Vol. 4, No. 6/June 1987/J. Opt. Soc. Am. B 977

Quadratic nonlinear properties of N-(4-nitrophenyl)-L-prolinol and of a newly engineered molecular compound

N-(4-nitrophenyl)-N-methylaminoacetonitrile:a comparative study

M. Barzoukas, D. Josse, P. Fremaux, and J. Zyss

Centre National d'Etudes des T6l6communications, 196 Avenue H. Ravera, 92220 Bagneux, France

J. F. Nicoud

ESPC I Laboratoire de Chimie et Electrochimie des Mat6riaux Moliculaires (UA CNRS No. 429), 10 rue

Vauquelin, 75231 Paris cedex 05, France

J. 0. Morley

Organics Division, Research Department, Imperial Chemical Industries, Blackley, Manchester, UK

Received December 10, 1986; accepted March 5, 1987

A new molecular engineering strategy is proposed that favors the packing of charge-transfer conjugated molecules to

enhance their crystalline quadratic nonlinear efficiency. A highly polar substituent is grafted to an achiralmolecule at a position remote from the donor-acceptor -r-electron conjugated system. Dipolar interaction forceswill act mainly toward the antiparallel coupling of local dipoles, while the remaining nonlinear portion of themolecule is freed, under other influences, to set up a noncentrosymmetric and possibly optimal structure. Amongother 4-nitroanilinelike compounds, N-(4-nitrophenyl)-N-methylaminoacetonitrile (NPAN) exemplifies this newapproach and is shown to have a powder second-harmonic generation efficiency of the same order as that of N-(4-ni-

trophenyl)-L-prolinol (NPP), i.e., more than. 2orders of magnitude above that of urea. The nonlinearity of bothmolecules (vector part of the fi tensor projected along the dipole moment) has been measured by use of electric-field-

induced second-harmonic (EFISH) generation in solution at 1.06 /m. The nonlinearity of the NPAN molecule is

roughly half that of NPP, but the transparency range of NPAN is significantly increased toward the UV comparedwith that of NPP. Two theoretical models, based, respectively, on a finite-field perturbation of the Hartree-Fockequations and on a sum-over-states expansion of tensor A3, both at a semiempirical level of approximation, are used

to compute the coefficients of the first-order hyperpolarizability of NPP and NPAN. A two-level quantum model isused to account for frequency dispersion, and theoretical crystalline coefficients are obtained from an oriented-gasdescription of the crystal. Theoretical molecular polarizabilities are in satisfactory agreement with the EFISHexperimental results. The experimental crystalline nonlinearity of NPP is also well accounted for by calculations,while the optimized nonlinear coefficient dzyY of crystalline NPAN is predicted to be of the order of 140 X 10-9 esu,

coming close to that of NPP.

1. INTRODUCTION

During the past decade, the nonlinear-optical properties oforganic molecules and molecular crystals have been investi-gated extensively.1-7 This interest is stimulated by a num-ber of potential applications,8,9 such as second-harmonicgeneration (SHG), frequency mixing, electro-optic modula-tion, and optical parametric emission, amplification, andoscillation.

Some organic molecules display hyperpolarizabilitiesmany times larger than those of most inorganics within the0.5-2-tum transparency domain. However, centrosymmetryor a misorientation of the molecule in the crystalline latticemay drastically reduce or cancel the second-order crystallinecoefficient.

The optimization of both the quadratic molecular hyper-polarizability a and the macroscopic quadratic susceptibilityd involves two related steps: molecular structure engineer-

ing and crystal structure engineering. A recently intro-duced strategy is exemplified by the discovery of a newmaterial, N-(4-nitrophenyl)-L-prolinol (NPP).1 0 The si-multaneous chiral and hydrogen-bonding character of theprolinol electron-donating group leads to a quasi-optimalangle, in terms of quadratic phase-matched nonlinear inter-actions, between the molecular transition moments and thetwofold axis of the monoclinic P21 crystal structure. A newstrategy is detailed in Subsection 2.A, which points out theimportance of 4-nitroaniline derivatives bearing a highlypolar substituent, such as the cyano group, at a positionindependent of the charge-transfer (CT) polar part. Thisapproach underlies the synthesis of a new material, N-(4-nitrophenyl)-N-methylaminoacetonitrile (NPAN) (Subsec-tion 2.B), which exhibits a powder SHG efficiency of the

same order as that of NPP. The crystalline structure of thematerial is described in Ref. 11 and shows an optimizedcrystalline structure for SHG. The measurement of the

0740-3224/87/060977-10$02.00 © 1987 Optical Society of America

Barzoukas et al.

978 J. Opt. Soc. Am. B/Vol. 4, No. 6/June 1987

cd molecular vector part of the quadratic hyperpolarizabilityA projected along the dipole moment of NPP and NPAN,cu using the electric-field-induced second-harmonic (EFISH)

generation technique, is detailed in Section 3. In Subsec-tion 4.A the microscopic origin of the higher nonlinear effi-

*- ciency of both molecules is investigated theoretically byCd means of quantum-chemistry-based calculations. It is con-U firmed, under nonresonant conditions, that the prolinol

O group is a better donor than the amino group. The theoreti-k cal crystalline coefficients of both compounds are then de-X rived, using an oriented-gas description. Calculation andX comparison with the experimental crystalline nonlinearity

of NPP are presented in Subsection 4.B.

2. MOLECULAR ENGINEERING OF NPAN

A. 4-Nitroaniline Derivative-Bearing Polar Group4-Nitroaniline derivatives (4-NA's) are among the mostwidely investigated organic materials in nonlinear optics.'2Their molecular structure exhibits a classical donor-accep-tor conjugated system, which has been shown for a long timeto lead to highly efficient quadratic nonlinear responseswithin the 0.5-2-,um transparency range. Several strategieshave already been attempted with good success to obtainefficient materials. One of them is chirality: the use of asingle enantiomer will necessarily ensure a noncentrosym-metric crystal structure, though not necessarily an optimalstructure as in the case of the first chiral nitroaniline deriva-tive, methyl-( 2 ,4-dinitrophenyl)-aminopropanoate (MAP). 4

The addition of hydrogen bonding to chirality led us to thediscovery of NPP material,' 0 a chiral derivative of 4-NA'sbearing the (L)-prolinol group as a donor substituent. Themonoclinic P21 crystal structure of NPP shows an angle of58.60 between the molecular CT axis and the helical twofoldcrystal axis close to the optimal 54.7° value for the phase-matchable d2 l coefficient Fig. 1(a).

