الفهرس 
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Abstract
Non-linear optics is a new and versatile branch of science that describes the
light-matter interaction when induced polarization depends non-linearly on the
external electric and magnetic elds. Here, we investigate the non-linear optical
properties (including: polarizability ( ), hyperpolarizability ( and
), and
second harmonic generation ( 2
SHG)) for a series of homogeneous (pure) and
heterogeneous (hybrid) fullerenes, where their geometrical, energetic, electronic,
and optical properties have been computed using the periodic software, CRYSTAL17.
The density functional theory (DFT-B3LYP) in combination with the
proper localized Gaussian basis set have been applied in order to model the series
of icosagens, crystallogens, and pnictogens fullerene-like nanocages. Over here
we have two groups of zero-dimensional (0D) molecular systems: pure fullerene
cages with the form of buckyball fullerene (C60), and hybrid Td Boron nitride
(B36N36) fullerene-like structure.
The geometry of all suggested models are fully relaxed, where their geometrical
and energetic properties were calculated. Then, the vibrational calculations
have been done in order to con rm that the obtained geometries represent global
minima on the potential energy surface (PES) via the absence of any imaginary
(negative) vibrational mode. If the frequency calculation produces one
(or more) negative frequency; then SCANMODE strategy that follows downhill
the negative frequency (generally, the largest obtained negative value) has been
performed. Such procedure allows to nd a minimum along this normal coordinate.
Based on the irreducible representation of the mode, the symmetry is
automatically reduced by the code. An overall optimization with this reduced
symmetry, followed by a frequency calculation in this new minimum, produces
in general a full set of positive frequencies.
The non-linear optical properties including: the full tensor of optical polarizability,
, and hyperpolarizability ( and
), as well as the second harmonic
generation (SHG) 2
SHG coecients, for all suggested nano-structures (global
minima on PES) have been computed and analysed. Due to the presence of
inversion center of symmetry in all pure icosahedral fullerenes, the rst hyper8
polarizability, tensor, and the second harmonic generation (SHG) coecients
are all null. The reason for which the hybrid Td fullerenes have been additionally
considered. Concerning pure fullerenes, the obtained optical responses have
been interestingly improved passing from parent fullerene, C60, to bismuthellene,
Bi60; = 498.06 (4095.15) bohr3 and the second hyperpolarizability,
= 0.26479
(13.45900) 105 au, for C60 (Bi60), respectively. It worth noting that, the static
polarizability has been improved by nearly one order of magnitude, while the
second hyperpolarizability increases by more than 50 times comparing to parent
C60 fullerene. However, the SHG coecients and rst hyperpolarizability are
always null due to symmetry restrictions.
Interestingly, hybrid B36N36 fullerene-like structure show Td symmetry, where
the SHG 2
SHG coecient and rst hyperpolarizability are non null. Not only,
the small SHG coecients for B36N36 fullerene, 2
SHG = 212 pmV1, but also
the expected improvement of all non-linear optical responses, were the motivation
behind modelling other hybrid BN-fullerene-like cages. Here, Sn36Si36 and
Al36P36 recorded the highest second harmonic generations susceptibility, 2
SHG
= 2409.63 pmV1 and 2386.31 pmV1, respectively; in addition to improve
by more than ve times for Sn36Si36 with respect to pristine B36N36 (650.41 au,
absolute value of xyz for Td B36N36).
The suggested models are expected to be promising materials for various nonlinear
optics applications such as optical signal processing, optical computers,
ultrafast switches, ultrashort pulsed lasers, sensors, laser ampli ers, and alloptical
modulations.