Journal of Physics and Chemistry of Solids 85 (2015) 117–131

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Journal of Physics and Chemistry of Solids

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n CorrE-m

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Linear and nonlinear optical properties of 3-nitroaniline (m-NA)and 4-nitroaniline (p-NA) crystals: A DFT/TDDFT study

M. Dadsetani n, A.R. OmidiPhysics Department, Lorestan University, Khorramabad, Iran

a r t i c l e i n f o

Article history:Received 29 January 2015Received in revised form5 May 2015Accepted 12 May 2015Available online 14 May 2015

Keywords:Organic compoundsAb initio calculationsElectronic structureOptical properties

x.doi.org/10.1016/j.jpcs.2015.05.01197/& 2015 Elsevier Ltd. All rights reserved.

esponding author. Fax: þ98 66 33120192.ail address: dadsetani.m@lu.ac.ir (M. Dadsetan

a b s t r a c t

We have studied the electronic structure and optical responses of 3-nitroaniline and 4-nitroanilinecrystals within the framework of density functional theory (DFT). In addition, the excitonic effects areinvestigated by using the recently published bootstrap exchange-correlation kernel within the timedependent density functional theory (TDDFT) framework. Our calculations based on mBJ approximationyield the indirect band gap for both crystals, but the larger one for m-NA. Due to the excitonic effects, theTDDFT calculations gives rise to the enhanced and red-shifted spectra (compared to RPA). Due to theweak intermolecular interactions, band-structure calculations yield bands with low dispersion for bothcrystals. This study shows that the substituent groups play an important role in the top of valence bandand the bottom of conduction band. Due to the linear structure of p-NA molecule, the highest peaks arelocated in the optical spectra of p-NA crystal, while m-NA has more sharp peaks, especially at lowerenergies. Both DFT and TDDFT calculations for the energy loss spectra show plasmon peaks around 27and 28 eV for p-NA and m-NA, respectively. Due to the non-centrosymmetric structure of m-NA crystal,we also have reported its nonlinear spectra and the 2ω/ω intra-band and inter-band contributions to thedominant susceptibilities. Findings indicate the opposite signs for these contributions, especially athigher energies. The comparison between nonlinear spectra and the linear spectra (as a function of bothω and 2ω) reveals the significant resemblance between linear and nonlinear patterns. In addition to thereasonable agreement between our results with experimental data, this study reveals the spectral si-milarities between crystalline susceptibility and molecular polarizability.

& 2015 Elsevier Ltd. All rights reserved.

1. Introduction

In recent years, a large number of studies have been devoted tosearching for different types of nonlinear optical (NLO) materials[1–7] which are applicable in modern communication technology,data storage and optical signal processing [8–10]. In particular,nonlinear organic materials have shown great promise in theseareas due to their useful physical and optical properties. In thesesolids, the molecular units are interacting through weak Van derWaals forces and the electronic properties of these solids aremainly dictated by the properties of the isolated molecules.

For optimizing the nonlinear properties of organic molecules,in addition to non-centrosymmetry, strong π-electron delocaliza-tion and intra-molecular charge transfer stimulated by the pre-sence of electron donor and acceptor groups are important factors.Typical organic chromophores which are of interest are the so-

i).

called push–pull or donor–accepter molecules due to their largevalue of hyperpolarizability [11,12]. Nitroanilines are good ex-amples of push–pull molecules due to the intra-molecular chargetransfer from the electron-donor (NH2) to the electron-acceptor(NO2) group. Despite enhanced charge transfer in push–pull mo-lecules, the application of these materials for nonlinear applica-tions has been rather limited since almost all of push–pull linearmolecular systems crystallize in a centrosymmetric structures inwhich the individual molecular second harmonic responses de-structively interfere. The p-NA and m-NA molecules which have anelectron donor Amino-group and an electron acceptor Nitro-group, are two of the smallest examples of the “push–pull” mo-lecule where the donor group “push” charges and the acceptoraids to “pull” charges to enhance the nonlinear optical activities(Fig. 1).

Although, the m-NA and p-NA molecules (C6H6N2O2) are iso-meric but the donor-group of m-NA occupies the meta position onthe benzene ring, which gives rise to a somewhat smaller mole-cular dipole moment and a lower molecular hyperpolarizability

Fig. 1. Molecular structure of m-NA and p-NA.

M. Dadsetani, A.R. Omidi / Journal of Physics and Chemistry of Solids 85 (2015) 117–131118

[14,15]. More importantly, dramatic differences are observed inthe second harmonic generation (SHG) capabilities of their crys-tals. In spite of having an appreciable hyperpolarizability, p-NAcrystallizes in centrosymmetric space group with no SHG activity[13]. On the other hand, the ground state dipole moment of m-NAis considerably smaller but it crystallizes in non-centrosymmetricstructure and shows large optical nonlinearity [14–31] and largeelectro-optic effect [18–21]. Furthermore, m-NA has been foundrecently to show piezoelectric [32] and ferroelectric [33] beha-viors. Also, its photoluminescence properties were studied bySzostak et al. [34]. In the case of p-NA, the presence of a desirableresonance structure, in addition to the intermolecular chargetransfer, leads to high value of polarizability and hyperpolariz-ability [35–38]. Its use as an end-group in thiol-based self-as-sembled monolayers has been reported [39]. Several experimentalpapers have been published focusing on the nonlinear opticalproperties of surfaces and nanostructures of p-NA crystals [40–43].

While there have been many ab initio full band structure cal-culations of linear optical response in semiconductors, there havebeen very few calculations of the nonlinear response, especially inmolecular crystals. Over the last decade, a number of ab initiostudies have appeared dealing with the theory of nonlinear opticin molecular crystals [44–48]. Most of these studies employ phe-nomenological models at various degrees of sophistication whichare generally accurate over a limited range of frequency. To thebest of our knowledge, an ab initio full band structure study on theelectronic structure and the optical properties of p-NA and m-NAcrystals has not been reported so far. So, our study has a goodnovelty among the computational studies on organic crystals.

In the present study, we adopted density functional theory(DFT) [49,50] to determine the electronic structure and opticalsusceptibilities of p-NA and m-NA crystals using the state-of-the-art full potential linear augmented plane wave (FP-LAPW) method.The FP-LAPW method provides currently the most reliable resultswithin density-functional theory. It should be noted that, due tothe interplay between different strengths of bonding types inmolecular crystals (i.e., the strong intra-molecular covalent bondsvs much weaker inter-molecular Van der Waals and possibly hy-drogen bonds), molecular crystals are one of the most difficultsystems to simulate with ab initio methods.