In spite of the chirality strategy, many optical-nonlinear-active achiral compounds in the 4-nitroaniline family arenow known. 2 -Methyl-4-nitroaniline (MNA) (Ref. 13) wasthe first of them, but many others showing powder test

(a) chiral compounds

N02

MAP: cIN

N H

H-C-COOCH3

CH3

(b) achiral compounds

NH2CH3MNA: 1J

NO2

NO2

NPP:

(2Y CH20H

H3C,~ .,HN .

MNMA: C

N02

HIN CH2 CHCH20H.

APNP: . 2

N02

H CH2 CH2., H3Cs ,CH3'"N 'CH2 ' COOH N

1 1/~~~~NHCOCH3 1NHCOCH3BANP: Yl DAN: N c PAN: INOCNO2 NO2 NO2

Fig. 1. Highly efficient ONL material of the 4-nitroaniline family.

Barzoukas et al.

values of I2 > 50 X 12w (urea) have been described.12 Someof them, 2 -methyl-4-nitro-N-methylaniline (MNMA), N-(4-nitrophenyl)-3-amino-1-propanol (APNP), 3-acetamido-4-dimethylaminonitrobenzene (DAN), and 3-acetamido-4-pyrrolidino-nitrobenzene (PAN), are shown here in Fig.1(b). The discovery of such materials was made possible bythe screening of hundreds of derivatives with the knowledgethat, statistically, a noncentrosymmetric crystal structureoccurs in about 29% of the cases for organic molecules. 14

The crystal structures of some compounds of Fig. 1(b),namely, MNA,13 DAN, and MNMA, are known. For DAN ithas been shown that intermolecular hydrogen bonds areinvolved to ensure an optimized monoclinic P21 crystalstructure.1 2 For MNMA the space group is Pna2i (ortho-rhombic mm2), also with an optimized orientation of themolecular CT axis.'5 It appears that for most of these mate-rials, the molecules bear potentially hydrogen-bonding sub-stituents. Only MNA seems to be an exception; however, itis the sole primary amine in the series.

These results show that compensation of the packingforces induced by the high permanent molecular-dipole mo-ments of 4-NA's (g = 6.9 D for 4-NA) by other intermolecu-lar forces often increases the chance of getting noncentro-symmetric crystal structures with optimized packing. Be-sides the use of hydrogen bonding in the so-called molecularengineering approach exemplified for NPP, we report here anew strategy leading to a new organic material built up from4-NA's and exhibiting a large second-order response togeth-er with good crystal growth potential.

In the present approach, we used achiral molecules with ahighly polar substituent, electronically and sterically inde-pendent of the CT polar part. With such tailor-made mole-cules the crystal packing was meant to be favorably influ-enced by the highly polar part, owing to dipole-dipole inter-actions. It is hoped that this will lead to a higher rate ofnoncentrosymmetric crystal structures and, among them, tosome optimized ones for efficient SHG. To check this strat-egy, the polar cyano group was chosen, owing to its highdipole moment (CN = 3.47 D).'6 Surprisingly, the two firstand simplest molecules so tailored exhibited high SHG effi-ciencies at the powder test stage. They are NPAN (1) andN-( 4 -nitrophenyl)-N-methylamino-propionitrile [NPPN(2)] materials (Table 1). The 5-nitropyridine analogs N-(5-nitro- 2 -pyridyl)-N-methylamino-autonitrile [NPyAN (5)]and N-(5-nitro-2-pyridyl)-N-methylamino-propionitrile[NPyPN (6)], on the other hand, have zero SHG efficiency,owing to their centrosymmetric crystal structure. This fact,although it is not yet understood, is not surprising sincealmost all the efficient 5-nitropyridine derivatives studied sofar for SHG are enantiomerically pure chiral compounds.Only 2 -N-cyclo-octylamino-5-nitropyridine (COANP), thecyclo-octylamine derivative, is an exception.12 Some otherachiral compounds whose chemical structure is close to thatof NPAN, such as N-(4-nitrophenyl)-N-methyl-3-amino-1-propyne (3) (NPAP) and N-(4-nitrophenyl)N-methylamin-oacetamide (4) (NPAA), prepared for comparison, also showno SHG signal at the powder test stage (Table 1). Thisagain shows how a minor change in the chemical structure,-C-CH instead of -C-N, for example, leads to a majorchange in the crystal packing. The polar cyano group playsa key role in the favorable crystal packing of NPAN."

W_s4

Vol. 4, No. 6/June 1987/J. Opt. Soc. Am. B 979

Table 1. Structural Formula and SHG Powder Tests ( = 1.06 Atm) of the New 4-NA DerivativesHaC >P O 2

R Z

SHGMelting Powder Test

R Z Compound Name Point (0C) (X Urea)

-CH2-C-N CH 1 NPAN 114 140

-CH2-CH2-C-N CH 2 NPPN 106 85 :-CH2-CCH CH 3 NPAP 97 0

-CH2-CONH2 CH 4 NPAA 177 0

-CH2-C-N N 5 NPyAN 87 0

-CH2-CH2-CN N 6 NPyPN - 0

t,

B. The NPAN Molecule: Physicochemical PropertiesNPAN and all other 4-NA's described here have been syn-thetized by using aromatic nucleophilic substitution (SNArreaction).'2 The preparation involves the reaction of 1-fluoro-4-nitrobenzene and the appropriate secondary or pri-mary amine in the presence of a base such as K 2CO3 ortriethylamine and using dimethyl sulfoxide as solvent.Nevertheless, in the case of NPAN the yield using this proce-dure is low; the product obtained has a substantial amountof black tar, probably due to the decomposition and poly-merization of the starting N-methylamino-acetonitrile.' 7

Now an improved synthesis of NPAN involving the Mannichreaction on N-methyl-4-nitroaniline, producing a materialwith high purity and good yield, has been worked out, thedetails of which will be published in a forthcoming paper.

