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A Series of Novel Derivatives with Giant Second HyperPolarizabilities, Based on Radiaannulenes, Tetrathiafulvalene, Nickel Dithiolene and Their Lithiated Analogues Aggelos Avramopoulos, Heribert Reis, Nicolás Otero, Panaghiotis Karamanis, Claude Pouchan, and Manthos G. Papadopoulos J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b02131 • Publication Date (Web): 05 Apr 2016 Downloaded from http://pubs.acs.org on April 6, 2016

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The Journal of Physical Chemistry

A Series of Novel Derivatives with Giant Second Hyperpolarizabilities, Based on Radiaannulenes, Tetrathiafulvalene, Nickel Dithiolene and Their Lithiated Analogues Aggelos Avramopoulos,a* Heribert Reis,a Nicolás Otero,b,c Karamanis,b Claude Pouchan,b Manthos G. Papadopoulos a* a

Panaghiotis

Institute of Biology, Pharmaceutical Chemistry and Biotechnology, National

Hellenic Research Foundation, 48 Vas. Constantinou Ave., Athens 11635, Greece. b

Equipe de Chimie Théorique, ECP Institut des Sciences Analytiques et de Physico-

chimie pour l’Environnement et les Matériaux (IPREM) UMR 5254, Hélioparc Pau Pyrénées 2 avenue du Président Angot, 64053 Pau Cedex 09, Pau, France. c

Departamento de Química Física, Universidade de Vigo,36310, Vigo, Galicia, Spain

ABSTRACT The main goal of this study was the design/recognition of a series of derivatives with exceptionally large hyperpolarizabilities, the understanding of the mechanism through which these properties are derived and the generalization of the resulting findings. Thus, we have studied the structure, a series of properties involving the excitation energies and the diradical character, but mainly the (hyper)polarizabilities of some oligomers of radiaannulene-tetrathiafulvalene (RA-TTF), radiaannulene-bis(ethylene1,2-dithiolato)nickel (RA-NiBDT), and their lithiated analogues. The employed methodology involves MP2 and DFT techniques; approaches for the computation of static and frequency dependent properties; techniques for the calculation of electronic and vibrational contributions. The polarizability has been partitioned be employing the fractional occupational Hirshfeld iterative method. Indices for the calculation of the diradical character of the NiBDT oligomers have been employed. We have found that: (i) Oligomerization increases γzzzz (second hyperpolarizability), (ii) Substitution of TTF with NiBDT leads to a very large increase of γzzzz and (iii) Lithiation leads to extremely large nonlinearities. The importance of NiBDT and lithium as building blocks for the production of NLO materials is highlighted. * Corresponding Author : [email protected]

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INTRODUCTION The optimization of non-linear optical (NLO) materials, which have a very large number of applications (e.g. photonics,1-2 material science,3-4 biology5), requires an in-depth understanding of the NLO properties at the microscopic level.6,7 Such an understanding

may

be

promoted

by

structure/(hyper)polarizabilities relationship.

the 5, 7-10

systematic

study

of

the

In this study we employ this

relationship for the design of some derivatives with exceptionally large hyperpolarizabilities. NLO molecular materials can be classified in to two categories: Inorganic and organic.11 Organic materials are advantageous over their inorganic counterparts due to: i) their fast non-linear response times, ii) their lower cost, iii) the greater easiness with which their structure is tuned to manipulate their physico-chemical properties, thus enhancing a specific NLO effect, iv) their inclusion within polymers and films, which are the building blocks of nano-NLO devices.12-13 The π-electron delocalization is one of the basic molecular structural factors required for achieving large γ (second hyperpolarizability) and χ3 (third-order susceptibility).11,

