13
A DFT Study of Linear and Nonlinear Optical Properties of 2Methyl-4-nitroaniline and 2Amino-4-nitroaniline Crystals M. Dadsetani* and A. R. Omidi Physics Department, Lorestan University, Khorramabad, Iran ABSTRACT: The electronic structure and linear and nonlinear optical susceptibilities of 2-methyl-4-nitroaniline (MNA) and 2-amino-4-nitroaniline (ANA) crystals have been studied using the full potential linear augmented plane wave method within density functional theory. In addition, we have investigated the excitonic eects by means of the bootstrap exchange-correlation kernel within time dependent density functional theory. Our calculations show indirect band gaps for MNA and ANA crystals. Both crystals have band structures with low dispersion which is a characteristic behavior of organic crystals. The crystalline ANA shows larger band dispersion, compared to MNA, due to the higher intermolecular interactions. Findings show that the substituent groups play major roles in enhancing the optical response of pushpull organic crystals. On the other hand, the intermolecular interactions make the band dispersion increase and the optical response, especially the nonlinear one, decrease. The MNA crystal shows larger values of nonlinear response, since all the constitutive molecules are mainly polarized along the same axis and there is less overlap between them. Moreover, the considerable below-band-gap anisotropy as well as the high values of nonlinear susceptibilities make these crystals suitable candidates for nonlinear purposes. In addition to the high potential of excitonic eects, both crystals have extremely small wavelengths of plasmon peaks. Finally, this study gives reliable results for the optical spectra in both linear and nonlinear regimes. 1. INTRODUCTION Since the invention of the laser in 1960, there have been signi- cant developments in the eld of nonlinear optical materials. Nonlinear optical (NLO) materials, dened as materials in which light waves can interact with each other, are key materials for the fast processing of information and optical storage applications. The important development in nonlinear optical materials occurred in 1970, when Davydov et al. reported a strong second harmonic generation (SHG) in organic materials which have electron donoracceptor groups. 1 During the last decades, extensive studies have been devoted to achieving a better understanding of factors that may lead to acentric crystals with large NLO responses. The results of these studies show that a good electron donoracceptor group can change the NLO response, considerably. Therefore, a wide range of organic materials which have electron donoracceptor groups have been synthesized particularly for second-order nonlinear optics. One of the most common donoracceptor molecules is para-nitroaniline (p-NA), since much interest in NLO proper- ties of substituted benzene derivatives stems from the basic studies on the chemistry and physics of the p-NA molecule. The p-NA molecule consists of a benzene ring in which an electron donor amino (NH 2 ) group is substituted in a para- position to an electron acceptor nitro (NO 2 ) group. These opposite ends of the conjugated system lead to maximum acentricity and large intramolecular charge transfer interactions. In spite of having an appreciable hyperpolarizability, p-NA crys- tallizes in the centrosymmetric space group, which restricts the observation of any macroscopic second-order optical eects. This drawback has led to the search for other molecular mate- rials. Several closely related derivatives of p-NA, with non- centrosymmetric crystallization, have been found. Replacing a meta-hydrogen with a methyl group (amino group) gives 2-methyl-4-nitroaniline (2-amino-4-nitroaniline) crystal (Figure 1). Such chemical substitutions give the maximum eccentricity to the molecules and provide crystals with noncentrosymmetric structure which have large values of nonlinear response. Contrary to 2-amino-4-nitroaniline (for brevity, we name it ANA), the 2-methyl-4-nitroaniline (MNA) crystal has attracted Received: June 6, 2015 Published: June 15, 2015 Article pubs.acs.org/JPCC © 2015 American Chemical Society 16263 DOI: 10.1021/acs.jpcc.5b05408 J. Phys. Chem. C 2015, 119, 1626316275

A DFT Study of Linear and Nonlinear Optical Properties ...A DFT Study of Linear and Nonlinear Optical Properties of 2‑Methyl-4-nitroaniline and 2‑Amino-4-nitroaniline Crystals

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Page 1: A DFT Study of Linear and Nonlinear Optical Properties ...A DFT Study of Linear and Nonlinear Optical Properties of 2‑Methyl-4-nitroaniline and 2‑Amino-4-nitroaniline Crystals

A DFT Study of Linear and Nonlinear Optical Propertiesof 2‑Methyl-4-nitroaniline and 2‑Amino-4-nitroaniline CrystalsM. Dadsetani* and A. R. Omidi

Physics Department, Lorestan University, Khorramabad, Iran

ABSTRACT: The electronic structure and linear and nonlinear optical susceptibilities of 2-methyl-4-nitroaniline (MNA) and2-amino-4-nitroaniline (ANA) crystals have been studied using the full potential linear augmented plane wave method withindensity functional theory. In addition, we have investigated the excitonic effects by means of the bootstrap exchange-correlationkernel within time dependent density functional theory. Our calculations show indirect band gaps for MNA and ANA crystals.Both crystals have band structures with low dispersion which is a characteristic behavior of organic crystals. The crystalline ANAshows larger band dispersion, compared to MNA, due to the higher intermolecular interactions. Findings show that thesubstituent groups play major roles in enhancing the optical response of push−pull organic crystals. On the other hand, theintermolecular interactions make the band dispersion increase and the optical response, especially the nonlinear one, decrease.The MNA crystal shows larger values of nonlinear response, since all the constitutive molecules are mainly polarized along thesame axis and there is less overlap between them. Moreover, the considerable below-band-gap anisotropy as well as the highvalues of nonlinear susceptibilities make these crystals suitable candidates for nonlinear purposes. In addition to the highpotential of excitonic effects, both crystals have extremely small wavelengths of plasmon peaks. Finally, this study gives reliableresults for the optical spectra in both linear and nonlinear regimes.

1. INTRODUCTION

Since the invention of the laser in 1960, there have been signi-ficant developments in the field of nonlinear optical materials.Nonlinear optical (NLO) materials, defined as materials inwhich light waves can interact with each other, are key materialsfor the fast processing of information and optical storageapplications. The important development in nonlinear opticalmaterials occurred in 1970, when Davydov et al. reported astrong second harmonic generation (SHG) in organic materialswhich have electron donor−acceptor groups.1 During the lastdecades, extensive studies have been devoted to achieving abetter understanding of factors that may lead to acentriccrystals with large NLO responses. The results of these studiesshow that a good electron donor−acceptor group can changethe NLO response, considerably. Therefore, a wide range oforganic materials which have electron donor−acceptor groupshave been synthesized particularly for second-order nonlinearoptics. One of the most common donor−acceptor molecules ispara-nitroaniline (p-NA), since much interest in NLO proper-ties of substituted benzene derivatives stems from the basicstudies on the chemistry and physics of the p-NA molecule.

