donor–acceptor diethynylsilane oligomers: a second-order nonlinear optical material

Donor–Acceptor Diethynylsilane Oligomers: A Second-Order

Nonlinear Optical Material

Ana E. De A. Machado,1 Leonardo A. De Souza,1,2 Helio F. Dos Santos,2

Wagner B. De Almeida1

1Laboratorio de Quımica Computacional e Modelagem Molecular (LQC-MM), Departamento de Quımica, ICEx, Universidade

Federal de Minas Gerais (UFMG), Campus Universitario, Pampulha, Belo Horizonte, MG 31270-901, Brasil

2Nucleo de Estudos em Quımica Computacional (NEQC), Departamento de Quımica, ICE, Universidade Federal de Juiz de Fora

(UFJF), Campus Universitario Martelos, Juiz de Fora, MG 36036-330, Brasil

Correspondence to: W. B. De Almeida (E-mail: [email protected])

Received 17 May 2011; revised 12 July 2011; accepted 12 July 2011; published online 9 August 2011

DOI: 10.1002/polb.22324

ABSTRACT: The interest in the study of oligomers has been

motivated mainly because of their solubility in common sol-

vents and also their capacity to be crystallized, which allowed

for chemical processing leading to important applications in

the area of material sciences. In this work, we carried out an

investigation of polydiethynylsilane (PDES) decamers substi-

tuted with electron donor (D) and acceptor (A) groups, which is

certainly of relevance, once PDES itself is known to display

large third-order optical susceptibility. Therefore, density func-

tional theory calculations of static first hyperpolarizability (b)were performed using various functionals with the 6-31G(d) ba-

sis set along with correlated MP2 calculation used as reference

for comparison. The influence of A and D substituents on the

magnitude of b was investigated by matching the acceptor

(dicyanovinyl, nitrobenzene) and donor (propyl, propoxy, and

phenylamine) groups attached at both ends of the oligomer.

The largest b value was predicted for the derivative having the

phenylamine and dicyanovinyl groups, which is around 30

times the relative value for the nonsubstituted decamer, what

is a very impressive enhancement reported for the first time in

the literature, strongly suggesting that disubstituted diethynyl-

silane decamers are potential building blocks for molecular-

based materials with second-order nonlinear responses. VC 2011

Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49:

1410–1419, 2011

KEYWORDS: density functional theory; disubstituted diethynylsi-

lane; first hyperpolarizability; NLO; polydiethynylsilane

INTRODUCTION Novel materials with large nonlinear coeffi-cients are required for advanced applications in nanoscienceand nanotechnology.1–3 Polymers are attractive molecular-based materials because of their mechanical, electrical, mag-netic, and chemical properties, with practical applications invarious fields.4–6 Polydiethynylsilane (PDES) is a conjugatedpolymer that displays large third-order optical susceptibilitywith exceptionally fast optical response on the sub-THz fre-quency range; these features are useful for manufacturingoptical modulators and switches.7 Early experimental andtheoretical studies demonstrated that this third-order nonlin-ear material has a four-membered backbone Si-ring struc-ture,8 as shown in Figure 1. Another investigation indicatedthat the electrical and optical properties of PDES must bedue to p-electrons in their carbon structures, because the sil-icon atoms are in their sp3-hybridized state.9 These materialssupport solitons and polarons as primary electronic excita-tions, which lead to larger shifts in the optical oscillatorstrength that contribute to increase cubic susceptibility.7,9

Other classes of nonlinear materials containing the Si atomhave been studied because of the relevant values of theirobserved hyperpolarizabilities.10–18 The Si atom itself andtheir clusters display significant nonlinear responses.19–21

Oligomers have been studied because of their solubility incommon solvents and their ability to be crystallized. Theseproperties are different from the polymers themselves, andtherefore, allow for their chemical processing.22–25 These fea-tures are essential for the construction of devices from mono-and multilayer films, single crystals, and other forms. In addi-tion, polymers and their oligomers have been experimentallyand theoretically characterized as prominent candidates asnonlinear materials.1–4,7,10,12,24,25 In particular, the modeltrimers of aniline simulate the observed experimental trendsfor the second hyperpolarizabilties at the Austin Model 1(AM1) level, using the time-dependent Hartree-Fock approach(TDHF), namely AM1/TDHF.26 Also, the large first hyperpolar-izability values obtained for the oligomers of the three neutralforms of the polyaniline showed the potential for second-

Additional Supporting Information may be found in the online version of this article.