14

One dimensional π-electron polymeric materials have been

extensively studied due to the variety of their structure, their fast NLO response and their incorporation into films.13 Conjugated oligomers with a chain length of several tens of nanometers may give large χ3 values.15 Other factors, which may contribute to development of materials with large third-order NLO properties are the low-lying excited states,16 planarity14, functionalization with proper groups (e.g π-electron rich) 11

and the increase of the diradical character (DC). DC has been found to significantly

affect the molecular second hyperpolarizability.17 Organic chromophores with small band gap have found applications in NIR photodetectors and NLO materials.1-2, 18-19 The NLO response of organic compounds can be extremely high under resonant conditions. 11 Annulenes are fully conjugated hydrocarbon monocycles20 and they have been used as a models to study aromaticity.21 [4n+2]-annulenes act as prototypes of onedimensional metals.22 Non-planar [4n]-annulenes have been employed as functional building blocks for electromechanical actuators and protecting groups for 2 ACS Paragon Plus Environment

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supermolecular interactions.22 Zhou et al. proposed that some annulene derivatives may be promising materials with high third-order NLO activity.23 Several groups have reported studies on their L&NLO properites.21, 24-25 Sarkar et al. reported experimental values of second-order NLO response of dehydrobenzo[18]-annulenes, by applying the hyper-Rayleigh scattering method.26 Radialenes are alicyclic organic compounds containing n-cross conjugated exocycling double bonds.27 Their interesting structure and unusual electronic properties have been studied by several research groups.28 [3]radialene,29 [4]radialene,30 [5]radialene

31

and [6]radialene32 have been synthesized. Expanded

radialenes are macrocyles that arise from the insertion of acetylic spacers into cyclic carbon-core.28, 33 The synthesis of expanded [3,4]radialenes has also been reported.28 Radiaannulenes (RA) are cyclic molecules, which have exo- and endocyclic double bonds34 and their structures lie between radialenes27 and annulenes.35 33, 36-38

radiaanulenes have been synthesized active in electron-accepting materials.

39

Several

and have been characterized as redox-

Combination of different functional groups

in radialenes and radiaannulenes may lead to the fabrication of

materials with

interesting optical and electronic properties.40 41 Our work was stimulated by the synthesis of a tetrathia-fulvalene-functionalized radiaannulene compound (TTF/RA), which has multiple redox states and could potentially lead to the development of advanced electrically conducting materials.34 A 2D π-conjugated nickel bis(dithiolene) complex nanosheet has been reported by using a bottom-up approach.42 Wang et al.43, demonstrated, by employing first-principles computations, that the synthesized 2D organometallic material, Ni3C12S2, can be identified as an organic topological insulator material with potential applications in spintronics and quantum computing.43 A 1D π-conjugated nickel bis(dithiolene) complex polymer has also been synthesized by using a liquid-liquid interfacial reactions.44 Previous studies of our group have shown that substitution of the central C=C of TTF by Ni has a large effect in the L&NLO properties.45-46

The resulting

bis(ethylene-1,2-dithiolato)nickel (NiBDT) has many interesting properties (e.g. photochemical and thermal stability, tunable properties), due to which it is considered to be a very promising material.47-49 Several theoretical studies have also shown that lithiation may lead to a significant increase of the second hyperpolarizability. 50,51-55 3 ACS Paragon Plus Environment


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Taking into account the above observations and findings, we set two objectives, the first of which was to design a series of oligomers, based on RA-TTF, RA-NiBDT and their lithiated derivatives, aiming at large second hyperpolarizabilities. Indeed, some of the proposed compounds have extremely large nonlinearities. The second objective of this study was to interpret the calculated large and interesting hyperpolarizabilities. To achieve the above goals we used a large array of computational techniques; these allowed to discuss several aspects of the molecular polarization. A longer term goal of this exercise is to develop a set of rules, which may guide one on the design of NLO materials with optimized properties. The article is organized as follows: In section II we describe the methods we have used, in section III we analyze our results and finally in section IV we give our concluding remarks.

