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Nonlinear Optical Properties of Ni(Me6pzS2)MX (M ) Ni, Pd, Pt; X ) Me2timdt, mnt) P. Romaniello,*,†,‡ M. C. D’Andria,§ and F. Lelj§ Laboratoire des Solides Irradie´s UMR 7642, CNRS-CEA/DSM, E´cole Polytechnique, and European Theoretical Spectroscopy Facility, F-91128 Palaiseau, France, and LaMI Dipartimento di Chimica and LaSCAMM, INSTM Sezione Basilicata, UniVersita della Basilicata, Via N. Sauro 85, Potenza 85100, Italy ReceiVed: NoVember 30, 2009; ReVised Manuscript ReceiVed: March 29, 2010
In this work we investigate the second-order response of complexes of formula Ni(Me6pzS2)MX (M ) Ni, Pd, Pt; X ) Me2timdt (monoanion of N,N′-disubstituted imidazolidine-2,4,5-trithione), mnt (maleonitriledithiolate)): by binding the porphyrazine to the metal-dithiolene, the electron asymmetry and π-conjugation of the latter is increased, and its second-order response can result enhanced. By performing ab initio calculations of the ground-state and response properties of these compounds, we predict the molecular first hyperpolarizability, we elucidate its electronic origin, and we illustrate its dependence on the metal and the dithiolene ligand. Our study indicates that these complexes show a very high second-order response, comparable to that of organic “push-pull” materials, and that the appropriate metal-dithiolene combination can significantly enhance it. I. Introduction With their wide range of possible applications, such as information processing, optical switching, optical frequency conversion, and telecomunications,1,2 nowadays nonlinear optical materials play an important role in the technological development.3,4 The properties of these materials have been studied experimentally and computationally with a major focus on organic compounds.5 The ultimate goal in developing nonlinear materials is to achieve large first hyperpolarizability, good optical transparency, and high photochemical stability in the same material. An essential step to reach this goal is the design of molecules that combine together these features: this has led to the modeling and successive synthesis of chromophores with remarkably large molecular first hyperpolarizabilities, such as 10 200 (×10-30) esu.5 Recently, there has been increasing interest in organometallic and coordination complexes.2,6–10 Metal 1,2-dithiolenes represent a very interesting class of coordination complexes due to their unique properties, such as high thermal and photochemical stabilities, reversibly connected oxidation states, and a very intense vis-IR absorption.11–14 In particular the dithiolenes derived from the dmit (1,3-dithiole2-thione-4,5-dithiolate) ligand together with the d8 metal ions are the most known due to their low temperature electrical superconducting properties.15–22 In the past decade, numerous dithiolenes of formula M(R,R′-timdt)2x- (M ) Ni, Pd, Pt; R,R′timdt ) monoanion of N,N′-disubstituted imidazolidine-2,4,5trithione; x ) 0, 1, 2) have been synthesized and fully characterized both experimentally and theoretically. In particular, the neutral form shows a very intense near-infrared (NIR) absorption, which has been attributed to a π f π* electronic transition between the HOMO and the LUMO and occurs at energy values depending on the nature of the R and R′ substituents, the metal, and the environment.12,23 The wavelength and the high intensity of this NIR absorption band together with the high thermal and photochemical stability makes this class * To whom correspondence should be addressed. † ´ Ecole Polytechnique. ‡ European Theoretical Spectroscopy Facility. § Universita della Basilicata.