In addition, this study tries to investigate the excitonic effectsin investigated crystals using Time Dependent Density FunctionalTheory (TDDFT) [51,52]. Such a study (on m-NA and p-NA crystals)has not been reported earlier. We have used Bootstrap approx-imation which is known to give optical spectra in excellentagreement with experiments [67], and is computationally less

expensive than solving the Bethe Salpeter equation. The clearsignature of excitons can be observed by comparing TDDFT resultswith those of RPA [53–55].

Since the nonlinear susceptibilities are very sensitive to theenergy gap, we have performed mBJ [56] calculations which canefficiently improve the band gap and give better band splitting.Studies have shown that the mBJ potential is generally as accuratein predicting the energy gaps of many semiconductors as themuch more expensive GW method [57]. Here, we have used an-other kind of calculation which is the most popular model forcrystals and provides a good physical insight for studding thelinear and nonlinear response in relation to crystal band structure[76].

Next section presents the basic theoretical aspects and com-putational details of our study. The calculated electronic structure,as well as the optical response are presented in Section 3. Lastsection is devoted to summary and principle conclusions.

2. Computational details

2.1. Calculation parameters

Our calculations were performed using the highly accurate all-electron full potential linearized augmented planewave (FP-LAPW)method based on DFT as implemented in the ELK code [58]. This isan implementation of the DFT with different possible approx-imation for the exchange correlation (XC) potentials. We have usedthe generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhoft [59] and the modified Becke–Johnson exchange po-tential (mBJ) [56,57] for the exchange-correlation potentials. ThemBJ exchange potential is available through an interface to theLibxc library [60]. Basis functions are expanded in combinations ofspherical harmonic functions inside non-overlapping spheres atthe atomic sites (muffin-tin spheres) and in plane waves in theinterstitial regions. The muffin-tin radii for oxygen (O), nitrogen(N), hydrogen (H) and carbon (C) was taken to be 1.14, 1.11, 0.78and 1.20 a.u., respectively. The interstitial plane wave vector cut offKmax is chosen such that RMTKmax equals 3.5 for all the calcula-tions. The convergence of the optical properties with respect toRMTKmax has been performed in a way that the smallest RMT isselected for the cutoff. The valence wave functions inside thespheres are expanded up to lmax¼10 while the charge density wasFourier expanded up to Gmax¼14. We found the optical responseto be sufficiently well converged with 192k-points in the IBZ. Theband structure has been computed on a discrete k mesh alonghigh-symmetry directions.

We have used the FHI-aims code [61] for relaxing the atomicpositions and structural parameters. FHI-aims uses numeric atom-centered orbitals as the quantum-mechanical basis set:

ru r

rY , 1i

ilmφ θ φ( ) =

( )( ) ( )

where Y ,lm θ φ( ) are spherical harmonics, and the radial parts, ui(r),are numerically tabulated. Hence, these basis are very flexible andany kind of desired shape can be achieved. This enables accurateall-electron full-potential calculations at a computational costwhich is competitive with, for instance, plane wave methods,without invoking a priori approximations to the potential. FHI-aims is an efficient computer program package to calculatephysical and chemical properties of condensed matter and othercases, such as molecules, clusters, solids, liquids based on a first-principles description of the electronic structure. It should benoted that, that the primary production method is density func-tional theory and the package is also a flexible framework foradvanced approaches to calculate ground-state and excited-state

M. Dadsetani, A.R. Omidi / Journal of Physics and Chemistry of Solids 85 (2015) 117–131 119

properties. We have performed the relaxation procedure so thatevery component of the forces acting on the atoms was less than10�4 eV/Å.

2.2. Linear and nonlinear optical response calculations

The linear optical properties of matter can be described bymeans of the transverse dielectric function ε(ω). There are twocontributions to ε(ω), namely, intraband and interband transi-tions. The contribution from intraband transitions is importantonly for metals while the titled crystals are semiconductor. Thecomponents of the dielectric function were calculated using thetraditional expression in the random phase approximation (RPA)[53–55]:

⎡⎣⎢⎢

⎤⎦⎥⎥

i iW

p k p k

i

p k p k

i

4 1

2

ij

ij

kk

cv vc

vci

cvj

vc

vci

cvj

vc

∑ ∑

ε ω

δ πω Ω ε ω ε η

ω ε η

( )

= + − (( ) ( )

( + + )

+( ( ) ( ))( − + )

)( )

⁎

Where the term in the bracket is optical conductivity (atomic unitsare used in the above formula). The sum covers all possible tran-sitions from the occupied to unoccupied states. The term pcv

j de-notes the momentum matrix element transition from the energylevel c of the conduction band to the level v of the valence band atcertain k-point in the BZ. ωℏ is the energy of the incident photonand εvc≡εv�εc is the differences between valence and conductioneigenvalue. Wk is the weight of the k-point over the Brillouin zone

Fig. 2. The primitive unit cells (a, b) and differe

and Ω is the unit cell volume. This formula is related to the directtransitions from valence bands to the conductions bands. Whenthe photon energy is close to the difference between valence andconduction bands, the denominator is very small which gives riseto the large value for the optical response. The energy eigenvaluesare calculated within the RPA approximation which ignores theelectron-hole interactions. Wherever the weight of k-points ishigh, the value of optical response will be enhanced giving peaksof optical spectra. This is the standard formula and has differentforms in the optical textbooks.

Time-dependent density-functional theory (TDDFT) [62], whichextends density-functional theory into the time domain, is anothermethod which is able, in principle, to determine neutral excita-tions of a system. The TDDFT method can handle large systemsand is, basically, exact. Hence, this study also covers the linearoptical responses within the framework of TDDFT. The key quan-tity of TDDFT (here, all the quantities are matrices on the basis ofreciprocal lattice vectors G) is the exchange-correlation kernel fxc,which, together with the Kohn–Sham (KS) single-particle density-response function χs, determines the interacting-particles density–response function χ, as follows [62]:

q qG q

f q, ,4

,3GG

sGG GG GG

xc1 12χ ω χ ω π δ ω

′( ) = ( ) ′( ) −

+ ′ −′( )

( )− −

While χs is constructed using the single-particle states obtainedwith a given approximation to the static exchange-correlationpotential Vxc(r) [46], fxc is a true many-body quantity, basically,containing all the dynamic exchange-correlation effects in a realinteracting system. Although formally exact, the predictions ofTDDFT are only as good as the approximation of the exchange-correlation kernel. A great amount of effort has been invested into

nt views of m-NA and p-NA crystals (c, d).