Electronic Absorption SpectraLike all N,N disubstituted 4-NA's, NPAN (1) displays anintense CT absorption band in the near UV (Fig. 2). Table 2gives the absorption characteristics of the CT band forNPAN together with those of two other related compounds,NPPN (2) and N,N-dimethyl-4-nitroaniline (7) (DMNA),for comparison. We observe an interesting behavior of thecyano compounds 1 and 2 relative to the parent compound 7.The acceptor properties of the cyano group lead to an in-creased energy gap of the CT band for both compounds, theresulting blue shift of the absorption maximum being morepronounced in NPAN (i.e., e 30 nm), where the cyano groupis closer to the nitroaniline moiety. This blue shift is ofgreat interest since, even with a decrease of molecular hyper-polarizability 3 due to dispersion, it leads to a wider trans-parency range than those of common 4-NA's. For example,Xmax = 390 nm, under the same conditions, for NPP.10

Nuclear Magnetic Resonance SpectraUndoubtedly, the cyano group influences the crystal pack-ing of NPAN, but in order to check for the occurrence ofother packing forces such as hydrogen bonding we carefullystudied the spectra of 'H and "3CNMR. Table 3 shows the'H nuclear magnetic resonance (NMR) chemical shifts 6,relative to tetramethylsilane (TMS), for compounds 1-4.The only appreciable difference is the deshielding of thearomatic NPAN protons H, and H2 in comparison with thesame ones for the three other products. However, these

differences are too small to consider intermolecular hydro-gen bonds. This is further confirmed by studying the crys-tal structure in Ref. 11. Protons H3 and H4 do not showunexpected values. Table 4 deals with some 13C NMRchemical shifts; again the carbon atoms in the ortho positionrelative to the donor amino group exhibit a little deshielding[1 part in 106 (ppm)] with respect to the unsubstituted par-ent compound 7 or 2.

n

NPAN NPP

2 0 250 300 350 400 450 0X(nm)

Fig. 2. Electronic absorption spectra of NPAN and NPP in ETOH.

Table 2. UV Absorption Spectra Data for NPAN,NPPN, and DMNAaY-H 2C/N Q NO2

H3C

Compound NPAN (1) NPPN (2) DMNA (7)Y -CN -CH2-CN -H

Xmax (nm) 358 374 387fmax 18440 19920 20000

a 5 X 10-5 M solutions in ETOH.

Barzoukas et al.

980 J. Opt. Soc. Am. B/Vol. 4, No. 6/June 1987

Table 3. H-NMR Data at 90 MHza(64,) H () H (6,)* ~Y-HC \

N 02H3C

(63) H (a2) H (8,)

Compound NPAN (1) NPPN (2) NPAP (3) NPAA (4)Y -CN -CH2-CN -C-CH -CONH2

6, 8.25 8.15 8.10 8.1062 6.85 6.72 6.7 6.763 3.15 3.20 3.15 3.1564 4.28 3.88 4.15 4.10

a 6 ppm from TMS in CDC13.

Table 4. 13C-NMR data at 20 MHza

R. (as) (±)

H3CIN0(63)

Compound NPAN (1) NPPN (2) DMNA (7)R -CH2-C-N -CH2-CH2-C=N H

61 126.0 126.2 126.462 113.2 110.8 110.763 39.3 39.2 30.3

a a ppm from TMS in CDC13.

3. MEASUREMENTS OF THE SECOND-ORDERPOLARIZABILITIES OF NPAN AND OF NPP

A. Electric-Field-Induced Second-Harmonic Generationin SolutionIn order to measure the molecular quadratic hyperpolariz-ability of NPP and NPAN, we have used the well-knownEFISH experiment'l5 -'

The nonlinear polarization in the solution, at frequency2w, is given by

p2w = FIJKLErE 2.IJKL JwE- (1)

Equation (1) is written in the laboratory frame. If the laserand the static electric field are both parallel to the X axis,the macroscopic susceptibility IJKL tensor reduces to a sin-gle component:

rL= xxxx. (2)It is convenient to introduce a mean microscopic hyperpo.larizability coefficient.'9 For a pure liquid,

rL = NfYXXXX = Nf'y0 (3)N is the number of molecules per unit volume; f is the local-field factor in the Lorentz approximation,

; ( ~~3 3 3 e,, + 2 4

where no, (n2,) is the fundamental (harmonic) refractiveindex, and e (en) is the static (high-frequency) dielectricconstant. e is taken equal to n2e,

For a polar liquid

,y, (5)

Barzoukas et al.

where (x, y, z) is a molecular frame, the z axis is taken alongthe permanent dipole moment of the molecule, and ye is thescalar part of the cubic hyperpolarizability tensor fyijkl:

Ye = '/5[Yxxxx + T yyyy + TYzzzz + /3e(Yxyyx + 'Yxxyy + Yxzzx

+ yzx + z + yyzzy + 2,yxyxy + 2,yyx + 2xzxz

+ 2zxzx + 2yzyz + 2zyzy)]. (6)

The PzI32w/5kT contribution originates from the partialorientation of the permanent dipole moment in the staticfield. i32, is the z component of the vector part of thequadratic hyperpolarizability tensor 0":

o2c = 0/3(3/2w + 02 + 2, + 2 +(7)

In highly conjugated molecules, the electronic term ye maybe considered negligible compared with the orientationalcontribution,

TO A X 0321/5KT.

The molecules of NPP and NPAN were dissolved in acetonefor further testing. Assuming no interaction between themolecules, an additive model can be used2 2:

rmix = f(Nl-y + N2-y'). (9)

N1,2 is the number of molecules per unit volume of 1 (sol-vent), 2 (solute).

It is convenient to introduce the mass ratio x = m2/m1.25Equation (9) then becomes

rmix = (x)f(x)N 7° + X7°2AL - 1 + MI M2} (10)

Ml and M2 are the molecular masses of the solvent and thesolute, and N is Avogadro's number. For small values of x (x' 10-2), we neglect the variations of the density p and of thelocal-field factor with respect to x:

= M2 [r[L(x)- L(o)].xpNf (11)

B. Experimental ResultsWe have used the wedge fringe technique of Maker et al.26The experimental setup is sketched in Fig. 3. The Q-switched Nd:YAG laser operates at 1.064 /tm, the pulse dura-tion is 20 nsec, and the repetition rate is 10 Hz.. The beam ispolarized vertically and focused into the cell. The visiblelight is filtered out with a Shott RG1000 filter. High-volt-age (H.V.) pulses of up to 10-kV amplitude and 2-,"sec dura-tion are applied synchronously to the laser pulses. Theinterelectrode distance is 2 mm. The electric field is essen-tially static and has a large known value inside the liquid.'9 "27It is oriented parallel to the electric laser field. The cell istranslated transversally by using a stepping motor (1 step =0.1 ,um). To filter the output beam, a BG18 filter, an inter-ference filter, and if necessary neutral densities are used.The second-harmonic light is then detected by a photomul-tiplier (P.M.). The signal is averaged, and the amplitude ofthe second-harmonic power is recorded as a function of time.Each measurement is referenced, at the beginning and at theend of each run, to a quartz wedge mounted on the sametranslation stage.

