1. INTRODUCTION:
Nonlinear optical materials have a great impact on
information technology and industrial applications [1-2]. For the last three
decades, the understanding of the nonlinear optical activities and their
relation to the structural characteristics of the materials has been
considerably improved. NLO effect has been observed in both inorganic and
organic compounds. Since the invention of LASER in the year 1960, inorganic
materials have been extensively used as optical materials [3-4]. However,
organic materials are considered to be better NLO materials while comparing
inorganic compounds due to flexible molecular design, faster
response time, greater optical threshold, higher
bandwidth, minimal processing cost and low voltage processing. However, low
thermal stability and problem in designing of large size crystals are
associated with the organic crystals. In the recent years, substantial progress
has been made in the field of crystal growth to find the suitable NLO material.
Non-centrosymmetric structure and large value of hyperpolarizabilities are the
main requirements of NLO materials. Especially, the π-electron conjugated
organic molecules have found to be suitable for certain applications where the
NLO effect play a vital role [5-9].
In recent years, several studies on chalcone
derivatives reported that they exhibit good nonlinear optical properties
[10-14]. Chalcone being an organic compound possess high tendency to
crystallize in a noncentrosymmetric structure suitable for easy charge
transfer. Chalcone and its derivatives have received the attention of
scientists due to their excellent SHG conversion efficiency and good optical
limiting behavior. Chalcone crystals are also found to be transparent and have
good thermal stability. The prominent nonlinear optical response of chalcone
derivatives is attributed to the delocalized π-electron conjugated systems
connecting donor and acceptor groups. This D-π-A like structure is
responsible for the asymmetric polarization of charges which enhances the
nonlinear optical behavior of the molecule [15-16]. In the present study, one
of the chalcone derivatives “1,3-Bis(3,4-dimethoxyphenyl)prop-2-en-1-one
(MDMC)” is exposed to DFT analyses, first and second order hyperpolarizability
studies and HOMO –LUMO analysis.
2. THEORETICAL BACKGROUND:
The non-linear optical response in organic compounds
is, generally, of molecular origin and is due to (hyper) polarization of the pi
electrons. When an electric field E interacts with the charge distribution of
the system, it produces a force (F = qE, where q is the charge), that causes
displacement of the electron density. This displacement of the centre of
electron density away from the nuclear framework results in a separation of
positive and negative charge and consequently, in an induced polarization or
induced dipole, 
. When a molecule is subjected to electric fields, the
induced polarization becomes the non-linear function of the field strength. The
approximation to formulate the non-linear polarization is to expand the total
dipole as a Taylor series,
3. COMPUTATIONAL DETAILS:
The
electronic structure and optimized geometry of the molecule were computed by
DFT method using the Gaussian 09 program [17] package employing basis set and
Becke’s three parameters (local, nonlocal, Hartree–Fock) hybrid exchange
functional with Lee-Yang-Parr correlation functional (B3LYP) [18–20]. The basis
set 6-311++g(d,p) augmented by d polarization functions on heavy atoms and p
polarization functions on hydrogen atoms were used [21,22]. The geometry was
fully optimized at the B3LYP/6-31G(d,p) level of theory with standard
thresholds defined by the 'Opt' keyword. For the computation of precise
polarizability and hyperpolarizability, 'Polar' keyword is used in the Gaussian
09 package.
4. GEOMETRY OPTIMIZATION:
The initial geometry taken from
crystallographic information file (CIF) of MDMC was minimized without any
constraint using B3LYP/6-31G(d,p)
level of theory and the optimized structural
parameters were obtained. The ground state optimized structure of CPP is shown
in Figure 1. From the theoretical values, it is found that some values slightly
deviates from the experimental values. These differences are probably due to
intermolecular interactions in the solid state. This structure is remarkably
similar to one of the crystallographic asymmetric unit and hence these
structural parameters are the basis for the calculation of the other
parameters. The self consistent field energy of the stabilized geometry of the
molecule, calculated by DFT method is - 997.6313 a.u. and the calculated
dipole moment is 3.1513 Debye.
Figure 1:
Optimized molecular structure of the molecule MDMC
The molecular structure consists of two rings (named
as Ring 1 and Ring 2) which are planar with dihedral angle C20-C19-C17-C15 =
179.99 and C11-C13-C14-C15= 179.97. Due to high electronegativity of the oxygen
than carbon, the carbonyl group is polar and has substantial dipole moments.