of dithiolenes a candidate for laser applications (see Mitsubishi patent24).25–27 In particular, the presence of an intense low-energy charge-transfer band, which involves a large difference between the dipole moment of the ground state and the excited state, could lead to a strong second-order response, as predicted by the two-level model.28 In this model, only one excited state is responsible for the second-order response, and the first hyperpolarizability tensor (second-harmonic generation, see later in the text) can be expressed as
βiii ∝
pωegfeg∆µieg [(pω)2eg - (2pω)2][(pω)2eg - (pω)2]
(1)
(in atomic units) where βiii represents the dominant tensorial component, pωeg and feg are the excitation energy and oscillator strength, respectively, of the transition to the selected excited state, ∆µeg is the difference between the excited-state and the ground-state dipole moments, and pω is the frequency of the external laser source. In ref 25 the second-order response of M(R,R′-timdt)2 metaldithiolenes has been investigated. This study shows that these compounds have a promising second-order response, which can be enhanced by increasing the charge-tranfer character of the NIR absorption. This is, indeed, the case in the MXY mixedligand compounds (M ) Ni, Pd, Pt; X,Y ) R2timdt, dmit, mnt (maleonitriledithiolate); X * Y),29 which exhibit an enhanced second-order response. This is in line with the well-established empirical observations that the second-order response can be enhanced by increasing the electronic asymmetry (stronger donator and acceptor moieties) and/or the π-conjugation between the donor and acceptor groups. These findings suggested us that one could obtain large second-order response by combining metal-dithiolenes with porphyrazines. The latter are molecules with high delocalized electronic structure in which the four pyrrole moieties are linked to each other by four aza bridges. Similar molecules, the porphyrins, which have carbon atoms in the meso bridge positions, have already been investigated, both theoretically and
10.1021/jp911353n 2010 American Chemical Society Published on Web 04/15/2010
Nonlinear Optical Properties of Ni(Me6pzS2)MX experimentally, for their nonlinear optical properties: conjugated, electronically asymmetric porphyrin-based chromophores show very large measured β values ranging from 650 to about 5000 (×10-30) esu.6–9 Recently, unsymmetrical porphyrazines bearing a peripheral functionality capable of binding metal ions have been investigated.30–35 The peripheral functionalities can significantly influence the electronic structure of the π-system in the porphyrazine, and consequently the optical spectrum. In this paper we focus mainly on the porphyrazine of the kind Ni[pz(A: B3)], where A and B are functional groups directly bound at the β-positions of the pyrroles. The peripheral B moieties involve alkyl groups. The peripheral A moieties can be an heteroatom of the kind of N or S (in our study it is a sulfur atom), which can bind a metal ions (M ) Ni, Pd, Pt) coordinated to a dithiolene (mnt and Me2timdt). These complexes have features in the UV-vis spectra that depend on the metal coordinating the “core” of the porphyrazine and on the peripheral substitution of the complex, hence allowing a fine-tuning of the electronic properties. Moreover, these complexes have two metals linked by a polarizable bridge. Similar push-pull bimetallic complexes have already been investigated in literature for their nonlinear optical properties.10,36,37 In this paper we investigate the molecular first hyperpolarizability of complexes of formula Ni(Me6pzS2)MX (M ) Ni, Pd, Pt; X ) Me2timdt, mnt). We calculate the ground-state and response properties using (time-dependent) density-functional theory (TDDFT). To get insight into the origin of the secondorder response we will use the two-level model1 for interpreting the TDDFT results of the β tensor: the comparison will indicate if there is a main excited state that dominates the second-order response or if, instead, more states are involved. The paper is organized as follows. In Section II we give some theoretical and computational details. In Section III we discuss the results calculated for the geometry, electronic structure, electronic excitations, and second-order response of these complexes, and we focus, in particular, on the role played by the peripheral metal and by the dithiolene ligand in the studied properties. We show, in particular, that increasing the electron asymmetry, passing from Me2timdt to mnt, and red-shifting the dominant low-energy excitation (if there is a dominant excitation that determines the second-order response), passing from Ni and Pt to Pd, the second-order response is very large and comparable to that of extended π-organics molecules. Finally, we draw our conclusions. II. Method and Computational Details All results showed in this paper refer to ab initio calculations based on density-functional theory. In particular, for the response calculations we used TDDFT. Within this approach, after the first-order equations have been solved, one can calculate the first hyperpolarizability tensors, which govern the second-order properties. In this work we will consider only the case in which the frequency of the external perturbation is either 0 or ω, which gives rise to the following first hyperpolarizability tensors: the static tensor β(0; 0, 0), and the tensors β(-2ω; ω, ω), β(-ω; 0, ω), and β(0;-ω, ω), which govern the second-harmonic generation (SHG), the electrooptic Pockels effect (EOPE), and the optical rectification (OR), respectively. Since d-metals are involved, scalar relativistic effects have been taken into account in all our calculations23 by using the zeroth-order regular approximation (ZORA).38 We used a valence double-ζ STO (Slater-type orbital) basis set with one polarization function (DZP) for main element atoms and a triple-ζ STO basis set with one polarization function (TZP) for
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Figure 1. Structure of the Ni(Me6pzS2)MX (M ) Ni, Pd, Pt; X ) mnt, Me2timdt) complexes. The system is placed in the xz-plane, with the dipole moment along the z-axis. For simplicity, we enumerated only the atoms involved in the bond lengths and angles discussed in the paper.