Cd

-4

A

4Q

Cd

,_e

0 .

z

Cd

Uyc;

.P4

O

00

.

(8)

I . - 1. . I �

Vol. 4, No. 6/June 1987/J. Opt. Soc. Am. B 981

DL and Dq are the attenuation coefficients of the second-harmonic intensity. The values of rL and lcL with respect tothe mass ratio x = m2/ml are presented in Figs. 4 and 5.The sign of rL(O) is already known; it is then possible todeduce the sign of y'. Its value is obtained, from experi-mental data, by using a least-mean-squares fit. The resultsare shown in Table 5. Since the dipolar moments of NPAN

1 &dAA samplelrecorder I I

Fig. 3. Experimental setup. The Q-switched Nd:YAG laser isoperating at 1.064 im, the pulse duration is 20 nsec, and the repeti-tion rate 10 Hz. The high-voltage pulses, up to 10-kV amplitudeand 2-psec duration, are applied synchronously to the laser pulses.

The experiment is performed using solutions of increasingconcentration in acetone. In all cases absorption was foundnegligible at w and 2w. Consequently the macroscopic sus-ceptibility is given by1927

30

27.5F

E

,25

(12)

IL and Iq are the mean intensities of the fringes of thesolution and of the quartz wedge, respectively, and

* NPPo NPAN

iI

22.5_

-( 0

(13)

5 10x.103 15 20

Fig. 4. Coherence length of NPP and NPAN in acetone as a func-tion of the mass ratio x. The accuracy is 2%.

Eq, Es, and EL x rL(x) represent the amplitude of the boundwave in the quartz wedge, in the fused silica, and in thesolution, respectively,

Eq = (l, )2 _-( q)2 1(l + nq) 10 (E@),

Es = - _ E 0 ( 2 10-DL/2 (Ew,)2,(n S ' - (n S)'2 + n~

(14)=i

0di

x*(15)

-167r icE 2 2n, 0

~L +nL X \1+ n S n~ + L(16)

ts= 2ns,/(1 + nsx). (17)

For quartz,'18 nq = 1.52413, n = 1.54702, and dq = 1.2 X10-9 esu. For fused silica, n = 1.449e, n = 1.4607, and s= 2.2 X 10-14 esu.

The coherence length of each solution can be deducedfrom the interfringe distance 6 and the angle a of the liquidwedge by

C= 1/2 X 6 X tan , (18)

and tan a is equal to 0.065.The variations of the refractive indices are negligible with

respect to x (x << 1). At 0.532/gm, the indices were measuredusing an Abbe refractometer:

nL= 1.3596, n = n2wL - X = 1.3494.W 1L~~~~~

0 5 10 15 20X i lo,

Fig. 5. DC SHG macroscopic susceptibility rL(X) of NPP andNPAN solutions in acetone. L(x) is given in 10-14 esu. Theaccuracy is 10%.

Table 5. Mean Microscopic Hyperpolarizabilities y2,and z Component of the Vector Part of the QuadraticHyperpolarizability Tensor #,2' along the Permanent

Dipole Momenta

X (Expt.) A (INDO) A7Molecule Solvent (nm) (D) (10-34 esu) (10-30 esu)

NPAN Acetone 360 7.2 7.9 ± 0.8 23 + 5NPP Acetone 397 7.3 15 ± 3 42 + 9

a The fundamental wavelength was X = 1.06 )m. The accuracy on j3! is 20%.

rL(X) = {: [+ I ] ts + TsEs} TLEt

nq; + nqTq 1 +1 + nL

ns + n2,Ll n2s + n2.L

nL + n2,,Lns + n2wL

l

Iu I

Barzoukas et al.

982 J. Opt. Soc. Am. B/Vol. 4, No. 6/June 1987

Table 6. Permanent Dipole Moment in the MolecularFrame xlylzla

Molecule u (INDO) u (CNDOVSB)

NPAN ptxl = -6.63 -8.04guy, = +0.62 +1.82gzl = -2.71 -3.95JIAII = 7.2 9.1

NPAM uxi = -6.75 -py = -0.43 _uz, = -0.43 -II I = 6.8 -

NPP jux1 = -6.92 -8.49my = -1.33 -1.48uz = +1.89 +1.89IlLll = 7.3 8.8

a All dipole moments are expressed in Debye units.

and of NPP have not yet been measured, the value calculat-ed by the INDO program was used (Table 6).

4. CALCULATION OF SECOND-ORDERMOLECULAR POLARIZABILITIES ANDCRYSTALLINE SUSCEPTIBILITIES

All components of the tensor of NPP and NPAN weredetermined by using two computational methods. In thefinite-field model, we have also determined the al coefficientsof a fictitious molecule, labeled NPAM, derived from NPANby substitution of a hydrogen atom for the cyano group inthe same orientation. This fictitious molecule differs in itsgeometrical structure from DMNA (7). The following mo-lecular coordinate system (xjyjzj) is used: the x axis liesalong the CT axis (i.e., nitrogen-nitrogen), and the z axis isorthogonal to the mean plane containing the six aromaticcarbons and the two nitrogen atoms (Fig. 6). The coeffi-cients and the vector components are also given, in theCNDOVSB program, in a rotated coordinate system (xyz),where z is parallel to the total molecular dipole moment.

The molecular hyperpolarizabilities are related to the val-ues of the macroscopic susceptibilities.

A. Calculation of the /3 Tensor

Finite-Field-Perturbed INDO ModelThe finite-field (FF) method, derived from the INDO equa-tions, was developed to calculate the dipole moments ofsingle isolated molecules, interacting with an external staticfield.28-30 Although this semiempirical model involves somedrastic approximations, it takes into account in a self-consis-tent way the electron-electron interactions in the presenceof the perturbing field. This procedure has also the advan-tage of dealing with all valence electrons, even for largemolecules (as many as 35 atoms). The perturbed ground-state dipole moment of the molecule can be developed inincreasing powers of E:

i = s19 + cAgE + /?j*kEjEk + - - - (19)

The coefficients AA, aij, /3jk stand for the permanent dipolemoment and the linear and nonlinear static polarizabilitiesof the molecule, respectively. It follows that the /3 compo-

Barzoukas et al.

nents are directly related to the derivatives, at zero-fieldvalue, of the dipole moment. It is convenient to use sym-metrical FF difference approximations of these derivativesto reach the 03-jk coefficients. This method eliminates thecontribution of the y components:

/30 = 1 jp. (Ex, 0, 0) + px(-E., 0, 0) -2px(0, 0, 0)1,

X.x 2E'2X

(20)

3yy = 2E2 px (0, Ey, 0) + px(0, -Eys, 0) -2px(0, 0, 0),

(21)

Pxxy 8E E 1p(Ex, Ey, 0) + px(-Ex - Ey, 0)8x~y

-Px(-Ex, Ey, 0) - px(Ex, -Eys, 0). (22)

The limited convergence of the dipole moment in the INDOmethod induces an error in /gjk. For instance,

A130 = 1 fApx(Exs, 0, 0) + Apx(-Ex, 0, 0) + 2Apx(O, 0, 0)1.