The carbonyl group is also planar with respect to the Ring 2 with a dihedral
angle O1-C14-C15-C17= -0.01. The methoxy groups are also
planer with respect to the associated rings. Such high degree of planarity in
structure increases electro-negativity within the π- conjugated molecular
system, which results in nonlinearity of the molecule.
5. HOMO-LUMO ANALYSIS:
The
highest occupied molecular orbital (HOMO) and lowest unoccupied molecular
orbital (LUMO) are very important parameters in quantum chemistry. HOMO and LUMO are used to determine the molecular
reactivity and the ability of a molecule to absorb light. The energy gap
between the highest occupied and the lowest unoccupied molecular orbital are
largely responsible for the chemical, and optical properties of the molecules
[24, 25]. The HOMO–LUMO energy gap of CPP was calculated at B3LYP/6-31G(d,p)
level using DFT theory. The ionization energy and electron affinity can be
expressed through HOMO and LUMO energies as (1 a.u = 27.211396 eV)
= 5.5294 eV and
= 1.7342 eV.
Energy
gap= 
The
smaller energy gap between HOMO and LUMO clearly indicates the higher
possibility of charge transfer takes place within the molecule, which increases
chemical activity of the molecule. Figure 2 displays the orbital lobes of the
HOMO & LUMO states and the energy gap. Using the HOMO and LUMO energies,
the global hardness (η), chemical potential (µ) and global
electrophilicity index (
) are given by the following relations, as proposed by
Parr et al. [26].
η
=(
/ = 1.8976 eV and
µ=
(
/ 2 = 3.6318 eV.
= 3.4754 eV
Figure 2: HOMO-LUMO plot of the molecule MDMC
6. NONLINEAR PROPERTIES:
The
first order and second order hyperpolarizabilities have been calculated at DFT
level by finite field approach [27], which is currently one of the methods for
obtaining numerically accurate NLO responses. The components of β are
defined as the coefficients in the Taylor series expansion of the energy in the
external field. The first order hyperpolarizability is a third-rank tensor that
can be described by 3x3x3 matrix. The 27 components in the matrix can be
reduced to 10 components due to Kleinman symmetry [28]. The total static dipole
moment (μ), the mean polarizability (α0)
and the mean first hyperpolarizability (β0), using the x, y and z components are defined as
μ = (μ2x+μ2y+μ2z)
1/2
α0 = (αxx+αyy+αzz)
/ 3
In
the present study, the values of μ and α0 are found to be
3.1522 Debye and -16.5664x10-24 esu respectively. The first
order hyper polarizability β was also calculated using the finite field
approach theory. The components of first hyperpolarizability can be calculated
using the following equation:
Using
the x, y and z components, the magnitude of the first hyperpolarizability
tensor can be calculated using the
following equation:
where
the components of β are given by following relations
The
first order hyperpolarizability of the title compound is calculated and is
found to be 1.245x10-30 esu. The calculated first order
hyperpolarizability of the title compound is 6.3 times that of the standard NLO
material urea (0.1947x10-30 esu) [29]. The obtained values in atomic
units were converted into esu unit using the following conversion factors
For
calculating α, 1 atomic unit (a.u.) = 0.1482 x 10-24
electrostatic unit (esu)
For
calculating β, 1 a.u. = 8.6393x10-33 esu and
For
calculating 
, 1 a.u. = 5.0367x10-40 esu.
Table 1:
Total static dipole moment (μ), the mean polarizability (α0),
the anisotropy of the polarizability (∆α), the mean first order
hyperpolarizability (β) and the mean Second order hyperpolarizability (
)
for MDMC.
|
Property
|
B3LYP/ 6-31G(d,p)
|
Property
|
B3LYP/6-31G(d,p)
|
Property
|
B3LYP/6-31G(d,p)
|
|
μx
|
-2.2268 Debye
|
βxxx
|
-232.6318 a.u.
|
|
-13154.30 a.u.
|
|
μy
|
2.2298 Debye
|
βxyy
|
75.4030 a.u.
|
|
-1628.53 a.u.
|
|
μz
|
-0.0736 Debye
|
βxzz
|
13.7085 a.u.
|
|
-148.62 a.u.