Table 1Optimized values of p-NA crystal by FHI-aims code.

Bond angle Optimized values (deg) Experimentaladata (deg) Bond length Optimized values (Å) Experimentaladata (Å)

C2–C1–C6 118.460 118.369 C1–C2 1.4244 1.4016C1–C6–C5 120.685 120.690 C2–C3 1.3790 1.3672C6–C5–C4 119.939 119.755 C3–C4 1.4096 1.3890C5–C4–C3 120.475 120.777 C4–C5 1.4086 1.3883C4–C3–C2 119.628 119.271 C5–C6 1.3752 1.3651C3–C2–C1 120.790 121.129 C6–C1 1.4244 1.4045H12–N11–H13 117.699 119.927 H10–C6 1.0889 0.9306H13–N11–C1 119.901 120.044 H9–C5 1.0868 0.9306N11–C1–C6 119.777 120.310 H8–C3 1.0879 0.9301C1–C6–H10 118.977 119.641 H7–C2 1.0891 0.9298H10–C6–C5 120.337 119.669 C1–N11 1.3489 1.3531C6–C5–H9 120.132 120.136 N11–H13 1.0265 0.8600H9–C5–C4 119.925 120.109 N11–H12 1.0161 0.8603C5–C4–N14 119.293 119.366 C4–N14 1.4234 1.4371C4–N14–O15 118.396 118.968 N14–O15 1.2612 1.2344O15–N14–O16 121.746 121.658 N14–O16 1.2512 1.2264O16–N14–C4 119.855 119.374N14–C4–C3 120.232 119.877C4–C3–H8 119.979 120.365H8–C3–C2 120.383 120.363C3–C2–H7 119.837 119.439H7–C2–C1 119.362 119.432C2–C1–N11 121.762 121.321C1–N11–H12 122.400 120.028

a Ref. [87].

M. Dadsetani, A.R. Omidi / Journal of Physics and Chemistry of Solids 85 (2015) 117–131120

the development of approximations to fxc of the crystalline semi-conductors and insulators [63–72]. In this study, we have used theBootstrap approximation for fxc[67] which has a wide applicabilityand is computationally less expensive than solving the BetheSalpeter equation.

The nonlinear procedure for calculating the second order sus-ceptibilities as well as their inter- and intra-band contributions(within RPA approximation) have been developed by Sipe and

Ghahramani [73], and Aversa and Sipe [74]. Eqs. (4)–(6) show thegeneral form of second-order optical susceptibilities,

2 , ,ijk2χ ω ω ω( − ), [75–80]. Here, n denotes the valence states, m

denotes the conduction states, and l denotes all states (l≠m,n). Twokinds of transitions take place in these equations: one of them isvcc’ which involves one valence band (v) and two conductionbands (c and c′) and the second transition is vv’c which involvestwo valence bands (v and v’) and one conduction band (c).

Table 2Optimized values of m-NA crystal by FHI-aims code.

Bond angle Optimized values (deg) Experimentaladata (deg) Bond length Optimized values (Å) Experimentaladata (Å)

C2–C1–C6 118.361 118.954 C1–C2 1.4075 1.3978C1–C6–C5 121.076 120.782 C2–C3 1.3932 1.3876C6–C5–C4 121.084 121.240 C3–C4 1.3969 1.3849C5–C4–C3 117.121 116.773 C4–C5 1.3947 1.3853C4–C3–C2 123.403 124.081 C5–C6 1.3939 1.3899C3–C2–C1 118.953 118.166 C6–C1 1.4133 1.3998H12–N11–H13 114.322 119.963 H10–C6 1.0886 0.9502H13–N11–C1 116.498 120.038 H9–C5 1.0904 0.9503N11–C1–C6 121.120 121.011 H8–C4 1.0865 0.9498C1–C6–H10 118.587 119.634 H7–C2 1.0866 0.9504H10–C6–C5 120.336 119.584 C1–N11 1.3887 1.3890C6–C5–H9 119.300 119.411 N11–H13 1.0205 0.8800H9–C5–C4 119.616 119.349 N11–H12 1.0253 0.8798C5–C4–H8 121.877 121.601 C3–N14 1.4664 1.4661H8–C4–C3 121.001 121.626 N14–O15 1.2327 1.2424C4–C3–N14 118.372 118.268 N14–O16 1.2252 1.2411C3–N14–O15 117.863 117.962O15–N14–O16 123.245 122.989O16–N14–C3 118.891 119.048N14–C3–C2 118.219 117.637C3–C2–H7 119.593 120.923H7–C2–C1 121.455 120.911C2–C1–N11 120.443 119.985C1–N11–H12 114.473 119.998

a Ref. [88].

M. Dadsetani, A.R. Omidi / Journal of Physics and Chemistry of Solids 85 (2015) 117–131 121

⎧⎨⎪⎪

⎩⎪⎪

⎡

⎣

⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥

⎫⎬⎪⎪

⎭⎪⎪

Wr r r

r r r r r r

2 ; ,

1

2

2

1

4

ijkinter

nmlkk

nmi

mlj k

ml mn

mn

lmk

mni

nlj

nl mn

nlj

lmk

mni

lm mn

ln

ln

{ }

{ } { }

∑

χ ω ω ω

Ω

ω ω ω ω

ω ω ω ω ω ω

( − )

=

→ →

( − )( − )

−( − )

→ → →

( − )−

→ → →

( − )( )

⎪

⎪⎧⎨⎩

⎡⎣⎢

⎤⎦⎥

⎫⎬⎪⎪

⎭⎪⎪

W

r r r r r r

ir r r r r

2 ; ,

1

82

22

5

ijkintra

kk

nml

mn

mnnlj

lmk

mni

ml lmk

mni

nlj

nm

nmi

mnj

nmk

mn mn nml

nmi

mlj k

ml

mn mn

2

ln

2

ln ln

2

{ } { }{ } { }

∑

∑

∑ ∑

χ ω ω ω

Ω

ωω ω

ω ω

Δ

ω ω ω

ω ω

ω ω ω

( − )

=

( − )→ → → − → → →

−

⇀ →

( − )+

⇀ → → ( − )

( − )( )

−

Fig. 3. Calculated band structure and total DOS of m-NA and p-NA crystals using m-BJ and GGA approximations.