the transition metals. The cores (C, N, O: 1s; S, Ni: 1s-2p; Pd: 1s-3d; Pt: 1s-4d) have been kept frozen. All the results are converged with respect to the basis set size. Geometries have been optimized by using the exchange-correlation potential proposed by Becke39 and Perdew40 (BP). Excited states have been computed by using the asymptotically correct potential proposed by van Leeuwen and Baerends (LB94)41 and the SAOP (statistical average of orbital potentials),42,43 and the hyperpolarizabilities by using the LB94 potential. The choice of these functionals has been motivated by our previous calculations on similar compounds.23,25,26,29,44,45 All the calculations have been performed using the ADF2003 computational package.46 Moreover, in order to get an estimation of the difference between the dipole moment of the ground-state and that of the low-lying excited states, we calculated the dipole moment of the lowest excited states using Gaussian09.47 We employed the LC-BLYP functional, which is a BLYP functional with the longrange correction proposed by Iikura et al.;48 we found that this functional yields transitions to the lowest-lying excited states with similar oscillator strengh and composition in terms of monoelectronic excitations as LB94 in ADF2003. III. Results In this section we present the results obtained for the geometry, the electronic structure, the excited states, and the second-order response of the Ni(Me6pzS2)MX (M ) Ni, Pd, Pt; X ) mnt, Me2timdt) complexes (see Figure 1). For simplicity, in the following we will indicate with A and B the series with X ) Me2timdt and X ) mnt, respectively, and with AM and BM (M ) Ni, Pd, Pt) the complexes of each series. A. Ground-State Properties. 1. Geometries. The geometries have been optimized assuming the system planar in the xz-plane (see Figure 1), with symmetry C2V and the singlet electronic ground state belonging to the A1 irreducible representation. The dipole moments are along the z-axis, and they have opposite direction in the two series. Although we have no experimental data for these complexes, the geometries show that the bond lengths and bond angles are in agreement with the experimental data found for similar complexes.30 In Table
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TABLE 1: Selected Bond Lengths (Å) and Angles (°) Calculated for Complexes BM (M ) Ni, Pd, Pt)a (s.r.) ZORA bond lengths (Å) and angles (°) M-S1 Ni-N1 Ni-N2 Ni-N3 S1-M-S2 N1-Ni-N2 N2-Ni-N3
Ni
Pd
Pt
expa
2.138 1.882 1.885 1.886 93.13 90.25 89.74
2.275 1.883 1.887 1.886 88.47 90.30 89.71
2.282 1.883 1.887 1.886 89.20 90.27 89.73
2.246 1.898 1.85 1.894 89.9 90.5 89.5
a For comparison, experimental data for the similar compound Ni [Pr6pz (NMe2) ]Pd (mnt) are also reported. Experimental data for Ni[Pr6pz(NMe2)2]Pd(mnt) are reported in ref 30.