II

Methods

All the reported data for the molecular structures, static and frequency dependent electronic (hyper)polarizabilities, vibrational contributions, EHOMO, ELUMO and the excitation spectrum of (TTF)m+1(RA)m, (NiBDT)m+1(RA)m, where m=1-3, and their lithiated derivatives have been calculated by employing a computational procedure which includes, ab-initio methods (MP256), Density Functional Theory (B3LYP57 (U)CAM-B3LYP,58 (U)BHandHLYP59 ); analytic60 and a finite field method for the computation of the (hyper)polarizabilities.61

The basis set effect. Most of the present results have been computed by employing two functionals, the (U)CAM-B3LYP and (U)BHandHLYP with the 6-31G*62 basis set for C, S, Li, H atoms. For Ni a quasi-relativistic, effective-core potential, ECP28MWB (SDD), was employed.63 To confirm the adequacy of the CAMB3LYP/6-31G* method, for the selected compounds, we have performed calculations, employing MP2 and a series of larger basis sets, involving more diffuse and polarization functions (Table 1).

It is observed that the effect of the added

polarization functions on C,S (6-31G/6-31G*) is significant for all the studied properties, especially for γzzzz. The CAM-B3LYP/6-31G* and MP2/6-31G* results demonstrate that there is a discrepancy for ELUMO and EHOMO-ELUMO (H-L). However, both methods give αzz and

γzzzz in satisfactory agreement. Addition of diffuse 4

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functions (6-31G*, 6-31++G*)

has a small effect on the considered properties. The

basis sets, 6-31G*/6-311++G** and 6-31G*/ aug-cc-pVDZ, give results, which are in reasonable agreement. A detailed study for the good performance of UBHandHLYP/6-31G* for NiBDT and related derivatives, has been presented elsewhere.64-65 The above results (Table 1) show that the (U)CAM-B3LYP/6-31G* is adequate for the study of the selected derivatives. Molecular Structures. All the employed molecular structures were optimized by using the B3LYP/6-31G* method (Figures 1 and 2). B3LYP has been successfully applied for the study of the structures and relative energies of polylithiated benzene compounds.66 In order to check the effect of basis set on the quality of structures, we optimized (TTF)2(RA) (2; Figure 1) at the B3LYP/aug-cc-pVDZ level. Both methods (B3LYP/6-31G*, B3LYP/aug-cc-pVDZ) gave similar geometries (Figure S1). The root mean square standard deviation, between the two optimized structures, is 0.043. All the (TTF)m+1(RA)m structures and their lithiated analogues are non-planar, having a rippled-like structure (Figure S2). The molecular structures of (NiBDT)m+1(RA)m and their lithiated derivatives were optimized by using the broken symmetry UB3LYP/6-31G* method. The latter approach has been shown to provide fairly accurate geometries for conjugated systems, including transition metal atoms.46 Both (NiBDT)m+1(RA)m and their lithiated analogues are planar and lie on the XoZ plane (Figures 1 and 2, Figure S2), with their longitudinal axis oriented along z axis. Planar structure has also been computed for the tetranuclear nickeladithiolene complex by using B3LYP/6-31G* method.44 For all structures employed in this study, vibrational analysis was used in order to verify that a stationary point has been found. Excitation Spectrum. The transition energies and transition dipole moments were computed by employing the time-dependent density functional theory (TD-DFT)67-68 using the CAM-B3LYP functional.58 The latter provided satisfactory estimates of transition energies for some organic dyes, compared with experiment.69-72 In Figures S3-S8, the first dominant transitions, computed with the aid of natural transition orbital pairs73, for compounds 2,3,6,5,8 and 11 are presented. Electronic (hyper)polarizabilities. When a molecule is set in a uniform static electric field F, its energy, E, may be expanded as follows: E= E0 – µiFi – (1/2)αijFiFj –(1/6)βijkFiFjFk – (1/24)γijklFiFjFkFl –...,

(1) 5

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where E0 is the field free energy of the molecule, Fi, Fj, Fk,Fl are the electric field components, µi, αij, βijk and γijkl are the tensor components of the dipole moment, linear dipole polarizability, first and second hyperpolarizability, respectively. Summation over repeated indices is implied. The considered systems have βijk, which is zero or close to zero, due to symmetry considerations. The components of the static αij(0;0), and αij(-ω;ω) were calculated analytically.60 For the computation of the static second hyperpolarizability components, γiiii (0;0,0,0), where i=x,z, the electro-optical Kerr effect (EOKE), γiiii (-ω;ω,0,0), and the electric-field-induced second-harmonic generation (EFISH) values, γiiii (-2ω;ω,ω,0), a finite field approach was employed. In order to safeguard the numerical stability for γiiii the Romberg-Rutishauser approach was used74-76. For all calculations, field strengths of magnitude 2mF, where m=0,1,2,3,4 and a base field (F) of 0.0004 a.u. were used.