Fig. 4. Projected density of states (PDOS) for different atoms of m-NA and p-NA molecules in their crystals.

M. Dadsetani, A.R. Omidi / Journal of Physics and Chemistry of Solids 85 (2015) 117–131122

Fig. 5. Calculated density of states for functional groups of m-NA and p-NA molecules.

M. Dadsetani, A.R. Omidi / Journal of Physics and Chemistry of Solids 85 (2015) 117–131 123

⎧⎨⎪⎪

⎩⎪⎪

⎡⎣⎢

⎤⎦⎥

⎫⎬⎪⎪

⎭⎪⎪

W

r r r r r r

ir r

2 ; ,

12

1

6

ijk

kk

nml mn mnnl lm

imnj

nlk

lm nli

lmj

mnk

nm

nmi

nmj

mnk

mn mn

mod

2

2

{ } { }{ }

∑

∑

∑

χ ω ω ω

Ω

ω ω ωω ω

Δ

ω ω ω

( − )

=

( − )→ → → − → → →

−

→ →

( − )( )

From these formulae (atomic units are used in these relations),we can notice that there are three major contributions to

2 , ,ijk2χ ω ω ω( − )( ) : the inter-band transitions, 2 , ,ijk

erintχ ω ω ω( − ), the

intra-band transitions, 2 , ,ijkraintχ ω ω ω( − ), and the modulation of

inter-band terms by intra-band terms, 2 , ,ijkmodχ ω ω ω( − ), where

n≠m≠l and i, j and k correspond to Cartesian indices.

The symbols knmiΔ (

→) and r k r knm

imlj{ }(⇀) (

→) are defined as follows:

k v k v k 7nmi

nni

mmiΔ (

→) = (

→) − (

→) ( )

r k r k r k r k r k r k8nm

imlj

nmi

mlj

nmj

mli1

2{ } ( )(⇀) (→

) = (→

) (→

) + (→

) (→

) ( )

where vnmi→ is the i component of the electron velocity (given as

v k i k r knmi

nm nmiω→ ( ) = ( ) (

→)). The position matrix elements between

band states n and m, r knmi (

→), are calculated from the momentum

matrix element pnm

i→ using the relation [81]: r knmi p k

im k

nmi

nm(→

) =ω

(→

)

(→

),

where the energy difference between the states n and m are givenby nm n mω ω ωℏ = ℏ( − ) and Wk is the weight of the k-point.

As mentioned before, p-NA is a centrosymmetric crystal with

no SHG activity, but m-NA belongs to the space group Pca21, andhence, it has seven independent nonlinear susceptibilities namely;xxz, xzx, yyz, yzy, zxx, zyy and zzz. Our calculation shows that xzx

2χ( )

and xxz2χ( ) possess the dominant below-band gap peaks, while zxx

2χ( )

has the largest peak above the energy gap.

3. Results and discussion

3.1. Crystal structure, electronic and linear optical properties

Fig. 2 represents the different views of p-NA and m-NA crystals.The p-NA molecule crystallizes in centrosymmetric monoclinicstructure (space group P21/n) with four molecules in the unit cell[82]. On the other hand, the X-ray diffraction experiments of m-NAcrystal which carried out at 15 different temperatures in the 90–350 °K range, show the non-centrosymmetric orthorhombicstructure (space group Pca21) with four molecules in the unit cell[83]. The X-ray crystallographic data [82,83] were optimized byminimization of the forces (10�4 eV/Å) acting on the atoms. Theoptimized lattice parameters for crystalline p-NA (a¼8.52 Å,b¼6.00 Å, c¼12.20 Å, α¼γ¼90° and β¼91.42°) and m-NA(a¼19.05 Å, b¼6.53 Å, c¼4.99 Å and α¼β¼γ¼90°) are found tobe in good agreement with the X-ray crystallographic data andearlier reported values [84–86]. The respective geometrical para-meters such as bond length and bond angle of optimized structureare given in Tables 1 and 2. This tables show that the calculatedC–H bonds are slightly longer than their experimental counter-parts. In addition, the C–H bonds which are near to the NO2 group(for example, C4–H8 in m-NA, and C3–H8 and C5–H9 in p-NAcrystal) are shorter than other C–H bonds. This phenomenon canbe attributed to the electron withdrawing property of Nitro-group.The NO2 group reduces the electron density at the ring carbonatom and the carbon atoms in substituted benzene ring exert alarger attraction on the valence electron cloud of the hydrogen

Fig. 6. Calculated imaginary ( ii2ε ) and real parts ( ii

1ε ) of principle components of dielectric function for m-NA and p-NA crystals within mBJ approximation.

Fig. 7. Calculated refractive indexes for m-NA and p-NA crystals.

M. Dadsetani, A.R. Omidi / Journal of Physics and Chemistry of Solids 85 (2015) 117–131124

atom resulting in an increase in the C–H force constant and adecrease in the corresponding bond length. In the case of p-NA,the calculated average C–C distance is 1.403 Å, and the bondsparallel to the long molecular axis (C2–C3 and C5–C6) are sig-nificantly shorter than the average. Of the other four bonds, thepair near the Nitro-group (C3–C4 and C4–C5) are shorter, whilethose near the Amino-group (C1–C2 and C1–C6) are significantly

longer than the average. On the other hand, in m-NA, the calcu-lated average C–C distance is 1.400 Å, and the bonds which arenear to the Amino-group (C1–C2 and C1–C6) are longer than theaverage, but those near the Nitro-group (C2–C3 and C3–C4) areshorter. Generally, the calculated bond angles are very close to theexperimental values, except for the positions of substitutions. Forexample in the case of m-NA, the bond angles of Amino-group

Table 3Calculated and experimental results for the refractive index and linear optical susceptibilities of m-NA crystal.

λ¼660 nm λ¼1064 nm λ¼1319 nm

Calc.[24] Exp.[23] This study Exp.[26] Exp.[23] This study Calc.[24] Exp.[23] This study

xx1χ( ) 1.946 1.925 2.00 1.82 1.83 1.92 1.844 1.809 1.90

yy1χ( ) 2.019 2.052 2.15 1.95 1.96 2.05 2.007 1.929 2.03

zz1χ( ) 1.719 1.755 1.80 1.66 1.66 1.7 1.644 1.640 1.69

λE630 nm

Exp.[19] Exp.[21] This study

nxx 1.74 1.715 1.73nyy 1.78 1.805 1.78nzz 1.69 1.675 1.68

Fig. 8. Absolute values of ijk2χ ( ) in units of (pm/V) for m-NA crystal.