1 we compare the most representative bond lengths and angles calculated for complex BPd with experimental data recorded for the similar compound Ni[Pr6pz(NMe2)2]Pd(mnt):30 the agreement is in line with previous studies on metal-dithiolenes.23,25,29,44 The geometry of the porphyrazine ring is not influenced by the nature of the metal, as is clear from the data reported in Table 1, as well as by the nature of the dithiolene ligand, since the bond lengths and angles of the porphyrazine ring are similar in the two series. The M-S1 (S2) (and similarly the M-S3 (S4)) bond length is influenced both by the metal and by the dithiolene ligand. This bond length increases passing from Ni to Pt, with a larger change from Ni to Pd than from Pd to Pt, as already
found in other metal-dithiolenes.23,25,29,44 The bond M-S3 is only marginally affected by the nature of the dithiolene ligand: the variation between the two series are of 0.017, 0.008, and 0.007 Å for Ni, Pd, and Pt, respectively, with series B showing the largest values. The bond M-S1, instead, strongly feels the nature of the dithiolene ligand: the variation between the two series are of 0.050, 0.035, and 0.037 Å for Ni, Pd and Pt, respectively, with series A showing the largest values. The remaining bond lengths as well as the bond angles show, in general, small changes among the members of the two series. 2. Electonic Structure. To better characterize these complexes we have analyzed the ground-state electronic structure in terms of the following fragments: the porphyrazine ligand Yx (Y ) Ni(Me6 pzS2)), the central metal M2+ (M ) Ni, Pd, Pt), and the dithiolene ligand Xy (X ) mnt, Me2timdt), with x ) 2-, y ) 0, for X ) Me2timdt, and x ) 0, y ) 2- for X ) mnt. This choice is based on the Mulliken population analysis and on the calculated values of the ground-state dipole moments (see later in the paper), which indicate as acceptor the porphyrazine ligand in series A and the dithiolene ligand in series B. In Figure 2 a schematic representation of the energy levels of the two series is depicted. The analysis of this figure leads to the following observations: the energy levels are similar within each series; in general, the energy levels of series A are higher than those of series B, as it can be expected since each complex of the former series has 8 electrons more than the corresponding complex of the latter series; the LUMO is quite far from the LUMO+1 in both series; the HOMO tends to
Figure 2. Energy level scheme for complexes AM and BM (M ) Ni, Pd, Pt). Only some selected molecular orbitals are depicted. For the sake of homogeneity here and in the following the orbital numbering of complexes APt and BPt does not include the 4f valence orbitals of Pt.
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Figure 3. Selected MOs and main percentage contributions from the peripheral metal (M ) Ni, Pd, Pt), porphyrazine ligand (Y ) Ni(Me6pzS2)), and dithiolene ligand (X ) Me2timdt) for complexes AM. Each percentage value is the sum of the main contributions from the MOs of each fragment. Where missing, the contributions are negligible. Notice that the orbitals 20b2 and 21b2 are the HOMO and the LUMO, respectively.