All the static γiiii

components were computed by the second order derivative of αii with respect to the applied electric field. The OKE values were calculated from the second derivative of αij(-ω;ω) with respect to the electric field. The EFISH values were computed from the first derivative of βiii(-2ω;ω,ω) with respect to the electric field. The values of βiii(2ω;ω,ω) were computed analytically, at ω=0.0182 a.u. All the static and frequency dependent molecular properties were computed by using the long range corrected version

of

B3LYP,

CAM-B3LYP,

which

yields

satisfactory

values

of

(hyper)polarizabilities of large and extended molecular systems.77 The reported linear and non-linear properties of (NiBDT)m+1(RA)m and their lithiated analogues have also been calculated

with the BHandHLYP functional, which provides

satisfactory

second hyper polarizability values of diradical molecules. 45 In this work we focus our attention, mainly, on the electronic contributions to (hyper)-polarizabilities. However, we have also computed some vibrational contributions to (hyper)polarizabilities of two test cases (2 and 8). The methods we have used for the calculation of the vibrational contributions are presented in the next section. Vibrational (Hyper)polarizabilities. The properties occurring in Eq. 1 generally refer to the geometry of the molecule without applied field, which means that they constitute the electronic contribution. However, the applied field may also change the geometry of the molecule, which thus acquires different electric properties. The difference between the property of the two sets of geometries is the so-called nuclear relaxation (NR) contribution, which is generally the largest part of the vibrational 6 ACS Paragon Plus Environment

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contributions to the NLO properties (for the remaining parts see below). NR contributions for compounds 2 and 8, were computed in the general framework of perturbation theory, as pioneered by Bishop and Kirtman.78-80

Specifically, two

methods were applied, in the first one, the so-called field-induced coordinates (FICs), as introduced by Luis et al81, were used for both compounds to compute the nuclear relaxation (NR) contribution to the static polarizability as well as the NR contribution to three different second hyperpolarizability effects, the electric field induced second harmonic generation, γ(−2ω;ω,ω,0), the electro-optic Kerr effect, γ(−ω;ω,0,0), and the intensity-dependent refractive index (IDRI) effect γ(−ω;ω,ω,−ω), in the infinite optical frequency approximation (IOFA), that is with ω→∞. In this limit, all NR contributions containing only non-zero frequencies in their sum-over-states expressions, such as THG γ(−3ω;ω,ω,ω), vanish. Although the frequency arguments for the IDRI effect are all non-zero, there are intermediate terms in the SOS equation for IDRI with a vanishing frequency, and which thus contribute to yield a non-zero NR contribution.81 Unfortunately, the computation of the NR contribution to the static second hyperpolarizability γ(0;0,0,0), is rather difficult using FICs,81 thus this property was computed using another approach introduced by Bishop, Hasan and Kirtman,82 which is based on the optimization of the geometries in different externally applied fields. As both approaches yield the static polarizability, this property allows a check of the consistency of applying perturbation theory for the molecules considered here, which show normal coordinates with rather small frequencies, and may thus have large anharmonic contributions. These may, in extreme situations, render the application of perturbation theory to the calculation of vibrational contributions to linear and non-linear optical properties questionable. In addition to the NR contributions, there are additional higher-order contributions called curvature effects, as well as contributions due the to zero-point vibrational average (ZPVA). Both effects are extremely expensive to calculate for molecules of the size considered here, and were thus not computed.

