Details of theoretical calculations
The crystal structure geometry was taken after normalizing the distances
involving H atoms to their typical neutron values (C–H= 1.083, N–H =
1.009 and O–H = 0.983 Å). The normalized model was used for Hirshfeld
surface analysis29 and
PIXEL energy
calculation.30-32 The
Hirshfeld surface analysis was performed with CrystalExplorer
program33 to
qualitatively analyze the intermolecular interactions. Further, the
intermolecular interaction energy (E tot) was
calculated for various dimers using the PIXEL method. TheE tot value decomposed into the Coulombic
(E coul), polarization
(E pol), dispersion
(E disp), and repulsion
((E rep) contributions. The PIXEL code handles up
to two-component system, but the title complex is a four-component
system (lysinium, mandalate and two water molecules) which cannot be
handled by PIXEL code. Therefore, the title complex was separated into
different combinations of two-component system which yielded five
different pairs. These pairs were: pair1: L-lysinium-L-mandelate, pair2:
L-lysinium-water1, pair3: L-lysinium-water2, pair4: L-mandelate-water1
and pair5: L-mandelate-water2. We followed this procedure as suggested
for the dihydropyrimidinium hydrochloride derivatives in the
literature.34 For each
pair, the electron densities have been obtained using the program
GAUSSIAN 0935 at
MP2/6-31G** level of theory. The intermolecular interaction energies
(E tot) of different dimers were computed by the
PIXEL method were further compared with those of dimeric energies
(ΔE cp) computed using the M06-2X/6-311++G(d,p)
level of theory with Grimme’s empirical dispersion
D3.36 Further, the
value of ΔE cp was corrected for basis set
superposition error (BSSE) using the counterpoise
method.37
The topological analysis within the framework of Bader’s QTAIM approach
was performed for different dimers identified in the title complex to
characterize the nature of bonding. To obtain wave function, single
point energy calculation (with the normalized X-ray structure geometry)
was carried out for these dimers at M06-2X-D3/6-311++G(d,p) level of
theory. From the calculation, we computed topological properties like
electron density ρ (r), Laplacian of the electron density
∇2ρ (r), potential energy density V (r),
kinetic energy density G (r) and total energy density H (r)
for intermolecular interactions at their bond critical points (BCPs)
using the AIMALL
package.38 Further, the
bond dissociation energies (D e =\(\frac{-V(r)}{2}\)) for all the intermolecular interactions were
calculated using the relationship of Espinosa et
al .39