separate from the other occupied MOs in series A, whereas it is quite close to the occupied MOs in series B; the HOMO-LUMO energy gap of series A complexes is larger than that of the corresponding series B complexes, with complexes APd and BPd showing the smallest gap (0.63 eV), and complex ANi the largest gap (0.76 eV). For both series the calculated MOs are, in general, mainly localized on the porphyrazine ligand. However, some of the orbitals that are involved in intense excitations of the systems, as we will see in the next section, have large contributions from the peripheral metal and from the dithiolene ligand as well. In Figures 3 and 4 we reported some selected orbitals (those which will be mainly involved in the low-energy excitations) with the percentage compositions in terms of the MOs of the fragments. In series A the HOMO (20b2) is delocalized both on the porphyrazine ligand and on the dithiolene ligand with a negligible contribution from the peripheral metal. In series B, instead, the HOMO (13a2) is localized mainly on the porphyrazine ligand with a small contribution from the peripheral metal orbital ndxy, namely, 9.8, 3.5, and 5.5% for BNi, BPd, and BPt, respectively. The LUMO (21b2 for series A and 19b1 for series B) is localized on the coordination sphere of the peripheral metal, which also contribute through the orbital ndyz with a percentage of 12.4, 8.9, and 10.6% for ANi, APd, and APt, respectively, and of 15.18, 10.5, and 13.4% for BNi, BPd, and BPt, respectively. The other selected orbitals in Figures 3 and 4 are mainly localized on the porphyrazine ligand in both the series; the orbitals 17b1 and 18b1 in series B have important contributions also from the dithiolene ligand (>20%). High thermal and photochemical stability is an essential requirement for materials used in laser applications. To have an indication of the stability of these complexes, we calculated the bonding energies by using the energy decomposition analysis based on the method proposed by Ziegler and Rauk.50 It results that these complexes are very stable, the total bonding energy being -3339.8, -3303.8, and -3463.9 kJ/mol for ANi, APd, and
Figure 4. Selected MOs and main percentage contributions from the peripheral metal (M ) Ni, Pd, Pt), porphyrazine ligand (Y ) Ni(Me6pzS2)), and dithiolene ligand (X ) mnt) for complexes BM. Each percentage value is the sum of the main contributions from the MOs of each fragment. Where missing, the contributions are negligible. Notice that the orbitals 13a2 and 19b1 are the HOMO and the LUMO, respectively.
APt, respectively, and -3457.1, -3411.1, and -3577.2 kJ/mol for BNi, BPd, and BPt, respectively. B. Electronic Spectra. We have calculated the excitation energies for the Ni(Me6pzS2)MX (M ) Ni, Pd, Pt; X ) mnt, Me2timdt) complexes in the range around 300-1000 nm using both the LB94 and the SAOP xc functionals. This choice of the functionals is justified by previous studies on metal-dithiolenes and porphyrazines:23,44,45,49 in that case the two functionals give substantially the same overall picture of the spectra, with the LB94 better describing the high wavelength range and the SAOP the lower wavelength range. The symmetry point group of these complexes is the C2V, with the singlet ground-state belonging to the A1 irreducible representation. The spin- and symmetry-allowed excitations are those to the singlet excited states belonging to the A1, B1, and B2 irriducible representations. In Figures 5 and 6 we reported the calculated excitation energies. All the complexes show a similar spectrum. Considering only the most dominant transitions (oscillator strength g0.1, mainly belonging to the A1 representation), the spectra can be arbitrarily separated in three main regions: the first two in the ranges 300-400 nm and 400-650 nm, which can be identified with the N, B, and Q bands, respectively, of the porphyrazine, and the third region at wavelengths higher than 650 nm, which can be identified with the excitations of the metal-dithiolene. Furthermore, for the near-infrared (NIR) peaks we observe within each series the same trend found for other metal-
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Figure 5. Excitation energies of complexes AM(M ) Ni, Pd, Pt) calculated using the LB94 (violet lines) and the SAOP (blue lines) xc functionals.
Figure 6. Excitation energies of complexes BM (M ) Ni, Pd, Pt) calculated using the LB94 (violet lines) and the SAOP (blue lines) xc functionals.
dithiolenes: a red-shift of the peaks in the complex with Pd with respect to the complexes with Ni and Pt. The analysis of the main excitations in terms of monoelectronic transitions reveals a similar nature of the spectra with the two xc functionals, although SAOP yields in general a stronger multiconfigurational character of the spectra, especially for low wavelengths. In general, the spectra of these complexes show strong charge transfers (CT) from/to the metals to/from the ligands, and inter/intraligands CT. Large charge transfers
from one side of the molecule to another can result in a large change in the dipole moment, which, in turn, can play an important role in the second-order response. Therefore, the analysis of the excitation energy spectrum and of the nature of the predominant transitions can give a first insight in the second-order response of these complexes. In particular, in Table 2 we reported the major monoelectronic transitions contributing to the LB94 excitations for λ > 650 nm (SAOP compositions are essentially similar).
