Coordination and Organometallic Complexes as Second-Order Nonlinear Optical Molecular Materials

Abstract

Coordination and organometallic complexes with second-order nonlinear optical (NLO) properties have attracted increasing attention as potential molecular building block materials for optical communications, optical data processing and storage, or electrooptical devices. In particular, they can offer additional flexibility, when compared to organic chromophores, due to the presence of metal–ligand charge-transfer transitions, usually at relatively low-energy and of high intensity, tunable by virtue of the nature, oxidation state, and coordination sphere of the metal center. This chapter presents an overview of the main classes of second-order NLO coordination and organometallic complexes with various ligands such as substituted amines, pyridines, stilbazoles, chelating ligands (bipyridines, phenanthrolines, terpyridines, Schiff bases), alkynyl, vinylidene, and cyclometallated ligands, macrocyclic ligands (porphyrins and phthalocyanines), metallocene derivatives, and chromophores with two metal centers. The coverage, mainly from 2000 up to now, is focused on NLO properties measured at molecular level from solution studies, as well as on NLO properties of bulk materials.

1 Introduction

Compounds with second-order nonlinear optical (NLO) properties are of great interest as molecular building block materials for optical communications, optical data processing and storage, or electrooptical devices [1–3]. Among them, organometallic and coordination metal complexes represent an emerging and growing class of second-order NLO chromophores that can offer additional flexibility, when compared to organic chromophores, due to the presence of metal–ligand charge-transfer (MLCT) transitions usually at relatively low energy and of high intensity, tunable by virtue of the nature, oxidation state, and coordination sphere of the metal center. Since the discovery of the second harmonic generation (SHG) for a ferrocenyl compound [4], increasing attention has been paid to organometallic and coordination complexes as potential second-order NLO chromophores. Extensive investigations have thus been carried out in this area. Early [5–9] and more recent [10–19] review articles on coordination and organometallic complexes with second-order NLO activity indicate the breadth of the active research in this field.

The goal of this overview is to report on the recent advances in order to analyze the main characteristics of second-order NLO organometallic and coordination complexes, and their potential as new NLO active molecular materials. After a brief introduction about the principles of nonlinear optics, this chapter illustrates the main classes of second-order NLO organometallic and coordination chromophores, producing examples of chromophores with monodentate nitrogen donor ligands (amines, pyridines, stilbazoles), chelating ligands (bipyridines, phenanthrolines, terpyridines, Schiff bases), alkynyl, vinylidene, and cyclometallated ligands, macrocyclic ligands (porphyrins and phthalocyanines), metallocene derivatives, and chromophores with two metal centers. The coverage, mainly from 2000 up to now, is not exhaustive, but allows the nonspecialist to get into this specific field and to understand its potentiality. Relevant older data of prototypical compounds are also reported. The focus is on both NLO properties measured at molecular level from solution studies and NLO properties of bulk materials.

2 Principles of Second-Order Nonlinear Optics

The principles of nonlinear optics, including the techniques to evaluate the second-order NLO properties, are briefly presented here. Major details can be found in excellent books [1–3] and various reviews [5–19].

2.1 Basic Concepts and Methods

Nonlinear optics deals with optical phenomena, caused by the interaction of applied electromagnetic fields to molecules or materials with emission of new electromagnetic fields which differ in frequency, phase, or other physical properties from the incident ones [1–3]. This kind of optical phenomena are related to the polarizability of a molecule or of a bulk material.

When a bulk material is subjected to an oscillating external electric field produced by an incident radiation, there is a polarization effect, expressed by

$$\overrightarrow P = \overrightarrow {P_0 } + \overrightarrow {P_{{\rm{ind}}} } = \overrightarrow {P_0 } + \chi ^{(1)} \overrightarrow E ,$$

(1)

where $\overrightarrow {P_0 }$ is the intrinsic polarity, $\overrightarrow {P_{{\rm{ind}}} }$ the induced polarization, and χ⁽¹⁾ the electrical susceptibility or linear polarizability tensor. If the electric field strength $\overrightarrow E$ of the incident radiation is very high, as is the case with laser pulses, the perturbation is not linear and the induced polarization is better expressed by a power series according to

$$\overrightarrow P = \overrightarrow {P_0 } + \chi ^{(1)} \overrightarrow E + \chi ^{(2)} \overrightarrow {E^2 } + \cdots + \chi ^{(n)} \overrightarrow {E^n } ,$$

(2)

where χ ⁽²⁾, χ ⁽³⁾, and χ ⁽ⁿ⁾ tensors are, respectively, the second-, third-, and n-order electrical susceptibilities, controlling the nonlinear response of the material.

If, instead of a bulk material, the applied electromagnetic field is interacting with a molecule, the induced polarization is expressed by

$$\vec P = \mu _0 + \alpha \vec E + \beta \vec E^{\,2} + \gamma \vec E^{\,3} +\ldots,$$

(3)

where μ ₀ is the molecular ground state electric dipole moment, α the linear polarizability tensor, β and γ the non linear quadratic and cubic hyperpolarizability tensors, respectively, responsible for second- and third-order NLO effects. It is important to underline that both β and χ ⁽²⁾ vanish in a centrosymmetric environment. Therefore, to have a second-order NLO effect, the acentricity requirement must be fulfilled. This is not true for γ and χ ⁽³⁾.

The second-order NLO properties are of interest for a variety of NLO processes [1–3]. One of the most relevant is the SHG, originated by the mixing of three waves; two incident waves with frequency ω interact with the molecule or the bulk material with NLO properties, defined by a given value of the quadratic hyperpolarizability, β, or of the second-order electrical susceptibility, χ ⁽²⁾, respectively, to produce a new electrical wave, named SH, of frequency 2ω. Another important second-order NLO process is the electrooptic Pockels effect which requires the presence of an external d.c. electric field, E(0), in addition to the optical $\overrightarrow E$ (ω) electrical field. This effect produces a change in the refractive index of a material proportional to the applied electric field, and can be exploited in devices such as optical switches and modulators [1–3].

To obtain molecular or bulk materials displaying significant second-order NLO effects, high values of β or of χ ⁽²⁾, respectively, are required. In the case of molecules, in 1977 Oudar gave a theoretical interpretation of the electronic factors controlling β [20, 21]. The quadratic hyperpolarizability of a molecule is originated by the mobility of polarizable electrons under the effect of a strong electric field $\overrightarrow E$ associated with an incident radiation. It follows that it is dependent on electronic transitions which, being associated with a significant electronic mobility, are of high CT character. Oudar assumed that, when the second-order NLO response is dominated by one major CT process, β _zzz can be defined according to

$$\beta _{zzz} = \frac{3}{{2h^2 c^2 }}\frac{{\nu _{{\rm{eg}}}^2 r_{{\rm{eg}}}^2 \Delta \mu _{{\rm{eg}}} }}{{\left( {\nu _{{\rm{eg}}}^{\rm{2}} - \nu _{\rm{L}}^2 } \right)\left( {\nu _{{\rm{eg}}}^2 - 4\nu _{\rm{L}}^{\rm{2}} } \right)}},$$

(4)

where z is the axis of the direction of the CT, ν _eg (cm⁻¹) the frequency of the CT transition, r _eg the transition dipole moment, Δμ _eg the difference between excited state μ _e and ground state μ _g molecular dipole moments, and ν _L the frequency of the incident radiation. Equation (4) is the so-called “two level” model, a way to estimate the frequency dependent quadratic hyperpolarizability for specific types of second-order NLO chromophores, characterized by a single dominant CT transition. Extrapolation to zero frequency (ν _L = 0.0 eV; λ = ∞) allows estimation, according to Eq. (5), of the static quadratic hyperpolarizability β ₀, a useful figure of merit to evaluate the basic second-order NLO properties of a molecule:

$$\beta _0 = \beta _\lambda \left[ {1 - \left( {{{2\lambda _{\max } } \mathord{\left/{\vphantom {{2\lambda _{\max } } \lambda }} \right.\kern-\nulldelimiterspace} \lambda }} \right)^2 } \right]\left[ {1 - \left( {{{\lambda _{\max } } \mathord{\left/{\vphantom {{\lambda _{\max } } \lambda }} \right.\kern-\nulldelimiterspace} \lambda }} \right)^2 } \right],$$

(5)

where β _λ is the quadratic hyperpolarizability value at λ incident wavelength and λ _max is the absorption wavelength of the controlling major CT. The molecular quadratic hyperpolarizability β can be expressed both in the cgs (cm⁴ statvolt⁻¹ = esu) or in the SI (C m³ V⁻²) unit systems (the conversion from the SI to the cgs system is given by the relation 10⁻⁵⁰ C m³ V⁻² = 2.694 × 10⁻³⁰ esu).

From the “two level” model it is possible to extrapolate the dipolar electronic requirements that a molecule must fulfill in order to show a significant second-order NLO response. It must be noncentrosymmetric, with CT transitions with large Δμ _eg and r _eg and at relatively low energy. This can be achieved, for instance, by separation of an electron-donor and an electron-acceptor group with a π-conjugated polarizable spacer, as occurs in classical 1D dipolar push–pull organic systems. Recently, multipolar systems, such as octupolar molecules, have been increasingly investigated, because it was shown that it is not only dipolar structures that may be the origin of significant SHG [1–3, 10–19].

From a theoretical point of view, various quantum mechanical methods allow the calculation of the molecular quadratic hyperpolarizability, β. Among them, the “sum over states” (SOS) approach also gives a useful way to define the electronic origin of the NLO response. Density functional theory (DFT) and time-dependent DFT (TD-DFT) or time-dependent HF (TD-HF) calculations [22, 23] are the most advanced theoretical methods. In particular, referring to the SOS method, it describes the tensor β _ijk in terms of all the electronic states interacting with the perturbing electric field, as an infinite expansion over a complete set of unperturbed excited states. Obviously, a simplification of this approach is the two-state model (Eq. 4) described above. These theoretical methods are a useful way of understanding hyperpolarizability–structure relationships, thus helping chemists to the design of new efficient molecular NLO chromophores.

Experimentally, mainly two techniques – the electric field induced second harmonic generation (EFISH) and hyper-Rayleigh scattering (HRS, also termed harmonic light scattering method) – are used in order to determine in solution the experimental value of the quadratic hyperpolarizability of molecular NLO chromophores.

The EFISH technique [24], suitable for dipolar neutral molecules, provides information on the molecular NLO properties through

$$\gamma _{{\rm{EFISH}}} = \left( {{{\mu \beta _{\rm{\lambda }} } \mathord{\left/{\vphantom {{\mu \beta _{\rm{\lambda }} } {5kT}}} \right.\kern-\nulldelimiterspace} {5kT}}} \right) + \gamma \left( { - 2\omega ;\omega ,\omega ,0} \right),$$

(6)

where ${{\mu \beta _{\rm{\lambda }} } \mathord{\left/{\vphantom {{\mu \beta _{\rm{\lambda }} } {5kT}}} \right.\kern-\nulldelimiterspace} {5kT}}$ represents the dipolar orientational contribution, and γ (−2ω; ω, ω, 0), β _λ a third-order term at frequency ω of the incident wavelength, is the electronic contribution which is negligible for many molecules with a limited electronic polarizability. β _λ is the projection along the dipole moment axis of β _VEC, the vectorial component of the β _ijk tensor of the quadratic hyperpolarizability, working with an incident wavelength λ of a pulsed laser. To obtain the value of β _λ , it is thus necessary to know the value of the ground state dipole moment μ of the molecule. Moreover, in order to avoid overestimation of the quadratic hyperpolarizabilty due to resonance enhancements, it is necessary to choose an incident wavelength whose second harmonic is far from any electronic absorption of the molecule.

