The BP86 functional and the following basis sets were employed: CP PPP) (41, 42) on Ni (core properties basis set as implemented in ORCA) and TZVP (43, 44) on N, C, H, O, and S. Tight convergence criteria was imposed on all calculations.
Descriptors were computed using Hartree-Fock theory using 6-31G(d) basis set as implemented in Gaussian 09 software.
Density functional theory was used with the 6-31G(d) basis set, as implemented in the Gaussian software package in conjunction with GaussView and Chem3D.
Before proceeding with our calculations, for the purpose of verification, we decided to perform the geometry optimization on our own using the B3LYP-based hybrid DFT approach employing the 6-311++g 6-311++g set as implemented in GAUSSIAN03 program [20].
In the DFT calculations, we adopted generalized gradient approximation (GGA) with the PW91 parameterization [33] and the double-numerical plus d polarization (DND) basis set as implemented in the DMol3 package [34].
Geometry optimizations and density of states (DOS) analysis were performed on a (5, 0) zigzag AlNNT (constructed of 40 Al and 40 N atoms) and different ethyl acetylene/AlNNT complexes at B3LYP level of theory with 6-31G (d) basis set as implemented in the GAMESS suite of program [11].
All atoms were initially optimized using the BP86 functional and LanL2DZ* basis set, as implemented in Gaussian 03.
VSEEs of the sodium-free DNA trimer fragments were computed by CIS (Foresman et al. 1992) using the 6-31G(d) basis set, as implemented in the GAMESS.
All relaxation for PG and PtG sheets in the present and absence of HF and SO3 molecules were done using B3LYP density functional with split basis set (for all atom excluding Pt the basis set was 6-31G (d,p), for Pt atom the basis set was lanl2dz) as implemented in Gaussian 09 suite of program [33].
Equations (28) are the basis of Cartesian FMM, such as implemented in Dehnen's ([2000], [2002]) falcON algorithm.