The calculations using FICs were conducted as

described in Ref.81, computing both the first-order FICs q1 as well as the harmonic components of the second-order FICs q2har, using a standard displacement of ∆q1= ∆q2har=0.04 a.u. for the calculation of numerical derivatives with respect to the FICs. The reliability of the numerical derivatives was checked by repeating the procedure with a second displacement with ∆q1= ∆q2har=0.02 au. For the field-dependent 7 ACS Paragon Plus Environment


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optimization approach (FDOA), several field strengths ±2nF a.u., where n=1-5, and F=0.0001 a.u., were applied, and the results were analyzed following ref. 83. A Romberg-Rutishauser approach was used for the numerical differentiations, with respect to the applied field.75-76 Property partitioning and electron delocalization indices. To partition the dipole polarizability in terms of atomic contributions, we relied on the fractional occupation Hirshfeld Iterative (FOHI) scheme.84-85 This extension of the Hirshfeld-I method is based on an idea of Hirshfeld,86 i.e., the use of diffuse boundaries resembling the isolated atom densities, but including the influence of the other atoms. Within the framework of this method, Otero and co-workers proposed an approach,,87-89 which allows to use standard visualization techniques to plot Mean Intrinsic Polarizability (MIP) densities in the form of surface and/or mapped representations, as any other density (e.g., electron or spin density). The term "intrinsic polarizability" refers to the pure polarizability of each atom of the molecule, free of charge transfer interactions (for more information see ref. 89 and references therein). In addition, for the needs of the discussion, we computed electron 2- and 5-center delocalization indices, which represent a measure of "how many" electrons are delocalized or shared among several atomic regions with respect to a null Fermi-hole density.90 These indices have been obtained through a real space scheme implementation (see supporting material of ref 91), via the Generalized Population Analysis.92 For these calculations we developed a FORTRAN code based on the QTAIM implementation of Mandado and coworkers.90, 93

In figure 3, we provide an application of both the above treatments on the

molecules of C5H5 and C3S2H3. For the sake of simplicity, only positive MIP isodensities are plotted (hereafter +MIP), representing regions in which the accumulation of the perturbed electron density is higher than in the unperturbed one (see discussion in ref 89). The numbers comprised in each of the above rings represent the 5-centerdelocalization indices (5-DI/au) computed at CAM-B3LYP/6-31G* level of theory. As seen, the more aromatic C5H5 is characterized by dramatically larger 5-DI values. All the computations were performed by employing the GAUSSIAN software.60


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III. RESULTS We shall consider the effect of: (i) oligomerization and (ii) the replacement of TTF with NiBDT, on EHOMO, ELUMO, |H-L| and the (hyper)polarizabilities -static and frequency dependent, electronic and vibrational contributions- of the designed derivatives as well as the effect of lithiation on the above properties. The experimental work which motivated us to perform the present study was based on 1 (Figure 1).34 To shed light on the nature of the dipole-polarizability, in terms of atomic contributions, we have applied a treatment based on the Fragmented Orbital Hirshefeld Iterative method (FOHI) on compounds 2, 3, 5, 9 and 12, which represent the most characteristic cases in the group of molecules we considered here. To facilitate our computations we removed the peripheral functional groups (e.g. EtS, iPr3S) and compared the properties of 1 with those of its truncated structure, 2. Of course, the (hyper)polarizabilities of 1 are larger than those of 2, but the basic physical phenomena, which are of interest in this work (e.g. conjugation, effect of Ni) are present in 2, thus, we shall base our study on it.

1.