(23)

The value of the perturbing field must not be too small ortoo large. In the former case, the FF expression approxi-mates the true dipole derivative more closely, but the nu-merical A from Eq. (23) increases, whereas in the latter caseconvergence of the Hartree-Fock scheme would not be en-sured.

In our calculations, we used E = 5 X 10-3 a.u. or 5 X 10+6V/cm. In order to test the overall symmetry in index per-

Y~~~~~

5-(N-C~\ S A~C -N

0

Fig. 6. NPAN and NPP molecules. The x axis lies along the CTaxis; the z axis is orthogonal to the mean plane containing the sixaromatic carbons and the two nitrogen atoms. The fictitious mole-cule NPAM is derived from NPAN by substitution of a hydrogenatom in the cyano group, keeping the same orientation.

W

cd

;

Cd

*i

Qo

Vol. 4, No. 6/June 1987/J. Opt. Soc. Am. B 983

Table 7. /3 Components of NPAN in the Molecularframe x1y 1z1a

/2jk CNDOVSB Method(10-30 esu) FF Method hw = 0 hw = 1.17 eV

/3x1x1x1 -11.9 ± 0.3 -11.56 -20.16

flYlYlYl -0.7 ±0.3 0.06 0.04

f#Z1zlZ, -0.1 ± 0.3 -0.05 -0.06

/3Xlylyl 2.3 4 0.3 1.59 2.73o3ynxly1 = /3yl ylX, 2.2 + 0.2 1.76

/3yixixi -0.4 4- 0.2 0.002 0.073xixlyl = l5xiylxl 0.1 + 0.3 0.02

#XZ1Z1 -0.1 4 0.3 0.04 0.043Zx1X1Z1 = /3z1Z1X, 0.2 + 0.3 0.05

OZIXX 0.7 + 0.3 0.14 0.19/3X1 Z1 = flX1Z1X1 0.7 + 0.3 0.25

/3y1Z1Z1 0.6 4 0.2 0.09 0.11#ZLY1Z1 = /3Z1Z1Y, 0.1 + 0.2 0.11

flz 1Y1y, 0.0 ± 0.2 -0.11 -0.14Oyiyzi = flyzLy, -0.05 4 0.2 -0.15

f3X1 y1z, = #Xz1y1 -0.05 ± 0.2 -0.03 -0.04f3yxiz, = 13y1z1X1 -0.4 4 0.2 -0.03flziXiy, = 13z1y1X, -0.1 4 0.2 -0.03

a In the FF method, all coefficients were calculated separately to test Klein-mann symmetry. The error margins take into account only the limitedconvergence of l. In the CNDOVSB method, results are given for two values ofthe fundamental wavelength: h = 0 and hw = 1.17 eV, as in the EFISHmeasurement. All ,B are in units of 10-30 esu.

mutation, we have determined all /3 components indepen-dently. This required 18 perturbating fields as well as thecalculation of the permanent dipole moment for each com-pound. Results are reported in Tables 6-9.

Sum-over-States Method, CNDOVSB ProgramThe CNDOVSB semiempirical program 31 32 has been param-eterized by a comparison of the calculated and experimentalvalues of molecular properties over a large wavelength range.This sum-over-states (SOS) method is based on quantumperturbation theory. The formulas for the /3 components,first given by Ward,3 3 contain summations over the groundand excited states of the unperturbed molecular system, i.e.,

2 /2w _-e r i k + rk rP rJijk + Aikj 4^,2 ((PgnPn nrng gn nn ngij-4h'2

n,n'

X {[(n'g - )(wng + 0)1'

+ [(wn'g + w)(Wng - }1'1 + (rinri' rg+ rgnr Pnrng)[(@ng + 2)(wng + co)]

(wng-2w)(wng - w)]'1 + (rgnx kpi

+ gn'r-nnrng)1w(-ng -)(Wng - 2w)IL'

+ [g + w)(wng + 20)E-1). (24)

For practical reasons, the number of states to be includedin the summations must be restricted. Additional terms areintroduced until the series converge to whatever accuracy is

required. Equation (24) is adequate as long as the processesinvolved are nonresonant, but, to avoid secular divergence (n= g and w = 0), the above expression must be transformed. 32

The /32w coefficients given in Tables 7 and 8 were deter-mined for two different values of the fundamental wave-length: h = 0 and hw = 1.17 eV, as in the EFISH measure-ment.

Results and ComparisonsCalculated values are compared with experimental data inTable 10. The vector component , is measured by theEFISH technique at the fundamental wavelength hw = 1.17eV. The CNDOVSB program directly provides a calculatedvalue of ,/3 within the rotated frame xyz. The FF modelcan be used only to determine static nonlinear coefficients.

Table 8. ,B Components of NPP (in 10-30 esu) in theMolecular Frame xjyjz

oB2.k FF Method CNDOVSB Method(10-30 esu) hw = 0 hw = 0 hw = 1.17 eV

flx1x1x, -17.2 + 0.3 -15.49 -29.46

flYlYlYl 0.3 ± 0.2 0.08 0.16

flz1Z1Z, -0.2 + 0.3 -0.01 -0.01

0xyly 2.3 + 0.3 1.95 3.743yiXiy = 3yiYnx, 2.3 ± 0.2 2.35

oyixx, 0.15 ± 0.3 0.07 0.005f3x1x1y1 = flxiy1x1 0.2 4 0.3 0.14

flx1z1z, 0.3 + 0.3 0.03 0.04#z 1 x1z, = #z1z1x, 0.3 + 0.3 0.04

#z1x1x1 0.2 ± 0.3 -0.12 -0.32flx1x1 z, = #x1z1xi 0.2 4- 0.3 -0.24

oyiziz, 0.1 ±0.2 0.01 0.01j#Z1Y1Z1 = flZ1Z1Y1 0.2 ±0.3 0.01

flzyiy -0.1 ± 0.3 0.05 0.09oyiYnz, = flylzlYl -0.1 4± 0.2 0.07

#x1y1z, = /3x1zLy, -0.1 ± 0.2 -0.05 -0.06oyixiz, = yizix, -0.1 0.2 -0.070Z3X1 Y1 = #ZLY1 X1 -0.1 4- 0.3 -0.07