The p-NA molecule consists of a benzene ring in which anelectron donor amino (NH2) group is substituted in a para-position to an electron acceptor nitro (NO2) group. Theseopposite ends of the conjugated system lead to maximumacentricity and large intramolecular charge transfer interactions.In spite of having an appreciable hyperpolarizability, p-NA crys-tallizes in the centrosymmetric space group, which restricts theobservation of any macroscopic second-order optical effects.This drawback has led to the search for other molecular mate-rials. Several closely related derivatives of p-NA, with non-centrosymmetric crystallization, have been found. Replacinga meta-hydrogen with a methyl group (amino group) gives2-methyl-4-nitroaniline (2-amino-4-nitroaniline) crystal (Figure 1).Such chemical substitutions give the maximum eccentricity tothe molecules and provide crystals with noncentrosymmetricstructure which have large values of nonlinear response.Contrary to 2-amino-4-nitroaniline (for brevity, we name it

ANA), the 2-methyl-4-nitroaniline (MNA) crystal has attracted

Received: June 6, 2015Published: June 15, 2015

Article

pubs.acs.org/JPCC

© 2015 American Chemical Society 16263 DOI: 10.1021/acs.jpcc.5b05408J. Phys. Chem. C 2015, 119, 16263−16275

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much attention in different studies. The linear and nonlinearoptical properties of MNA have already been the topic ofseveral experimental2−6 and theoretical7−12 studies. The FT-IRspectra of crystalline MNA deposited on a poly substrate werestudied by Vallee and co-workers.13,14 Nogueira et al.15 reportedthe longitudinal optical (LO) and transversal optical (TO)wavenumbers of polar vibrations found in the unpolarized FT-IRreflectivity spectra of MNA crystals. Intra- and intermolecularelectronic transitions were calculated for MNA molecular clustersby Guillaume et al.16 Okwieka et al. have measured the polarizedFT-IR, Raman, neutron scattering, and UV−visible spectra ofMNA crystal plates, powder, and solutions.17 There are a fewstudies on optical spectra of ANA. In one of them, Kolev et al.studied the properties of 2-amino-4-nitroaniline by means of UVand linear polarized IR spectroscopy.18

It is worth mentioning that theoretical simulations for non-linear optics are often used to understand relationships at themolecular level, and fewer investigations have tackled the pre-diction and interpretation of the NLO response at the macro-scopic level. Early studies only considered the bulk susceptibili-ties which were calculated from a straightforward tensor sumover the microscopic (molecular) properties.19,20 Improvedapproaches incorporate the local field effects, either by usingLorentz-like expressions or by evaluating these within electro-static interaction schemes.21−25 A more comprehensive approachis the full treatment of periodic crystals by means of bandstructure theory, although a few studies have used the ab initiofull band-structure model to calculate the linear and nonlinearoptical responses of crystals. During the past few years, a numberof studies have been published on the linear and nonlinearoptical properties of molecular crystals within band structuretheory.26−30 To the best of our knowledge, this is the first abinitio full band-structure study that reports the electronic struc-ture and optical properties of MNA and ANA crystals. Thus, weexpect it to be useful for future investigations.It should be noted that even predicting the linear optical

properties for molecular crystals is quite challenging, due to theinterplay between different strengths of bonding types in mole-cular crystals (i.e., the strong intramolecular covalent bonds vsmuch weaker intermolecular van der Waals and possibly hydro-gen bonds). Hence, this study is important and interestingenough to deserve attention.In the present study, we adopted density functional theory

(DFT)31,32 to determine the electronic structure and opticalsusceptibilities of MNA and ANA crystals using the state-of-the-art full potential linear augmented plane wave method.

Currently, the FP-LAPW method provides the most reliableresults within density functional theory.For the first time, this study tries to investigate the excitonic

effects of MNA and ANA crystals using time dependent densityfunctional theory (TDDFT).33,34 We have used the Bootstrapapproximation which is known to give optical spectra in excel-lent agreement with experiments,56 and is computationally lessexpensive than solving the Bethe−Salpeter equation. Thedifferences between TDDFT and RPA results show clearsignatures of excitonic effects.35−37

Since the nonlinear susceptibilities are very sensitive to theenergy gap, we have performed mBJ38 calculations which canefficiently improve the band gap and give better band splitting.Studies have shown that the mBJ potential is generally asaccurate in predicting the energy gaps of many semiconductorsas the much more expensive GW method.39

In the present study, we have selected two organic molecules,with similar chemical formula but different crystal structures, toobserve the effect of molecular arrangement on optical spectra.Findings show that the linear response is basically molecule-dependent but the nonlinear response is crystal-dependent,since it is very sensitive to the band structure and inter-molecular interactions. Contrary to other works, this studyclearly shows that the intermolecular interactions can changethe band dispersion and nonlinear optical response, consid-erably. According to the results of our study, the higher linearresponses do not necessarily lead to higher nonlinear responses.In the case of organic crystals, the present work is one of thefew studies which provides an excellent opportunity to comparetheoretical and experimental optical spectra in both linear andnonlinear regimes. The results of TDDFT calculations showthat the excitonic effects can be very dramatic, particularly nearthe band edge. However, this study provides new importantinformation for the electronic structure, band structure, energyloss, and linear and nonlinear optical spectra of investigatedcompounds. We hope that our work will lead to comprehensiveexperimental studies of these compounds which have promisinglinear and nonlinear optical susceptibilities.The next section presents the basic theoretical aspects and

computational details of our study. The calculated electronicstructure and the optical response are presented in section 3.The last section is devoted to the summary and principleconclusions.

2. COMPUTATIONAL DETAILSA. Calculation Parameters. Our calculations were

performed using the highly accurate all-electron full potentiallinearized augmented plane wave (FP-LAPW) method basedon DFT as implemented in the ELK code.40 This is an imple-mentation of the DFT with different possible approximationsfor the exchange correlation (XC) potentials. We have used thegeneralized gradient approximation (GGA) of Perdew−Burke−Ernzerhoft41 and the modified Becke−Johnson exchangepotential (mBJ)38,39 for the exchange-correlation potentials.The mBJ exchange potential is available through an interface tothe Libxc library.42 Basis functions are expanded in combina-tions of spherical harmonic functions inside nonoverlappingspheres at the atomic sites (muffin-tin spheres) and in planewaves in the interstitial regions. The muffin-tin radii for oxygen(O), nitrogen (N), hydrogen (H), and carbon (C) were takento be 1.16, 1.16, 0.6, and 1.20 au, respectively. The interstitialplane wave vector cutoff Kmax is chosen such that RmtKmax equals3.5 for all of the calculations. The convergence parameter RmtKmax,

Figure 1. Molecular structures (a, b) and different views of 2-methyl-4-nitroaniline and 2-amino-4-nitroaniline crystals (c, d).