|
|
μ
|
3.1522 Debye
|
βyyy
|
26.0096 a.u.
|
|
-2493.13 a.u.
|
|
αxx
|
-88.7537 a.u.
|
βyzz
|
-2.4652 a.u
|
|
-2773.29 a.u.
|
|
αyx
|
11.2990 a.u.
|
βyxx
|
-35.7175 a.u.
|
|
-318.022 a.u.
|
|
αyy
|
-115.339 a.u
|
βzzz
|
-0.1110 a.u.
|
Static
|
-2.63*10-36 esu
|
|
αzx
|
0.0009 a.u.
|
βzxx
|
-1.9141 a.u.
|
|
|
|
αzy
|
-0.0023 a.u.
|
βzyy
|
-0.2707 a.u.
|
|
|
|
αzz
|
-131.259 a.u.
|
β
|
144.05 a.u.
|
|
|
|
αo
|
-16.5664*10-24
esu
|
β
|
1.245*10-30 esu
|
|
|
|
∆α
|
5.5123*10-24
esu
|
|
|
|
|
7. STRUCTURE-NLO PROPERTY RELATIONSHIP:
The
title compound MDMC has a D-π-A type push–pull structure. The methoxy
groups in the molecule are almost coplanar with the attached rings. Ring 2
along with carbonyl group (–C=O–) acts as an electron acceptor and Ring 1 acts
as an electron donor. This donor–acceptor groups are connected by –C=C– which
forms the π-conjugation path for the effective intramolecular charge
transfer.
The
β value of MDMC is compared with some of the reported chalcone derivatives
and urea (which is considered as a reference material for NLO studies) and is
tabulated in Table 2. It is clear from these results that the substitution of
methoxy groups at the phenyl rings does not give results better than the
substitution of chlorine groups at the ortho and the meta positions of the
phenyl ring. This may be due to the fact that the electron donating ability of
the chlorine group is more than that of the methoxy group. If a strong electron
donating chlorine/fluorine group is substituted in the para position of the
phenylene group, it leads to a push–pull effect that results in an easy flow of
charges towards the electron accepting carbonyl group. A high value of β
is reported in the compound 4N4MSP that may be attributed to the substitution
of nitro group and sulfide group at the para position of the phenyl rings. This
substitution will increase the charge transfer across the molecule and the NLO
activity.
Table 2:
Comparison of first order hyperpolarizability (β) of various chalcone
derivatives NLO crystals
|
Crystal
|
β (x10-30 esu )
|
|
MDMC
|
1.2450
|
|
HMCBI [34]
|
4.7400
|
|
4N4MSP [35]
|
12.4900
|
|
2C6F2SC [36]
|
5.3405
|
|
Urea [37]
|
0.3728
|
HMCBI; 2-hydroxy-3-methoxy-N-(2-chloro-benzyl)-benzaldehyde-imine
4N4MSP;
(2E)-3-[4-(methylsulfanyl) phenyl]-1-(4-nitrophenyl) prop-2-en-1-one
2C6F2SC;
3-(2-Chloro-6-fluorophenyl)-1-(2-thienyl) prop-2-en-1-one
8. CONCLUSION:
Density
functional theory (DFT) computations using (B3LYP) level with 6-31 G (d, p)
basis set gave the optimized structure of MDMC molecule. Energy gap between the
HOMO and LUMO orbitals of MDMC was found as 
by HOMO-LUMO analysis. The lower energy gap confirmed
the higher possibility of charge transfer within the molecule. From the
estimated NLO parameters, we found that first order hyperpolarizability and
second order hyperpolarizability of the molecule is 1.245x10-30 esu
and -2.63x10-36 esu, respectively. The methoxy functional groups are
planer with the corresponding rings and carbonyl group, thus making the
structure easy for intramolecular charge transfer which leads to the increase
of nonlinearity. This nonlinear optical analysis reveals the NLO behavior of
the material. The comparative NLO study of MDMC with other chalcone derivative
may enhance the researchers to implement these molecules in different
applications based on the requirement of NLO response for the particular
system.
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The effect of substitution of methoxy group to the
ortho and para position of the rings are studied and the structure and the
nonlinear optical response have been analyzed and compared with the other
chalcone derivatives. Low energy band gap and planer structure suggest easy
charge transfer within the molecule and hence a potential candidate for
nonlinear optical response.