Table 9. Comparison between NPAN and NPAM bythe FF Methoda

i:.jk(10-30 esu) NPAN NPAM

0x1x1x1 -11.9 ± 0.3 -11.8 ± 0.2oYlylyy -0.7 + 0.3 -0.29 ± 0.1flZZ1 iz1 -0.1 + 0.3 +0.02 ± 0.1oxyly, 2.3 + 0.3 2.4 0.1oyixix1 -0.4 + 0.2 +0.3 ± 0.1#x1z1z1 -0.1 + 0.3 0.2 0.10z1x1x, 0.7 + 0.3 0.3 0.1#1yiz1z 0.6 + 0.2 0.01 ± 0.10z1yLY1 0.0 + 0.2 0.15 ± 0.1oxiyz, -0.4 + 0.4 -0.2 4 0.1

0iik coefficients are given in the molecular frame xjyjzj in units of 10-3Qesu. Margins of error reflect the limited convergence of INDO.

Barzoukas et al.

984 J. Opt. Soc. Am. B/Vol. 4, No. 6/June 1987

Table 10. Calculated and Experimental Values of the /3- Component (z along the Permanent Dipole) at theFundamental Wavelength h, 1.7 eVa

,u (INDo) X (Expt.) X (CNDOVSB) (10-30 esu)Molecule (D) (nm) (nm) Expt. FF CNDOVSB

NPAN 7.2 360 316 23 5 25 16NPP 7.3 397 334 42±9 42 26

a 2 is given in units of 10-30 esu.

To account for the dispersion, a two-level quantum sys-tem30 34 is used to describe the molecule:

= 3e2h2WfAA/12m[W2 - (2hw)2][W2 - (ho)2]], (25)

where W is the transition energy to the first excited state, f isthe oscillator strength, and A is the difference of dipolemoments between the excited and ground states. This mod-el takes into account only the predominating CT processthat occurs between the donor and the acceptor groups.

Equation (25) can be contracted into the following equa-tion:

/X1x = F(W, w) X /30 , (26)

where 0xixi is the static coefficient and F(W, w) is a disper-sion factor given by

F(W, co) = 1/[1 - (2hw/W)2][1 - (hw/W)2]J. (27)

The results, given in Table 9, show satisfactory agreementbetween the calculated and measured values. It appearsthat the SOS method overestimates the value of the perma-nent dipole moment and underestimates the /2w coefficients;this is also true when the values of the static /30 componentsare compared in Tables 7 and 8. However, this differenceincreases when the values are calculated at the fundamentalwavelength hi = 1.17 eV, since the CNDOVSB method under-estimates, by nearly 0.8 eV for NPP and 0.5 eV for NPAN,the transition energy to the first excited state. Thus thedispersion, which is directly accounted for in Eq. (24), isunderestimated. Nevertheless, the results confirm the util-ity of both methods and justify the approximations madethroughout the calculation.

Let us now examine in more detail the values of the static/30 components reported in Tables 7 and 8. First, the goodagreement between the two methods must be pointed out.For both molecules, the ratio B (CNDoVs)//3,,,xI (FF) isclose to 0.9. The symmetry requirement is, in the FF meth-od, well taken into account within error margins. However,the Kleinman relations are no longer valid at hw = 1.17 eV.

Clearly, the / tensor expressed in the molecular framexlyizi is one dimensional along the amino-nitro CT axis.For NPP as well as for NPAN, the nonlinear polarizability isdue primarly to a CT between r electrons of the donor(prolinol or amino) and of the acceptor groups, through theconjugated aromatic ring. The components involving theout-of-plane z axis are 2 orders of magnitude smaller than/XX3XX. This indicates that, because of steric constraints, thecyano group added in NPAN does not take part in the CTprocess. This is further confirmed by a comparison of the:/values of NPAN and of NPAM. The results displayed inTable 10 show that the molecular nonlinearity is nearlyunchanged. On the other hand, the interactions that occur

between the cyano dipoles lead to a noncentrosymmetriccrystal structure, which is highly optimized for efficientSHG."'

At first sight, it might seem surprising that the 00,ylylcoefficient is significantly larger than that of . This isa direct consequence of the molecular symmetry. We havealready shown that the active part of the molecule is similarto 4-nitroaniline. If we neglect the out-of-plane protons ofthe amino group, which do not contribute to the CT process,yl is a symmetry axis. It is clear that any component involv-ing an odd number of y1's will vanish. This is not exactly thecase, because of the approximations involved. Neverthe-less, our calculations confirm the relative weakness of 1x°

compared with O' IXl.Finally, the results given in Tables 7 and 8 enable us to

compare the efficiency of NPP and NPAN at zero-frequencyvalues. Both methods yield nearly the same ratio:

/l3~xlx, (NPAN, CNDoVSB)//XJX'XJ (NPP, CNDOVSB) = 0.75

and

/3xlx, (NPAN, FF)//3lIxlx (NPP, FF) = 0.70.

This comparison confirms that, under nonresonant condi-tions, the prolinol group is a better donor than the aminogroup. At h = 1.17 eV the same ratio drops to 0.68 with theCNDOVSB method. However, what is lost in hyperpolariza-bility may be recovered in transparency.

B. Molecular Crystalline Nonlinearities

NPPThe crystal structure of NPP is monoclinic, with space groupP21 and two molecules in the unit cell.10'3 5 The mean plane,containing the six aromatic carbons and the CT axis, isalmost coincident with the (110) crystallographic plane.The angle 0 between the binary axis b Y and the CT axis x1is 58.6°, a highly favorable value for SHG. The X and Zdielectric axes are not imposed by symmetry. However,neglecting the out-of-plane bonds, we have defined X as theintersection of the molecular plane and the (011) plane (Fig.7).

Assuming a one-dimensional / tensor and Kleinman sym-metry, there are two major nonlinear macroscopic tensorcomponents 35 ,36:

yyy = Nf yyy cos3 x1xxX

d2cX = Nfyxx cos 0 sin2 0o2X

(28)

(29)

where N is the number of molecules per unit cell (=3.68 X1021 m 3 ) and f the local-field factor in the Lorentz approxi-

,

;1

0.

0

bz;0

cB

Barzoukas et al.