M. Dadsetani, A.R. Omidi / Journal of Physics and Chemistry of Solids 85 (2015) 117–131 125

(C1–N11–H12 and C1–N11–H13) have more deviation compared toother angles and the sum of angles around the Amino nitrogen is345.293°, which indicate the nonplanarity form for the Amino-group. One can see that the experimental details of m-NA crystalstructure [85,86] are very close to optimized results in this study. Itis interesting to note that the sum of angles around the Aminonitrogen in p-NA is 360.00, which indicate the planarity form forthe Amino-group of p-NA. On the other hand, the planarity ofNitro-group in m-NA and p-NA is very reasonable, in accord withthe experimental findings and our calculations. In addition, theelectron-donating and electron withdrawing substituents distortthe symmetry of the benzene ring, yielding ring angles smallerthan 120° at the position of NH2 group and slightly larger than120° at the point of NO2 group. The above-described results pro-vide conclusive evidence that the p-NA molecular structure is veryclose to planar but the Amino hydrogens of m-NA are out of themolecular plane. It should be noted that, the shortest inter-molecular distances are between the hydrogens of Amino-groupand the oxygens of Nitro-group (especially in p-NA crystal) whichincrease the number of hydrogen-bonding interactions in the in-vestigated crystals.

In the following, the electronic band structure and the total andpartial density of electron states are presented. The calculatedelectronic band structure and corresponding total DOS with GGAand mBJ approximations are represented in Fig. 3. As can be seenthe mBJ approximation push the valence bands to lower energiesand the conduction bands to higher energies, yielding improvedresults for the band gap. In addition, both mBJ and GGA

approximations give small band dispersions, since the investigatedcrystals have weak intermolecular interactions. Compared to in-organic crystals, band dispersions in the two studied compoundsare small, a characteristic behavior of the molecular crystals as aresult of the weak van der Waals interactions between molecules.One can see that, on going from GGA to mBJ approximation, anempty regionwith no energy bands appears in the range of 4‐6 eV.Despite close similarity between band structures, the p-NA one(due to the lower intermolecular distances) is rather more dis-persed. However, our results show that mBJ gives a better bandgap value and corresponding bands splitting. Thus, we will showour results using mBJ only. Our calculations based on mBJ ap-proximation show that p-NA (m-NA) crystal possesses a funda-mental indirect band gap by about 2.42 eV (2.45 eV) in the ГC–UV

(YC–ГV) direction while the smallest direct band-to-band transi-tion is in the UC–UV (YC–YV) direction by about 2.47 eV (2.50 eV).In an experiment which carried out by Shkir et al. [87] the ab-sorbance data was used to calculate the optical absorption coeffi-cient and the optical band gap of p-NA crystal. They have reportedthe band gap of 2.43 eV, which is very close to our result. In asimilar experiment, Suresh [88] has used the transmittance data tocalculate the optical absorption coefficient and the optical bandgap of m-NA crystal. He has reported the value of 3.35 eV for theenergy gap, which is larger than our result by about 0.9 eV.

The unit cell of examined crystals contains 4 molecules. Fig. 4shows the angular momentum decomposition of the atoms pro-jected density of states (PDOS) for one of molecules. This figureindicate that, in both crystals, the top of valence band come pre-dominantly from N-p states of Amino group, while the bottom ofconduction band mainly originate from N-p and O-p states of Nitrogroup. As can be seen the N-s state of Amino group in m-NAcrystal has more contribution to upper valence band in compar-ison to that of p-NA. It should be noted that the role of Aminonitrogen in the bottom of conduction band and the contribution ofNitro nitrogen to the top of valence band is negligible. In addition,the H-s, N-s and O-s states have negligible contribution to the low-energy conduction bands. The structures of valence band at en-ergies between �11.0 eV and �1 eV, originate mainly from N-p,O-p, and C-p states with small admixture of O-s, H-s, N-s, and C-sstates. Generally, C-s and H-s states have small contributions to thevalence bands and to the negative energies above �5 eV, respec-tively. Furthermore, this figure shows the strong hybridizationsbetween different states at energies under �1 eV, which is a signof strong covalent intra-molecular bondings.

It is worthwhile to study the density of states for functionalgroups, separately. As can be seen in Fig. 5, the bottom of con-duction band, in both crystals, origins mainly from the Nitro-groupwhile the top of valence band comes mainly from both Benzene-

Table 4

Calculated total, intra-band and inter-band contributions to Re 0ijk2χ ( )( ) in units of

(pm/V).

Component xxz xzx yyz yzy zxx zyy zzz

Re intra(ω) �0.901 �0.192 5.62 3.43 �0.256 4.60 4.55Re intra(2ω) �1.13 �1.13 8.65 8.65 �1.62 �11.60 �12.19Re inter(ω) �2.59 1.97 �2.09 �2.85 �3.33 �0.865 �2.61Re inter(2ω) 4.77 4.77 4.46 4.46 �2.57 8.20 7.09Re total intra �2.031 �1.322 �3.03 �5.22 �1.876 �7.00 �7.64Re total inter 2.18 6.74 2.37 1.61 �5.90 7.34 4.48Re total 0.506 5.77 �3.12 �6.08 �7.80 �1.59 �5.44

Fig. 9. Calculated (2ω and ω) inter-band and intra-band contributions to Im xxzχ , Im xzxχ and Im zxxχ in units of (pm/V) for m-NA crystal (the vertical dashed line indicate theborder of band gap).

M. Dadsetani, A.R. Omidi / Journal of Physics and Chemistry of Solids 85 (2015) 117–131126

ring and Amino-group. It should be noted that, due to the non-linearity of m-NA molecule, the contribution of its Nitro-group tothe top of valence band is smaller than that of p-NA. In addition,this figure shows that the Nitro-group also has a main role atenergy values around �4 eV and �9 eV. Generally, the Benzene-ring (Amino-group) has a major (minor) contribution to the higherconduction bands and to the lower valence bands.