The HRS technique [25–27] involves the detection of the incoherently scattered second harmonic generated by the molecule in solution under irradiation with a laser of wavelength λ, leading to the mean value of the β × β tensor product. By analysis of the polarization dependence of the second harmonic signal, which can be evaluated selecting the polarization of the incident and scattered radiation, it is possible to obtain information about the single components of the quadratic hyperpolarizability tensor β. Unlike EFISH, HRS can also be used for ionic molecular species and for nondipolar molecules such as octupolar molecules. In this chapter, the quadratic hyperpolarizability measured with an incident wavelength λ by the EFISH and HRS techniques will be indicated as β _λ (EFISH) and β _λ (HRS), respectively.

Since the “two level” model (Eq. 4) applies well to NLO chromophores characterized by a major CT transition, the solvatochromic method may afford a way to evaluate the quadratic hyperpolarizability, but only the component along the major CT direction, β _λ (CT), by recording electronic absorption spectra of this absorption band in a series of solvents covering a wide range of dielectric constants and of refraction indexes [28]. This method, which does not require sophisticated instrumentation, can give a fair to good estimate of the quadratic hyperpolarizability, for instance in the case of 1D dipolar push–pull molecules, and at the same time it may allow the evaluation of the contribution of a given absorption band to the β value. This method may be more accurate in the case of fluorescent compounds, by combining the solvatochromic study of both absorption and emission spectra [28]. It should be emphasized that β _λ (EFISH) and β _λ (CT) values can be compared only when the dipole moment axis and the direction of the CT are roughly the same.

The static hyperpolarizability β ₀ can also be evaluated by means of Stark (electroabsorption) spectroscopy, which affords the value of Δμ _eg by analyzing the effects of an applied electric field on the shapes of the major absorption bands of CT character [29–31]. The contribution of each transition to the quadratic hyperpolarizability value is thus obtained according to the “two level” model (Eq. 4). However, the estimated β ₀ are generally approximate, especially when dynamic β data are resonantly enhanced, or when many excited states contribute to the NLO response [32].

In the case of bulk materials or films the second-order susceptibility values, χ ⁽²⁾, can be obtained by means of the investigation of the SHG [1–3]. The Kurtz–Perry technique [33] is often used to compare the intensity of the SHG of a powder sample with that of a reference sample of known χ ⁽²⁾, such as quartz or urea. Although this technique is limited (the magnitude of the response is also dependent on particle size), it is a simple and rapid method for screening a large number of powder materials.

2.2 Organic Molecular Materials

Although this chapter deals with molecular second-order NLO chromophores based on organometallic and coordination complexes, for the sake of clarity we report here a brief summary of the structural features of molecular organic second-order NLO chromophores, which have been extensively investigated [1–3]. In this way, we can give a description of the actual approach to the design of second-order NLO active chromophores.

As stated in the previous paragraph, the noncentrosymmetry is generally a prerequisite for second-order NLO activity of a molecule. However, in order to obtain efficient second-order molecular responses, intense, low-energy electronic transitions having CT character are required. With these concepts in mind, various synthetic strategies, through an appropriate molecular design, also recently based on sophisticated theoretical approaches, such as TD-DFT or TD-HF, have been developed in order to produce efficient second-order molecular NLO chromophores. Actually, for material chemists involved in the investigation of NLO properties, this is one of the most important topics of the latest two decades.

Two main families of organic molecular NLO chromophores can be identified: dipolar and octupolar species. The former, which are not centrosymmetric, follow a general scheme involving a polarizable molecular structure (e.g., a π-conjugated pathway) having an asymmetrical charge distribution (e.g., with donor and/or acceptor group substituents) to form a donor–π–conjugated bridge-acceptor (D–π–A) network. The prototypical example of a dipolar molecule is represented by p-nitroaniline. The second-order optical nonlinearity originates from the existence of D→A electronic CT transitions mediated by the π-conjugated-bridge, which in many cases are referred to the lowest-energy transition, so that the “two level” model applies quite well. To this category of molecular materials belong most conjugated organic species.

Octupolar molecules, instead, may be centrosymmetric but they imply the existence of twofold (D ₂) or threefold (D ₃) rotational axes. They are characterized by multidirectional CT excitations. The theoretical description of nonlinearity of such systems implies, even in the simplest case, a three-level approach. The prototypical example of an octupolar molecule is represented by 1,3,5-triamino-2,4,6-trinitrobenzene.

2.3 Coordination and Organometallic Complexes

Second-order NLO active coordination and organometallic complexes have progressively occupied in the last decade a relevant role in the panorama of molecular NLO chromophores because of the unique, structural and electronic characteristics associated with a metal center interacting with organic ligands [5–19]. Actually, compared to organic molecules, coordination and organometallic complexes can offer a larger variety of electronic structures, controlled by the metal electronic configuration, oxidation state, coordination sphere, etc. In particular, in the case of dipolar NLO chromophores, the metal center may act as the donor, or as the acceptor, or even as the bridge of a donor–acceptor network. In fact, as coordination and organometallic complexes may possess intense, low-energy MLCT, ligand-to-metal CT (LMCT), or intraligand CT (ILCT) excitations, the metal can effectively act as the donor, the acceptor, or the polarizable bridge of a donor–acceptor network. Finally, metal ions are well suited to build molecular structures based on octupolar coordination of organic ligands with D ₂ or D ₃ symmetry.

In the following paragraphs is reported an overview, mainly limited to the last 8–10 years, on coordination and organometallic second-order NLO active chromophores, focusing the attention only on specific and relevant aspects associated with each class of NLO chromophores; therefore the overview is not exhaustive.

3 Coordination and Organometallic Complexes for Second-Order Nonlinear Optics

3.1 Complexes with Amine, Pyridine, and Stilbazole Ligands

3.1.1 Amines

Coe et al. investigated deeply the second-order NLO properties of various ruthenium amine complexes with pyridine ligands [18, 34–51]. In particular, they systematically investigated, in acetonitrile solution by the HRS technique working at 1.064 μm incident wavelength, Ru^II NLO chromophores such as trans-[Ru(NH₃)₄(L^D)(L^A)][PF₆] _n (n = 2 or 3) where L^D (e.g., 4-(dimethylamino)pyridine) and L^A (e.g., 4-acetylpyridine or N-methyl-4,4′-bipyridinium, MeQ⁺) are electron-rich and electron-deficient ligands, respectively [35]. In such chromophores, intense Ru^II → L^A MLCT transitions dominate the β(HRS) value. A rather high β ₀(HRS) value was reported for the chromophores [Ru(NH₃)₅(MeQ⁺)][PF₆]₃ (1, 123 × 10⁻³⁰ esu) and trans-[Ru(NH₃)₄(4-Me₂N–C₅H₄N)(MeQ⁺)][PF₆]₃ (130 × 10⁻³⁰ esu). Complexes with the charged MeQ⁺ ligand show larger β ₀ values, when compared with their analogs with neutral pyridine L^A ligands, due to a more extended π-conjugation and to the presence of a ligand carrying a positive charge [35].

N-Arylation of the 4,4′-bipyridinium cation leads to an even higher β ₀(HRS) value (2, 410 × 10⁻³⁰ esu) [37], and, by placing a trans-ethylene bridge between the pyridine and pyridinium rings of L^A, β ₀ increases up to 50% [41].

Besides, replacement of a neutral L^D ligand such as 4-Me₂N–C₅H₄N with a presumably N-coordinated thiocyanate anion (see 3) increases the electron-donating strength of the Ru^II center and consequently the β ₀(HRS) value to 513 × 10⁻³⁰ esu [42]. The β ₀ values obtained by the HRS technique for these Ru^II chromophores were confirmed by means of the method based on Stark spectroscopy [41, 42]. Also, calculations based on TD-DFT gave values of β ₀ reasonably in agreement with the experimental β ₀(HRS) values [46]. Interestingly, an [Ru(NH₃)₅NC₅H₄-]²⁺ moiety is more effective than a 4-NMe₂–C₆H₄- moiety as a π-electron-donor, in terms of enhancing β ₀(HRS) [47].

Within three series of pyridyl polyene chromophores 4, the β ₀ values obtained by the HRS technique or Stark spectroscopy (about 100–600 × 10⁻³⁰ esu) maximize when n = 2. This is in contrast with the behavior of known organic chromophores based on an electron-donor–acceptor system linked by a polyene bridge, in which β ₀(HRS) increases steadily with the increase of the π delocalization of the polyene bridge [48, 49]. TD-DFT calculations show that the HOMO level of these Ru^II complexes gains in π character as n increases; consequently, the lowest energy transition usually considered as purely MLCT in character has some opposite ILCT contribution which becomes significant when n >2 and which increases with the conjugated pathlength, causing the value of β ₀(HRS) to decrease [49]. Electrochemical studies, ¹H NMR, and an investigation based on Stark spectroscopy all confirm that the role of an extended conjugated π-system is more effective in the purely organic chromophores than in their Ru^II analogs [50, 51].

Remarkably, the β ₀(HRS) values of certain complexes (e.g., 1) can be reversibly and very effectively (10- to 20-fold) attenuated by a Ru^III/Ru^II redox process involving chemical reagents such as H₂O₂ [39, 40, 43–45].

The redox-switching of the linear optical absorption of self-assembled monolayers and Langmuir–Schäfer films of [Ru(NH₃)₅(4,4′-bipyridinium)]³⁺ complexes [52–54] and a redox-switching of the NLO response of Langmuir–Blodgett thin films based on 5 were recently reported. Oxidation to Ru^III causes ca. 50% decrease of the intensity of the SHG, which is almost completely restored by reduction to Ru^II [55].

3.1.2 Pyridines and Stilbazoles

The effect of coordination to a metal center on the second-order NLO response of pyridine and stilbazole ligands has been deeply studied mainly by Marks, Ratner et al., and by Ugo et al. [10–16]. The quadratic hyperpolarizability β, measured in solution by the EFISH technique, of para-substituted pyridines and stilbazoles, such as 4-R-C₅H₄N and 4,4′-trans or trans,trans-R-C₆H₄(CH═CH) _n −C₅H₄N (R = donor or acceptor substituent; n = 1, 2), increases upon coordination to various metal centers, the enhancement factor (EF) being modulated by the nature of the metal (electronic configuration, oxidation state, coordination sphere) which can act as an electron-acceptor or an electron-donor. For example, the quadratic hyperpolarizability, measured by the EFISH technique of 4,4′-trans-Me₂N–C₆H₄CH═ CHC₅H₄N increases by a factor of 2 (β _1.06(EFISH) goes from 28.2 × 10⁻³⁰ to 61 × 10⁻³⁰ esu) upon coordination to a zerovalent “W(CO)₅” moiety which acts mainly as electron-acceptor [56]. Similarly, coordination of a pyridine or stilbazole ligand bearing an electron-withdrawing group to a low oxidation state organometallic fragment such as “M(CO)₅” (M═Cr, W), that may also act as electron-donor, could produce a relevant increase of the absolute value of the second-order NLO response. Thus, the β _1.91(EFISH) value of 4-COH–pyridine (−0.10 × 10⁻³⁰ esu) increases its absolute value (−12 × 10⁻³⁰ esu) upon coordination to a zerovalent “W(CO)₅” [56–58].

This ambivalent donor or acceptor role of a zerovalent metal has suggested two different mechanisms controlling the second-order NLO response of this kind of NLO organometallic chromophores [56] (Scheme 1).

