Synthetic and Computational Studies on Factors Controlling Structures of Molecular Triangles and Squares and Their Equilibrium in Solutions

Reactions of (en*)Pd(NO3)2 (en* = N,N,N′,N′-tetramethylethylenediamine)with a series of organic bridging ligands of pyrazine, 1,2-bis(4-pyridyl)ethylene, 1,2-bis(4-pyridyl)acetylene, and 1,4-bis(4-pyridyl)benzene are carried out to investigate factors controlling the supramolecular structures and the equilibrium between the molecular triangles and the squares in solutions. The molecular structures of solid triangular [(en*)Pd(Ln)]3(NO3)6 with 1,2-bis(4-pyridyl)ethylene and 1,2-bis(4-pyridyl)acetylene bridging ligands are determined by X-ray crystallography: [(en*)Pd(1,2-bis(4-pyridyl)ethylene)]3(NO3)6, monoclinic Pn (No. 7), a = 17.3242(3) Å, b = 15.0804(3) Å, c = 17.3223(3) Å, β = 103.5100(10)°, V = 4400.33(14) Å3, Z = 2; [(en*)Pd(1,2-bis(4-pyridyl)acetylene)]3(NO3)6, orthorhombic Aba2 (No. 41), a = 14.6642(3) Å, b = 27.8763(5) Å, c = 21.4233(4) Å, V = 8757.5(3) Å3, Z = 4. In contrast, an infinite chain structure of {[(en*)Pd(pyrazine)](NO3)}∞ (monoclinic P21/m (No. 11), a = 14.4740(7) Å, b = 8.9209(3) Å, c = 28.9705(13) Å, β = 89.974(2)°, V = 3740.7(3) Å3, Z = 2) is observed with the shortest pyrazine. The steric hindrance between the supporting and the bridging ligands or the neighboring supporting ligands would contribute to the formation of the infinite chain complex 1. The N(Py)−Pd−N(Py) angles in the solid molecular triangles monotonically increased closely to 90° with the increase in the lengths of the bridging ligands, indicating the relaxation of the steric hindrance between the supporting and the bridging ligands. The structures of the molecular triangles and squares in solutions are optimized with density functional theory (DFT) calculations using the conductor-like polarizable continuum model (C-PCM), and the resulting structures are almost the same as those in the solid state. The 1H NMR spectra indicate that (i) the equilibrium between the molecular triangles and the squares is attained upon the introduction of the methyl substituents into the en supporting ligands (en*), (ii) the ΔG° values decreased with the increase in the lengths of the straight bridging ligands, and (iii) the equilibrium constants depend on the kinds of solvents. The 1H NMR spectra estimated with the gauge invariant atomic orbital DFT (GIAO−DFT) calculations well reproduce the experimental data, and the single-point energy DFT calculations with C-PCM in the presence of the solvents approximately reproduce the facts (i)−(iii).