In search of the ‘impenetrable’ volume of a molecule in a noncovalent complex

ABSTRACT

We propose to characterise the “impenetrable” volumes of molecules A and B in a complex A---B by finding that contour of its electronic density that separates the molecular surfaces of A and B but leaves them almost touching. The volume of the complex within that contour is always less than within the 0.001 au contour. The percent difference measures the interpenetration of the two molecules at equilibrium, and is found to directly correlate with the binding energy of the complex. We interpret the volume of each molecule that is enclosed by the almost-touching contour as that molecule's impenetrable volume relative to its particular partner. The percents by which the molecules' relative impenetrable volumes differ from their 0.001 au volumes in the free states also correlate with the strengths of the interactions. This allows the “absolute” impenetrable volume of any molecule to be estimated as ～25% of its 0.001 au volume in the free state. However this absolute impenetrable volume is only approached by the molecule in a relatively strong interaction.     

Pyrromethene–BF2 complexes as laser dyes:1.

Condensations between 3-X-2,4-dimethylpyrroles (X = H, CH₃, C₂H₅, and CO₂C₂H₅) and acyl chlorides gave derivatives of 3,5,3′,5′-tetramethylpyrromethene (isolated as their hydrochloride salts): 6-methyl, 6-ethyl, 4,4′,6-trimethyl, 4,4′-diethyl-6-methyl, and 4,4′-dicarboethoxy-6-ethyl derivatives for conversion on treatment with boron trifluoride to 1,3,5,7-tetramethylpyrromethene–BF₂ complex (TMP–BF₂) and its 8-methyl (PMP–BF₂), 8-ethyl, 2,6,8-trimethyl (HMP–BF₂),2,6,-diethyl-8-methyl (PMDEP–BF₂), and 2,6-dicarboethoxy-8-ethyl derivatives. Chlorosulfonation converted, 1,3,5,7,8-pentamethylpyrromethene–BF₂ complex to its 2,6-disulfonic acid isolated as the lithium, sodium (PMPDS–BF₂), potassium, rubidium, cesium, ammonium, and tetramethylammonium disulfonate salts and the methyl disulfonate ester. Sodium 1,3,5,7-tetramethyl-8-ethylpyrromethene-2,6-disulfonate–BF₂ complex was obtained from the 8-ethyl derivative of TMP–BF₂. Nitration and bromination converted PMP–BF₂ to its 2,6-dinitro-(PMDNP–BF₂) and 2,6-dibromo- derivatives. The time required for loss of fluorescence by irradiation from a sunlamp showed the following order for P–BF₂ compounds (10⁻³ to 10⁻⁴ M) in ethanol: PMPDS–BF₂, 7 weeks; PMP–BF₂, 5 days; PMDNP–BF₂, 72 h; HMP–BF₂, 70 h; and PMDEP–BF₂, 65 h. Under similar irradiation PMPDS–BF₂ in water lost fluorescence after 55 h. The dibromo derivative was inactive, but each of the other pyrromethene–BF₂ complexes under flashlamp excitation showed broadband laser activity in the region λ 530–580 nm. In methanol PMPDS–BF₂ was six times more resistant to degradation by flashlamp pulses than was observed for Rhodamine-6G (R-6G). An improvement (up to 66%) in the laser power efficiency of PMPDS–BF₂ (10⁻⁴ M in methanol) in the presence of caffeine (a filter for light <300 nm) was dependent on flashlamp pulse width (2.0 to 7.0 μsec).