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where Kmax is the plane wave cutoff and Rmt is the smallest of allatomic sphere radii, controls the size of the basis. The valencewave functions inside the spheres are expanded up to lmax = 10,while the charge density was Fourier expanded up to Gmax = 14.Convergence tests have shown that 64 k-points in the irreduciblewedge of the Brillouin zone are sufficient, as more k-points giveno appreciable change in the energy or properties. However, wehave used a dense mesh of 512 k-points for the opticalcalculations. Self-consistency was achieved by an iterative processwith energy convergence up to 0.0001 eV in less than 60iterations. The band structures have been computed on a discretek-mesh along high-symmetry directions. We have used 1000k-points for the band structure and DOS plot.We have used the FHI-aims code43 for relaxing the atomic

positions and structural parameters. FHI-aims uses numericatom-centered orbitals as the quantum-mechanical basis set

φ θ φ=ru r

rY( )

( )( , )i

ilm (1)

where Ylm(θ, φ) are spherical harmonics and the radial ui(r)parts are numerically tabulated. Hence, the bases are veryflexible and any kind of desired shape can be achieved. Thisenables accurate all-electron full-potential calculations at a com-putational cost which is competitive with plane wave methods.FHI-aims is an efficient computer program package44−50 to cal-culate physical and chemical properties of condensed matterand other cases, such as molecules, clusters, solids, and liquids. Itshould be noted that the primary production method is densityfunctional theory and the package is also a flexible framework foradvanced approaches to calculate ground-state and excited-stateproperties. However, we have relaxed the structures (includingvan der Waals corrections) in a way that every component of theforces acting on the atoms was less than 10−4 eV/Å.B. Mathematical Framework of Optical Response. The

linear optical properties of matter can be described by means ofthe transverse dielectric function ε(ω). There are two contribu-tions to ε(ω), namely, intraband and interband transitions. Weignored the intraband contribution, since it is important onlyfor metals. The components of the dielectric function werecalculated using the traditional expression in the random phaseapproximation (RPA)35−37

∑ ∑ε ω δ πω ε ω ε η

ω ε η

= + −Ω + +

+*

− +

⎡⎣⎢⎢

⎛⎝⎜⎜

⎞⎠⎟⎟⎤⎦⎥⎥

i iW

p k p k

i

p k p k

i

( )4 1 ( ) ( )

( )

( ( ) ( ))

( )

ij ij

kk

cv vc

vci

cvj

vc

vci

cvj

vc (2)

where the term in the brackets is optical conductivity (atomicunits are used in the above formula). The sum covers allpossible transitions from the occupied to unoccupied states.The term pcv

j denotes the momentum matrix element transitionfrom the energy level c of the conduction band to the level v ofthe valence band at certain k-points in the Brillouin Zone (BZ).ℏω is the energy of the incident photon, and εvc ≡ εv − εc is thedifference between the valence and conduction eigenvalues.Wk is the weight of k-points over the Brillouin zone, and Ω isthe unit cell volume.Time-dependent density functional theory (TDDFT),51

which extends density functional theory into the time domain,is another method which is able, in principle, to determineneutral excitations of a system. The TDDFT method can

handle large systems and is, basically, exact. Hence, this studytries to cover both the RPA- and TDDFT-based linear opticalresponses. The key quantity of TDDFT is the exchange-correlationkernel f xc, which, together with the Kohn−Sham (KS) single-particle density-response function χs, determines the interacting-particles density-response function χ, as follows:51

χ ω χ ω π δ ω= −| + |

−′−

′−

′ ′q qG q

f q( , ) ( ) ( , )4

( , )GG GG GG GG1 s 1

2xc

(3)

While χs is constructed using the single-particle statesobtained with a given approximation to the static exchange-correlation potential Vxc(r),

32 f xc is a true many-body quantity,basically, containing all the dynamic exchange-correlationeffects in a real interacting system. Although formally exact,the predictions of TDDFT are only as good as the approxi-mation of the exchange-correlation kernel. A great amount ofeffort has been invested into the development of approx-imations to f xc of semiconductors and insulators.52−61 In thisstudy, we have used the Bootstrap approximation for f xc

56

which has a wide applicability and is computationally lessexpensive than solving the Bethe−Salpeter equation. The exactrelationship between the dielectric function and the kernel f xcfor a periodic solid can be written as

ε ω δ χ ω

δ χ ω

ω χ ω

= +

= +

− +

′−

′ ′ ′

′ ′ ′

′ ′ ′−

q v q q

q v q

v q f q q

( , ) ( ) ( , )

( , ) ( ){(1

[ ( ) ( , )] ( , )}

GG GG GG GG

GG GG GG

GG GG GG

1

s

xc s 1(4)

Here v(q) is the bare Coulomb potential. All of these quantitiesare matrices on the basis of reciprocal lattice vectors G. TheBootstrap exchange-correlation is approximated by

ωε ωε ω

ε ωχ ω

= −== −

===

− −f q

q v qq

qq

( , )( , 0) ( )( , 0) 1

( , 0)( , 0)xc

boot1

000

1

000

(5)

where ε0(q,ω) = 1 − v(q)χ(q,ω) denotes the dielectric functionin the RPA. The superscript 00 indicates that only the G = G′ =0 component is used in the denominator. This coupled set ofequations is solved by first setting f xc

boot = 0 and then solvingeq 4 to obtain ε−1. This is then “bootstrapped” in eq 5 to find anew f xc

boot, and the procedure is repeated until self-consistencybetween the two equations at ω = 0 is achieved.In addition to the linear response, this study tries to cover the

nonlinear response of investigated crystals. The mathematicalrelations for calculating the second order susceptibilities as wellas their inter- and intraband contributions have been developedby Sipe and Ghahramani62 and Aversa and Sipe.63 Generally,the complex second-order nonlinear optical susceptibility tensorscan be written as64−70

χ ω ω ω

ω ω ω ω ω ω

ω ω ω ω

− −

−−

× −

− −

⎧⎨⎩

⎡⎣⎢⎢

⎤⎦⎥⎥⎫⎬⎭

Wr r r

r r r r r r

( 2 ; , )

1 2 { }( )( 2 )

1( )

{ }( )

{ }( )

ijk

nmlkk

nmi

mlj

lnk

ln ml mn mn

lmk

mni

nlj

nl mn

nlj

lmk

mni

lm mn

inter

(6)

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∑ ∑

χ ω ω ω

ωω ω

ω

ωω ω ω

ω ωω ω ω

=Ω −

− −Δ

+ −−

⎧⎨⎩

⎫⎬⎭

W r r r

r r r ir r

r r r

( 2 ; , )