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TABLE 2: Low-Energy Excitations (λ > 650 nm) and Major One-Electron Transition Contributions Calculated for Complexes AM and BM (M ) Ni, Pd, Pt) Using the LB94 xc Functionala state 1 A1 2 A1
3 A1
a
ANi 926 (0.12) 76% 20b2 f 21% 20b2 f 885 (0.23) 49% 20b2 f 30% 19b2 f 15% 20b2 f 776 (0.15) 58% 19b2 f 20% 20b2 f
APd
APt
941 (0.14) 79% 20b2 f 19% 20b2 f 923 (0.24) 51% 20b2 f 34% 19b2 f 11% 20b2 f 808 (0.13) 58% 19b2 f 23% 20b2 f
22b2 21b2 21b2 21b2 22b2 21b2 21b2
22b2 21b2 21b2 21b2 22b2 21b2 21b2
945 (0.07) 88% 20b2 f 10% 20b2 f 890 (0.29) 57% 20b2 f 34% 19b2 f
BNi 22b2 21b2 21b2 21b2
780 (0.24) 56% 19b2 f 21b2 28% 20b2 f 21b2
BPd
BPt
1049 (0.04) 61% 17b1 f 19b1 35% 18b1 f 19b1 836 (0.02) 88% 16b1 f 19b1
1100 (0.05) 70% 17b1 f 26% 18b1 f 875 (0.06) 80% 16b1 f 15% 18b1 f
19b1 19b1
1057 (0.05) 60% 17b1 f 19b1 37% 18b1 f 19b1 833 (0.03) 86% 16b1 f 19b1 8% 18b1 f 19b1
713 (0.26) 47% 18b1 f 19b1 28% 17b1 f 19b1 8% 16b1 f 19b1
798 (0.24) 52% 18b1 f 19b1 21% 17b1 f 19b1 18% 16b1 f 19b1
726 (0.32) 47% 18b1 f 19b1 29% 17b1 f 19b1 12% 16b1 f 19b1
19b1 19b1
In brackets the oscillator strengths are reported as well.
TABLE 3: βvec (×10-30 esu)b Values Calculated for Complexes AM and BM (M ) Ni, Pd, Pt) at 0.35 eV (3.50 µm) Using the LB94 xc Functionala ANi static βvec SHG βvec EOPE/OR βvec
µz
68.8 (69.8) 78.2 (80.2) 71.7 (72.9) 1.95
c
APd
APt
BNi
BPd
BPt
39.4 (40.6) 33.5 (36.0) 38.4 (39.8) 1.93
82.5 (83.3) 94.3 (95.9) 86.1 (87.1) 1.73
136.4(-134.7) 270.1(-257.5) 165.7(-162.8) -14.28
166.4(-163.7) 355.5(-333.6) 205.2(-201.0) -14.84
140.7(-138.9) 280.1(-268.8) 171.6(-168.6) -14.49
The calculated dipole moments along the z-axis, µz (D), are also reported. b Here βvec ) (µzβz)/(|µ|), with βz ) 1/3Σi(βzii + βizi + βiiz), (i ) x,y,z), and z is the axis of the dipole moment. c In brackets the dominant component of the hyperpolarizability tensor, i.e., βzzz, is reported. a
1. UV-Wis-IR Spectrum of Ni(Me6pzS2)M(Me2timdt]) Complexes. We first analyze the spectrum of complexes ANi, APd, and APt. In general, the spectrum of complex ANi has a dominant ligand-to-ligand (both inter and intraligand) and metal-to-ligand charge transfer character. However, due to the complexity of the molecules, also metal-to-metal and ligand-to-metal charge transfers are present. In the low-energy region (λ > 650 nm) there are three main excited states responsible for the absorption, namely 1A1, 2A1, and 3A1, which we have reported in Table 2. Intra/interligand and metal-to-ligand charge transfers are predominant, as it becomes clear from Table 2 and from the MOs depicted in Figure 3. In particular, we observe that there are two opposite tendencies in the one-electron excitations involved in the low-energy absorption: charge transfers from the porphyrazine ligand toward the metal and the dithiolene ligand (namely 19b2 f 21b2), but also the vice versa (namely 20b2 f 22b2). This might result in a small dipole moment in the related excited state, as confirmed by our calculations of the dipole moment in the lowest-lying excited states of the complex ANi: as an example, the difference between the dipole moment of the excited state 2A1 and of the ground state is found to be ∆µeg ) -0.45 D. Furthermore, only the one-electron excitation 20b2 f 21b2 (HOMO f LUMO) involves MOs with large overlap, which explains also why the excited state 2A1 shows the largest oscillator strength. Note also that, unlike the corresponding symmetric metal-dithiolenes, the NIR absorption is not predominantly due to the HOMO f LUMO transition. Complexes APd and APt show similar spectral features; in particular, the low-energy region has essentially a similar nature as in complex ANi. 2. UV-Wis-IR Spectrum of