Vol. 4, No. 6/June 1987/J. Opt. Soc. Am. B 985

mation. Since the refractive indices of NPP have not yetbeen measured, we have used f 3. The optimum value ford/2wyx is 0 = 54.7°, close to the actual 58.60 value. Equation(27) provides a means to account for the dispersion. Butsince the solid-state spectra are not available, we have as-sumed a 40-nm shift from the value of the maximum absorp-tion wavelength measured in acetone. This estimation isbased on results published for 4-nitroaniline, giving a 50-nmshift from the value in a nonpolar solvent to that in thecrystalline compound.37 For 0B1XIX1 we have taken both theFF and the CNDOVSB values. Calculated and measured val-ues3 4 using a thin crystalline film of NPP are given in Table11. It appears that this method overestimates the d compo-nents by as much as 40o if the FF /3 value is used. This caneasily be understood by recalling the drastic approximationsinvolved: local-field factor, dispersion factor, and Klein-man symmetry. Nevertheless, it provides the right order ofmagnitude, allowing us to extend this approach to NPAN,for which no experimental data are available.

NPANThe crystal structure of NPAN is orthorhombic with spacegroup Fdd2 and 16 molecules in the unit cell." The mole-cules are closely stacked along the c Z axis. The layerordering along the (110) crystallographic plane has a dislo-cated appearance, and the CT axis is out of this plane. Theangle 0 between the CT x axis and the binary c Z axis is58.60, the same value as for NPP. The XYZ dielectric axesare imposed by symmetry (Fig. 8).

Assuming a one-dimensional /3 tensor and Kleinman sym-metry, it may be shown that there are three nnnegligiblenonlinear coefficients 3 8:

d2.Xx = NfZxx cos(Z, xl)cos2(X, XJ)flX)3X1 , (30)

d2yy = Nfzyy cos(Z, x)cos'(Y. Xxx (31)

d 2z, = Nfzzz cos3(Z, XJ)02. (32)

twofold axis

Fig. 7. Crystal structure of NPP (space group P21 , Z = 2 molecules).a = 5.261 A, b = 14.908 A, c = 7.185 A, g = 105.180.

Table 11. Calculated and Experimental Values of dCoefficients for NPP Crystal at the Fundamental

Wavelength h = 1.17 eVa

Expt.diK FF CNDOVSB (Thin Single Crystal)

d 2x 270 250 197 28dyyy 100 90 73± 11

a d is given in units of 10-9 esu.

twofold axis

,XI

:74.4

Fig. 8. Crystal structure of NPAN (orthorhombic Fdd2, Z = 16molecules). a = 25.9222 A, b = 33.956 A, c = 4.319 A. The anglebetween the z1 axis and the (011) crystallographic plane is less than60.

Table 12. Calculated Values of d Coefficients forNPAN Crystal at the Fundamental Wavelength hw =

1.17 eVa

d 2K FF CNDOVSB

d 2x, 15 15dZYY 140 135d 2. 60 55

a d is given in units of 10-9 esu.

where N = 16/abc = 4.21 X 102l cm 3 , NPAN is more denselypacked than NPP, f 3, and the dispersion factor is 2.7(compared with 3.8 for NPP) assuming a similar 40-nm shiftfrom the Xmax value measured in acetone. Cos(X, x) =0.26896, cos(Y, xi) = 0.80936, and cos(Z, xi) = 0.52211. Theangular projection factor weighting /32X, in Eq. (31) is 0.34,a value quite close to the value of 0.38 for the dYXx compo-nent of NPP. In that sense, the crystal packing of NPANcomes close to optimizing the dyy nonlinear coefficient.Table 2 shows the d components that we determined byusing the FF and CNDOVSB results for /3O0

To compare the efficiencies of NPAN and of NPP, wehave calculated the following ratios:

dzwyy (NPAN)/d"x (NPP) = 0.56,

d'z (NPAN)/d.y~ (NPP) = 0.66

for both sets of results.This rather crude estimate points out the promising non-

linear properties of NPAN, which has a wider transparencyrange than NPP (Fig. 2).

5. CONCLUSIONS

In this paper we have reported a new molecular engineeringstrategy. This new approach has led us to the preparationof a new nitroanilinelike compound, NPAN, which comparesquite favorably with the already known NPP compound.

We have also presented quantum-chemical calculationsfor the purpose of comparison with experimental measure-ments and for the determination of all components of the tensor. The results have been used to calculate the macro-scopic nonlinear coefficients of both compounds, which havenot yet been determined experimentally in the case ofNPAN.

The estimated nonlinear coefficients of NPAN show thepotential of this material. It would therefore be of great

Barzoukas et al.

X

986 J. Opt. Soc. Am. B/Vol. 4, No. 6/June 1987

interest to grow thin crystalline layers and bulk crystals ofNPAN, in view of the preliminary successful attempts togrow single crystalline fibers of this material in hollow capil-laries.

ACKNOWLEDGMENTS

It is a pleasure to acknowledge assistance from I. Ledoux inmaking the EFISH measurement and from L. Brunet foraccess to the computing facilities.

REFERENCES

1. D. J. Williams, ed., "Nonlinear optical properties of organic andpolymeric materials," ACS Symp. Ser. 233 (American ChemicalSociety, Washington, D.C., 1983).

2. J. Zyss, "New organic molecular materials for nonlinear optics,"J. Non-Cryst. Solids 47, 211-225 (1982).

3. J. Zyss, D. S. Chemla, and J. F. Nicoud, "Demonstration ofefficient nonlinear optical crystals with vanishing moleculardipole moment: second-harmonic generation in 3-methyl-4-nitropyridine-1-oxyde," J. Chem. Phys. 74, 4800-4811 (1981).

4. J. L. Oudar and R. Hierle, "An efficient organic material fornon-linear optics: methyl-(2,4-dinitrophenyl)-aminopropan-oate," J. Appl. Phys. 48, 2699-2704 (1977).

5. K. Jain, J. I. Crowley, G. H. Hewig, Y. Y. Cheng, and R. J. Tweig,"Optically nonlinear organic materials," Opt. Laser Technol.13, 297-301 (1981).

6. A. F. Garito and K. D. Singer, "Organic crystals and polymers, anew class of nonlinear optical materials," Laser Focus 18(2), 59-68 (1982).

7. I. Ledoux, J. Zyss, A. Migus, J. Etchepare, G. Grillon, and A.Antonetti, "Generation of high peak power subpicosecondpulses in the 1.0-1.6-,um range by parametric amplification inan organic crystal," Appl. Phys. Lett. 48, 1564-1566 (1986).