1( )

[ { }

{ }] 8{ }

( 2 )

2{ }( )

( 2 )

ijk

kk

nml

mn

mnln nl

jlmk

mni

ml lmk

mni

nlj

nm

nmi

mnj

nmk

mn mn

nml

nmi

mlj

lnk

ml ln

mn mn

intra

2

2

2(7)

∑ ∑

χ ω ω ω

ω ω ωω

ωω ω ω

=Ω −

− − Δ−

⎧⎨⎩

⎫⎬⎭

W r r r

r r r ir r

( 2 ; , )

12

1( )

[ { }

{ }]{ }( )

ijk

kk

nml mn mnnl lm

imnj

nlk

lm nli

lmj

mnk

nm

nmi

nmj

mnk

mn mn

mod

2

2(8)

From these formulas (atomic units are used in these relations),we can notice that there are three major contributions toχijk(2)(−2ω, ω, ω): the interband transitions χijk

inter(−2ω, ω, ω), theintraband transitions χijk

intra(−2ω, ω, ω), and the modulation ofinterband terms by intraband terms χijk

mod(−2ω, ω, ω), where n ≠m ≠ l and i, j, and k correspond to Cartesian indices.Here, n denotes the valence states, m denotes the conduction

states, and l denotes all states (l ≠ m, n). Two kinds of transi-tions take place: one of them is vcc′ which involves one valenceband (v) and two conduction bands (c and c′), and the secondtransition is vv′c which involves two valence bands (v and v′)and one conduction band (c). The symbols Δnm

i (k) and {rnmi (k)

rmlj (k)} are defined as follows

Δ = − k v k v k( ) ( ) ( )nmi

nni

mmi

(9)

= + r k r k r k r k r k r k{ ( ) ( )}12

( ( ) ( ) ( ) ( ))nmi

mlj

nmi

mlj

nmj

mli

(10)

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

vnmi (k) = iωnm(k)rnm

i (k)). The position matrix elements betweenband states n and m, rnm

i (k), are calculated from the momentummatrix element p nmi using the relation71 rnm

i (k) = (pnmi (k)/

imωnm(k)), where the energy differences between the states nand m are given by ℏωnm = ℏ(ωn − ωm) andWk is the weight ofk-points.As mentioned before, both ANA and MNA are non-

centrosymmetric crystals. ANA has six second order nonlinearsusceptibilities, xyz, xzy, yxz, yzx, zxy, and zyx, while MNA has14 components, xxx, xxz, xyy, xzx, xzz, yxy, yyx, yyz, yzy, zxx,zxz, zyy, zzx, and zzz. Our calculations show that χzyx

(2) and χxyz(2)

are the dominant components of ANA but χzzz(2) is the dominant

one in MNA.

3. RESULTS AND DISCUSSIONA. Crystal Structure and Electronic and Linear Optical

Properties. The molecular and crystalline structures of2-methyl-4-nitroaniline (MNA) and 2-amino-4-nitroaniline(ANA) are represented in Figure 1. Studies have shown that2-methyl-4-nitroaniline crystallizes in the monoclinic system,space group Ia, with four molecules in the unit cell.72 Thecrystallographic a and b axes are parallel to the optical x and yaxes, respectively, but the c-axis deviates from the z-axis by

about 4°. On the other hand, 2-amino-4-nitroaniline crystallizesin the chiral noncentrosymmetric orthorhombic, space groupP212121, again with four molecules in the unit cell. Here a, b,and c are selected to be along the optical x, y, and z axes,respectively.18 The X-ray crystallographic data were optimizedby minimizing the forces acting on the atoms. The optimizedlattice parameters for crystalline MNA (a = 7.40 Å, b = 11.70 Å,c = 8.17 Å, α = γ = 90°, and β = 94.05°) and ANA (a = 3.67 Å,b = 10.24 Å, c = 17.12 Å, and α = β = γ = 90°) are found to bein good agreement with the X-ray crystallographic data. As canbe seen in Figure 1, the dipole molecules tend to be along thez-axis. Hence, in both crystals, εzz exhibits the maximum valuesof the dielectric function. On the other hand, the molecularplanes are principally perpendicular to the x-axis which makesεxx the smallest, since there is very little electronic response outof the molecular plane. As we go along the y-axis, the polari-zation of ANA molecules changes alternately which gives rise tohigher intermolecular attractions. In addition, the small inter-molecular distance, especially in ANA, provides strong interac-tion between π-electrons. Altogether, these conditions showthat the crystalline ANA tends to have higher intermolecularinteractions and greater band dispersion.In Tables 1 and 2, we have presented the respective geo-

metrical parameters such as bond length and bond angle ofoptimized structure. These tables show that the calculatedC−H bonds are slightly longer than their experimental coun-terparts. Due to the electron withdrawing effects of the nitro-group, those C−C bonds which are along the long molecularaxis (i.e., C2−C3 and C5−C6) are shorter than other C−Cbonds. In addition, the C−C bonds which are near the amino-group (C1−C2 and C1−C6) are longer than those which arenear the nitro-group (C3−C4 and C4−C5). Such differencesshow that the benzene ring (as a molecular bridge) plays amajor role in electron delocalization. Due to the near dipolarstructure, those bond lengths which are located in the meta-position (C2−N7 in ANA and C2−C7 in MNA) are longerthan those located in the para-position (C1−N11). The opti-mization procedure (including van der Waals corrections)makes the ANA molecule be nonplanar, although the para-amino group tends to be planar, due to the high intermolecularinteractions. Except for substitute positions, all the optimizedbond angles agree well with the experimental values. Forexample, the bond angles of the meta-amino group (C2−N7−H17, C2−N7−H17, and H18−N7−H17 in ANA) and thebond angle of the methyl-group (C2−C7−H17 in MNA) havemore deviation compared to other angles. In addition, theelectron donating and electron withdrawing characteristics ofsubstituent groups distort the symmetry of the benzene ring,yielding ring angles smaller and larger than 120° at the substi-tute positions.In what follows, the electronic band structure and total and

partial densities of electron states are presented. Figure 2 showsthe calculated electronic band structure and the correspondingtotal DOS of investigated crystals. As can be seen, the mBJapproximation pushes the valence bands to lower energies andthe conduction bands to higher energies, yielding improvedresults for the band gap. As a result of low intermolecularinteractions, both the GGA and mBJ approximations give bandstructures with low dispersions. Moreover, when we go fromGGA to mBJ, an empty region with no energy bands appears inthe range 4−6 eV. Despite close similarity, ANA shows moreband dispersion (due to the higher intermolecular interactions).It should be noted that mBJ gives a better band gap and better

