Proceedings - Interdisciplinary Center for Nanotoxicity

Conference on Current Trends in Computational Chemistry 2009
construct the quantum mechanical structure of molecule, which is known as molecular graph
(MG) [11]. The MG of studied molecule has been depicted in Figure 1b.
The AIM analysis for the optimized structures (Figure 1a) has been performed to obtain
the topological properties of the bonds, such as the Laplacian of b ρ ( 2
∇ ρb
), total energy
density (Hb) at BCPs, bond critical points (BCPs), ring critical points (RCPs) and also the bond
2
paths (BPs). As is known, ∇ ρb
and/or Hb identifies whether the charge of the region is shared
2
2
interactions ( ∇ ρ b < 0 and/or H b < 0 ) or closed shell interactions ( ∇ ρ b > 0 and/or H b > 0 ).
The former characterizes shared interactions (covalent bonds), where the electron density
concentrates in the inter nuclear region, whereas the latter is typically associated with
interactions between closed‐shell systems (ionic bonds, hydrogen bonds, and vander waals
molecules).
a b
Figure 1. (a) The optimized geometry of FOX‐7 at level of MP2/aug‐cc‐pVDZ. (b) The 3D
molecular graph (MGs) of the equilibrium geometry of FOX‐7 (Red points are Bond Critical
Points: BCPs; Yellow points are Ring Critical Points: RCPs. The lines are Bond Paths: BPs).
The complete list of bond critical points of electron density (where ∇ρ = 0 ) and their
mathematical characters have been gathered in Table 1 for FOX‐7 with RHF, B3LYP and MP2
levels and aug‐cc‐pVDZ basis set. The completeness of critical point (CP) analysis has been
checked by the satisfaction of Poincare‐Hopf rule [11,12].
n − b + r − c = 1
Where n is the number of nuclei and b, r and c are the number of bond, ring and cage
critical points, respectively.
In attention to Gillespie‐Popelier discusión [12], and Table 1, represent the following
2
bonding natures: the most of bonded interactions are shared covalent ( ∇ ρ b < 0 , H b < 0 and
ρ b order of 10 ‐1 2
a.u.) and O(s)‐H(s) and O(t)‐O(t) interactions with ∇ ρ b > 0 and H b > 0 are
closed shell. O(s)‐H(s) is hydrogen bond and O(t)‐O(t) is not meaning classically. The vibrational
mode of O(t)‐O(t) interaction along with bending of C
NO 2
NO 2
in RHF, B3LYP and MP2 levels are
313.6, 293.2 and 268.4 cm ‐1 respectively. So the normal mode is populated in room
temperature and the BCP between O(t)‐O(t) can be disappeared.
95