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order nonlinear material in agreement with the experimentalresults.26 Furthermore, the introduction of substituents onthese oligomers increase the b hyperpolarizability values byseveral times according to AM1/TDHF calculations.27

PDES presents two structural forms (PDES-I and PDES-II),which are almost energetically degenerate.28 Early studies onthe functionalization of diethynylsilane oligomers with sub-stituents at the silicon atom resulted in larger values of thelongitudinal second hyperpolarizability (c) compared withother important polymers, revealing an efficient strategy toincrease the nonlinear response.29 Recently, AM1/TDHF calcu-lations indicated that that electron donor (D)–acceptor (A)-substituted PDES-II derivatives present very large first hyper-polarizabilities (b) compared with the substituted PDES-I andnonsubstituted forms.30 Spectroscopy measurements associ-ated with theoretical characterization indicated that PDES con-sists of a four-membered ring backbone for which two kindsof dimerization forms are energetically almost degenerate(�0.02 kcal mol�1).7 It is well established that the D–A elec-tronic strength, dimensionality, molecular asymmetry, size andnature of the linker between the donor and acceptor substitu-ents, and molecular conformation are usually strongly corre-lated with the b values of organic-based materials.2,3 In addi-tion, the lowest energy electronic absorption (charge transferprocess) contributes to the enhancement of the first hyperpo-larizability according to models based on the perturbationtheory. Hence, the transparency and stability are fundamentalfor nonlinear optical (NLO) materials to be used as optoelec-tronic and photonic devices.

A survey of theoretical reports shows that molecular-basedmaterials have potential applications as second- and third-nonlinear materials, as the transition metal complexes,31 por-phyrins.25,32,33 phtalocyanines,34 among others.35–43 Novelmaterials with large nonlinear coefficients are needed foradvanced technologies, as well as the implementation of pho-tonics. Hence, theoretical methods have been considered asuseful techniques for prediction of polarizabilities (a) andhyperpolarizabilities (b) mainly due to the possibility ofscreening a great number of potential candidate moleculeshaving a high value of hyperpolarizability, avoiding a largeamount of experimental synthetic work which are expensiveand time consuming and at the end may not lead to a com-pound with desired NLO properties. It has also been shownthat the nonlinear properties can be estimated with increasedaccuracy through the use of post-Hatree–Fock (post-HF)

methods. However, semiempirical (Parametric Method 3(PM3) and AM1), HF, and density functional theory (DFT)approaches have also been satisfactorily applied to relativelylarge molecules, for which more rigorous methods such asnth-order Møller–Plesset perturbation theory (MPn) andcoupled cluster (CC) are prohibitive.2,21,44,45 The choice of thebasis set also plays a role in the quality of the results. Accord-ing to the literature, calculations using a large basis set withpolarization and diffuse functions are required to reproducethe experimental magnitude of b.2,44,46 Nonetheless, severalsystematic theoretical studies indicate that the inclusion of anaugmented set does not promote large differences in the bvalues for extended systems, with calculated values being inaccordance with the experimental data even when medium-size basis sets are used.2,44–48 Furthermore, for very largemolecules, such as those studied in this work, the small 6-31G(d) basis set seems to be appropriate for structural deter-mination as well as for calculation of the hyperpolarizability,because our main goal is to screen molecules with enhancednonlinear responses within a specific class of compounds.Therefore, the relative hyperpolarizability values are more im-portant than the absolute values.26 DFT calculations based onstandard hybrid functionals generally overestimate the b val-ues in comparison with more rigorous post-HF MPn and CCmethods.2,44,48 However, as already mentioned, these ab initiocorrelated methods are prohibitive for large systems, such asthose studied in this work; therefore, DFT methods are thebest in terms of accuracy and computational time.2,47 DFT cal-culations have been reported for several classes of moleculesincluding boroxine-based octupolar molecules,47 bis-[4-(dime-thylamino)phenyl]squaraine27 and D/A-substituted benzenesand stilbenes48 among others.49 In addition, DFT single-pointcalculations, with PM3 optimized geometries, have beenapplied for predicting the first hyperpolarizability of azo-dyesderivatives, with results that are in qualitative agreement toexperimental measurements.50

In this work, A–D pairs were introduced in diethynylsilaneoligomer structures (Fig. 1) to identify new derivatives withenhanced second-order NLO properties. The D and A groupswere attached at both ends of the diethenylsilane oligomer,which contains 10 heterocyclic rings. We used propyl, pro-poxy, and phenylamine as D groups and dicyanovinyl andnitrobenzene as A groups. The decamer missing the substitu-ent groups was also investigated to account for the effect ofthe D and A groups in promoting an increase in the firsthyperpolarizability. We report DFT calculations of b and afor the nonsubstituted decamer and six substituted deriva-tives using various functionals. According to the literature,calculations of a value for nonextended molecules using DFTfunctionals are accurate in comparison to post-HF results,contrasting with the results for b which were more depend-ent on the specific functional used.2 Therefore, in an attemptto assess which DFT functional is more suitable for the cal-culation of b for substituted PDES derivatives, we performedMP2 calculation for the nonsubstituted decamer, what iscomputational viable, and take this b value as referencefor comparison with DFT results using 10 functional.This study predicted much enhanced values of first

FIGURE 1 Schematic representation of substituted oligomers

(R1-Oligomer-R2), where R1 is an electron acceptor group, R2

an electron donor group and n is equal to 10 (decamer).