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band splitting. Thus, we will report our results using mBJ only.The mBJ-based calculations show that MNA (ANA) possessesa fundamental indirect band gap by about 2.63 eV (1.83 eV) inthe ΓC−ZV (XC−ΓV) direction, while the smallest direct band-to-band transition is in the ΓC−ΓV (ΓC−ΓV) direction by about2.67 eV (2.14 eV). The transmittance spectra of MNA crystalwere measured by Levine et al.2 According to the results of thatstudy, the onset of transmittance appears at around λ ∼ 450 nm= 2.76 eV which is very close to the band gap calculated in thepresent study. As can be seen, due to the higher overlap betweenπ-orbitals along the x-axis, the band dispersion along Γ−Z andΓ−Y is much smaller than the band dispersion along Γ−X. TheANA crystal shows more band dispersion, since there is smallerdistance and hence higher intermolecular overlapping. In orderto understand the role that van der Waals interaction plays incrystal structures, two optimization calculations have been per-formed: (i) with van der Waals correction and (ii) without vander Waals correction. Findings show that this factor is veryimportant for optimization, since, when we ignore the van derWaals correction, the relaxed structure shows larger intermo-lecular distance, higher band gap, and lower band dispersion,. Forexample, the GGA approximation gives the band gap value of1.23 (1.72) eV for ANA with (without) van der Waals correc-tion. In sum, van der Waals interactions can change the banddispersion and hence the optical response (particularly, thenonlinear one) considerably.In order to show the role that different groups play, we have

reported the partial density of states for functional groups,

separately. As can be seen in Figure 3, the total DOS mainlycomes from the p-states of the benzene ring and nitro group.The nitro and amino groups have important roles in thebottom of conduction bands and top of valence bands, respec-tively. It is worth mentioning that, compared to its counterpart(the meta-amino group of ANA), the methyl group has anegligible contribution to the top valence bands and thebottom of conduction bands. On the other hand, in comparisonto the para-amino of ANA, the amino group of MNA has morecontributions to the top valence bands. In addition, this figureindirectly gives a clear illustration for the electron withdrawingand electron donating effects. As can be seen, the acceptorgroup (such as the nitro group) has a higher density of states atconduction bands, since it can absorb the excited electrons,while the methyl and amino groups, which have a negligibledensity of states at conduction bands, tend to be donors. Theelectron delocalization in the benzene ring is well pictured inthis figure, since the benzene ring itself injects the electronsinto the conduction bands and absorbs the exited electronssimultaneously. As a result of this figure, the benzene ring andthe substituent groups play major roles in producing the mainpeaks of optical spectra, since these peaks mainly come fromthe low-energy transitions between the higher valence bandsand the lower conduction bands. In what follows, the imaginaryand real parts of the dielectric function and the different com-ponents of refractive indices are represented. Assuming thatthey give a small contribution to the dielectric functions, weignored the indirect interband transitions involving scattering of

Table 1. Optimized Values of MNA Crystal by FHI-aims Code

bond angle optimized values (deg) experimentala data (deg) bond length optimized values (Å) experimentala data (Å)

C2−C1−C6 118.395 119.440 C1−C2 1.4148 1.3913C1−C6−C5 122.422 121.138 C2−C3 1.3782 1.3811C6−C5−C4 118.954 118.841 C3−C4 1.3910 1.3986C5−C4−C3 119.398 121.267 C4−C5 1.3660 1.3873C4−C3−C2 122.606 120.162 C5−C6 1.3699 1.3776C3−C2−C1 118.203 119.145 C6−C1 1.4074 1.4043H12−N11−H13 115.835 119.995 H10−C6 1.0584 0.9302H13−N11−C1 118.060 119.996 H9−C5 1.0749 0.9303N11−C1−C6 120.963 119.498 H8−C3 1.0564 0.9299C1−C6−H10 117.722 119.437 C7−C2 1.4822 1.5046H10−C6−C5 119.856 119.424 C1−N11 1.3462 1.3583C6−C5−H9 122.798 120.568 N11−H13 0.9910 0.8596H9−C5−C4 118.247 120.591 N11−H12 1.0149 0.8599C5−C4−N14 118.996 119.387 C4−N14 1.4160 1.4332C4−N14−O15 120.269 118.524 N14−O15 1.2426 1.2307O15−N14−O16 120.304 121.800 N14−O16 1.2216 1.2326O16−N14−C4 119.423 119.672 C7−H19 1.0660 0.9596N14−C4−C3 121.606 119.344 C7−H18 1.0050 0.9604C4−C3−H8 118.214 119.873 C7−H17 1.0992 0.9604H8−C3−C2 119.179 119.966C3−C2−C7 122.503 121.419C7−C2−C1 119.284 119.438C2−C1−N11 120.626 121.052C1−N11−H12 123.821 120.010H19−C7−H17 108.932 109.493H19−C7−H18 107.985 109.454H18−C7−H17 106.362 109.477H19−C7−C2 108.909 109.487H18−C7−C2 112.318 109.470H17−C7−C2 112.195 119.477

aReference 72.

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phonons.26−30 Recent studies have shown that, although withoutphonon contributions, DFT calculations can generate exper-imental results very well.73 The calculated imaginary and realparts of principle components of dielectric functions arepresented in Figure 4. There is a high degree of similaritybetween the linear optical spectra of MNA and ANA crystals.Three spectral structures (A, B, and C) in the imaginary partsof the dielectric function can be seen. The dominant peaks are

located in part A, and there is large anisotropy here. As men-tioned before, the high intensity of ε2

zz(ω) can be attributed tothe fact that the molecular polarizations of MNA and ANAmolecules are mainly along the z-axis, which results in thestrong light−matter interaction. It should be noted that theANA crystal shows higher values of the dielectric function,since its long molecular axis is closer to the z-axis. On the otherhand, the molecular planes are mainly perpendicular to the

Table 2. Optimized Values of ANA Crystal by FHI-aims Code

bond angle optimized values (deg) experimentala data (deg) bond length optimized values (Å) experimentala data (Å)