In the following part of this section, the imaginary and realparts of dielectric function and the components of refractive in-dices are represented. The calculated imaginary ( xx

2ε ω( ), yy2ε ω( ) and

zz2ε ω( )) and real parts ( xx

1ε ω( ), yy1ε ω( ) and zz

1ε ω( )) of principle com-ponents of dielectric functions are represented in Fig. 6. The op-tical spectra are scissors corrected using scissors corrections of0.01 eV and 0.9 eV for p-NA and m-NA crystals, respectively. Thisvalues are the difference between the calculated energy gap usingmBJ and the earlier reported values [87,88]. Generally, one can seetwo main structures (regions below 10 eV and beyond 10 eV) in

the imaginary spectra of dielectric function. Regarding the firststructure (under 10 eV) in m-NA crystal, the component yy

2ε ω( ) isdominant and the smallest values are in zz

2ε ω( ), while in the case ofp-NA, the component zz

2ε ω( ) is dominant and yy2ε ω( ) has smaller

values. The polarization vector of m-NA and p-NA molecules isalong Nitro-group to Amino-group. As can be seen in Fig. 2c and d,the smaller angle between polarization vector and y-axis in m-NAcrystal, (z-axis in p-NA crystal) yields the strong interaction be-tween light and matter along y-axis (z-axis). So, the largest peaksof absorptive spectra are observable in yy

2ε ω( ) and zz2ε ω( ) of m-NA

and p-NA crystals, respectively. Both crystals show several smallpeaks (α, β, γ, s, η) in the first part of ii

2ε ω( ), but the m-NA spectrahave more of them. In the case of m-NA, comparison betweenFigs. 6 and 5 shows that the first peak (α) is located around 3.65 eVand come from the electron transitions between a-valence bandsto the e-conduction bands (a-e). The position of other peaksvaries with components and they have different origins. For ex-ample the second peak of xx

2ε ω( ) (βxx) is located around 5.58 eV andcome from d-e transitions, while βyy and βzz both located around4.85 eV and come from b-e transitions. The dominant peak of yy

2ε(γyy) is located around 5.78 eV and originates from a-f transi-tions. In the case of p-NA, the first peaks of all components (α)have same positions (located around 2.75 eV) and come from a-etransitions. The second peaks of xx

2ε and yy2ε (βxx and βyy) are lo-

cated around 4.67 eV and come from a-f transitions, while βzz islocated around 5.5 eV and originates from a-g transitions. As canbe seen, the dominant peak of p-NA (αzz) has lower energy buthigher intensity compared to its counterpart in m-NA crystal (γyy).In spite of smaller angle between y-axis and polarization vector ofm-NA molecule, the p-NA crystal possesses the largest peak since

Fig. 10. Linear optical response compared to nonlinear one in m-NA crystal (the leftvertical solid line indicate the border of band gap).

M. Dadsetani, A.R. Omidi / Journal of Physics and Chemistry of Solids 85 (2015) 117–131 127

its molecule has linear structure and hence the stronger polar-ization. Additionally, Fig. 5 shows that the Nitro-group (benzene-ring) of p-NA (m-NA) plays an important role in the dominantpeaks of spectra.

The second structure (above 10 eV) of ii2ε ω( ) in m-NA (p-NA)

crystal is a wide peak around 18 eV (17 eV) with admixture ofsmaller peaks which located around 11, 15, 16, 17, and 18 eV (15and 17 eV).

It is worthwhile to mention that, due to the higher polarizability ofp-NA molecules, the average value of ε(0)/ε(1) in p-NA crystal islarger than that of m-NA (around 4.17 for p-NA but 3.30 for m-NA).Here ε(0) is the static dielectric constant, and ε(1) is the so called“static high frequency” dielectric constant. So, the ionic behavior inp-NA crystal is more observable compared to m-NA one.

The refractive index spectra of investigated compounds arerepresented in Fig. 7. Although, this figure shows an almost biaxialrather than uniaxial behavior for m-NA and p-NA crystals, but bothof them represent close values for nxx and nyy in the below-bandgap region. For example, the values of nxx(0), nyy(0) and nzz(0) inm-NA crystal are 1.70, 1.73 and 1.63, and these values in p-NAcrystal are 1.83, 1.87 and 2.04, respectively. So, in the below bandgap spectra, m-NA (p-NA) behaves like a negative (positive) uni-axial crystal. Fig. 7 also shows that p-NA crystal behaves as anisotropic crystal at energy values around 2.7 eV (all refractive in-dex components have similar values). In addition, p-NA has thelargest values of refractive index at energies around 2.4 eV.Moreover, this figure shows that both p-NA and m-NA crystalshave sufficient anisotropy in the non-absorbing region of spectrawhich is important for phase matching. Finally, one can see the

close similarity between dispersion of refractive indices with thoseof real parts of dielectric function ( ii

1ε ω( )). We also notice that therefractive index spectra of m-NA has more oscillation compared top-NA, and such a behavior can be seen in the real part of dielectricfunction, too. As shown in Table 3, there is a very good agreementbetween our results for linear susceptibilities and refractive in-dices of m-NA crystal with experimental data and other computedresults. As can be seen in this table, our results for the linearsusceptibilities are larger than experimental results by about0.1 which is a reasonable difference. Such differences betweentheoretical and experimental results can be improved by choosingproper values for the scissor correction and broadening factors. Inthe case of p-NA crystal, we could not find valid experimental datafor comparison to calculated results in this study.

3.2. Nonlinear optical response

Due to the non-centrosymmetric structure of m-NA crystal,here we have presented the nonlinear optical spectra for thiscrystal only. The mathematical relations of nonlinear suscept-ibilities are more complicated than their linear counterparts, andnonlinear susceptibility tensors are much more sensitive to slightchanges in the band structure dispersions. So, regarding numericalmethods, the k-space integration must be performed more care-fully and more conduction bands must be taken into account toreach a reasonable accuracy. In addition, the nonlinear suscept-ibilities are very sensitive to the band gap due to the 2ω and ωresonances which appear in imaginary and real parts of χ(2).Physical interpretation of nonlinear results is very hard, since bothvalence to valence and conduction to condition inter- and intra-band transitions are active in nonlinear procedure.

At the beginning of this section, we have represented the ab-solute values of nonlinear susceptibilities in Fig. 8. Following thisfigure, one can see that all xzx

2χ( ), xxz2χ( ) and zxx

2χ( ) components have amain peak in the violet–ultraviolet region (around 3 eV), but thelargest peak of this figure is attributed to zxx

2χ( ) and is located around

5.5 eV. In addition, yyz2χ( ) has a considerable peak in the near ultra-

violet region but the main peaks of other components are confinedto visible region. The green emission of m-NA crystal for wave-lengths around 1064 nm, have confirmed the SHG in m-NA crystal[19,88]. Our results shows that zzz

2χ( ) has the largest values for wa-velengths around 1064 nm.