Oligomers of TTF and NiBDT

Structure. Compounds 2-4 are non-planar, while 5-7 are planar (Figure 1). The structures are displayed in SI (Figure S2). EHOMO, ELUMO, |H-L|. There is a very small variation of these properties with the size of the molecule (Table 2). Specifically, EHOMO of 2-4 and 5-7 decreases and increases, respectively, as the size of the molecules increases. ELUMO of 2-4 decreases with the increasing size of the molecule. |H-L| of 2-4 and 5-7 decreases as the size of the molecule increases. A noticeable decrease of EHOMO and ELUMO is observed by replacing the central C=C of TTF by Ni, for example EHOMO(4)-EHOMO(7) = 0.022 a.u. Excitation Energies. The results for the first excitation energies, Eexc (Tables 2 and 3) show two distinct trends: First, Eexc of the TTF oligomers (including their lithiated derivatives) increases with the size of the oligomer, second, Eexc of the NiBDT ( including the lithiated ones) compounds, decreases as the oligomer increases in size. The experimental value for the first excitation of 1 is 1.9 eV,34 while our computed value (CAM-B3LYP/6-31G*) is 2.15 eV.



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Electronic Polarizabilities. αzz> αxx, for 2-4, however, these properties do not have significantly different magnitude; αzz is much larger than αxx, for 5-7 (Table 2). In Figure 4 we show positive mean intrinsic polarizability (+MIP) density contrasts, mapped on the molecular plane and the atomic intrinsic polarizabilities of some selected atoms for 2, and +MIP mapped-sphere representations for 3. FOHI analysis suggests that the most polarizable areas of both molecules are primarily located in the vicinity of the S atoms and, secondarily, at the external acetylenic units. The eight sulfur atoms, in 2, account for the 50% of the total molecular mean intrinsic polarizability, while in 3, the corresponding contribution of the twelve S atoms amounts to 46 %.

Interestingly, going from 2 to 3 the average value of the intrinsic atomic

polarizabilities of S atoms remains practically unchanged (7.5 au in both molecules). In terms of functional groups, the two -H2C6S4 fragments contribute an amount of ~63 and ~56% of the total intrinsic polarizabilities of 2 and 3 respectively. For the transition from 2 to 5, the mean intrinsic atomic polarizabilities of the S atoms decrease from an average value of 7.5 to 5.75 a.u., due to the presence of Ni atoms. In this molecule the two C4S4Ni units account for 63% of the mean intrinsic molecular polarizability, a value that matches the contribution of TTF-unit (-C6S4) in 2. The density contour plots shown at the bottom of figure 5 represent the deformation of +MIP density for the transition from the most stable electronic configuration of 5, open-shell-singlet in character, to the corresponding singlet-closed-shell state. It is obvious that the most intense +MIP-density differences occur mostly on the C4S4Ni fragments due to the presence of Ni, and implicate all of their atoms. Electronic Hyperpolarizabilities. γxxxx is smaller than γzzzz and their difference increases with the increasing molecular size. In particular, for 5-7, their difference is very large, for example γzzzz (6)/γxxxx(6)=552(UCAM-B3LYP/6-31G*; Table 2). Thus, our analysis will focus on γzzzz. Addition of the first and second TTF units contribute 25.3x105a.u. and 32.2x105a.u., respectively, while the contributions of the first and second RA-NiBDT units are 1293x105a.u. and 2483x105a.u., respectively. These contributions have been calculated with the UCAM-B3LYP functional. The corresponding values with the UBHandHLYP are 894x105a.u. and 1830x105a.u., respectively. The index: γzzzz/N=PEC gives the per electron contribution to γzzzz, where N is the number of electrons of the corresponding molecule. PEC for 2-4 varies from 4.2 to 9.2x103a.u., while this index for 5-7 varies from 65.9 to 500 10 ACS Paragon Plus Environment

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x103a.u.(method: (U)CAM-B3LYP). The corresponding variation for UBHandHLYP is 51.7-362.5 x103a.u. The PEC index values for 2-4 and 5-7 should be compared with the corresponding value of C6H6, which is 42.3 a.u. (CAM-B3LY/6-31G*). This comparison is useful, since benzene is the prototype of second order NLO materials. These results (Figure 6) clearly demonstrate the great effect of oligomerization and NiBDT on the second order hyperpolarizability (γzzzz). The following definitions are used for the anisotropy of the

polarizability and second hyperpolarizability,

respectively: α = αzz - αxx and γ = γzzzz - γxxxx. We observe for the TTF oligomers (Τable 1):

[(TTF)2(RA)1]: α = 38.0 a.u., γ = 3.110 . .,

[(TTF)3(RA)2]: α = 109.3 a.u., γ = 20.310 . . and [(TTF)4(RA)3]: α = 245.0 a.u, γ = 44.010 . .