C2−C1−C6 119.068 119.461 C1−C2 1.4373 1.4277C1−C6−C5 121.324 120.831 C2−C3 1.3835 1.3785C6−C5−C4 118.955 118.789 C3−C4 1.4059 1.3965C5−C4−C3 121.129 121.821 C4−C5 1.4044 1.3870C4−C3−C2 120.545 119.979 C5−C6 1.3764 1.3829C3−C2−C1 118.973 119.107 C6−C1 1.4202 1.4052H12−N11−H13 116.046 119.945 H10−C6 1.0914 0.9301H13−N11−C1 120.552 120.050 H9−C5 1.0863 0.9307N11−C1−C6 119.990 120.169 H8−C3 1.0869 0.9301C1−C6−H10 118.638 119.562 N7−C2 1.4110 1.4219H10−C6−C5 120.073 119.607 C1−N11 1.3508 1.3670C6−C5−H9 121.315 120.599 N11−H13 1.0263 0.8603H9−C5−C4 119.726 120.611 N11−H12 1.0218 0.8601C5−C4−N14 119.551 119.165 C4−N14 1.4179 1.4411C4−N14−O15 119.543 118.837 N14−O15 1.2654 1.2460O15−N14−O16 121.405 121.890 N14−O16 1.2576 1.2377O16−N14−C4 119.042 119.267 N7−H18 1.0249 0.8600N14−C4−C3 119.290 118.994 N7−H17 1.0231 0.8595C4−C3−H8 119.627 120.004H8−C3−C2 119.779 120.017C3−C2−N7 120.751 121.120N7−C2−C1 120.227 119.736C2−C1−N11 120.938 120.369C1−N11−H12 122.898 120.006H18−N7−H17 109.024 120.048H18−N7−C2 110.383 119.982H17−N7−C2 113.970 119.709

aReference 18.

Figure 2. Calculated band structure and total DOS of MNA and ANA crystals using m-BJ and GGA approximations.

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x-axis, which makes ε2xx(ω) smallest. The values of peaks in

parts B and C are much smaller than the main peak of part A,although there are more small peaks in part B. The weakness ofstructures at parts B and C, compared to A, can be attributed tothe fact that ε2(ω) scales as 1/ω

2. The crystalline ANA has twopeaks at part A; the major peak comes from the transitionsbetween the flat part (T−Y−Γ−Z) of the top valence bandto the low conduction band. Due to the small dispersion ofband structure as well as the small volume of the unit cell, thecorresponding peak is very sharp. On the other hand, the minorpeak can be attributed to the transitions from the other flat part(S−X−U−R) of the top valence band to the lowest conductionbands. As shown in Figure 1, the electric field produced by the

surrounding molecules, which seems as opposite rows ofdipoles in the y−z plane, enhances the molecular polarizabilityand hence the linear optical response of ANA crystal. On theother hand, the molecular packing along the x-axis increases theband dispersion and gives smaller values of nonlinear response.Furthermore, both crystals show large values of ε(0)/ε(∞),whose deviation from one is a sign of the polarity of materials,but it is a little higher in ANA.The variations of refractive indices of investigated com-

pounds are represented in Figure 5. According to this figure, wecan see considerable anisotropy again, particularly in thenonabsorbing region. It should be noted that this anisotropy isnecessary for phase-matching conditions. The MNA crystal hasbeen shown to be phase-matchable for SHG at λ ∼ 1064 nm2.Figure 5 shows a biaxial, rather than uniaxial, behavior in bothcrystals. For example, our calculations for crystalline MNA(ANA) give the static values of 1.55, 1.83, and 2.18 (1.52, 1.85,and 2.55) for nxx(0), nyy(0), and nzz(0), respectively. We alsohave represented the experimental spectra of refractive indices.In the case of MNA,6 the numerical data agree well with theexperimental results. As can be seen, both theoretical and ex-perimental results show similar patterns for the dispersion ofrefractive indices. In addition to the noticeable differences(nxx < nyy < nzz), both works agree that nzz (nxx) has a higher(lower) rate of growth compared to other components. Itshould be noted that the scissor correction can give a muchbetter agreement between calculated results and experimentaldata. In the case of crystalline ANA, we could not find validexperimental data for a conclusive comparison. However, accordingto this figure, both MNA and ANA crystals have sufficient aniso-tropy in the IR-VIS region, which makes them promising crystalsfor SHG.

Figure 3. Calculated density of states for the functional groups of MNA and ANA molecules.

Figure 4. Calculated imaginary and real parts of the principlecomponents of dielectric function for MNA and ANA crystals withinthe mBJ approximation.

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B. Nonlinear Optical Response. The mathematicalrelations of nonlinear susceptibilities are more complicatedthan their linear counterparts, and they are much more sensitiveto slight changes of band dispersion. Regarding numerical methods,the k-space integration must be performed more carefully andmore conduction bands must be taken into account to reach areasonable accuracy. In addition, the nonlinear susceptibilitiesare very sensitive to the band gap value, due to the 2ω and ωresonances which appear in the imaginary and real parts of χ(2).Physical interpretation of nonlinear results is very difficult, since,in addition to valence−valence and conduction−conductiontransitions, both inter- and intraband transitions can participatein the nonlinear procedure.As mentioned before, the MNA and ANA crystals have

14 and 6 elements of nonlinear susceptibilities, respectively.

The absolute values of nonlinear susceptibilities, as well as theimaginary and real parts of the dominant components, arerepresented in Figure 6. The crystalline MNA shows muchhigher values of nonlinear response compared to ANA. Forexample, the dominant components of ANA (χzyx

(2) and χzxy(2))

have smaller values compared to the dominant component ofMNA (χzzz

(2)), since all the MNA molecules are mainly polarizedalong the z-axis and there is less overlap between them. Inaddition, the crystalline ANA shows larger band dispersionwhich makes the nonlinear response smaller. In the case ofMNA, the upper valence bands and the lower conduction bandsbehave as parallel lines giving enhanced two-photon absorption.The fact that the molecular packing along the x-axis gives riseto the smaller values of first hyperpolarizability and the non-linear susceptibility has been approved by other studies.12,16

Figure 5. Theoretical and experimental results for the refractive indices of MNA and ANA crystals.

Figure 6. Absolute values of χijk(2) in units of (pm/V) for MNA and ANA crystals (left). Calculated imaginary and real parts of the dominant nonlinear

susceptibilities (right).

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In the same way, our study shows that the molecular packingalong the x-axis increases the band dispersion and hencereduces the nonlinear response, especially in ANA crystal.According to the results of our study, the crystals in questionhave sufficient anisotropy and high values of nonlinear responsewhich make them promising candidates for SHG in the IR-VISregion. In addition to our results, the experimental results2 haveshown that the MNA crystal is transparent at both of thefundamental wavelengths in the infrared region (λ = 1064 nm)and the second harmonic wavelengths in the visible region (λ =532 nm).It should be noted that different studies2,3,5,9,10 have used

different directions for MNA molecule, but all of them agreethat d33 = (1/2)χzzz (when the long molecular axis tends to bealong the z-axis) is the dominant component. As pointed outby Levin et al.,2 d33 is phase matchable using the usual indexbirefringence and has the enormous figure of merit of 2000times larger than LiNbO3. In Figure 7, we have plotted the