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hyperpolarizabilities, reported for the first time in the litera-ture, which strongly stimulates experimental investigationswith the substituted oligomers reported here.

COMPUTATIONAL ASPECTS

Geometries of the diethenylsilane decamer and their D–Asubstituted derivatives (see Fig. 1) were fully optimized

using the DFT51 method with the B3LYP hybrid func-tional52,53 and the 6-31G(d) polarized basis set54–57 (here-after abbreviated as B3LYP/6-31G(d)). DFT single-point cal-culations of first hyperpolarizability and polarizability wereperformed for the nonsubstituted decamer (structure I,Fig. 2) using various functional with the 6-31G(d) basis setusing the B3LYP/6-31G(d) optimized geometry, to investigate

FIGURE 2 B3LYP/6-31G(d) fully optimized structures for the investigated oligomers. (a) I (R1 ¼ H; R2 ¼ H): nonsubstituted oligomer. (b) II (R1

¼ p-NO2-phenyl; R2 ¼ CH3CH2CH2A). (c) III (R1 ¼ p-NO2-phenyl; R2 ¼ CH3CH2CH2AOA). (d) IV (R1 ¼ p-NO2-phenyl; R2 ¼ p-NH2-phenyl). (e) V

(R1 ¼ (CN)2C¼¼CHA; R2 ¼ CH3CH2CH2A). (f) VI (R1 ¼ (CN)2C¼¼CHA; R2 ¼ CH3CH2CH2AOA). (g) VII (R1 ¼ (CN)2C¼¼CHA; R2 ¼ p-NH2-phenyl).



the effect of a given functional on the calculated value of b. It isworth to remind that in DFT methodology the exact exchange(HF) energy for a single determinant51 is replaced by a moregeneral expression, the exchange-correlation functional, whichcan include terms accounting for both exchange energy and theelectron correlation which is omitted from the HF theory. Inaddition to pure ab initio methods, DFT hybrid functionals,where a percentage of the exchange functional is given by theHF exchange, have became very popular in the area of physicalorganic chemistry and material sciences and have producedvery stimulating results. The following functionals were used inthis work: B3LYP,52,53 PBE1PBE58,59 (this is equivalent to thehybrid PBE0 functional60,61), BLYP,52,62 BP86, 58,62,63 PW91,64

B97-2,65 CAM-B3LYP (Coulomb-attenuating method applied toB3LYP),66 BH and HLYP,52,62 and the newly developed meta-GGA functional M06-2X of Truhlar and coworkers.67–69 TheLocal Density Approximation correlation functional using theSlater exchange term (SVWN)70,71 was also used, since thelower computer time required for hyperpolarizability calcula-tions using the SVWN functional can be of great aid for treatinglarge molecular systems. In addition, HF72 and Møller–Plessetsecond-order perturbation theory (MP2)72 hyperpolarizabilitycalculations were also carried out for the nonsubstitutedoligomer (structure I), with the MP2 b value taken as referencefor comparison reason. For the substituted oligomers (struc-tures II–VII), the B3LYP, PBE1PBE, SVWN, and M06-2X func-tional were used as representative, in the light of the resultsobtained for structure I. Single-point calculations with the 6-31G(d,p) basis set,54–57 which includes a polarization functionon hydrogen atoms as well, were also performed, but no signifi-cant changes were observed (see Supporting Material). In thenotation used here, the double slash indicates a single-point cal-culation at the B3LYP/6-31G(d) optimized geometry (i.e.,PBE1PBE/6-31G(d)//B3LYP/6-31G(d)).

