Computational Details
All the geometries were optimized at non-local DFT level of theory using
Becke’s exchange functional[27] in conjugation
with Perdew’s correlation functional[28] (BP86).
Basis function of triple zeta quality with two sets of polarization
functions were used. This level of theory is denoted as BP86/TZ2P.
Scalar relativistic effects were considered using Zeroth Order Regular
Approximation (ZORA)[29-34] and the core electrons
were treated by the frozen-core approximations. The geometry
optimizations were performed using ADF 2018 program
package.[35,36] The atomic charge and populations
analysis were carried out by Natural population analysis implemented in
Natural Bonding Orbital (NBO version 3.1),[37]while aromatic nature of the ring system was evaluated by Nuclear
Independent Chemical Shift (NICS)[38] analysis.
NBO and NICS analysis were carried out at the M06/def2-TZVPP level of
theory using the Gaussian 09 program package.[39]The electrostatic potential (ESP) of
S2N2 molecule at molecular isosurface
were created using Multiwfn version 3.6[40] and
VMD version 1.9.3[41] softwares. Topological
analysis of electron density using Bader’s quantum theory of atoms in
molecules (QTAIM)[42-44] were also performed by
Multiwfn 3.6[40] program packages. Using the
Gaussian 09 program package, [39] the wavefunction
file for the ESP plot and for the QTAIM analysis were generated at the
M06/def2-TZVPP level of theory. QTAIM analysis is applied to describe
the electronic properties of the molecules by calculating bond paths,
bond critical points (BCP) and ring critical points
(RCP).[45-47] The atomic interactions are revealed
by the various descriptors at the critical points such as electron
density ρ(r) , laplacian of electron density∇2(r) , potential energy density V(r) ,
kinetic energy density G(r) , total energy density H(r) and
ellipticity (ε ). These were done by single point calculations at
the meta-GGA exchange-correlation functional
M06[48] with def2-TZVPP[49]basis set on geometries optimized at the BP86/TZ2P level of theory. The
EDA-NOCV calculations were carried out using BP86/TZ2P geometries with
the ADF 2018 program package.[50,51]
The bonding nature between molecular fragments in a molecule have been
investigated by means of an energy decomposition analysis (EDA, also
termed extended transition state method -ETS) developed independently by
Morokuma[52] and by Ziegler and
Rauk.[53] The EDA focuses on the analysis of the
instantaneous interaction energy Eint, which gives a
quantitative picture of the chemical bond formation between fragments in
the frozen geometry of the molecule. The interaction energy
(Eint) can be partitioned into three physically
meaningful parameters, viz. electrostatic interaction
(Eelstat), Pauli repulsion
(EPauli) and orbital (covalent) interaction
(Eorb).
ΔEint = ΔEelstat +
ΔEPauli + ΔEorb (1)
Eelstat gives the quasiclassical electrostatic
interaction between the fragments, EPauli is the
repulsive exchange interaction between electrons of the fragments having
same spin and Eorb is the orbital (covalent)
interaction which comes from the orbital relaxation and the orbital
mixing between the fragments. The Eorb term can be
partitioned into contributions from orbital having different symmetries.
The EDA-NOCV scheme breaks down the Eorb term into
pairwise contributions of interacting orbitals of the two fragments.
NOCV (Natural Orbital for Chemical Valence) is defined as the eigen
vectors of the valence operator, \(\hat{V}\), given by the equation:
\(\hat{V}\)ѱi =
𝜐iѱi (2)
The total orbital interaction E orb may
moreover be derived from pairwise orbital interaction energies
Δ\(E_{k}^{\text{orb}}\) that are associated with the deformation
densities Δρk , which is the difference between
the densities of the fragments before and after bond formation.
Eorb = \(\sum_{k=1}^{N/2}E_{k}^{\text{orb}}\)=\(\sum_{k=1}^{N/2}\upsilon\)k \(\left[-F_{-k,-k}^{\text{TS}}\ +\ F_{k,k}^{\text{TS}}\right]\)(3)
The terms \(-F_{-k,-k}^{\text{TS}}\) and \(F_{k,k}^{\text{TS}}\) are
diagonal transition-state (TS) Kohn–Sham matrix elements corresponding
to NOCVs with the eigenvalues –υk and
υk , respectively. The Δ\(E_{k}^{\text{orb}}\)term of a specific kind of bond are allocated by visual assessment of
the shape of the deformation density, Δρ k. The
EDA-NOCV scheme in this manner, gives quantitative
(ΔEorb) data about the strength of orbital interactions
in chemical bonds.