2 Computational Details
All theoretical calculations were performed via the Gaussian 16
suite of programs[31]. The
dispersion-corrected density functional theory (DFT-D3) methods were
used to study the systems we chose. The structures of all the monomers
and the complexes included in this study were fully optimized at
the
B3LYP-D3/6-311+G(d,p) level of theory. The vibrational frequencies of
the optimized structures were carried out at the same level and used to
obtain the zero-point vibrational energy (ZPE). All stationary points
were characterized as a local energy minimum on their potential energy
surfaces by verifying that all the corresponding frequencies were real.
The interaction and the binding energy were obtained using the
double-hybrid functional method B2PLYP-D3 with jun-cc-pVTZ as the basis
set. Both B3LYP-D3 and B2PLYP-D3 methods used in present study are all
DFT methods including a version of Grimme’s D3 dispersion model
(DFT-D3)with BJ-damping[32,
33]. Due to the inclusion of both long
and medium-range dispersion effects, these DFT methods have been widely
used and show generally satisfactory performance in the calculations of
non-covalent interactions in similar systems[34-36].
Jun-cc-pVTZ is a modified version of aug-cc-pVTZ by removing itsf -type diffusion basis function. This modification significantly
facilitates the convergence of the geometry optimization process while
the loss of accuracy is trivial[37].
The interaction energy, denoted by
ΔE int, is
defined as the difference between the complex and the sum of energies of
monomer whose geometries come from the optimized structure of the
complex. As for the binding energy, denoted by
ΔE bin, the energy of the monomer used as the
reference point is derived from the energetic minima of the isolated
monomers. The deformation energy, denoted byE def, is
calculated as the difference between ΔE bin and
ΔE int of the complexes, which is the energy
difference between the monomers in their equilibrium geometries and at
their relaxed geometries in the complexes, and its value is positive
since the complexation results in changes of the structure of monomers[38,
39]. The basis-set superposition error
(BSSE) was obtained using the counterpoise correction method proposed by
Boys and Bernardi[40] to correct
both ΔE int and ΔE bin. The
total interaction energy in the ternary system, denoted by
ΔE (ABC) or ΔE total, is calculated as the
difference between the energy of ternary complex and the energy sum of
the monomers which is frozen in the geometry of the ternary complexes.
The cooperative effects can be explained by the many-body interaction
analysis [41,
42]. The two-body terms, denoted by
ΔE (AB), ΔE (BC), and ΔE (A-C)far, are
defined as the difference between the energy of each binary system and
the energy sum of the monomers, which come from the geometry of ternary
complexes. The interplay between the two interactions in the ternary can
be estimated with the cooperative energy, denoted byE coop, which are obtained by the following
formulas:E coop=ΔE (ABC)-ΔE (AB)-ΔE (BC)-ΔE (A-C)far.
This methodology has been widely used to study how the different
interactions affect each other in the complexes[43,
44].
Molecular electrostatic potentials (MEPs) maps of the isolated monomer
were calculated with the Wave Function Analysis-Surface Analysis Suite
(WFA-SAS) program[45] at the
B3LYP-D3/6-311+G(d,p) level on the 0.001 a.u. contour of electronic
density to locate the position and the value of the minima and maxima.
To unveil the nature of the intermolecular interactions, the
atoms-in-molecules (AIM) topological analysis were carried out with the
use of the Multiwfn package[46] based on the
wavefunctions generated at the B3LYP-D3/6-311+G(d,p) level. The
following characteristics of bond critical points (BCPs) corresponding
to the intermolecular interaction were analyzed including the electron
density (ρBCP), the Laplacian of the electron density
(∇2ρBCP), and the electronic energy
density (HBCP), which is decomposed into electronic
kinetic energy density (GBCP) and the electronic
potential energy density (VBCP). The Visual Molecular
Dynamics (VMD) program[47]was applied to
visualize the weak interaction. The natural bond orbital (NBO) analysis
was performed via the NBO 3.1
program[48]implemented in Gaussian 16 to estimate the orbital-orbital interactions
as well as charge transfer (CT).