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 density2(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.