theoretical and experimental5 dispersion of |χzzz(2)| for crystalline

MNA. As can be seen, the results herein corroborate well withthe experimental results. For example, both of them show large(small) values of nonlinear response at lower (higher) wave-lengths. Although our results give rise to a steeper curve, scissorshift correction can reduce the rate of growth and give betteragreement. While the scissor correction gives only a blue shiftto the linear response, it can change the nonlinear spectra, con-siderably. As shown in other studies,28,29 the nonlinear responseis highly sensitive to the scissor correction, since valence−valence−conduction and valence−conduction−conductiontransitions are both active in the nonlinear regime. Unlike thelinear spectra, the features in the nonlinear spectra are verydifficult to identify from the band structure, because of thepresence of 2ω and ω resonances. Generally, whenever theinterband peaks appear, the intraband peaks appear simulta-neously. Since the magnitude of interband transitions isrealizable from ε2(ω), one could expect the nonlinear structuresto be realized from the features of ε2(ω). Hence, we find ituseful to compare absolute values of nonlinear susceptibilitieswith the imaginary parts of the dielectric function, as a functionof both ω and 2ω (Figure 8). This figure shows significantsimilarities between linear and nonlinear spectra. The coloredarrows indicate the agreement between nonlinear and linearpeak positions (as a function of both ω and 2ω). For example,at below-band-gap spectra, both linear and nonlinear structureshave a main peak (the black arrows), although ANA hasanother small peak just below the band gap (green arrow).

In addition, this figure shows that the below-band-gapnonlinear structures originate from the 2ω resonances, whilethe nonlinear small peak which is located just above the bandgap (the brown arrow) mainly comes from the ω resonances. Itcan be seen that the nonlinear structures at energy values above8 eV come from the 2ω resonances but those structures locatedin the range 5−6.5 eV mainly originate from the ω resonances.In the case of ANA, this figure shows that both ω and 2ωresonances contribute to the nonlinear optical small peaksaround 3 eV. Finally, this figure shows that, when we movefrom the linear regime to the nonlinear one, the low-energypeaks are enhanced and shifted to lower energies but the high-energy peaks tend to be small. As mentioned before, the mole-cular crystals possess a band structure with small dispersions,particularly around the band gap, which enhances the two-photon absorption at lower energies. On the other hand,increase in band dispersion at higher energies makes the two-photon absorption diminish. Another reason for this reductioncould be explained by the fact that χ2(ω) scales as 1/ω

2. As aresult of valence−valence and conduction−conduction tran-sitions, it is almost impossible to predict the exact behavior ofnonlinear response, although the general behavior can berecognized from the combination of ε2(ω) and ε2(2ω).Finally, we can estimate the values of first order hyper-

polarizabilities (tensor βijk) of MNA and ANA molecules byusing the expression (βijk = χijk/Nf

3) given in refs 74 and 75.Here, N is the number of molecules/cm3 and f is the local fieldfactor with a value varying between 1.3 and 2.0. The calculatedvalues for βzzz of MNA and βzxy of ANA (at λ ≈ 1064 nm) arefound to be 42 × 10−30 (esu) and 35 × 10−30 (esu), respec-tively. This is very interesting to notice that the calculated valuefor βzzz (of MNA) is the same as the experimental resultmeasured by Levine et al.2

C. TDDFT Calculations and Excitonic Effects. Recentstudies show that TDDFT kernels (such as Bootstrap kernel)which have a long-range 1/q2 contribution in the long-wavelengthlimit are able to capture the exciton formation in solids,54,60 withlow computational cost.We have used the bootstrap kernel56 (within the framework

of time dependent DFT) to investigate the excitonic effects inMNA and ANA crystals. Both RPA and TDDFT calculationsfor the imaginary and real parts of the dielectric function ofinvestigated crystals are represented in Figure 9. We see astrong indication of excitonic effects in bulk MNA and ANA bycomparing our TDDFT results with those of RPA. It is clearthat, despite the extremely good overall agreement between

Figure 7. Theoretical and experimental dispersion of d33 = (1/2)χzzz(2) in

units of (pm/V) for MNA crystal.

Figure 8. Linear optical response in comparison with the nonlinearone for MNA and ANA crystals (the vertical dashed line indicates theborder of the band gap).

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RPA and TDDFT results, the bootstrap procedure tends toenhance the low-energy structures. In addition, there is a slightred-shift in going from RPA to TDDFT calculations. Althoughthe excitonic effects have minor roles at higher energies, theygive considerable high-energy deviations (energy valuesbetween 10 and 18 eV) only along the x-axis.At the end part of this section, we have shown the electron

energy loss spectra for MNA and ANA crystals in Figure 10.The energy loss function, L(ω) = Im[−1/ε], is an importantfactor which illustrates the energy loss of a fast electrontraversing in a material. Generally, the energy loss spectra showtwo main structures. The low-energy peaks (under 10 eV) canbe attributed to the interband transitions between valence andconduction bands. Hence, there is a clear correspondencebetween the loss peak positions with those of Im εii, but theloss peaks have slight blue-shifts. It is important to note that,when an interband transition gives rise to a feature in Im εii atthe frequency ωk, it gives rise to a peak in the loss function,occurring at a larger frequency, where ωk

2 = ωk2 + ( f k

2ωp2/γ).76

The second main structure of the loss spectra is a wide peakaround 27 eV (28 eV) which corresponds to the collectiveplasmon excitations in MNA (ANA) crystal. The plasmonpeaks correspond to the abrupt reduction of ε2(ω) and to thezero crossing of ε1(ω). As can be seen in this figure, the RPA

structures are very close to those of TDDFT, but the excitoniceffects make the low-energy peaks enhance. In both crystals, Lxxhas a lower intensity of the plasmon peak, since the x-axis ismainly perpendicular to the molecular planes. We also note thatdifferent components of MNA tend to have different values of

Figure 9. Calculated imaginary and real parts of εxx, εyy, and εzz within the framework of RPA and TDDFT for MNA and ANA crystals.

Figure 10. RPA and TDDFT results for the energy loss spectra ofMNA and ANA crystals.

