M. Velayutham Pillai et al. / Journal of Molecular Structure 1100 (2015) 447e454
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3.3. Theoretical study
3.3.1. Molecular geometry
Theoretical study has been carried out using HF/6e31G (d, p)
and B3YLP/DFT 6e31G (d, p) methods in Gaussian 09 program. The
full geometry optimization was carried out using 6e31G (d, p) basis
set both by HF and DFT methods. The optimized geometry for the
molecule predicted in the gas phase is shown in Fig. 5 and the
optimization parameters such as bond lengths, bond angles and
dihedral angles along with the experimental data obtained from X-
ray diffraction are given in the Table S2 (in supplementary file) for
comparative purpose. From the table, it is noticeable that there is
considerable agreement between theoretical and experimental
values of parameters such as bond lengths, bond angles. Despite
some deviations in bond angles and dihedral angles, the stereo-
chemical orientations of the substituents are not changed much.
The variations observed between theoretical and experimental
parameters could be understandable form the fact that in the solid
state, intra as well as intermolecular interactions (such as hydrogen
bonding and van der Waal's forces of attraction) play an important
role in the molecular packing and stability of the molecule. More-
over, in the theoretical study an isolated molecule in the gaseous
state is considered for calculations.
3.3.2. HOMOeLUMO energies
The HOMO and LUMO energies calculated by HF 6e31G (d, p)
are ꢁ8.7890 eV and ꢁ5.4422 eV respectively while that by DFT
6e31G (d, p) are ꢁ8.7639 eV and ꢁ5.4776 eV respectively. The
LUMO and HOMO are being measures of electron affinity (A) and
ionization energy (I) as - ELUMO ¼ A and -EHOMO ¼ I respectively. The
energy gap between the LUMO and HOMO is also indicative of the
global hardness (
the stability of the system while the term chemical potential (
given by ½[ELUMO þ EHOMO]. Further, the global electrophilicity in-
dex ( ) is derived from the relation . The above molecular
2/2
h
¼ ½[ELUMOꢁEHOMO]) which is associated with
m) is
u
u
¼
m
h
properties calculated are depicted in Table S3 (in the
supplementary file). The energy gap between the HOMO and the
LUMO as calculated by HF and DFT methods are 3.3468 eV and
3.2863 eV respectively which suggests that the molecule is soft,
more polarizable, associated with appreciable chemical reactivity.
Moreover, the HOMO and LUMO energy gap explains the eventual
charge transfer interactions that take place within the molecule
which are responsible for the bioactivity of the molecule.
The HOMO and LUMO diagrams of compound 4 as predicted by
HF and DFT methods are shown in Fig. 6. It is observed from the
HOMO and LUMO orbital diagrams [HF 6e31G (d, p)] that in the
HOMO, the electron density is localized mainly over the piperidine
ring only while in the LUMO; the electron density is distributed
mainly over the coumarin ring only and this also indicates that the
Fig. 6. HOMO and LUMO diagrams of compound 4.
hyperpolarizability calculated by theoretical study are shown in
Table S4 (in supplementary file). The dipole moment value equal to
4.2929 D (HF) and/or 3.9144 D (DFT) indicates the polar nature of
the molecule. The highest value of dipole moment is observed for
the component my equal to 2.7613 (HF) and/or 1.9532 (DFT) in the
molecule. The calculated polarizability is higher for the component
ayy ¼ ꢁ203.757 (HF) and/or ꢁ205.343 (DFT) and the hyper-
polarizability is higher for the bxxz component [75.9377 (HF) and/or
66.0241 (DFT)]. It is interesting to note that the calculated polar-
HOMO is made up of setype and LUMO is mostly petype orbitals.
The HOMOeLUMO diagram as per the DFT method reveals that the
electron density in HOMO is concentrated mainly in the piperidine
ring and there is only a partial distribution of electrons over phenyl
and coumarin rings. However, the LUMO has the electron density in
the coumarin and piperidine part but the phenyl rings attached to
the piperidine ring don't contribute to the LUMO and the phenyl
ring attached to the pyran ring is having a partial electron delo-
calization over it. It is notable that, when electronic transitions
occur from HOMO to LUMO in the molecule, electron density
significantly increases in the coumarin ring which thereby behaves
as an electron acceptor in the molecule and the remaining part of
the molecule act as the electron donor.
izability (
a
) value for compound 4 is equal to 62.209 ꢂ 10ꢁ24 e.s.u.
(HF) and/or 61.119 ꢂ 10ꢁ24 e.s.u. (DFT) which is almost 2½ times
greater than that of penitroaniline, a typical NLO material [21,22].
Also the comparison of hyperpolarizability [
b
, 0.98719 ꢂ 10ꢁ30
e.s.u. (HF) and/or 0.82098 ꢂ 10ꢁ30 e.s.u. (DFT)] of compound 4
(which is greater than that of the standard NLO material urea [23],
3.3.3. NLO properties
b
¼ 0.72137 ꢂ 10ꢁ30 e.s.u.) reveals that the former could be used as
The NLO properties such as dipole moment, polarizabilty and