8. N. Bloembergen, Nonlinear Optics (Benjamin, New York,1965).

9. H. Rabin and C. L. Tang, Quantum Electronics (Academic,New York, 1965.

10. J. Zyss, J. F. Nicoud, and M. Coquillay, "Chirality and hydro-'gene bonding in molecular crystals for phase-matched secondharmonic generation: N-(4-nitrophenyl)-L-prolinol (NPP),"J. Chem. Phys. 81, 4160-4167 (1984).

11. P. V. Vidakovi6, M. Coquillay, and F. Salin, "N-(4-nitro-phenyl)-N-methylamino-aceto-nitrile: new organic materialfor efficient second-harmonic generation in bulk and waveguideconfigurations. I. Growth, crystal structure, and characteriza-tion of organic crystal-cored fibers," J. Opt. Soc. Am. B 4, 998-1012 (1987).

12. J. F. Nicoud and R. J. Twieg, "Design and synthesis of organicmolecular compounds for efficienty second harmonic genera-tion," in Nonlinear Optical Properties of Organic Moleculesand Crystals, D. S. Chemla and J. Zyss, eds. (Academic, Orlan-do, Fla., 1986), Vol. 1.

13. J. F. Lipscomb, A. F. Garito, and R. S. Narang, "An exceptional-ly large linear electrooptic effect in the organic solid MNA," J.Chem. Phys. 75, 1509-1516 (1981).

14. A. D. Mighell, V. L. Himes, and J. R. Rodgers, "Space groupfrequencies for organic compounds," Acta Cryst. A39, 737-740(1983).

15. R. J. Twieg, IBM Almaden Research Center, San Jose, Califor-nia 95102-6099 (personal communication).

16. V. I. Minkin, 0. A. Osipov, and Yv. A. Zhdanov, Dipole Mo-ments of Organic Chemistry (Plenum, New York, 1970).

17. N-Methylaminoacetonitrile is commercially available (fromTokyo Chemical Industry, Tokyo) or easily prepared: A. H.

Cook and S. F. Cox, "The preparation of a-N-alkylamino-ni-trile, -amide, and acids," J. Am. Chem. Soc. 1949, 2334-2337(1949).

18. J. L. Oudar and H. Le Person, "Second order polarizabilities ofsome aromatic molecules," Opt. Commun. 15, 258-262 (1976).

19. J. L. Oudar, "Optical nonlinearities of conjugated molecules.Stilbene derivatives and highly polar aromatic compounds," J.Chem. Phys. 67, 446-457 (1977).

20. B. F. Levine and C. G. Bethea, "Ultraviolet dispersion of thedonor-acceptor charge transfer contribution to the second or-der hyperpolarizability," J. Chem Phys. 69, 5240-5245 (1978).

21. C. G. Bethea, "Experimental technique of dc induced SHG inliquids: measurement of the nonlinearity of CH 2 I2," Appl. Opt.14, 1447-1451 (1975).

22. B. F. Levine and C. G. Bethea, "Effects on hyperpolarizabilitiesof molecular interactions in associating liquid mixtures," J.Chem. Phys. 65, 2429-2438 (1976).

23. B. F. Levine, "Donor-acceptor charge transfer contributions tothe second order hyperpolarizability," Chem. Phys. Lett. 37,516-520 (1976).

24. K. D. Singer and A. F. Garito, "Measurements of molecularsecond order optical susceptibilities using dc induced secondharmonic generation," J. Chem. Phys. 75, 3572-3580 (1981).

25. I. Ledoux and J. Zyss, "Influence of the molecular environmentin solution measurements of the second order optical suscepti-bility of urea and derivatives," Chem. Phys. 73, 203-213 (1982).

26. P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage,"Effects of dispersion and focusing on the production of opticalharmonics," Phys. Rev. Lett. 8, 21-22 (1962).

27. B. F. Levine and C. G. Bethea, "Second and third order hyper-polarizabilities of organic molecules," J. Chem. Phys. 63, 2666-2682 (1975).

28. J. Zyss, "Hyperpolarizabilities of substituted conjugated mole-cules. I. Perturbated INDO approach to monosubstitutedbenzene," J. Chem. Phys. 70, 3333-3340 (1979).

29. J. Zyss, "Hyperpolarizabilities of substituted conjugated mole-cules. II. Substituent effects and respective av-r contribu-tions," J. Chem. Phys. 70, 3341-3349 (1979).

30. J. Zyss, "Hyperpolarizabilities of substituted conjugated mole-cules. III. Study of a family of donor-acceptor disubstitutedphenylpolynes," J. Chem. Phys. 71, 909-916 (1979).

31. V. J. Dorcherty, D. Pugh, and J. D. Morley, "Calculation of thesecond order electronic polarizabilities of some organic mole-cules," J. Chem. Soc. Faraday Trans. 2 81, 1179-1192 (1985).

32. S. Allen, J. D. Morley, D. Pugh, and V. J. Docherty, "A CNDOVSBprogram for the calculation of second-order molecular polariza-bilities and its application," in Molecular and Polymeric Op-toelectronic Materials, L. G. DeShazer, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 682 (to be published).

33. J. F. Ward, "Calculation of nonlinear optical susceptibilitiesusing diagrammatic perturbation theory," Rev. Mol. Phys. 37,1-18 (1965).

34. J. L. Oudar and D. S. Chemla, "Hyperpolarizabilities of thenitroanilines and their relations to the excited state dipole mo-ment," J. Chem. Phys. 66, 2664-2668 (1977).

35. I. Ledoux, D. Josse, P. Vidakovic, and J. Zyss, "Highly efficientsingle crystalline organic thin films for quadratic nonlinear op-tics," Opt. Eng. 25, 202-210 (1986).

36. J. L. Oudar and J. Zyss, "Structural dependence of nonlinearoptical properties of methyl-(2,4-dinitrophenyl)-aminopropan-oate crystals," Phys. Rev. A. 26, 2016-2027 (1982).

37. F. Bertinelli, P. Palmieri, A. Brillante, and C. Taliani, "Elec-tronic excited states of nitroanilines. II. A configuration in-teraction study and U.V. Spectrum of the paranitroaniline sin-gle crystal," Chem. Phys. 25, 333-341 (1977).

38. J. Zyss and J. L. Oudar, "Relations between microscopic andmacroscopic lowest order optical nonlinearities of molecularcrystals with one or two dimensional units," Phys. Rev. A 26,2028-2048 (1982).

c)

*+a

Cd1

'e4

0

zd

Barzoukas et al.