Both α γ , increase with the number of TTF and RA units (Figure S10).

The following anisotropies have been found for the NiBDT oligomers (Table 2):

[(NiBDT)2(RA)1] α = 730.5 a.u., γ = 222.110 . .,

[(NiBDT)3(RA)2] α = 2036.9 a.u., γ = 1514.210 . . and

[(NiBDT)4(RA)3] α = 3573.7 a.u.

These values were computed with UCAM-B3LYP/6-31G*. It is observed that: i) α γ significantly increase with the number of NiBDT units (Figure S9) and ii) α γ , of [(NiBDT)m+1(RA)m] are remarkably larger, compared with those of [(TTF)m+1(RA)m] (Figure S10). Similar trends have been found for the values computed with the UBHandHLYP functional. A very substantial increase of γzzzz(-2ω;ω,ω,0) in comparison with γzzzz(-ω;ω,0,0) is observed for 5 (Table 4). Interpretation of Electronic Hyperpolarizabilities. In this section we report a qualitative explanation of why γzzzz(5)>γzzzz(2), or why substitution of TTF with NiBDT leads to a large enhancement of the second hyperpolarizability. This discussion will be based on the Sum-Over-States (SOS) approach. The analytical expression of γ can be partitioned into three terms:94 γ =γΙ + γΙΙ +γΙΙΙ

(2)



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Specific expressions for the above terms, which have been computed by employing the CIS/6-31G* (configuration interaction singles) method, are given in the SI. A validation study for the adequacy of the CIS method is also reported in SI. γI for 2 and 5 is zero, since they are centro-symmetric. The results of γIIzzzz(=γII) and γIIIzzzz (=γIII) for compounds 2 and 5 are reported in SI (Table S1). It is observed that for both compounds |(γΙΙΙ)| > | (γΙΙ)|, implying that γzzzz>0.0. The SOS computed values are: (γΙΙ +γΙΙΙ) (5) =10289a.u. and (γΙΙ +γΙΙΙ) (2) = 6424 a.u. The SOS computed inequality, γzzzz(5) > γzzzz (2), is in agreement with that shown by the DFT results (Table 2). For 5, the ground to excited states transitions lie in the range 3.08-4.63eV (5.29-5.85 eV), while the excited to excited state transitions are in the range 3.20-6.28 eV (4.07-7.99eV). The transition energies in parentheses are the corresponding values for 2. Thus, qualitatively, one may say that the higher γzzzz(5), in comparison with γzzzz (2), is due to the observed lower lying excited states of 5, compared with those of 2. A similar reasoning have also been used to rationalize the higher hyperpolarizability of NiBDT(γzzzz=558x103 a.u.) in comparison to that of TTF (γzzzz=32.9x103 a.u.).64 It has been found that in TTF (tetrathiafulvalene) a single transition (πσ*) is present below 3eV,95 but NiBDT has no less than 16 states in the visible spectrum.45

2.

Lithiated oligomers of TTF and NiBDT

Table 3 presents the effect of lithiation on EHOMO, ELUMO, |H-L| and the (hyper)polarizabilities of the considered derivatives. In the two classes of oligomers, RA-TTF and RA-NiBDT, the two terminal hydrogens bonded to TTF or NiBDT are substituted with Li. Structures. Lithiation does not affect the shape of the derivative as comparison of TTF (or NiBDT) oligomers with their lithiated counterparts shows (SI; Figure S2 ). EHOMO, ELUMO, |H-L|. Lithiation leads to an increase of EHOMO, ELUMO and decrease of |H-L|. Electronic Polarizabilities. In all cases αxx

A Series of Novel Derivatives with Giant Second ... - ACS Publications

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