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plasmon intensity (Lxx < Lzz < Lyy), while ANA shows closevalues for Lzz and Lyy.To sum up, we have used a full ab initio treatment for

handling the nonlinear response of periodic crystals within theframework of band structure theory. This study gives reliabledispersions for linear and nonlinear optical spectra in bothabsorbing and nonabsorbing regions. In addition, since theexperimental measurement of nonlinear susceptibilities isexpensive and somewhat cumbersome, such studies providean extremely useful guide for research on nonlinear organiccrystals. In spite of the structural similarity between ANA andMNA molecules, the intermolecular interactions can modify thecrystalline band structure and optical response, considerably.Hence, the intermolecular interactions should be considered asimportant factors in the nonlinear response of organic crystals.According to the results of this study, the higher values of linearresponse do not necessarily lead to higher values of nonlinearresponse, since the crystalline ANA shows higher dielectricresponse, larger band dispersion, and lower nonlinear response.This study shows that the linear response is mainly part-dependent,but the nonlinear response is basically bulk-dependent, since it isvery sensitive to the molecular arrangement and intermolecularinteractions. This study provides new valuable information aboutthe optical properties of investigated solids which are a major topic,both in basic research and for industrial applications. This workshows that both MNA and ANA crystals have sufficient anisotropyin the nonabsorbing region which is important for phase matching.According to our study, the investigated crystals are transparentat both the fundamental wavelengths in the infrared region andsecond harmonic wavelengths in the visible region. Thus, bothMNA and ANA crystals can be considered as proper candidates forSHG in the IR-VIS region. Moreover, our calculations show thatvan der Waals interactions play major roles in the band structureand optical response of organic crystals. Finally, a satisfactorycoincidence of both the theoretical prediction and the experimentalresults was achieved. This confirms the capability of our computersimulation.

4. CONCLUSIONS

We have studied the electronic structure as well as the linearand nonlinear optical properties of MNA and ANA crystalswithin the framework of DFT and TDDFT. The full potentialcalculations show that the MNA (ANA) crystal possesses anindirect energy gap of 2.63 eV (1.83 eV). The dielectricfunction shows the largest values, when the applied electric fieldtends to be along the molecular axis. The substituent groups,especially the nitro group, play major roles in the band struc-ture and hence in the optical spectra. Among the substitutedgroups, the methyl group has a minor contribution to the mainpeaks of optical response. In spite of the structural similaritybetween ANA and MNA molecules, this study shows that inter-molecular interactions can modify the crystalline band structureand nonlinear optical response, considerably. We have shownthat the higher values of linear response do not necessarilylead to higher values of nonlinear response. For example, thecrystalline ANA has higher dielectric response and larger banddispersion but lower values of nonlinear response. The MNAcrystal shows high values of nonlinear response, since all themolecules are mainly polarized along the same direction, andthere is small overlap between them. In addition to the highvalues of nonlinear susceptibilities, the investigated crystalshave high dielectric constants as well as sufficient anisotropy

which make them suitable candidates for SHG in the IR-VISregion.The TDDFT calculations show that the excitonic effects have

a very dramatic influence on the optical properties of investi-gated semiconductors, particularly near the band edge. Further-more, both DFT and TDDFT calculations for the energy lossspectra yield a plasmon peak around 27 (28) eV for MNA (ANA)crystal. Due to the extremely small wavelengths of plasmon peaks,the crystals in question can be useful in plasmon-based electronic,computer chips and high-resolution lithography and microscopy.This study reproduces the experimental results very well; inaddition to the molecular hyperpolarizability, our calculations givereliable results for both the linear and nonlinear spectra.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected]. Phone/fax: +98-66-33120192.NotesThe authors declare no competing financial interest.

■ REFERENCES(1) Davydov, B. L.; Derkacheva, L.D.; Dunina, V. V.; Zhabotinski, M.K.; Zolin, V. K.; Kreneva, L. G.; Samokhina, M. A. ConnectionBetween Charge Transfer and Laser Second Harmonic Generation.JEPT Lett. 1970, 12 (16), 9−12.(2) Levine, B. F.; Bethea, C. G.; Thurmond, C. D.; Lynch, R. T.;Bernstein, J. L. An Organic Crystal with an Exceptionally Large OpticalSecond Harmonic Coefficient: 2-Methyl-4-nitroaniline. J. Appl. Phys.1979, 50, 2523−2527.(3) Lipscomb, G. F.; Garito, A. F.; Narang, R. S. Large LinearElectro-Optic Effect in a Polar Organic Crystal 2-methyl-4-nitroaniline.Appl. Phys. A 1981, 38, 663−665.(4) Morita, R.; Kondo, T.; Kaneda, Y.; Sugihashi, A.; Ogasawara, N.;Umegaki, S.; Ito, R. Mutiple-Reflection Effects in Optical Second-Harmonic Generation. Jpn. J. Appl. Phys. 1988, 27, L1134−1136.(5) Morita, R.; Kondo, T.; Kaneda, Y.; Sugihashi, A.; Ogasawara, N.;Umegaki, S.; Ito, R. Dispersion of Second-Order Nonlinear OptricalCoefficient d11 of 2-Methyl-4-Nitroaniline (MNA). Jpn. J. Appl. Phys.1988, 27, L1131−1133.(6) Grossman, C. H.; Garito, A. F. Brewster Angle Method forRefractive Index Measurements of Biaxial Organic Systems. Mol. Cryst.Liq. Cryst. 1989, 168, 255−267.(7) Jayatilaka, D.; Munshi, P.; Turner, M. J.; Howard, J. A. K.;Spackman, M. A. Refractive Indices for Molecular Crystals from theResponse of X-ray Constrained Hartree-Fock Wavefunctions. Phys.Chem. Chem. Phys. 2009, 11, 7209−7218.(8) Kanoun, M. B.; Botek, E.; Champagne, B. Electrostatic Modelingof the Linear Optical Susceptibilities of 2-methyl-4-nitroaniline, m-nitroaniline, 3-methyl-4-nitropyridine N-oxide and 2-Carboxylic Acid-4-nitropyridine-1-oxide Crystals. Chem. Phys. Lett. 2010, 487, 256−262.(9) Kanoun, M. B.; Champagne, B. Calculating the Second-OrderNonlinear Optical Susceptibilities of 3-methyl-4-nitropyridine N-oxide,2-carboxylic acid-4-nitropyridine-1-oxide, 2-methyl-4-nitroaniline, andm-nitroaniline Crystals. Int. J. Quantum Chem. 2011, 111, 880−890.(10) Seidler, T.; Stadnicka, K.; Champagne, B. Investigation of Linearand Nonlinear Optical Properties of Molecular Crystals Within theLocal Field Theory. J. Chem. Phys. 2013, 139, 114105.(11) Howard, S. T.; Hursthouse, M. B.; Lehmann, C. W.; Mallinson,P. R.; Frampton, C. S. Experimental and Theoretical Study of theCharge-density in 2-methyl-4-nitroaniline. J. Chem. Phys. 1992, 97,5616−5630.(12) Castet, F. Champagne, B. Semiempirical AM1Model Inves-tigation of 3-methyl-4-nitroaniline Crystal. J. Phys. Chem. A 2001, 105,1366−1370.(13) Vallee, R.; Damman, P.; Dosiere, M.; Toussaere, E.; Zyss, J.Nonlinear Optical Properties and Crystalline Orientation of 2-methyl-

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