The NLO properties were calculated at the DFT and MP2 lev-els through numerical differentiations (EnOnly Gaussianoption) using the finite field method73–76 with field strengthof 0.001 au, where the tensor elements bijk (where i, j, and kare equal to x, y, and z, respectively) are obtained by partialderivatives of the molecular energy perturbed by the exter-nal time-dependent electric field. From the tensor elementsbijk, the Cartesian components bx, by, and bz can be calcu-lated according to eq 1:

bi ¼1

3

Xik

bikk þ bkik þ bkkið Þ 8 k ¼ x; y; z; i ¼ x; y; z (1)

Thus, the total molecular first hyperpolarizability (bmol) iscalculated according to eq 2.

bmol ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffib2x þ b2y þ b2z

q(2)

As explained in ref. 77, the Gaussian quantum mechanicalpackage78 uses the relationship bij ¼ bji and provides a ten-sor with only 10 elements. In the electric field-inducedsecond-harmonic generation (EFISH) experiment, only thevector component of b along the dipole moment direction

(denominated bvec)3 is measured. We also analyzed the val-

ues of bvec defined by eq 3, which can have positive or nega-tive values, where l is the dipole moment, and x is thefrequency of the applied field.

bvecð�2x;x;xÞ ¼X3i¼1

libilj j (3)

The averaged polarizability is evaluated according to eq 4:

aav ¼ 1

3axx þ ayy þ azz� �

(4)

The average value of the first hyperpolarizability (bav)50 and

the total intrinsic quadratic hyperpolarizability (btot)3 are

virtually the same as bmol. All calculations were carried outusing the Gaussian-03 and G-09 programs.78

RESULTS AND DISCUSSION

Spatial views of the B3LYP/6-31G(d) fully optimized geome-tries for the seven molecules studied are depicted in Figure2. The B3LYP Cartesian coordinates, from which atomic dis-tances, bond angles, and dihedral angles can be easilyobtained, are provided in Supporting Information. All opti-mized geometries for the PDES oligomers keep a reasonableplanarity, which is in agreement with the experimental find-ings for other related systems.7,8 DFT optimized geometriesare usually in better agreement with experimental structuraldata than semiempirical results, so we believe that theB3LYP/6-31G(d) level of calculation used in this work isadequate to predict the structure of extended systems, suchas those investigated here. In addition, it was confirmed thatthe PBE1PBE and B3LYP optimized geometries for the non-substituted oligomer (structure I) are essentially the same,what should also hold for the substituted PDES decamers,therefore, justifying the use of single-point calculations usingthe B3LYP/6-31G(d) fully optimized structure.

In a first place, we considered that an investigation of theeffect of a chosen DFT functional on the calculation of b wasof primarily importance, using the post-HF MP2/6-31G(d)calculated b as a reference value for comparison. DFT, MP2,and also HF bmol results for the nonsubstituted oligomer(structure I) are given in Table 1, with a values being alsoreported. The percent deviation with respect to the MP2 ref-erence value is quoted in parentheses. Energy gap and dipolemoment values, including calculations with the 6-31G(d,p)basis set, are provided in Supporting Information (see TableS1). It can be anticipated that the use of the 6-31G(d,p) ba-sis, with polarization function added to hydrogen atoms, didnot cause significant changes in the calculated hyperpolariz-ability values. It can be promptly seen from Table 1 that thePBE1PBE functional seems very adequate for the calculationof first hyperpolarizabilities for the series of substitutedoligomers studied here as compared with the MP2 referenceresult, having a deviation of only 8%. The B3LYP and B97-2functionals overestimate the value of b, compared with theMP2 value, in 81% and 59% respectively. The BP86, PW91,



SVWN, and BLYP functional predicted too high values of bwith a deviation much more than 100%. The M06-2X, CAM-B3LYP, and BH and HLYP functional yielded underestimatedvalues in 71%, 70%, and 91%, respectively. The HF resultsare also underestimated in 85%. It should be mentioned thefact that MP2 and PBE0 b values agree for one case (nonsub-stituted oligomer, structure I) does not mean that this func-tional will be well suitable for other systems. For example,it is shown in ref. 79 that MP2 and coupled cluster withsingle, double and perturbative triple excitations (CCSD)(T)results differ considerably (with the CCSD(T) value beinggenerally smaller than MP2), so being close to MP2 datacannot be considered a definitive criterion to choose thebest functional to be used. In addition, for long oligomers,especially when charge transfer (CT) character is importantlike in push–pull systems, it is well recognized that long-range separated hybrids are much more reliable (see refs.80–82). In a very recent paper published by Lu,83 where acomputational study of static first hyperpolarizability of do-nor–acceptor substituted (E)-benzaldehyde phenylhydra-zone was reported using various DFT functional and theMP2 level of theory used as reference result, the BH andHLYP and CAM-B3LYP functional were recommended as thebest choice for the estimation of molecular nonlinearity ofhydrazones. However, in this study for PDES decamer thePBE1PBE functional was found very suitable for the calcula-tion of b. This is indeed a very interesting situation, reveal-ing that we are still far away to find an ‘‘adequate’’ DFTfunctional that works very satisfactorily for any molecularstructure exhibiting nonlinear responses. What we observedis a rather strong dependence of DFT b results using agiven functional with a specific molecular spatial arrange-ment. Therefore in our discussion on the substituted PDESdecamers, the PBE1PBE/6-31G(d)//B3LYP/6-31G(d) b val-ues will be used, with other DFT results given in Support-ing Information (see Table S2). Polarizability results arealso reported in Table 1 only for reason of comparison. Itcan be seen that the DFT a results are considerably overes-timated with respect to the MP2 reference data, with theHF value showing the least deviation from MP2.