The origin of spectral peaks can be evaluated by consideringvarious contributions to the nonlinear process. We have shown theimaginary parts of 2ω/ω inter- and intra-band contributions of thedominant components (Im xzx

2χ( ), Im xxz2χ( )and Im zxx

2χ( )) in Fig. 9. Unlike thelinear spectra, the sign of imaginary parts of nonlinear spectra canbe both positive and negative. A number of results can be deducedfrom this figure, such as; (i) the 2ω-contributions start con-tributing at energy values above 1/2Eg but the ω-resonances forenergy values above Eg (Eg is the fundamental band-gap), (ii) 2ω-contributions are more important than ω-resonances. For examplethe main peaks come from 2ω-inter-band contributions. (iii)Generally, intra- and inter-band contributions act in opposite di-rections and weaken each other. For example, they representsymmetric patterns at higher energies and cancel each other.(iv) As a result of this figure and mathematical relations the2ω-resonces are invariant under permutation of the last two in-dices, but these contributions are very sensitive to the permuta-tion of the first two indices. For example 2ω-resonances of xxz

2χ( ) and

xzx2χ( ) have similar behaviors. Hence, xzx

2χ( ) and xxz2χ( ) have similar be-

low-band gap peaks at same positions, but xzx2χ( ) and zxx

2χ( ) do not.Following this rule, one can say that the positions of below-bandgap peaks in yzy

2χ( ) are similar to those of yyz2χ( ) .

Fig. 11. Calculated imaginary and real parts of xxε , yyε and zzε within the framework of RPA and TDDFT for m-NA and p-NA crystals.

M. Dadsetani, A.R. Omidi / Journal of Physics and Chemistry of Solids 85 (2015) 117–131128

The values of all components at zero-frequency limit are listedin Table 4. Here, the sums of inter- and intra-band contributionsare not equal to the total values, and this inequality can be at-tributed to the modulation term. However, the effect of the intra-band motion is revealed to be as important as that of the inter-band transition at zero frequencies. As can be seen in this table,the 2ω-contributions of xxz (yyz) component is as same as that ofxzx (yzy).

Unlike the linear spectra, the features in the nonlinear spectraare very difficult to identify from the band structure because of thepresence of 2ω and ω resonances. Generally, whenever the inter-band peaks appear, the intra-band peaks also appear (but usuallyhave opposite directions and weaken each other). Since themagnitude of inter-band transitions are realizable from ε2(ω)spectra, one could expect that the structures in Im ijk

2χ ( )(and ijk2χ ( ) )

could be realized from the features of ε2(ω). So, it would be usefulto compare absolute values of nonlinear susceptibilities ( xxz

2χ( ) , xzx2χ( )

and zxx2χ( ) ) with the imaginary parts of dielectric function, as a

function of both ω and 2ω (Fig. 10). This figure shows the sig-nificant similarity between linear and nonlinear spectra. For ex-ample at below-band gap spectra (part A), both linear and non-linear structures have distinguished peaks around 1.8, 2.4. 2.9 and

3.2 eV, and both of them have similar peaks at energy values aboveband gap (part B) around 3.8, 4.3, 4.7, 5.5, 6.0 and 6.4 eV. In ad-dition, either of them have another small peaks around 7.3, 7.8,8.8 and 9.4 eV in part C. The clear similarity between linear andnonlinear structures at part A shows that the below-band gapnonlinear structures originate from 2ω-resonances. Also, it can beseen that the nonlinear structures at energy values above 7 eVcomes from 2ω-resonances but those structures which situatedbetween 6 and 7 eV, mainly originate from ω-resonances. Finally,one can see that when we move from linear response to nonlinearone, the low-energy peaks are enhanced and shifted to lowerenergies, but the high-energy peaks are weakened. The bandstructure of m-NA has small dispersion around the band gap (theyarranged as a set of parallel lines around the band gap), and hencethere is a good potential for two photon absorption at any k-pointof IBZ. While, at higher energies, the dispersion of conductionband increases yielding bad conditions for two photon absorption.

Although, the general behavior of ijk2χ ( ) spectra can be re-

cognized from the combination of ε2(ω) and ε2(2ω), but the exactprediction is impossible, since as well as valence to conductiontransitions both valence to valence and conduction to conductiontransitions take part in the nonlinear process.

At the end of this section, we can estimate the values of first

Fig. 12. The average molecular polarizability in comparison with crystalline linearsusceptibility for p-NA.

M. Dadsetani, A.R. Omidi / Journal of Physics and Chemistry of Solids 85 (2015) 117–131 129

order hyperpolarizability (tensor βijk) of m-NA molecules by usingthe expression (βijk¼χijk//Nf3) given in Refs. [89,91]. Here, N is thenumber of molecules/cm3 and f is the local field factor which itsvalue is varying between 1.3 and 2.0. For example, the value of βzxxis found to be equal to 0.5�10�30 esu and 8.4�10�30 esu at thestatic limit and at λE400 nm, respectively. Although the calcu-lated results fall within the range of calculated values by

Fig. 13. The RPA and TDDFT results for the ener

Krishnakumar [90], but due to the clear differences between Car-tesian-framework of crystal with that of molecule, there is not aclose agreement between our results with those of Ref. [90]. Inaddition there are many intermolecular effects in the bulk-phasewhich are ignored for molecular calculations.

At the end of this section it is worthwhile to mention that,although p-NA is a centrosymmetric crystal but it has higher linearresponse and hence higher potential of photon-absorption. Inaddition to sufficient anisotropy, this study shows that it istransparent in the infrared and visible regions and hence has agood potential for third harmonic generation. The fact that p-NAcrystal has higher values of linear response, compared to m-NA, isa sign of higher polarisability and hyperpolarizability in p-NAmolecule. So, p-NA molecules and p-NA nanostructures (withoutcentrosymmetric design) can be suitable candidates for SHG.

3.3. TDDFT calculations and excitonic effects

Since solving the Bethe–Salpeter equation (BSE) is numericallyvery expensive, one can observe the excitonic effects in a simplerway by using time dependent calculations with proper exchange-correlation kernels. Recent studies show that TDDFT kernels (suchas Bootstrap kernel) which have a long range 1/q2 contribution inthe long-wavelength limit are able to capture the exciton forma-tion in solids [65,71], with low computational cost.

