Discovering the stacking landscape of a pyridine-pyridine system

Abstract

Extremely extensive calculations of potential energy surfaces for the parallel-displaced configuration of pyridine dimer systems have been carried out using a dispersion-corrected density functional. Instead of focusing on stationary geometries these calculations provide much deeper insight into the "landscape" of the interaction energies of the particular systems-one can learn how the pyridine dimer stability changes along with various geometrical parameters. Other calculations such as natural bond orbital and energy decomposition have also been applied. The interplay of two significant factors, electrostatic forces and electron correlation effects, have been evaluated. The role of π···π interactions in the stacked pyridine systems has also been confirmed, and surprisingly, this happened to be true even for the geometries where the formation of C-H···π interactions might be proposed instead. The combination of many different methods has revealed the complexity of the stacking interactions. Apart from providing a "literal new look" into pyridine interaction patterns another picture has emerged. A stacking interaction in a pyridine dimer system is perceived as a combination of many different sources of the interaction energy, including orbital ones, and this is true for many different geometries.

Keywords: Density-functional theory; Energy decomposition analysis; Natural bond orbital analysis; Pyridine; Stacking interactions.

Fig. 1

Interaction energy curves created on the basis of data from Sx66 data set [52, 53] for both stacked (a) and hydrogen bonded (b) pyridine dimer systems. Distance scaling factors are the factors used for scaling the closest intermolecular distance starting from the equilibrium geometries [52, 53]. The curves were created using splicing interpolation. CBS stands for complete basis set extrapolation

Fig. 2

Atom HLY charge values (a), EPS map (b) calculated for a pyridine molecule and the geometrical model of a pyridine dimer (c) used in presented calculations (d, the aromatic ring center distance; α, the twist angle between the monomers; β, the angle between the line connecting the aromatic ring centers and the normal line to the aromatic ring in which the connecting center line starts). For all parameters equal to zero, the atom positions of one monomer are the same as the corresponding atom positions of the second one. HLY charge values (a) are given in e (elementary electric charge), the EPS map (b) is superimposed on the isodensity surface with 0.005 au

Fig. 3

PES maps of the studied pyridine dimer systems created on the basis of energy minima found for the systems with the given β and d parameter values (1) as well as for the systems with the given α and β values (2). These PES maps are shown together with corresponding twist angles between the aromatic rings (1) and the corresponding aromatic ring centers distances (2)

Fig. 4

PES maps of the studied pyridine dimer systems along with the maps depicting the corresponding α (°) and d (Å) values. The PES maps were created on the basis of energy minima (kcal mol^-1) found for the systems with the given β and d values (on the left) as well as for the systems with the given α and β values (on the right)

Fig. 5

PES maps of the studied pyridine dimer systems created on the basis of energy minima found for the systems with the given α and γ parameters values and for β = 90° and d = 6.1 Å

Fig. 6

Geometries of the pyridine-pyridine systems that are associated with the found energy minima, together with the atom HLY charge values (e) and the atom numbering scheme (integers) used in NBO analysis. PP1_opt, PP2_opt, and PP3_opt are the configurations that resulted from the optimization of PP1, PP2, and PP3 systems

Fig. 7

PP1_opt, PP2_opt, and PP3_opt configurations of pyridine dimers with the selected NBO orbitals (drawn with the isovalue equal to 0.015 au) taking part in the intermolecular interactions

Fig. 8

Interaction energy curve created on the basis of data corresponding to energy minima found for the systems with the given β. The system configurations are presented in the picture. The curve was created using splicing interpolation

Fig. 9

Interaction energy curve created on the basis of data corresponding to energy minima found for the systems with the given α. The system configurations are presented in the picture. The curve was created using splicing interpolation

Fig. 10

Selected configurations of pyridine dimers where the formation of C-H···π interactions might be proposed. The selected NBO orbitals (drawn with the isovalue equal to 0.015 au) taking part in the intermolecular interactions are shown