Table 2 reports the bmol and bvec values, calculated with thePBE1PBE functional, for all structures shown in Figure 2,with aav results being also given. It can be seen that there isa remarkable increase in the b values due to the presence ofthe A–D substituents attached at both ends of the PDESdacamer. The relative increase can be better seen in Figure3, where the increasing factor (F) defined as the ratiobetween the bmol value of a given substituted structure andthe value for the nonsubstituted decamer, structure I, (F ¼bmol/bmol

Str-I) is plotted using four DFT functionals (B3LYP,PBE1PBE, SVWN, and M06-2X) for reason of comparison. Itcan be seen from Figure 3 that all functionals show a regularincrease of bmol for structures II–VII, with the SVWN andM06-2X functional predicting a very modest increase com-pared with the B3LYP and PBE1PBE functional, which is inline with the results given in Table 1 for the SVWN andM06-2X underestimated bmol values. The maximum increaseof bmol is also indicated in Figure 3, which is 27 and 35times for B3LYP and PBE1PBE values, respectively, and 8 forSVWN and M06-2X functional. In any case, a very remark-able enhancement of the first hyperpolarizability is pre-dicted. It can also be seen from Figure 3 that both B3LYPand PBE1PBE functional showed the same profile for the Ffactor and could be equally used for estimate relative bmol

values for substituted oligomers, besides deviating consider-ably in the prediction of absolute values of bmol according to

TABLE 1 Calculated Polarizability (aav, 10225 cm3) and First-Hyperpolarizabilitya (bmol, 10

230 cm5 esu21) for the Nonsubstituted

Oligomer [Str. I, See Fig. 2(a)] Using 10 DFT Functionals and the HF and MP2 Levels with the 6–31G(d) Basis Set (Single-Point

Calculations Using the B3LYP/6–31G(d) Fully Optimized Geometry)

MP2 PBE1PBE B3LYP B97–2

aav 1,804 3,107 3,261 3,227

bmol (deviation from MP2) 1,411 1,527b (þ8%) 2,553 (þ81%) 2,244 (þ59%)

BP86 PW91 BLYP SVWN

aav 4,263 4,255 4,251 4,283

bmol (deviation from MP2) 10,998 (>>100%) 10,881 (>>100%) 11,266 (>>100%) 11,088 (>>100%)

M06–2X CAM-B3LYP BHandHLYP HF

aav 2,464 2,480 2,577 2,247

bmol (deviation from MP2) 402 (�71%) 417 (�70%) 127 (�91%) 209 (�85%)

The percent deviation from MP2 reference data is given in parentheses.a First-hyperpolarizability (b): 1 a.u. ¼ 8.639418 � 10�33 cm5 esu�1.

b PBE1PBE/6–31G(d,p) fully optimized geometry aav and bmol values are,

respectively: 3,017 (/10�25 cm3) and 1,462 (/10�30 cm5 esu�1).

TABLE 2 Calculated Polarizability (aav/10225 cm3) and First-

Hyperpolarizabilitya (bmol/10230 cm5 esu21) for Free (I) and

Substituted Oligomers (II–VII), Using PBE1PBE/6–31G(d) Single-

Point Calculations with B3LYP/6–31G(d) Fully Optimized

Geometries (PBE1PBE/6–31G(d)//B3LYP/6–31G(d))

I II III IV V VI VII

aav 3,107 3,871 4,084 4,571 4,361 4,798 5,604

bmol 1,527 8,540 14,158 21,961 22,131 34,743 53,265

bvec 1,527 4,798 �8,548 �6,832 �21,811 �34,667 �51,269

a The bmol and bvec are defined according to eqs 2 and 3, respectively.



the results reported in Table 1 (see also Supporting Informa-tion, Table S2). As mentioned before, the most important isthe right prediction of relative bmol values with respect to areference, which in our case is the nonsubstituted oligomer(structure I). Other results are given in Supporting Informa-tion. Analyzing Figure 3, it can be concluded that structureVII has an increasing factor F ranging from 8 to 30 (depend-ing on the functional used) and is certainly a good candidateto be experimentally tested as a material exhibiting second-order nonlinear response. It is worth noting that the mole-cule VII shows the highest polarizability value, as well asfirst hyperpolarizability.