Scheme 1

Two mechanisms controlling the second order NLO response

When the R substituent is a strong electron-donating group, the increase of the value of the quadratic hyperpolarizability β is dominated by an intraligand CT (ILCT) transition, with the metal center, which behaves as an electron-acceptor, producing a red-shift of this transition and therefore an increase of the value of β according to the “two level” model [20, 21]. In contrast, when R is a strong electron-accepting group, the quadratic hyperpolarizability β is dominated mainly by an MLCT transition. In this latter case the negative sign of β is due to a reduction of the dipole moment in the excited state of the MLCT transition (Δμ _eg <0), according to the “two level” model [20, 21].

An extended EFISH investigation of the second-order NLO response of cis-[M(CO)₂Cl(4-R-C₅H₄N)] (M = Rh, Ir) and fac-[Os(CO)₃Cl₂(4-R-C₅H₄N)] (R = electron-donor or -acceptor substituent) has confirmed such interpretation of the ambivalent role of the metal center. In fact, the ambivalent acceptor or donor role is controlled by the intrinsic softness of the metal center and by the presence in the pyridine ligand of an electron-donor or -acceptor group R [59]. For instance, the values of β _1.06(EFISH) of cis-[M(CO)₂Cl(4-R-C₅H₄N)] (M = Ir^I (5d ⁸), Rh^I (4d ⁸)) are dependent upon the nature of R: (1) β >0 with strong electron-donating groups (e.g., R = NMe₂ and M = Ir, β _1.06(EFISH) = 9 × 10⁻³⁰ esu); (2) β is positive but very small with weak electron-donating groups (e.g., R = CMe₃ and M = Ir, β _1.06(EFISH) = ca. 0.1 × 10⁻³⁰ esu); (3) β <0 with strong electron-withdrawing groups (e.g., R = CN and M = Ir, β _1.06(EFISH) = −9 × 10⁻³⁰ esu). Independently from the strong electron-donating or withdrawing properties of the R group, a very strong enhancement of one or two orders of magnitude of the absolute value of β _1.06(EFISH) of the pyridine ligands occurs upon coordination [16].

Remarkably, it is possible to modulate the NLO response of a pyridine ligand by an increased acceptor or donor strength of the metal centers, which is controlled by their oxidation state and ancillary ligands [16]. Thus, coordination of 4-Me₂N–C₅H₄N to “cis-M(CO)₂Cl” (M = Rh^I, 4d⁸ or Ir^I, 5d⁸) or “fac-Os(CO)₃Cl₂” (Os^II, 5d⁶) produces an increase of the β _1.06(EFISH) value about tenfold higher than coordination to the less accepting zerovalent “Cr(CO)₅” moiety (Cr⁰, 3d⁶). Besides, the quadratic hyperpolarizability β _1.91(EFISH) of [W(CO)₅(4-MeCO–C₅H₄N] (−9.3 × 10⁻³⁰ esu) is larger than that of the complex of this substituted pyridine with the “Os^II(CO)₃Cl₂” moiety, due to the better donor properties of the “W(CO)₅” fragment [56, 57, 59]. Moreover, the value of β _1.34(EFISH) decreases upon substitution of the carbonyl ligands of “cis-M(CO)₂Cl” (M = Rh^I or Ir^I) with cyclooctadiene or with two cyclooctene ligands, according to a decrease of the acceptor properties of the metal center [59].

In push–pull 1D organic chromophores, an increase of the delocalized π-electron bridge between the donor and the acceptor groups leads to a significant increase of the second-order NLO response [60, 61]. In contrast, there is a buffering of the second-order NLO response upon coordination, because the effect due to coordination becomes less relevant by increasing the length of the π-delocalized bridge of the nitrogen donor ligand. For example, on going from 4-Me₂N–C₅H₄N to 4,4′-trans-Me₂N–C₆H₄CH═CHC₅H₄N the EF of β _1.34(EFISH) is of the order of 10³ while on going from cis-[M(CO)₂Cl(4-Me₂N–C₅H₄N)] to cis-[M(CO)₂Cl(4,4′-trans-Me₂N–C₆H₄CH═CHC₅H₄N)] the EF is only ten times [59]. Coordination to “cis-Ir(CO)₂Cl” of 4,4′-trans-Me₂N–C₆H₄CH═CHC₅H₄N causes an EF of β _1.34(EFISH) of only 2.3, quite small when compared to the large EF produced when 4-Me₂N–C₅H₄N is coordinated to the same metal moiety [59].

Also, a zerovalent trimeric cluster core such as “Os₃(CO)₁₁” shows this ambivalent acceptor-donor effect on the second-order NLO response of para-substituted stilbazole ligands. However, strangely enough, its acceptor and donor strengths are comparable to those of “fac-Os(CO)₃Cl₂” and “cis-Ir(CO)₂Cl” [62]. While one expects a significant MLCT electron transfer from the “Os₃(CO)₁₁” core to the π* orbital system of a stilbazole ligand carrying in para position an electron-withdrawing substituent such as CF₃, in consideration of a significant polarizability of the d electron density of a trimeric cluster core with metals in the zero oxidation state, the significant σ acceptor properties of the zerovalent “Os₃(CO)₁₁” core when the stilbazole carries an electron-donor group such as NMe₂, comparable to that of an Os^II metal carbonyl center, is unexpected [62].

In contrast to the effect of coordination to a low oxidation state metal carbonyl moiety, the β _1.34(EFISH) value of 4,4′-trans-Me₂N–C₆H₄CH═CHC₅H₄N is almost unaffected by coordination to the relatively soft “cis-PtCl₂” moiety and, strangely enough, also to the less soft “Zn(CH₃CO₂)₂” Lewis acid moiety, in agreement with an irrelevant red-shift upon coordination of the ILCT transition of the stilbazole [63]. However, a more significant red-shift occurs upon coordination to harder “ZnY₂” (Y = Cl⁻ [63], CF₃CO₂ ⁻ [63], CF₃SO₃ ⁻ [64, 65]) Lewis acid moieties. It appears that the β EF is function of the ancillary ligands Y which tune the acceptor properties of the Zn^II center (CH₃CO₂ ⁻ <Cl⁻ <CF₃CO₂ ⁻ <CF₃SO₃ ⁻), as confirmed by both EFISH measurements and solvatochromic investigations [63–65].

For instance, at concentrations higher than 1 × 10⁻⁴ M, the value of β _1.91(EFISH) of [Zn(CF₃SO₃)₂(4,4′-trans-Me₂N–C₆H₄(CH═CH) _n C₅H₄N)₂] (n = 1,2) is increased by a factor of about 4–6 times, when compared to that of the related complexes with the CH₃CO₂ ⁻ ancillary ligand, in agreement with a higher Lewis acidity of the Zn^II center, as confirmed by the much higher red-shift of the ILCT transition upon coordination (for n = 1, Δλ _max = 2 and 116 nm when Y = CH₃CO₂ ⁻ and CF₃SO₃ ⁻, respectively). Of interest is the unexpected evidence that, in CHCl₃ solution at concentrations lower than about 10⁻⁴ M, the β _1.91(EFISH) value of these triflate complexes increases abruptly by decreasing concentration, up to very large values, while this effect is not observed for the related acetate or trifluoroacetate complexes. Such behavior was attributed to an increased concentration of the cation [Zn(CF₃SO₃)(4,4′-trans-Me₂N–C₆H₄(CH═CH) _n C₅H₄N)₂]⁺ (n = 1,2), characterized by a stronger second-order NLO response due to the positive charge, produced by the facile solvolysis of the triflate ligand, as confirmed by electrical conductivity measurements which evidenced a sharp conductivity increase at concentrations below 10⁻⁴ M for the triflate complexes [64, 65]. A similar behavior of the quadratic hyperpolarizability in CHCl₃ solution by dilution was observed for Zn^II complexes with the same stilbazoles and with ancillary ligands such as the methansulfonate or para-toluensulfonate anions [66].

3.2 Complexes with Chelating Ligands

3.2.1 Bipyridines and Phenanthrolines

The second-order NLO response of various bipyridine and phenanthroline ligands increases upon coordination to a metal center, as in the case of pyridines and stilbazoles (see Sect. 3.1.2), the EF of the quadratic hyperpolarizability still depending on the electronic configuration of the metal, its oxidation state, and its sphere of ancillary ligands [10, 16].

An investigation was carried out on powders of Re, Pd, and Pt complexes with 2,2′-bipyridine, which exhibit modest second-order NLO activities as evidenced by the Kurtz technique [67]. A more extended investigation on the second-order NLO response of various Re^I, Zn^II, and Hg^II complexes with donor-substituted vinyl bipyridines (for examples, 6 and 7) was done by the EFISH technique, working at 1.34 μm incident wavelength [10, 68, 69].

β _1.34(EFISH) increases with the strength of the electron-donor substituent group (NBu₂ is more efficient than Ooctyl) and with the Lewis acidity of the metal center (the relative increase of the acceptor strength, which parallels the increase of the red-shift of the ILCT transition upon coordination, follows the order: “Hg(OAc)₂” < “HgCl₂” < “Zn(OAc)₂” < “ZnCl₂” < “Re(CO)₃Br”), the best value being obtained for a complex with “ZnCl₂” (for 7 with M = Zn, β _1.34(EFISH) = 152 × 10⁻³⁰ esu; μβ ₀ = 831 × 10⁻⁴⁸ esu). The complexes with “Re(CO)₃Br” were less efficient than the corresponding Zn complexes due to the presence of two vectorially opposed CT transitions (MLCT and ILCT) [68, 69].

In the related complexes 8, for a given donor group, a slight increase of the value of μβ _1.34(EFISH) occurs by replacing CH with N. However, the significant increase of the NLO response seems to be mainly controlled by resonant enhancement [70]. Interestingly, the μβ _1.34(EFISH) value of 8a [70] is twice that of the structurally related nonchelated complex [ZnCl₂(4,4′-trans-Me₂N–C₆H₄CH═CHC₅H₄N)₂] [63], due to the rather planar arrangement of the chelated ligand upon coordination and consequently to a shift of the ILCT transition at lower energy [16].

Very recently, the efficient photoswitching of the second-order NLO responses of some dipolar photochromic Zn^II complexes (9) was reported [71]. The NLO activity for the open forms is very small, as expected for the absence of π-conjugation between the two thiophene rings. Upon conversion to the closed form in the photo-stationary state, the NLO activity increases dramatically (μβ ₀(EFISH) from 75–160 × 10⁻⁴⁸ to 1,020–1,800 × 10⁻⁴⁸ esu). This substantial enhancement reflects a more efficient delocalization of the π-electron system in the closed forms favoring an efficient on/off switching of the NLO responses [71].

Two-dimensional second-order NLO, positively charged, chromophores incorporating the “Ru(NH₃)₄ ²⁺” moiety linked to two structurally related electron-accepting N-methyl/aryl-pyridinium systems (either two monodentate pyridine ligands or one bipyridine chelated ligand) were studied (10) [72]. The β _0.80(HRS) for the chelated complexes (32–48 × 10⁻³⁰ esu) are smaller than those of the nonchelated counterparts (135–160 × 10⁻³⁰ esu). The possibilities for redox-switching of the NLO properties, by exploiting reversible Ru^III/II oxidation processes and ligand-based reductions, were investigated [72].

The quadratic hyperpolarizability of 5-R-1,10-phenanthroline (R = donor group such as OMe, NMe₂, trans-CH═CHC₆H_4–4′-NMe₂ and trans,trans-(CH═CH)₂C₆H_4–4′-NMe₂) increases upon coordination to a Zn^II center but not to the softer Cd^II center [63]. The EF of β _1.34(EFISH) upon coordination to “Zn(CH₃CO₂)₂” is, as expected, higher for the donor group NMe₂ (EF = 4.6) than for the donor group OMe (EF = 3.2). Such enhancement becomes less and less relevant by increasing the length of the π-delocalized bridge between the donor group NMe₂ and the phenanthroline chelated ligand, as already observed in the case of 4-R-pyridines (Sect. 3.1.2) [63]. Notably, the second-order NLO chromophore 11 (R = trans,trans-(CH═CH)₂C₆H_4–4′-NMe₂) is characterized by a good value of β _1.34(EFISHG) (112 × 10⁻³⁰ esu) [63].