Ni(Me6pzS2)M(mnt) Complexes. In general, ligand-to-ligand and metal-to-ligand charge transfers are predominant in the spectra of series B, as in series A. However, the nature of the low-energy region is different from series A. First, the lowest excitation energy for these complexes (related to the excited state 1B2) is a pure HOMO f LUMO transition; since it is very weak (oscillator strength 1000 nm in these complexes, whereas it falls at λ < 1000 nm in series A. C. Second-Order Response. The analysis of the excitation energies in the previous section showed that combining a metal-dithiolene with a porphyrazine one builds complexes in which there can be intense excitations that fall at low energies and for which the difference in the dipole moment between the ground-state and the relative excited state (∆µeg) can be large. According to the two-level model (see in the Introduction) this could lead to a large second-order response. Therefore, we have calculated the off-resonance (0.35 eV) second-order response of these complexes. In Table 3 the vector component of the β tensors along the dipole moment direction (the z-axes in the studied complexes) and the predominant tensorial component βzzz are reported. We have also reported the value of the dipole moment, in order to indicate the electronic asymmetry in the ground-state. The studied complexes show a significant secondorder response, much larger than that calculated for the (quasi)symmetric- and mixed-ligand dithiolenes previously investigated.25,29 Series B shows a larger second-order response than series A, with complex BPd having the largest values of β -30 esu). The low-energy excitations are (βSHG vec ) 355.5 × 10 probably the main responsible for the second-order response in these complexes, since they fall at very low energies and they can have strong oscillator strengths. Moreover, these excitations are characterized by ∆µeg values that can be expected larger in series B than in series A, in line with the larger β values calculated in the former. The trend of the β values within series B is consistent with the expectations deriving from the two-level model, if one
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assumes that the excited state 3A1, which has the largest oscillator strength in the low-energy region, gives the dominant contribution to the first hyperpolarizability. To show this, we stress that the three main excitations in the low-energy region have similar nature (hence one could assume a similar ∆µeg) and similar oscillator strengths among the complexes of the series. Furthermore, for each complex of the series the three excitations show a similar nature, whereas the oscillator strengths are very different, with the excited state 3A1 showing a much larger oscillator strength than 1A1 and 2A1. If one assumed this excited state as the main responsible for the second-order response in series B, then complex BPd, which has the lowest-energy excitation, would have the largest β vector according to the two-level model and in line with the values of β reported in Table 3. The trend of the β values in series A is, instead, not consistent with the two-level model. In this case, assuming a predominant excitation in the low-energy region and using the same arguments valid for series B, one would get the largest secondorder response for complex APd, whereas the results in Table 3 show the trend βAPt > βANi > βAPd. This inconsistency suggests that more excited states, and not only one, contribute to the second-order response. This can be explained by the fact that the nature of the three main excited states in the low-energy region is not as uniform as in series B and is not coherent with the trend of the oscillator