According to the results reported in Table 2, the introductionof the D and A groups resulted in higher values of linearpolarizability (a) for the diethynylsilane derivative, but amuch less extent compared with bmol, with the maximumincreasing factor being only 2. The a values are severalorders of magnitude higher than those for the Si4 cluster,21

cis- and trans-butadiene,84 and push–pull conjugated systemsamong others,19 which have been calculated using post-Har-tree–Fock and DFT methods. Compounds with high polariz-ability values are required for applications such as opticalfibers. The a values obtained using the DFT functional arelarger than those calculated with other methods, as con-firmed by the MP2 data reported in Table 1 for structure I.The a values using the PBE1PBE functional were smallerthan those calculated with the B3LYP functional, but withsimilar order of magnitude (see Table 1), also showing aconsiderable deviation from the MP2 value. Maroulis andPouchan demonstrated that the B3LYP functional performswell for the calculation of a (and c hyperpolarizability) valuefor the Si4 cluster when compared with other DFT function-als and post-Hartree–Fock methods.21 In a recent paper byPaschoal et al.,85 the B3LYP functional was also used to cal-culate the electronic properties of push–pull benzene deriva-tives, with the reported results for polarizability in excellentagreement with MP2 and experimental data.

The first hyperpolarizability of organic molecules is stronglycorrelated with the size of the alternated conjugation of thebridge group linking the D–A pair as well as the nature andstrength of the donor–acceptor pair.2,3,24,77,86 We analyzedboth features using appropriate molecular descriptors.Extension of the electronic conjugation can be investigatedby the topological bond-length alternation (BLA) parameter,which is the difference between the average single and dou-ble bond lengths in the conjugation pathway.86 Using theB3LYP/6-31G(d) fully optimized geometries, we determinedthe BLA values for the systems investigated here (Table 3).The nonsubstituted oligomer (structure I) has a BLA valueequal to 0.071 Å and the lowest bmol (Tables 2 and 3). Forsystem VII with the largest bmol value (see Table 2), the BLAof the linker between D and A is 0.061 Å. The overall trendpredicted at the PBE1PBE/6-31G(d)//B3LYP/6-31G(d) levelof calculation is shown in Figure 4(a). bmol decreases withincreasing BLA values, as expected for conjugated poly-mers.87,88 For molecules I to IV, the NLO response is quitesensitive to the structural changes induced by the substitu-ents, showing a quadratic increase with the respectivedecrease of the BLA parameter. This behavior was smoothedfor molecules V–VII. In general, the D–A pair promotes anincrease in the double bond length and a decrease in the sin-gle bond length in the polyenic moiety. Although for p-conju-gated systems it is well known from the literature that theB3LYP functional underestimates the BLA parameter in con-trast with the results obtained with other functional, such asM06-2X and CAM-B3LYP, and the long-distance correctionDFT scheme,89–92 the results obtained in this work using theB3LYP hybrid functional show that this parameter is stronglycorrelated with the bmol value, independent on the functionalused for the calculation of the hyperpolarizability, predictingthe same increasing order of b for the series of substitutedoligomers. Early ab initio and semiempirical results forpush–pull polyenes showed that the effect is stronger in theregion close to the D and A substituents.7,88 Considering thecalculations at the B3LYP/6-31G(d) level (and alsoPBE1PBE/6-31G(d)), we conclude that the conjugated moi-ety geometry near the acceptor is significantly different from

FIGURE 3 B3LYP/6-31G(d), PBE1PBE/6-31G(d), SVWN/6-31G(d)

and M06-2X/6-31G(d) bmol increasing factor (F ¼ bmol/bmolStr-I)

relative to the nonsubstituted oligomer (structure I) calculated

using B3LYP/6-31G(d) fully optimized geometries. The

double slash means a single-point calculation with the opti-

mized geometry indicated on the right side.

TABLE 3 BLA and Total Hammett Electronic Parameter (rt) for

the Systems Investigated

Moleculesa


BLA (A) 0.071 0.069 0.068 0.067 0.0665 0.066 0.061

rtb 0.00 0.39 0.51 0.66 0.65 0.77 0.92

The BLA values were calculated at the B3LYP/6–31G(d) level.a I (R1 ¼ H; R2 ¼ H): nonsubstituted oligomer. II (R1 ¼ p-NO2-phenyl; R2