The β _1.91(EFISH) value of a large series of square planar M(substituted 1,10-phenanthroline)(dithiolate) complexes (M = Pt^II, Pd^II, Ni^II) was measured [73]. In these second-order NLO chromophores, the HOMOs are a mixture of metal and thiolate orbitals whilst the LUMOs are phenanthroline π* orbitals. Therefore, the presence of an electron-donor group on the dithiolate ligand, acting on the HOMOs level, increases the value of the quadratic hyperpolarizability by acting on the energy of the CT involving the HOMO–LUMO transition. The best NLO response is obtained when M = Pt^II (12, β _1.91(EFISH) = −39 × 10⁻³⁰ esu; μβ ₀ = −260 × 10⁻⁴⁸ esu) since this latter Pt^II complex shows an increased oscillator strength of the HOMO–LUMO transition when compared to that of the related Pd^II or Ni^II NLO complexes. The structurally related complex 13, which shows a μβ ₀ value between −523 and −669 × 10⁻⁴⁸ esu, dependent on the nature of the solvent, was also investigated [74].

The quadratic hyperpolarizability of various one-dimensional push–pull carboxylate ligands increases upon coordination to a “(1,10-phenanthroline)Zn^II” center. For example, 14 has a β ₀(HRS) value of 39 × 10⁻³⁰ esu, much higher than that of the related carboxylate ligand (6.6 × 10⁻³⁰ esu) [75].

Metal ions are excellent templates to build D _2d and D ₃ octupolar second-order NLO chromophores; therefore their associations with functionalized bipyridyl ligands give rise to octahedral and tetrahedral metal complexes with large quadratic hyperpolarizabilities [76]. The adequate functionalization of these octupoles allows their incorporation into macromolecular architectures such as polymers and metallodendrimers [76]. Various D ₃ octupolar tris chelated Ru^II complexes are characterized by a significant second-order NLO response as evidenced by HRS [18]. For example, the β ₀(HRS) value of 15, when M = Ru^II and R = NBu₂, is 380 × 10⁻³⁰ esu [77, 78]. Similar values are obtained upon substitution of PF₆ ⁻ with other anions such as TRISPHAT⁻ (tris(tetrachlorobenzendiolato)phosphate anion) [79]. Polarized HRS investigations and Stark spectroscopic measurements support a second-order NLO response of 15 controlled by multiple degenerate dipolar CT transitions, rather than by an octupolar transition. In accordance the transitions dominant on the NLO response are ILCT excitations red-shifted by coordination to Ru^II and MLCT transitions with a CT process opposite as direction [78, 80].

Holding fixed the bipyridine carrying R = NBu₂, but changing the metal, substitution of Ru^II with Fe^II causes a decrease of β ₀(HRS) due to both a blue-shift of the ILCT and a red-shift of the MLCT [78, 81]. The analogs Zn^II or Hg^II complexes, which have only the ILCT transition, show β ₀(HRS) values of 380 and 256 × 10⁻³⁰ esu, respectively, in accordance with the different Lewis acidity of the metal center [78]. By introducing the less donor R = Ooctyl group in the Ru^II NLO chromophore, the β ₀(HLS) value decreases due to a ILCT absorption band at higher energy [78]. The NLO chromophore 15, with M = Zn^II and R = trans-CH═CHC₆H₄NBu₂, exhibits the highest value of the quadratic hyperpolarizability reported for an octupolar NLO chromophore (β ₀(HRS) = 657 × 10⁻³⁰ esu; β _1.91(HRS) = 870 × 10⁻³⁰ esu) [82].

Tetrahedral D _2d octupolar metal NLO chromophores (where the metal center M is Cu^I, Ag^I, Zn^II) with the same functionalized bipyridyl ligands were studied. Their quadratic hyperpolarizabilities, measured by HRS at 1.907 μm incident wavelength, are much lower when compared to those of the related octahedral D ₃ NLO chromophores (β ₀(HRS) = 70–157 × 10⁻³⁰ esu and 200–657 × 10⁻³⁰ esu for D _2d and D ₃ complexes, respectively) [82].

Le Bozec and coworkers have incorporated the Ru^II NLO chromophore 15, adequately functionalized with an appropriate R = amino group, into macromolecular systems of interest as building blocks for the preparation of second-order NLO active bulk materials [83–86]. A thermally stable polyimide derivative of 15 shows, in CH₂Cl₂ solution, a β _1.91(HRS) value of 1,300 × 10⁻³⁰ esu, larger than that of the monomeric counterpart [83], whereas a dendrimeric species 16 with seven units shows a β _1.91(HRS) value of 1,900 × 10⁻³⁰ esu (in CH₂Cl₂) [84, 85]. The quasi-optimized octupolar ordering of the dendrimeric structure is responsible for the greater second-order NLO response compared to that of a linear arrangement of 14 basic units of the polyimide derivative [84, 85].

A star-shaped arrangement based on an octupolar Zn^II second-order NLO chromophore containing three photoisomerizable ligands (in two geometries) such as 4,4′-bis-(styryl)-2,2′-bipyridine functionalized with a dialkylamino-azobenzene shows a β _1.91(HRS) value of 863 × 10⁻³⁰ esu in CH₂Cl₂ solution [87]. By using both photophysical and second-order NLO properties of this chromophore, all-optical poling, an interference process between one- and two-photon excitations that locally induces macroscopic second-order effects in polymeric films, was investigated. Grafting these chromophores onto the polymer network improves the stability of the macroscopic photoinduced nonlinearity [88].

Coe et al. investigated some related tris-chelate complexes of Ru^II and Fe^II, with bipyridines substituted with electron-withdrawing pyridinium groups (17) [89]. In these particular octupolar chromophores the second-order NLO response is dominated by two MLCT transitions; HRS measurements working with a 0.800 μm incident wavelength have produced larger quadratic hyperpolarizabilities for the Ru^II chromophores (170–290 × 10⁻³⁰ esu) than for the Fe^II analogs (78–110 × 10⁻³⁰ esu). However, this is probably due to the presence of a resonant enhancement in the case of the Ru^II chromophores. A Stark spectroscopic investigation and computations based on TD-DFT theory and the finite field method have shown in fact that the second-order NLO response of these chromophores is controlled by two substantial components producing slightly larger β ₀ values for the Fe^II chromophore (86–151 × 10⁻³⁰ esu) than for the Ru^II chromophore (68–114 × 10⁻³⁰ esu) [89]. Since MLCT transitions determine the second-order NLO response of these chromophores, NLO redox switching based on these Fe^II/Fe^III or Ru^II/Ru^III species is possible.

3.2.2 Terpyridines

The second-order NLO properties of metal complexes with terpyridine ligands were recently studied for the first time [90, 91]. Coordination of a terpyridine such as 4′-(1-C₆H₄-p-NBu₂)-2, 2′: 6′, 2″-terpyridine to Zn^II, Ru^III, and Ir^III metal centers (18) induces a significant enhancement of its second-order NLO response measured by the EFISH technique working with an incident wavelength of 1.34 μm [90, 92]. In all these chromophores the ILCT transition of the terpyridine at about 416–465 nm is red-shifted by coordination, due to an increased π delocalization of the ligand upon chelation. The enhanced value upon coordination of the terpyridine to the Lewis center “ZnY₂” (β _1.34(EFISH) = 67 and 88 × 10⁻³⁰ esu for Y = Cl⁻, CF₃CO₂ ⁻, respectively) remains positive, as expected for an ILCT transition dominating the second-order NLO response [16], the EF being higher for the more electron-withdrawing ancillary ligand CF₃CO₂ ⁻. However, coordination of these terpyridine metal centers with different dⁿ configurations such as Ir^III (5d ⁶ in “Ir(4-EtPhCO₂)₃”) or Ru^III (4d ⁵ in “Ru(CF₃CO₂)₃”), produces an NLO response no longer influenced just by the ILCT transition, but also by MLCT and/or LMCT transitions, in such a way that these latter transitions can even change the sign of the quadratic hyperpolarizability. This relevant role of MLCT and LMCT transitions was confirmed by solvatochromic [92] and TD-DFT investigations [93]. As expected, the relevance of the MLCT transition increases when the terpyridine is carrying an electron-withdrawing substituent (β _1.34(EFISH) from −70 to −230 × 10⁻³⁰ esu for R = NBu₂ and NO₂, respectively, when the terpyridine is coordinated to “Ir(4-EtPhCO₂)₃”) [92].

Langmuir–Blodgett films of Zn^II and Ir^III complexes of 4′-(1-C₆H₄-p-NMe(C₁₆H₃₃))-2, 2′: 6′, 2″-terpyridine have been investigated, measuring their SHG at 1.064 μm incident wavelength. Rather low χ ⁽²⁾ values were unexpectedly obtained, probably due to a scarce noncentrosymmetric ordering of these rather bulk chromophores [94].

Recently, the second-order NLO properties of new lanthanide complexes of the type [Ln(NO₃)₃–L] (Ln = La, Gd, Dy, Yb, Y; 19), where L is a rather rigid terpyridine-like ligand, have been determined by HRS, working with a nonresonant incident wavelength of 1.907 μm. The value of the quadratic hyperpolarizability β _1.91(HRS) increases by increasing the number of f-electrons, from 186 to 288 × 10⁻³⁰ esu [95]. The dependence of the second-order NLO response on the nature of the lanthanide metal center suggests that f-electrons may contribute to the second- order NLO response [95].

3.2.3 Schiff-Bases

Schiff-bases, arising from condensation of substituted salicylaldehydes with various bridging diamines, represent suitable templates to generate noncentrosymmetric molecular architectures. Various bis(salicylaldiminato)M^II (M = Fe, Co, Ni, Cu, Zn) complexes have been investigated as second-order NLO molecular chromophores [96, 97], exploring various aspects of their second-order nonlinear optics. In these NLO chromophores the metal ion templates noncentrosymmetric structures and acts as donor counterpart of a donor (D)–acceptor (A) system involving MLCT transitions. Starting from the more simple unsubstituted species (20), for the first time the role of the metal-d configuration was demonstrated in controlling the second-order NLO response, when MLCT transitions are dominating such a response. In particular, on passing from the closed-shell Ni^II (d ⁸) (β _1.34(EFISH) = −20 × 10⁻³⁰ esu) to the open-shell Cu^II (d ⁹) (β _1.34(EFISH) = −50 × 10⁻³⁰ esu) and Co^II (d ⁷) (β _1.34(EFISH) = −170 × 10⁻³⁰ esu) homologues, the substantial increase of the absolute values of the quadratic hyperpolarizability is clearly related to the increased accessibility of lower-lying CT states [98, 99]. However, in the presence of strong donor/acceptor substituents on the Schiff-base structure, the metal ion mostly acts as a bridge, and its role in controlling the second-order NLO response becomes less defined. Tunable values of the quadratic hyperpolarizability, ranging from negative to positive values [97], were obtained for these molecular NLO chromophores, depending upon the strength of the donor/acceptor substituents. The symmetric donor–acceptor substitution in dipolar planar Schiff-base complexes also allowed investigation of the in-plane two-dimensional (2D) NLO properties (21), of interest for the development of polarization-independent materials.