Here we have used the bootstrap kernel [67] (within the fra-mework of time dependent DFT) to investigated the excitonic ef-fects in m-NA and p-NA crystals. Both RPA and TDDFT calculationsfor the imaginary and real parts of dielectric function of in-vestigated crystals are represented in Fig. 11. We see a powersignature of excitonic effects in bulk m-NA and p-NA by comparingour TDDFT results with those of RPA. It is clear that, despite theextremely good overall agreement between RPA and TDDFT re-sults, the bootstrap procedure tends to enhance the low-energystructures. In addition, there is a slight red-shift in going from RPAto TDDFT calculations. We also notice that the enhancement andred-shift phenomena in m-NA crystal are clearer and more

gy loss spectra of m-NA and p-NA crystals.

M. Dadsetani, A.R. Omidi / Journal of Physics and Chemistry of Solids 85 (2015) 117–131130

interesting compared to p-NA crystal.Due to the small intermolecular interactions in organic crystals,

the large susceptibilities of these crystals can be traced to theelectronic properties of the constituent molecules [88]. Two sim-ple formulas for the relation between microscopic and macro-scopic susceptibilities are: χijkENf3βijk and χijENfαij, where N isthe density of unit cell and f is the local field factor, χij and χijk arethe linear and second-order susceptibilities of crystal, αij and βijk

are the polarizability and first hyperpolarizability of molecule[89,92]. So, one can expect clear similarities between the mole-cular polarizability spectra with that of crystalline susceptibility.The relationship between the molecular and the crystal suscept-ibilities has been reported for various crystal classes [93]. Recently,Takimoto et al. have performed molecular TDDFT calculations todetermine the dynamical polarizability of p-NA molecule [94]. Inorder to check the reliability of our calculations, we have re-presented the calculated Takimoto's results for the molecular po-larizability and our TDDFT results for the crystalline susceptibilityin Fig. 12. As shown, there is a good overall similarity betweenpolarizability and linear susceptibility spectra, but due to the in-termolecular interactions in bulk-phase, the linear susceptibilitybehaves as a spectral broadening of polarizability with a lightshifting to lower energies. As a result of this figure, it is clear thatthe band gap of bulk-phase is smaller than its gas-phase coun-terpart. It addition, due to the dispersion characteristic of energyeigenvalues in bulk-phase, the crystal spectra has a smootherform, especially at higher energies. Moreover, this figure showsthat the intermolecular interactions can change the molecular ei-genvalues and hence the optical spectra. For example, the mole-cular spectra has sharp peaks around 8, 9, 10, 18, 22 and 34 eV,which are absent in the crystalline spectra.

At the last part of this section, we have shown the energy lossspectra for m-NA and p-NA crystals in Fig. 13. The energy lossfunction, L(ω)¼(‐1/ε)¼ Im[�1/ε] is an important factor describingthe energy loss of a fast electron traversing in a material. The low-energy peaks can be attributed to the inter-band transitions be-tween valence and conduction bands, while the main high-energypeaks at around 27 eV (28 eV) are correspond to the collectiveplasmon excitations in p-NA (m-NA) crystal. The plasmon peakscorrespond to the abrupt reduction of ε2(ω) and to the zerocrossing of ε1(ω). As can be seen in this figure, the RPA structuresof the energy loss spectra are very close to the TDDFT one, but dueto the excitonic effects, the low-energy peaks are enhanced inTDDFT calculations. It should be noted that the plasmon peaks inm-NA crystal have similar values, while Lyy in p-NA crystal hashigher intensity compared to other components. Unfortunately,the lack of experimental spectra for energy loss prevents anyconclusive comparison with experiment.

At the end of this paper, it is worthwhile to mention that DFTtheory has its limitations [95,96]. As discussed by Cohen et al. [95]the weaknesses of DFT can be traced back to two main errors ofstandard density-functionals: the delocalization error and thestatic correlation error. In the DFT theory, the electron density (orelectron cloud) is artificially spread-out due to an incorrect be-havior of the standard functionals. This problem has its root in thefact that when using DFT even if you have only one electron, thedensity of that electron (a non-local object) interacts with theelectron itself (a local object). Such errors reflected in the under-estimation of the barriers of chemical reactions, the band gaps ofmaterials, the energies of dissociating molecular ions, and chargetransfer excitation energies. Density-functional approximationsalso overestimate the binding energies of charge transfer com-plexes and the response to an electric field in molecules and ma-terials. Despite these limitations, DFT is widely and successfullyapplied in simulations throughout engineering and sciences.

4. Conclusions

We have studied the electronic structure as well as the linearand nonlinear optical properties of m-NA and p-NA crystals usingthe FP-LAPW method within the framework of DFT and TDDFT.Our calculations based on mBJ approximation give rise to the in-direct band gap for both crystals, but the larger one for m-NA. Thelow dispersion of band structure (due to the weak intermolecularinteractions) with the clear band splitting results in a number ofdistinguished sharp peaks in the low-energy spectra (especially inm-NA crystal). We have shown that both crystals have high valuesof linear response, as a characteristic behavior of organic crystals.

This study has shown that the m-NA crystal has considerablepotential as a second-harmonic generator. In addition to highnonlinear susceptibilities, it has high dielectric constants as well assufficient anisotropy which make it a suitable candidate for non-linear purposes. Although the p-NA crystal has centrosymmetricstructure, it shows higher dielectric constants and much betteranisotropy in the non-absorbing region. In addition, it has a low-dispersion band structure which enhances the resonance condi-tions and makes it a suitable crystal for the higher-order nonlinearresponse. The fact that p-NA crystal has higher values of linearresponse, compared to m-NA, is a sign of higher polarisability inp-NA molecule. So, p-NA molecules and p-NA nanostructures canbe suitable candidates for SHG.

The TDDFT calculations show that the excitonic effects have avery dramatic influence on the optical properties of investigatedsemiconductors, particularly near the band edge. Furthermore,both DFT and TDDFT calculations for the energy loss spectra yieldplasmon peaks around 27 and 28 eV for p-NA and m-NA crystals,respectively. Due to the extremely small wavelengths of Plasmonpeaks, the investigated crystals can be useful in Plasmon-basedelectronic, computer chips and high-resolution lithography andmicroscopy. The important role of Nitro- and Amino-group in theband structure and low-energy optical response of investigatedcrystals shows that the substituted groups can be considered asimportant factors for designing new optical crystals. It should benoted that our results are in good agreement with other experi-mental and theoretical results.

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