¼ CH3CH2CH2A). III (R1 ¼ p-NO2-phenyl; R2 ¼ CH3CH2CH2AOA). IV (R1 ¼p-NO2-phenyl; R2 ¼ p-NH2-phenyl).V (R1 ¼ (CN)2C¼¼CHA; R2 ¼CH3CH2CH2A). VI (R1 ¼ (CN)2C¼¼CHA; R2 ¼ CH3CH2CH2AOA). VII (R1 ¼(CN)2C¼¼CHA; R2 ¼ p-NH2-phenyl).b rt ¼ rA � rD, where rA and rD stand by the Hammett parameters for

each individual acceptor and donor substituent, respectively. The values

used here were þ0.52 (dicyanovinyl), þ0.26 (nitrobenzene), 0.00 (hydro-

gen), �0.13 (propyl), �0.25 (propoxy), and �0.40 (phenylamine).



that near the donor group for all disubstituted systems.Thus, the introduction of D and A groups markedly changesthe PDES oligomers’ geometries and consequently, the valuesof the nonlinear coefficients. All of the studied systems have10 double bonds in the alternated carbon chain linking theD and A groups; thus, the difference between the dipolemoments of the ground and excited states is expected to besimilar among systems with equivalent linkers. According tothe simple two-level model, the first hyperpolarizability isdirectly related to the oscillator strength and inversely to theenergy gap.2,3 Therefore, the investigated systems can beoptimized for instance by increasing the oscillator strengthand decreasing the frequency of the lowest energy electronictransition.

Figure 4(b) shows the nice correlation between bmol and thetotal Hammett parameter, which is defined as rt ¼ rA � rD,where rA and rD are the Hammett parameters for each indi-vidual acceptor and donor substituent, respectively. We usedvalues of þ0.52 (dicyanovinyl), þ0.26 (nitrobenzene), 0.00(hydrogen), �0.13 (propyl), �0.25 (propoxy), and �0.40(phenylamine),93 with positive values for the acceptorgroups (rA) and negative values for the donor groups (rD).The rt values (included in Table 3) represent the strength ofthe polarization effect induced on the molecule by the sub-stituents. The results clearly show an increase in bmol withrt at the DFT level, regardless of the type of functional andbasis set used. As found for the BLA descriptor, a quadraticincrease of bmol is predicted with rt. For molecules IV (D ¼phenylamine and A ¼ nitrobenzene) and V (D ¼ propyl andA ¼ dicyanovinyl), we determined very close rt values of0.66 and 0.65 and also equally close bmol values of 21961and 22131 e.s.u., respectively (PBE1PBE/6-31G(d)//B3LYP/6-31G(d) values). These findings support the usefulness ofthe descriptor rt for the structure–property relationshipsestablished in this study.

The introduction of the D–A pairs is found to reduce theHOMO–LUMO gap (eHL) of all disubstituted oligomers (see

Table 4). The HOMO–LUMO gap is the difference betweenthe HOMO and LUMO energies in according to the Koop-mans’ theorem. Molecule VII with the phenylamine–dicyano-vinyl pair presents the smallest HOMO–LUMO gap accordingto the DFT calculations (1.19 eV at the PBE1PBE/6-31G(d)//B3LYP/6-31G(d) level). The experimental one-dimensionalgap of the PDES conjugated polymer is estimated to be�2.0 eV,7,28 which is in perfect agreement with the PBE1PBEresults for the nonsubstituted PDES decamer value of2.00 eV (see Table 4). Several systems characterized in theliterature having the strong acceptor dicyanovinyl displayvery low energy transitions for the charge transfer processes,which contribute to the increase in the nonlinear coeffi-cients.94,95 In addition, theoretical studies revealed largenonlinear responses for various polyenic and aniline deriva-tives with the acceptor dicyanovinyl group.2,25,87,88,96,97 Sev-eral experimental and theoretical studies have shown thatthe magnitude of the first hyperpolarizability of organic mol-ecules is associated with lower values of the HOMO–LUMOgap.2,3,24,56,57,96–99 As found in this work, the DFT resultsshowed that introduction of the D–A pairs decreases theground-state dipole moment (l) of the PDES derivatives incomparison with the nonsubstituted oligomer (see Table 4).The donor–acceptor decamers VI and VII display the highest

FIGURE 4 Structure–property relationships for the substituted-PDES polymers. The calculated property is the static first hyperpo-

larizability (bmol, PBEPBE/6-31G(d) values), and the structure is represented by (a) the topological BLA parameter and (b) the total

Hammett electronic descriptor (rt).

TABLE 4 Calculated HOMO–LUMO Gap (eHL, eV) and Dipole

Moment (l, D) for Free (I) and Substituted Oligomers (II–VII),

Using PBE1PBE/6–31G(d) Single-Point Calculations with B3LYP/

6–31G(d) Fully Optimized Geometries (PBE1PBE/6–31G(d)//

B3LYP/6–31G(d))


eHL 2.00 (2.0)a 1.73 1.60 1.55 1.39 1.26 1.19

l 10.39 3.66 2.70 1.46 4.86 8.53 8.00

The experimental gap is given in parentheses.a Experimental one-dimensional gap for the PDES conjugated

polymer.7,28



ground-state dipole moments among the substituted oligom-ers according to the DFT calculations.