Dipolar 1D donor/acceptor systems are generally characterized by a prevalent single hyperpolarizability tensor, namely β _zzz , parallel to the dipolar z axis of the molecule. However, an appropriate donor/acceptor substitution pattern on the bis(salicylaldiminato) framework, resulting in a C _2v molecular symmetry, leads to large off-diagonal β _ijk tensors components (e.g., 21, D = NEt₂; A = Cl, β _{zzz (1.34)}(HRS) = 43 × 10⁻³⁰ esu; β _{zxx (1.34)}(HRS) = 20 × 10⁻³⁰ esu) [100], due to the existence of CT transitions (21), perpendicular to the two axes, μ(x)_ge [100, 101].

A further variety of noncentrosymmetric Schiff-base structures can be envisaged, either by an unsymmetrical donor/acceptor substitution on the bis(salicyli-dene) ligand of a series of Cu^II complexes (22) [102], or by an unsymmetrical [N₂O₂] tetradentate coordination in M^II (M = Ni, Cu, Zn, VO) complexes (23) [103], or finally in a series of Ni^II complexes with ligands derived by a monocondensation of the bridging diamine [104]. Appreciably optical nonlinearity has been achieved (e.g., 23, M = Zn; R = N₂Ph, β _1.91(EFISH) = −280 × 10⁻³⁰ esu) [103]. Therefore a large diversity of structures can produce second-order nonlinearity in this class of NLO chromophores. Further examples of second-order NLO chromophores based on Schiff bases are represented by a series of octahedral M^II (M = Fe, Co, Ni, Zn) metal complexes of N-2′-pyridylmethylene-4-aminopoly(phenyl) ligands, in which the molecular quadratic hyperpolarizability is strongly influenced by the metal electronic configuration and parallels the number of unpaired electrons. The largest values of the quadratic hyperpolarizability are those of the Mn^II complexes with a 3d ⁵ electronic configuration [105]. Moreover, the switching of the second-order NLO response can be envisaged in the case of spin-crossover of Fe^II complexes. Bimetallic NLO chromophores involving dicopper(II) [106] or Cu^II-Gd^III [107] complexes have been investigated with the aim of finding possible interplay between magnetism and second-order NLO response. These “multifunctional” molecular chromophores, even possessing a rather modest optical nonlinearity, represent interesting models for further investigations of this field of research.

The use of chiral diamines in Schiff bases complexes allowed exploration of the powder SHG efficiency of crystalline materials based on this class of NLO chromophores, otherwise inactive because of the almost always crystal centrosymmetry. Relatively high powder SHG efficiency (up to 13 times that of urea) has been achieved in the case of the (1R,2R)-(+)-1,2-diphenylethylenediamine Ni^II derivative [108]. Analogous Zn^II complexes using the chiral (R)-(+)-1-phenylethylamine have given appreciable powder SHG efficiencies [109]. This strategy has been extended using a series of chiral amino alcohols [110] and amino acids [111] to obtain noncentrosymmetric crystals based on Sn^IV derivatives, with an attempt to correlate their SHG efficiencies with the molecular chirality.

In spite of the above studies on molecular NLO chromophores, investigations as NLO materials based on these chromophores remain almost unexplored. Monolayers of Ni^II complexes on glassy [112] or Si(100) [113] substrates have been obtained, but their second-order NLO activity has not yet been investigated.

3.3 Complexes with Metallocene Ligands

Since the first report in 1987 by Green et al. [4], metallocene derivatives represent one of the most widely investigated classes of second-order NLO metal-based chromophores [114–116]. Starting from the prototypical stilbene (trans)-1-ferrocenyl-2-(4-nitrophenyl)ethylene derivative (24, β _1.91(EFISH) = 31 × 10⁻³⁰ esu) [117] and related phenylethenyl oligomers [118], a very large variety of ferrocenyl species have been investigated. They range from various polyenes having a terminal acceptor group [119], such as N-alkylpyridinium salts (e.g., 25, β _1.06(HRS) = 458 × 10⁻³⁰ esu) [120], fullerene [121], sesquifulvalene (e.g., 26, β _1.06(HRS) = 1,539 × 10⁻³⁰ esu; β ₀(HRS) = 821 × 10⁻³⁰ esu) [122], fluorene (e.g., 27, R = CO₂Me, μβ _1.54(EFISH) = 5,000 ± 1,500 × 10⁻⁴⁸ esu) [123], indanone [124], thiazole [125], dicyanomethylene (e.g., 28, μβ _1.00(EFISH) = 1,120 × 10⁻⁴⁸ esu), [126] and related derivatives [127–129], including some (dicyanomethylene)indane species (e.g., 29, μβ _1.91(EFISH) = 5,200 (8,720) × 10⁻⁴⁸ esu) [130], and various bimetallic (see Sect. 3.7) [131–133] and trimetallic [134] compounds, connected to the ferrocenyl unit through a conjugated π-linker. The values of the quadratic hyperpolarizability of these species parallel the strength of the acceptor group and, generally, increase with the length of conjugated π-network, as usually observed for related organic chromophores [60, 61]. In all cases, the metallocene unit represents the donor group of the donor-acceptor system connected by a π linker. Actually, the ferrocene unit possesses ionization energy and redox potential features comparable to those of the best organic donors. However, the values of the quadratic hyperpolarizability of the NLO chromophores based on ferrocene as donor group indicate a donor capability of the ferrocenyl group comparable to that of the poorly donor organic methoxyphenyl group. These relatively poor donor properties are due to a weak electronic coupling between the metal-d orbitals of the metallocenyl donor group and the π-network of the linker connecting the donor-acceptor push-pull systems. Thus, the very large hyperpolarizability values observed for some of the NLO chromophores reported above are in some cases due to resonant enhancement effects. On the other hand, even extrapolated β ₀ values [117–134] cannot be considered reliable [32], since it has been assessed that, for ferrocenyl derivatives, many electronic states contribute to optical nonlinearity [115, 116].

Some related ruthenocene species have also been investigated [117], almost always showing lower quadratic hyperpolarizabilities, in accordance with the higher ionization energy of the ruthenocene vs ferrocene moiety [115].

The interest in this class of NLO chromophores is also due to their capability to crystallize in noncentrosymmetric structures characterized by a high SHG, because the acceptor substituents are usually bulky species [135] or pyridinium salts [4, 136] which favor noncentrosymmetric packing. Also relevant is the possibility of engineering crystalline structures through chirality of the ferrocenyl group (e.g., 30, powder efficiency 100 times that of urea) [137], or by an appropriate substituent on the second cyclopentadienyl ring (e.g., 31, powder efficiency 140 times that of urea) [138]. Actually, the crystalline species based on ferrocene NLO chromophores are among the most SHG efficient organometallic materials, e.g., the pyridinium derivative 32 possesses powder efficiency 220 times that of urea [136].

The large variety of molecular NLO chromophores based on metallocenes rends them suitable for the investigation of various bulk second-order NLO materials. Thus, some studies devoted to electrically poled polymers including a metallocene NLO molecular chromophore as guest [126, 139], or to self-assembled nanostructures of these metallocene NLO chromophores [140, 141], appeared quite recently in the literature. Moreover, the facile and reversible accessibility to the ferrocenium oxidized species [142], allowed the redox switching of the SHG signal in self-assembled monolayers [140] or the molecular multifunctional (linear optical, NLO, and magnetic properties) redox switching [143] to be obtained.

3.4 Complexes with Alkynyl and Vinylidene Ligands

(Cyclopentadienyl) (alkylphosphine) metal σ-acetylides of group 8, group 10, and group 11 metals represent a widely investigated class of second-order NLO chromophores, mainly developed by Humphrey et al., whose relevant results are summarized in recent review articles [11, 19, 144].

Analogous to metallocenes, in these complexes the metal acts as the donor group of a donor-acceptor system connected by a π-linker. The second-order nonlinearity is controlled by low-energy MLCT excitations. Large values of the quadratic hyperpolarizability, even if resonantly enhanced, have been achieved [11, 19, 144]. Accordingly, with the relative oxidizability (Ru^II > Ni^II > Au^I) [11, 19] the largest values of the quadratic hyperpolarizability have been obtained for the readily oxidizable Ru^II centers (e.g., 33, β _1.06(HRS) = 1,455 × 10⁻³⁰ esu), followed by the Ni^II complexes (e.g., 34, β _1.06(HRS) = 445 × 10⁻³⁰ esu), and by the 14-valence-electron, less readily oxidizable, Au^I species (e.g., 35, β _1.06(HRS) = 120 × 10⁻³⁰ esu) [11]. Group 8 complexes, in particular Ru^II compounds, consist of the largest group of acetylides studied [11, 19, 144–147], possessing the highest values of the quadratic hyperpolarizability (e.g., 36, β _1.06(HRS) = 2,676 × 10⁻³⁰ esu; β ₀(HRS) = 342 × 10⁻³⁰ esu) [145], thus resulting in very efficient donors. As expected, the quadratic hyperpolarizability [11, 19, 144–147] increases upon increasing the chain length of the acetylide bridge (e.g., 36 vs 37, β _1.06(HRS) = 351 × 10⁻³⁰ esu; β ₀(HRS) = 55 × 10⁻³⁰ esu, for the latter) [145], and increasing the strength of the acceptor (e.g., 37 vs 38, β _1.06(HRS) = 120 × 10⁻³⁰ esu, for the latter) [145]. Moreover, replacement of the cyclopentadienyl ligand by a tertiary-phosphine, always produces a substantial increase of the quadratic hyperpolarizability (e.g., 33 vs 36). Compared to metallocene based second-order NLO chromophore, σ-acetylide based second-order NLO chromophores, which possess an almost linear M–C≡C–R structure, give rise to a better coupling between the d metal orbitals and the π* system of the σ-acetylide bridge and, hence, to larger second-order nonlinearity (e.g., 24, β _1.91(EFISH) = 31 × 10⁻³⁰ esu vs 37). Bimetallic complexes involving σ-acetylide Ru^II complexes as donor and the “W(CO)₅” fragment as acceptor have also been investigated [19] (see Sect. 3.7).

Vinylidene [11, 145], aryldiazovinylidene [148], and alkenyl [149] species represent parallel families closely related to σ-acetylides. However, their second-order optical nonlinearity is generally lower [11]. Their interest is mostly related to the possibility of switching the NLO properties by virtue of the facile interconvertibility of acetylide and protonated vinylidene pairs via protonation/deprotonation sequences (e.g., 36 vs 39, β _1.06(HRS) = 441 × 10⁻³⁰ esu; β ₀(HRS) = 74 × 10⁻³⁰ esu, for the latter) [145] (Scheme 2).

Scheme 2

Swtiching of second-order NLO response in the acetylide/vinylidene pairs upon protonation/deprotonation sequences

σ-Acetylide Ru^II complexes have also been investigated as octupolar and dendrimeric species [144, 150]. Actually, starting from the 1,3,5-substituted aromatic species, e.g., 40, a variety of octupolar (e.g., 41, √〈β ² _1.06〉 = 1,220 × 10⁻³⁰ esu; √〈β ² ₀〉 = 254 × 10⁻³⁰ esu measured by HRS) or dendrimeric (e.g., 42, √〈β ² _1.06〉 = 1,880 × 10⁻³⁰ esu; √〈β ² ₀〉 = 350 × 10⁻³⁰ esu measured by HRS) structures have been synthesized and investigated [150]. They involve very large static and dynamic hyperpolarizabilities with an improved efficiency/transparency trade-off for SHG applications (e.g., 37, λ _max = 477 nm vs 41, λ _max = 459 nm).

Applications of these molecular NLO chromophores, to produce second-order bulk NLO materials or structured films, are very limited. Actually, in spite of their very large molecular hyperpolarizabilities, they exhibit crystalline materials with modest bulk SHG efficiency [11], e.g., the most efficient crystalline material shows a powder efficiency of only eight times that of urea [11], in consequence of the reluctance of acetylide complexes to crystallize in noncentrosymmetric structures.

