3, 4, and 5 are in agreement with ab initio theoretical calculations on these compounds; particularly, the planar conformations of 3 and 4 reflect the previously calculated low rotation barriers of these molecules.     

A comment on the potential in heavy quarkonium quantum-mechanical systems

I discuss the characteristics of the non-relativistic potential responsible for the ψ and ? systems. In particular a comparison is made between the recently advocated flavour independent power behaved potential and the QCD inspired Coulomb + linear potential. The ratios $\text{ΔM}{}_{\mathrm{?}}\text{ΔM}{}_{\mathrm{\psi }}$ of radical excitation energy level differences are used as sensitive tests to the r dependence of V(r). Deviations of these ratios from a constant value may indicate a gradual increase in the effective power of the potentials as r increases (in agreement with the Coulomb + linear potential). Decisive tests have to come from the not yet discovered toponium family where the ratios $\text{ΔM}{}_{\mathrm{T}}\text{ΔM?}$ should start to become greater than 1 if a singularity of the potential exists at r → 0.     

Conditions for equality of decomposable symmetric tensors. II.

We derive consequences of a condition for the equality of two star products given by the second author. We also study another method for the same problem which consists of comparing the components, in an appropriate basis, of the star products involved.