Finally, it is important to clarify that there are various waysof expressing b mathematically as given by eqs 1–3. Table 2shows a comparison between the bmol and bvec values calcu-lated at the PBE1PBE/6-31G(d)//B3LYP/6-31G(d) level. Thedefinition of bvec depends on the x, y, and z dipole momentcomponents, so it can be positive or negative. For structure Imissing the A and D groups, we found that bvec ¼ bmol, indi-cating that the charge transfer is unidirectional and parallelto the molecular dipole moment, which is in the x direction(|l| ¼ lx with ly ¼ lz ¼ 0). The definition of bvec impliesthe use of a frequency-dependent field to generate the bi val-ues; however, our calculations concern static hyperpolariz-ability. Nevertheless, for structures V, VI, and VII, the abso-lute values of bvec and bmol are practically the same (Table2), so the second-order response to the applied field will besampled in electric field-induced second-harmonic genera-tion (EFISH) measurements. Structure VII has the highestvalue of b independent of the way it is defined and is cer-tainly a prominent candidate for applications in the nonlin-ear optics field.

CONCLUSIONS

The search for molecules possessing a large value of firsthyperpolarizability (b) is a key step toward the optimizationof new materials for NLO response applications. Theoreticalmethods have been considered as useful techniques for pre-diction of polarizabilities and hyperpolarizabilities avoidingan expensive large amount of experimental synthetic workthat precedes the measuring of NLO properties, what maynot lead to a desired compound for practical applications.The main goal of this work was to screen molecules withenhanced nonlinear responses within a specific class of com-pounds. Therefore, the relative hyperpolarizability values aremore important than the absolute values, and we showedthat DFT-based methods can be of great aid in searching fornew nonlinear chemical compounds. Our results indicatedthat the PBE1PBE/6-31G(d) level of calculation, using eitherPBE1PBE or B3LYP optimized geometries, is adequate forthe calculation of first hyperpolarizabilities of PDES-substi-tuted oligomer and related molecular systems. In addition,the relative increase in the bmol values along a series ofoligomers (I–VII) is equally described at the B3LYP/6-31G(d) level and can also be satisfactorily predicted by theSVWN or M06-2X functional. All DFT calculations predictedmuch enhanced values of the static first hyperpolarizability(bmol) for the donor–acceptor derivatives of diethynylsilane,ranging from 8 to 35 times the value of the nonsubstitutedoligomer (structure I) depending on the specific functionalused. In addition, reliable structure–property relationshipswith the first hyperpolarizability were determined for theclass of molecules investigated (BLA and Hammet parame-ters). The presence of an electric field as well as a solventwould further increase the nonlinear coefficients of the stud-ied systems. Further enhancement of the magnitude of the bhyperpolarizability can also be achieved by introducing D

and/or A groups in the Si heteroatom on the rings of thePDES decamer, which should increase the molecular asym-metry. The results obtained in this work demonstrate thatdisubstituted diethynylsilane decamers might be used aspotential building blocks for molecular-based materials witha second-order nonlinear response. Furthermore, the model-ing resulted in derivatives that display very large a values,indicating that they may also be interesting for other practi-cal applications.

The calculated vector component of b along the dipolemoment direction (bvec) values indicated that the second-order response to the applied field will probably be sampledin EFISH measurements for some structures, including V, VI,and VII, where the magnitude of bvec is almost the same asbmol. Although PDES that is a p-conjugated polymer incorpo-rating Si have been theoretically and experimentally charac-terized as third-order NLO material, the remarkable b valuespredicted for the donor–acceptor PDES oligomers in thisinvestigation demonstrated their potential also for second-order nonlinear applications. Our very high DFT valuesobtained for the first hyperpolarizability, reported for thefirst time in the literature, will certainly stimulate experi-mental measurements of nonlinear properties for these oli-gomeric systems. In addition, emphasis must be placed inthe evaluation of the effect of thermal nonlinearities and theelectron–phonon interactions including anharmonic ones onthe b values, because it can contribute for further increaseof the nonlinear coefficients.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the financial support fromthe Conselho Nacional de Desenvolvimento Cientıfico e Tecno-logico (MCT/CNPQ) and Fundaçao de Amparo a Ciencia e Tec-nologia do Estado de Minas Gerais (FAPEMIG) to ourlaboratories. A. E. De A. Machado thanks the FAPEMIG for apostdoctoral grant.

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donor–acceptor diethynylsilane oligomers: a second-order nonlinear optical material

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