Recently, poled polymer films involving, as guest, a dipolar Fe^II σ-acetylide NLO chromophore have shown the traditional temperature-dependent SHG properties [151], while a film of an Ru^II oligothienylacetylide NLO chromophore incorporated into a PMMA matrix revealed an acoustically induced SHG signal, reaching values (χ⁽²⁾ = 0.80 pm V⁻¹) among the highest reported so far for this kind of unusual way to induce SHG [152].

In the last few years, this class of molecular materials has attracted renewed interest by virtue of their remarkable third-order NLO properties [11, 19, 150].

3.5 Cyclometallated Complexes

Recently, three classes of cyclometallated complexes have been reported to show interesting second-order NLO properties, therefore opening a novel route for the design of new efficient second-order NLO chromophores.

New orthopalladated NLO chromophores based on a parallel alignment of two different push-pull ligands have been synthesized by Centore et al. [153] and their second-order NLO activity has been measured by the EFISH technique working in CHCl₃ with an incident wavelength of 1.907 μm. The maximum value of μβ _1.91(EFISH) (610 × 10⁻⁴⁸ esu) was obtained for the NLO chromophore 43.

Corona-poled thin polymeric films of 44 containing as guests this kind of NLO chromophores are characterized by large macroscopic NLO coefficients d ₃₃ (25 pm V⁻¹), as determined by means of SHG measurements working with an incident wavelength of 1.064 μm [154].

Recently, Labat et al. [155] studied the second-order NLO properties of a new cyclometallated Ru^II complex (45) for which the HRS technique, working in acetonitrile, gives a β ₀(HRS) value of 230 × 10⁻³⁰ esu. In this particular NLO chromophore the Ru^II moiety seems to act as the donor group of a push–pull system.

Finally, in the last 3 years, ionic cyclometallated Ir^III complexes with chelated π-delocalized ligands, such as bipyridines [156, 157] or phenanthrolines [158–160], have shown interesting photoemissive properties with potential applications in electroluminescent devices. Ugo et al. have extended their investigations on the second-order NLO response of these chromophores, such as for instance [Ir(cyclometallated-2-phenylpyridine)₂(5-R-1,10-phenanthroline)][PF₆] (R = H, Me, NMe₂, NO₂; 46) and [Ir(cyclometallated-2-phenylpyridine)₂(4-R′,7-R′-1,10-phenanthroline)][PF₆] (R′ = Me, Ph; 47) [160]. The quadratic hyperpolarizability was measured by the EFISH technique working with a nonresonant 1.907 μm incident λ in a low polarity solvent, like CH₂Cl₂, which allows by ion-pairing the extension of the use of this technique to ionic compounds. These Ir^III complexes show a large negative second-order response (μβ _1.91(EFISH) ranging from −1,270 to −2,230 × 10⁻⁴⁸ esu). Most notably, they do not show strong absorptions above 450 nm so that a significant SHG may be obtained without a significant cost in transparency. The highest absolute μβ _1.91(EFISH) value is that of the complex carrying the phenanthroline with the strong electron-withdrawing group NO₂ [161]. A SOS-TDDFT theoretical investigation confirmed that the second-order NLO response of these Ir^III NLO chromophores is mainly controlled by the MLCT transition from the HOMOs phenylpyridine-Ir based orbital of the cyclometallated moiety to the LUMOs π* orbitals of the phenanthroline [161]. Therefore, the second-order NLO response is strongly controlled by the donor or acceptor properties of the substituent on the phenanthroline ligand.

Substitution of cyclometallated 2-phenylpyridine with the more π-delocalized cyclometallated 2-phenylquinoline does not affect significantly the NLO responses, while a lower NLO response is obtained for the Ir^III NLO chromophore with a cyclometallated 3′-(2-pyridyl)-2,2′:5′,2″-terthiophene (ttpy), since the structure of ttpy induces a significant downshift of the HOMO's energy, compared to that of cyclometallated 2-phenylpyridine and 2-phenylquinoline [162].

3.6 Compounds with Macrocyclic Ligands

3.6.1 Metalloporphyrins

The macrocyclic structure of porphyrins, consisting of an extended π system formed by four pyrrolic rings connected by methine bridges, is a typical example of a very polarizable architecture with a variety of low lying excited states. Therefore the presence of various substituents in the meso or pyrrolic position of the porphyrin ring could produce significant perturbations. These structural features, together with the high chemical and thermal stability, can explain the widespread interest in these chromophores during the last few decades in the area of new optical materials.

Due to the high polarizability of the electronic cloud of the porphyrin ring, a large amount of work has been devoted to third-order NLO responses. For instance, we can refer to some comprehensive reviews [13, 163, 164] for applications based on third-order responses such as optical limiting (OL), for which metalloporphyrins are of great interest, given their tendency to show reverse saturable absorption (RSA) behavior because of their strong absorbing, long-lived triplet excited states and their transparency gap between the intense Soret (B) and Q π−π* absorption bands (in the range 400–500 nm and 600–700 nm, respectively). A certain amount of work has been devoted to two-photon absorption (TPA) responses of asymmetric porphyrinic structures [165]. The aim is not only that of possible applications in OL devices, requiring a high TPA absorption cross section, but also of exploiting their application in the field of photodynamic therapy [166]. In the last two decades a significant amount of work has also been devoted to the investigation of the second-order NLO properties of porphyrin architectures of increasing complexity; a recent review has been partially devoted to this specific area [164].

Taking into account the significant third-order NLO response of the porphyrin ring, when the asymmetric substitution of such a ring is too weak, the determination of the quadratic hyperpolarizability by the EFISH technique can be affected by significant errors because the third-order electronic contribution γ (−2ω; ω, ω, 0) to γ _EFISH cannot be neglected [167].

Pizzotti et al. reported [168] an EFISH investigation, working in CHCl₃ solution with a nonresonant incident wavelength of 1.907 μm, on the second-order NLO response of various push–pull tetraphenylporphyrins and their Zn^II complexes substituted at the β pyrrolic position by a π-delocalized organic substituent carrying either an electron-withdrawing or electron-donating group (48).

Interestingly, the porphyrin ring shows in these push-pull NLO chromophores an ambivalent character as donor (due to the high polarizability of its electronic cloud) or as acceptor (due to the presence of various low-lying excited-states). When the substituent is an electron-acceptor group, the porphyrin ring behaves as a significant donor group, comparable to a ferrocenyl group. The value of β _1.91(EFISH) decreases only slightly on going from the free porphyrin to its Zn^II complex, in agreement with the assumption that the second-order NLO response is controlled by a CT process, favored by π conjugation, from the occupied π levels of the pyrrolic ring, acting as a push system, to the π* antibonding orbitals of the linker. This latter process should be scarcely affected by coordination of the porphyrin ring to Zn^II. In contrast, when the substituent is a strong electron-donor π-system, the β _1.91(EFISH) is not only higher but it increases by complexation to Zn^II, as expected for an increased acceptor property.

Diphenyl porphyrins and their Zn^II complexes substituted in the meso position by a π-delocalized substituent carrying an electron-donor or an electron-withdrawing group (49) were also investigated by the EFISH technique [169]. These second-order NLO chromophores have confirmed the ambivalent role of the polarizable porphyrin ring, which, in the ground state, already acts as a donor or acceptor, depending on the nature (acceptor or donor) of the substituent in the meso position. There is a significant increase of β _1.91(EFISH) for the same π-delocalized substituent carrying an electron-acceptor group, going from the substitution in the meso position to that in the β pyrrolic position. When the π-delocalized substituent is carrying an electron-donor group, the position of the substitution (meso or β pyrrolic) is influential on the value of β _1.91(EFISH). Interestingly, when the electron-acceptor substituent is in position meso, the donor property of the porphyrin ring becomes quite similar to that of the organic strong donor system trans-4-NMe₂C₆H₄CH═CH₂.

A combined electrochemical, HRS and theoretical DFT investigation has also been carried out on meso-tetraphenylporphyrin (H₂TPP) and its first transition series metal complexes (MTPP) (50) [170].

While neutral MTPP, due to their centrosymmetric structure, have a zero second-order NLO response, the one and two-electron oxidized products of CuTPP and ZnTPP show significant β(HRS) values (β _1.06(HRS) = 351 and 371 × 10⁻³⁰ esu, for CuTPP⁺ and CuTPP⁺⁺; β _1.06(HRS) = 407 and 606 × 10⁻³⁰ esu, for ZnTPP⁺ and ZnTPP⁺⁺), confirmed by TD-DFT calculations. Electrochemical switching of their optical nonlinearity between the neutral and the oxidized forms has been achieved, but its repetition was demonstrated only for the first oxidation step.

Axial coordination of stilbazoles like 4,4′-trans or trans,trans-Me₂N–C₆H₄(CH═CH) _n C₅H₄N (n = 1, 2) to tetraphenylporphyrinates of Zn^II, Ru^II, and Os^II [171] does not produce the increase of the quadratic hyperpolarizability which usually occurs when this kind of stilbazoles coordinates to hard or soft Lewis acid metallic centers (see Sect. 3.1.2). This lack of increase of the second-order NLO response upon axial coordination can be interpreted as being due to a significant axial π backdonation from the d_π orbitals of the metal into the π* antibonding orbitals of the stilbazoles. This effect produces a contribution, opposite to that of σ donation, to the quadratic hyperpolarizability of the stilbazole, thereby giving rise to a balance of the positive (σ−donation) and negative (π-backdonation) effect on the quadratic hyperpolarizability. When 4,4′-trans-F₃C–C₆H₄(CH═CH)C₅H₄N is axially coordinated, the axial π backdonation becomes very relevant and prevails, thus resulting in a threefold increase of the EFISH quadratic hyperpolarizability. Therefore, the role of the axial π backbonding, when π-delocalized ligands, like stilbazoles, are axially coordinated to metal porphyrinates, causes the metal atoms of porphyrinates to act not only as σ acceptors, but also as π donors according to the nature of the stilbazoles.

From HRS measurements, working in CHCl₃ solution with a resonant incident wavelength of 1.064 μm, asymmetric meso-tetraaryl-metallo porphyrins such as 51 (Cu^II) and 52 (Zn^II) [172] have shown a relatively low second-order NLO response (β _1.06(HRS) = 118 and 92 × 10⁻³⁰ esu, respectively) when compared to asymmetric arylethynyl push–pull porphyniric NLO chromophores like 53 (Cu^II) and 54 (Zn^II) [173] (β _1.06(HRS) = 1,501 and 4,933 × 10⁻³⁰ esu, respectively), for which a very strong coupling between the donor and the acceptor substituents occurs [173]. In this latter case, the porphyrin ring acts mainly as a very polarizable and long π linker. The value of β _1.06 of 54, deduced from both an absorption and electroabsorption investigation (Stark effect), has been subsequently reported to be lower (β _1.06 = 1,710 × 10⁻³⁰ esu), although still very high [174]. For 55, carrying a Ni^II instead of a Zn^II or Cu^II metal center, much lower values have been measured by the EFISH technique working in CHCl₃ with a nonresonant incident wavelength of 1.907 μm [175]. Similar low values (β _1.91(EFISH) = 66–124 × 10⁻³⁰ esu) of the quadratic hyperpolarizability have been reported for structurally related porphyrin arylethynyl push–pull NLO chromophores measured by EFISH under the same experimental conditions [176]. Such striking differences have suggested that the metal could strongly influence the second-order NLO response of this kind of push-pull NLO chromophores. However, recent theoretical DFT or HF and coupled-perturbed (CP) DFT or HF investigations on the linear and second-order nonlinear properties of 53, 54 and 55 [177] have shown that their second-order NLO response is barely affected by changing the metal. Moreover, the values of β ₀ of 54–55 calculated by CP-HF and CP-DFT level of theory are similar and in the range 61–66 × 10⁻³⁰ esu and 301–327 × 10⁻³⁰ esu, respectively, with β _1.91(CP-HF) values in the range 76–79 × 10⁻³⁰ esu. These are much lower values than those reported for 54, when measured by HRS working at a resonant incident wavelength of 1.064 μm. The discrepancy of the experimental measurements is probably due to the different incident wavelengths, as confirmed by the comparison of the calculated β _1.06 and β _1.91 values of 54 at HF level of theory, with the former showing a much higher value, as a result of a resonance between the second harmonic (532 nm) and the strong Q band at about 600 nm.

An attempt to link covalently an NLO chromophore structurally related to 54 to a polymeric network has been made by introducing a methacrylate group on the donor part of the molecule and a carboxylic acid function on the acceptor one (56) [178]. Copolymerization with glycidyl methacrylate has been successfully carried out, affording a composite polymeric film whose electrooptical properties are under investigation.

In order to improve the second-order NLO response, working at 1.30 μm incident wavelength, new push-pull NLO chromophores based on the porphyrin ring have been synthesized, coupling to the porphyrin ring thiophene or thiazole rings.

The second-order NLO response of molecular architectures such as 57 and 58 [179] or 59 and 60 [180] (structurally related to 58a) has been determined by the HRS technique in THF solution. β _1.30(HRS) values from 650 to 4,350 × 10⁻³⁰ esu have been measured for 57 and 58 (the highest value was obtained for 57c). The lower values of the quadratic hyperpolarizability have been measured when thiophene or oligothiophene units are linked to the porphyrinic core through a C≡C triple bond (58). For the NLO chromophores 59 and 60, β _1.30(HRS) values of about 785–1,400 × 10⁻³⁰ esu have been measured, with 60b showing the highest value. It must be pointed out, however, that the second harmonic at 0.65 μm (650 nm) is in the region of intense Q absorption bands. Therefore, it is possible that the values of the quadratic hyperpolarizabilities could be affected by a significant enhancement due to resonance effects. A detailed theoretical analysis of the origin of the quadratic hyperpolarizability of these NLO chromophores, which is beyond the scope of this review, can be found in [179] and [180]. In conclusion, chromophores such as 57–60 may be interesting for long-wavelength optoelectronic applications.

The effect of the central metal ion on the value of the quadratic hyperpolarizability has been studied for chromophores similar to 58b, but carrying in the phenyl ring in 5,15 positions a CH₃ instead of a 3,5-bis(3,3-dimethyl-1-butyloxy)phenyl substituent. Metals such as Mg, Co, Ni, Cu, and Zn have been considered [181]. Their quadratic hyperpolarizabilty was theoretically evaluated by semiempirical ZINDO/CV calculations, which have shown that metalloporphyrins, due to significant CT transitions, may display values of the quadratic hyperpolarizability about one order of magnitude higher than that of the free porphyrins. Moreover, by varying the metal atom, an increase of the quadratic hyperpolarizability could be achieved, the highest value being computed for the NLO chromophore with Mg as metal center (β _1.91 = 1,120 × 10⁻³⁰ esu).

In order to investigate how the second-order NLO properties of this kind of NLO chromophores are affected by aggregation of many porphyrin rings, push-pull metalloporphyrins carrying two or three porphyrin rings, such as those reported below (61) [182] where the single porphyrin rings are connected by two C≡C triple bonds, have been theoretically investigated.

Semiempirical ZINDO/CV calculations have suggested that the quadratic hyperpolarizability of dimers and trimers are about one order of magnitude higher than that of the monomer [182]. A DFT/TDDFT investigation on the NLO chromophores 57b and 58b [183] has confirmed an almost planar architecture, which enhances the π-conjugation of the push–pull system and, as a consequence, the quadratic hyperpolarizability.

Structures with a Zn^II porphyrin cycle and a metal^IIpolypyridyl connected through the 10,20 meso position of the porphyrin by a C≡C linker have been studied by HRS working in CH₃CN solution with a 0.80 μm incident wavelength (62) [184]. HRS depolarization experiments have shown that the second-order NLO response of these architectures is mainly due to conformers in which the torsional angles between the polypyridyl unit and the porphyrin core are opposite in sign but equivalent in magnitude (θ ≈ −φ). These species can thus be considered as interesting building blocks for nonpolar chiral electrooptic materials.

3.6.2 Metallophthalocyanines

Phthalocyanines are macrocycles characterized by an extensive 2D planar and centrosymmetric 18 π-electron system. For this reason they have been widely investigated as third-order NLO materials and in particular as potential materials for OL; some recent reviews have appeared in this specific field [163, 185, 186]. Only in the last decade have the second-order NLO properties been investigated and some of the reviews reported above describe the first significant results [164, 185]. Hereafter, we will highlight the must relevant results achieved since 2003 in the field of phthalocyanines showing second-order NLO properties.

By means of the EFISH technique, working in CHCl₃ with a nonresonant incident wavelength of 1.907 μm, the second-order NLO response of the asymmetric phthalocyanine 63 has been measured and compared to that of phthalocyanines 64 and 65 [187].

The dipole moments of push-pull NLO chromophores 63 and 64a are exceptionally high (38.8 D and 33.6 D, respectively), while the measured γ(EFISH) values are negative for all of them (γ(EFISH) = −41.3 × 10⁻³⁴ esu for 64a; γ(EFISH) = −57.4 × 10⁻³⁴ esu for 64b; γ(EFISH) = −16.8 × 10⁻³⁴ esu for 65) except for 63 (γ(EFISH) = 5.25 × 10⁻³⁴ esu). The high value found for the centrosymmetric phthalocyanine 64b clearly shows that, for this kind of second-order NLO chromophores, the electronic contribution γ (−2ω; ω, ω, 0) to the EFISH measurement is significant and cannot be neglected. The comparison between the positive value obtained for 63 and the negative value measured for 64a, which bears a similar substitution pattern but without a triazolehemiporphyrazine bridge between the donor and the acceptor part of the molecule, suggests a change in the sign of Δμ _eg.

In a further investigation [188], a new family of substituted push-pull phthalocyanines (66 and 67), carrying triple bonds as linkers between the donor and the acceptor groups, has been investigated.

The second-order NLO response of these push–pull NLO chromophores has been measured by means of both EFISH (in CHCl₃, working at 1.064 and 1.907 μm incident wavelength) and HRS (working at 1.064 μm incident wavelength) techniques. The largest β _1.91(EFISH) and β _1.91(HRS) values (522 × 10⁻³⁰ esu and 530 × 10⁻³⁰ esu, respectively) were obtained for 66b, which exhibits the highest degree of dipolar asymmetry. The ethynyl based linker seems, therefore, to be an excellent spacer for enhancing the second-order NLO response of this kind of asymmetric push-pull phthalocyanines.

In order to overcome the nonlinearity transparence trade-off (the lengthening of the π conjugation increases the second-order NLO response of this kind of second-order NLO chromophores, but at the same time decreases their transparency), a bisphthalocyanine, with the CT between the donor and the acceptor guaranteed through space by a [2,2] paracyclophane unit (68), has been synthesized [189] and its second-order NLO response measured in CHCl₃ by both EFISH and HRS, working at 1.064 μm incident wavelength; a significant value of β _1.06(HRS) (180 × 10⁻³⁰ esu) was measured.

Of particular interest for their high second-order NLO response are the intrinsically noncentrosymmetric phthalocyanines analogs called subphthalocyanines. These cone-shaped macrocycles, consisting of three isoindole moieties with a central boron atom coordinated to an axial halogen ligand, have been studied for both their dipolar and their octupolar characters, given that they possess not only a dipole moment along the B-halogen bond, but also an octupolar charge distribution within their three-dimensional aromatic architecture [185]. For instance, the NLO chromophore 69 is characterized by a significant β _1.34(HRS) value (104 × 10⁻³⁰ esu), due to the strong octupolar character of the subphthalocyanine core and to a fair γ _1.34(EFISH) value (17.9 × 10⁻³⁴ esu) corresponding mainly to the dipolar orientational contribution to γ _1.34(EFISH). A fine-tuning of the dipolar and octupolar contributions was reached by varying the substituents of the subphthalocyanine core [190].

The effect of a static electric field on the SHG of the centrosymmetric copper phthalocyanines 70 has been investigated, applying an external d.c. voltage to an Au-phthalocyanine film-Au system that induces a second-order polarization [191]. A SHG signal has also been obtained at the interface of a Langmuir-Blodgett film of 70b, deposited on a metal-coated glass slide [192] and from a film obtained by vacuum-evaporation of 70a at a metal electrode interface [193].

3.7 Bimetallic Complexes

The investigation of the second-order NLO response of asymmetric bimetallic complexes in which the electron-accepting and donating properties of two metal- based fragments are combined has been an area of interest in the past few years [13, 19].

The ferrocenyl moiety has a donor strength comparable to that of a methoxyphenyl group [194]; therefore many bimetallic complexes containing a ferrocenyl moiety linked via a π-delocalized bridge to another organometallic fragment, acting as acceptor group, have been investigated [13, 19]. For example, when η⁷-cycloheptatrienyltricarbonylchromium is used as acceptor group, a high quadratic hyperpolarizability has been measured by HRS (71, β _1.06(HRS) = 570 × 10⁻³⁰ esu) [195].

The “W(CO)₅” fragment, which can behave as donor or acceptor in monometallic NLO chromophores (see Sect. 3.1), appeared as an efficient acceptor group in these NLO chromophores with ferrocene as donor. For example, the β _1.06(HRS) value of trans-(1-ferrocenyl-2-(4-pyridyl)ethylene] increases by a factor of about 5 upon coordination to “W(CO)₅” (72, β _1.06(HRS) = 101 × 10⁻³⁰ esu). The EF is less significant when changing the metal and it decreases in the order “W(CO)₅” >“Mo(CO)₅” >“Cr(CO)₅,” probably due to the higher π-backdonation of the electron d density in the case of W, if compared to Cr and Mo [196]. Interestingly, no significant EF is observed upon coordination of the pyridyl ligand to “Re(CO)₃Br” [197]. As expected, an increase in the conjugation length of the linker, for instance by insertion of a vinylenephenylene between the ethylene and the ferrocenyl, results in higher β _1.06(HRS) values (for trans,trans-(η⁵-C₅H₅)Fe{η⁵-C₅H₄CH═CHC₆H₄CH═CH–C₅H₄N–W(CO)₅, 535 × 10⁻³⁰ esu [120]). Coordination of trans-[1-ferrocenyl-2-(4-cyanophenyl)ethylene] to “W(CO)₅” (73) also leads to an enhancement of the β _1.06(HRS) value (by a factor of 3.6; β _1.06(HRS) = 375 × 10⁻³⁰ esu), less significant than that of the related ferrocenyl system based on the donor pyridine ligand (72) [196].

Various bimetallic complexes with ferrocenyl as electron-donor group linked via a π-delocalized system and pyridine coordination to electron-deficient “Mo^II(NO)Tp*X” (Tp* = tris(3,5-dimethylpyrazolyl)borate; X = Cl, Br, I) or “W(CO)₅” centers have been studied by McCleverty et al. [132]. For example, the complex 74 is characterized by a β _1.06(HRS) value of 205 × 10⁻³⁰ esu. Although the measured HRS data are resonance enhanced, the β _1.06(HRS) trends imply the following conclusions: (1) the quadratic hyperpolarizability increases when the ligand Cl⁻ or Br⁻ is replaced by I⁻, which is reasonable in the light of the more substantial polarizability of I⁻ when compared with Cl⁻ and Br⁻; (2) methylation of ferrocene increases its electron-donor ability; and (3) the electron-accepting abilities of the “Mo^II(NO)Tp*Cl” and “W(CO)₅” moieties are similar. Furthermore, chemical oxidation of the ferrocenyl donor group or chemical reduction of the molybdenum nitrosyl acceptor fragment in selected NLO chromophores caused a reduction of between 25% and 100% of the NLO response, therefore allowing redox-induced switching of the NLO responses [132].

Jayaprakash et al. [198] reported the series of push–pull bimetallic polyene complexes [(CO)₅M═C(OCH₃)(–CH═CH–) _n (η⁵C₅H₄)Fe(η⁵C₅H₅)] (M = W, Cr; n =1–4) with ferrocene as donor and a carbene complex of Cr or W as acceptor. The β _1.06(HRS) values increase with increasing the conjugation of the π linker; for the same π linker, the chromophore based on W exhibits higher second-order NLO responses than that based on Cr, as expected for a more efficient π backdonation from the W atom. The quadratic hyperpolarizability of these bimetallic push-pull polyene NLO chromophores exhibits significant solvent polarity dependence, suggesting a CT from the ferrocene donor to the carbene acceptor along the polyene backbone with significant Δμ _eg. The highest β _1.06(HRS) value (780 and 2,420 × 10⁻³⁰ esu, in hexane and acetonitrile, respectively) was reached for the NLO chromophore with M = W and n = 4.

In this kind of bimetallic chromophores, another efficient electron-donor group is a ruthenium σ-acetylide complex [13, 19] which can lead to large β _1.06(HRS) values (535 and 700 × 10⁻³⁰ esu for 75 and 76, respectively [199]). Comparison with complexes 72 and 73 confirms that a ruthenium σ-acetylide complex is a better donor than the 1-ferrocenyl-ethylene moiety. In all these NLO chromophores, “W(CO)₅” is an efficient acceptor group, better than “Cr(CO)₅” [199].

Significant quadratic hyperpolarizabilities for two mixed-valence bimetallic complexes have also been reported [13, 19]; for example complex 77 is characterized by a β _1.06(Stark) of 37 × 10⁻³⁰ esu [200]. In such NLO chromophores, the electron-accepting d ⁵ Ru^III center is stabilized by strongly basic amine ligands, whilst the electron-donating d ⁶ Ru^II is stabilized by π-accepting cyanides.

The second-order NLO response of a class of asymmetric push–pull bimetallic complexes, organometallic counterpart of classical push–pull aromatic chromophores, having pyrazine (pyz) and trans-1,2-bis(4-pyridyl)ethylene (bpe) as π-polarizable linkers between a metal carbonyl fragment acting as donor group (“W(CO)₅”) and a metal carbonyl fragment acting as acceptor group (e.g., “cis-Rh(CO)₂Cl”), was investigated [201]. Coordination of (CO)₅W(pyz, or bpe) to “cis-Rh(CO)₂Cl” leads to an increase of the absolute value of the quadratic hyperpolarizability (β _1.91(EFISH) = −33 and −41 × 10⁻³⁰ esu, for 78 and 79, respectively), dominated by a red-shift of the MLCT (W⁰→π*) transition of the W(CO)₅(pyz or bpe) moiety, due to the stabilization by interaction with the “cis-Rh(CO)₂Cl” acceptor group of the π* acceptor orbitals of the pyz or bpe bridge [201].

The CT is in the direction opposite to that of the ground state dipole moment, leading to a negative quadratic hyperpolarizability. In these NLO chromophores, the MLCT process (W⁰→π*), dominating the NLO response, remains localized on the part of the π bridge close to the push donor center (“W(CO)₅”) even after coordination at the other end of the bridge of a metallic center acting as pull acceptor center. Therefore, the electronic process controlling the second-order NLO response never assumes a MMCT (metal-to-metal CT) character, with the CT process involving both the donor and acceptor metal centers via the polarizable π bridge as it occurs between the donor and acceptor groups in structurally related classical push-pull aromatic 1D chromophores. In accordance, in these bimetallic NLO chromophores the quadratic hyperpolarizability is not strongly influenced by increasing the length of the π-delocalized bridge between the push and pull groups, while in structurally related organic π-delocalized push–pull 1D chromophores the second-order NLO response increases by increasing the length of the π-delocalized bridge [60, 61]. Consequently the value of β _1.91(EFISH) of 78 is, as absolute value, higher than that of para-nitro dimethyl aniline (12 × 10⁻³⁰ esu), whereas that of 79 is lower than that of trans-4-dimethylamino, 4-nitro stilbene (73 × 10⁻³⁰ esu) [201]. Theoretical TD-DFT and TD-HF calculations have confirmed such a view of the origin of the second-order NLO response in these push–pull NLO chromophores [202].

An interesting effect due to metal–metal bonding was studied in the case of bimetallic NLO chromophores such as [(CO)₃(1,10-phenanthroline)W-fac-MCO)₃Cl₂] (M = Ru^II, Os^II) and [(CO)₃(1,10-phenanthroline)W-cis-MCO)₂Cl] (M = Rh^I, Ir^I) which show an increased negative second-order NLO response (β _1.91(EFISH) from −25.8 × 10⁻³⁰ up to −76 × 10⁻³⁰ esu), the best value being measured for the Os^II derivative. The increase of the absolute value of the second- order NLO response when compared to that of the monometallic NLO chromophore [W(CO)₄(1,10-phenanthroline)] (β _1.91(EFISH) = −13 × 10⁻³⁰ esu) is due, as shown by a solvatochromic investigation, to the additional negative contribution produced by a new absorption band involving the W(CO)₃(1,10-phenanthroline) moiety at around 385–450 nm, in addition to the contribution of the MLCT (W⁰→π*phen) absorption band at around 499–526 nm, typical of [W(CO)₃(1,10-phenanthroline)L] (L = CO, CH₃CN) [203].

Recently Coe et al. synthesized some new push–pull bimetallic complexes with trans-[Ru^IICl(pdma)₂]⁺ (pdma = 1,2-phenylenebis(dimethylarsine)) as electron-donor group, linked via a π-conjugated bridging ligand to fac-[Re^I(biq)(CO)₃]⁺ (biq = 2,2′-biquinolinyl) as electron-acceptor group [204]. The bridging units were 4,4′-bipyridyl (4,4′-bpy; 80), trans-1,2-bis(4-pyridyl)ethylene (bpe; 81), or 1,4-bis[trans-2-(4-pyridyl)ethenyl]benzene (bpvb; 82). The electronic absorption spectra of these bimetallic species are dominated by intense and opposite Ru^II→π*(4,4′-bpy/bpe/bpvb) and Re^I→π*(biq) MLCT transitions. Cyclic voltammetric studies reveal both Ru^III/II oxidation and ligand-based reduction processes and show no evidence for significant electronic communication between the two metal centers. Stark spectroscopic studies on the MLCT bands show that extending the π conjugation of the linker leads to an increase of the dipole moment change (Δμ _eg) and of the transition dipole moment (r _eg). These effects combine to afford an increase of the static quadratic hyperpolarizabilities, β ₀, estimated by applying the “two level” model (β ₀(Stark) = 47, 114 and 122 × 10⁻³⁰ esu, for 80, 81, and 82, respectively). Comparisons with monometallic Ru^II complexes reveal that methylation of the free pyridyl nitrogen, to generate a pyridinium center, leads to larger β ₀ responses (β ₀(Stark) = 113, 123, and 131 × 10⁻³⁰ esu, for the alkylated monometallic Ru^II complex with 4,4′-bpy, bpe, or bpvb, respectively) than does coordination to the fac-[Re^I(biq)(CO)₃]⁺ center. The outcome can be attributed to the evidence that the Re^I moiety is a weaker net electron-acceptor. In fact, it is a Lewis acceptor but it also behaves as a π donor, and this offsets partially its electron-withdrawing effect. In contrast, an N-methylpyridinium group does not possess such an ambivalent electronic behavior [204].

As evidenced from these examples, the introduction of two metal centers as donor and acceptor groups in a push–pull NLO chromophore can allow tuning of the electronic properties for a better second-order NLO response, affording relatively large quadratic hyperpolarizabilities.

4 Conclusions and Perspectives

This short and not exhaustive overview illustrates the actual level of the control of the structure – second-order NLO activity relationship in organometallic or coordination compounds and therefore their potentiality as second-order NLO chromophores.

Many coordination or organometallic compounds with various ligands such as substituted stilbazoles, bipyridines, phenanthrolines, terpyridines, Schiff bases, alkynyl and vinylidene ligands, metallocenes, or macrocycles such as metalloporphyrins, metallophthalocyanines, or the new emerging class of cationic cyclometalated or of bimetallic coordination complexes, have been investigated as second-order NLO chromophores in the last 10 years. They are characterized by rather large β _λ (HRS), μβ _λ (EFISH), or μβ ₀(EFISH) values which can be favorably compared with that of the prototypical organic 1D push-pull NLO chromophore Disperse Red One (trans-4,4′-O₂NC₆H₄N═NC₆H₄NEt–(CH₂CH₂OH), μβ ₀(EFISH) = 450 × 10⁻⁴⁸ esu) currently proposed for electrooptic polymeric poled films [205, 206]. Moreover, a variety of push-pull Ru^II ammine salts and of octupolar metal (in particular of Ru^II) complexes, recently studied, are characterized by large static quadratic hyperpolarizabilities, as determined by HRS.

It appears from this overview that the interaction with a metal center represents a flexible way to tune the second-order NLO response of organic NLO chromophores acting as ligands. By the modulation of the electronic nature and the oxidation state of the metal and of its coordination sphere through ancillary ligands or chelation, such a response can not only be increased, sometimes in a very significant way, but its sign can also be changed. Besides, the metal may act as template for the stabilization of octupolar D ₃ and D _2d structures, based on various chelated organic ligands, or of asymmetric Schiff-bases complexes, producing second-order NLO chromophores, either octupolar or dipolar, with significant and tunable second-order NLO response. Finally, it is possible to produce bimetallic push-pull NLO chromophores where metal based moieties, acting as donor or acceptor groups, are connected by a π organic linker. In these cases, there are significant differences with the corresponding traditional push–pull organic NLO chromophores about the general trends and the origin of the quadratic hyperpolarizability. The metal can also act as a bridge, thus permitting electron-transfer processes between various sites of its coordination sphere such as in some push–pull metal porphyrins or Schiff bases complexes and in the new cyclometallated chromophores. The great potentiality of TD-DFT, CP-DFT, and CP-HF theoretical approaches has recently given a way to understand better the electronic origin of the second-order NLO response of many NLO chromophores based on metal complexes or organometallic compounds. These useful theoretical tools may allow today the design of new and efficient coordination and organometallic second-order NLO chromophores.

Sufficiently large second-order NLO responses have already been achieved; therefore the research now hinges also on considerations such as thermal and chemical stability and multifunctionality (for example, combining second-order NLO response with emission or magnetic properties). Nanoorganization of second-order NLO chromophores based on metal complexes or organometallic compounds, for example in Langmuir–Blodgett films or in polymeric electrically poled films, has been investigated but is still under study in order to reach large and stable in time SHG. In the last few years, increasing effort has also been dedicated to achieve the switching of the second-order NLO response, for example by redox-induced switching or photo-switching controlled by the metal. Therefore, metal complexes and organometallic compounds are attractive not only for their interesting second-order NLO properties but also for their potentiality as multifunctional materials. Up to now, however, no stable and efficient nanostructured materials or electro-optical devices based on coordination and organometallic compounds have reached the stage of real applications and commercialization. But this is normal for a relatively young field of research, of which almost all scientific contributions have appeared in the last two decades. In any case, given the rapid progress made over recent years, future prospects for applications seem possible.