strengths and excitation energies. To be more specific, the excited states 1A1 and 3A1 show a stronger CT character than the excited state 2A1, but a lower oscillator strength. Therefore, there might not be a predominant excitation, but rather the whole region at λ > 700 nm could be responsible for the second-order response. IV. Conclusions We investigated the ground-state and response properties of Ni(Me6pzS2)MX (M ) Ni, Pd, Pt; X ) Me2timdt, mnt) complexes within (time-dependent) density-functional theory. These compounds combine together a porphyrazine, which has a very delocalized π-system, with a metal-dithiolene, which, with their intense π f π* NIR band and high thermal and photochemical stabilities, are promising candidates for laser applications. From the analysis of the ground state it results that, whereas in the complexes with X ) Me2timdt (series A) the charge is quite uniformly distributed (small dipole moment) in the molecules, in the complexes with X ) mnt (series B) there is a net tendency of the porphyrazine ligand to behave as donor and the dithiolene ligand as acceptor, which resembles the structure of nonlinear push/pull organic materials. The calculation of the excitation energies shows that also these complexes exhibit intense low-energy absorptions with strong change transfers between the two ligands and between the ligands and the peripheral metal. Series A shows charge transfers from the porphyrazine ligand to the metal and dithiolene ligand and viceversa, which can result in a small dipole moment in the exited states; series B, instead, shows a net CT from the porphyrazine to the metal and dithiolene ligand, which can be a signal of a large dipole moment in the excited states. All these features can lead to a large second-order response. Indeed, our values of the first hyperpolarizability tensors, calcuclated offresonance (0.35 eV) for the second-harmonic generation(SHG), the EOPE, and the OR, respectively, show that all the complexes have a second-order response comparable to the typical push/ pull organic molecules. In particular, the response is strongly enhanced in series B (βvec > 100 × 10-30), with the complex of palladium showing the largest values of the β tensors (βSHG vec )
Romaniello et al. 355.5 × 10-30). The trend of the β values in series B is consistent with the expectations deriving from the two-level model, assuming one of the low-energy excitations as the main responsible for the second-order response. In series A, instead, all the main low-energy excitations are probably responsible for the second-order response. Note Added after ASAP Publication. This Article was published ASAP on April 15, 2010. Figures 5 and 6 were interchanged. The corrected version was reposted on April 16, 2010. References and Notes (1) Marder, S. R.; Sohn, J. E.; Stucky, G. D.; Eds. ACS Symposium Series 455; American Chemical Society: Washington, DC, 1991. (2) Benson, M. T.; Cundari, T. R.; Lim, S. J.; Nguyen, H. D.; PierceBeaver, K. J. Am. Chem. Soc. 1994, 116, 3955–3966. (3) Wagner, R. W.; Lindsey, J. S.; Seth, J.; Palaniappan, V.; Bocian, D. F. J. Am. Chem. Soc. 1996, 118, 3996–3997. (4) Reimers, J. R.; Lu, T. X.; Crossley, M. J.; Hush, N. S. Chem. Phys. Lett. 1996, 256, 353–359. (5) see e.g., Cheng, Y.-J.; Luo, J. D.; Huang, S.; Zhou, X.-H.; Shi, Z. W.; Kim, T.-D.; Bale, D. H.; Takahashi, S.; Yick, A.; Polishak, B. M.; Jang, S.-H.; Dalton, L. R.; Reid, P. J.; Steier, W. H.; Jen, A. K.-Y. Chem. Mater. 2008, 20, 5047–5054, and references therein. (6) LeCours, S. M.; Guan, H. W.; DiMagno, S. G.; Wang, C. H.; Therien, M. J. J. Am. Chem. Soc. 1996, 118, 1497–1503. (7) Priyadarshy, S.; Therien, M. J.; Beratan, D. N. J. Am. Chem. Soc. 1996, 118, 1504–1510. (8) Karki, L.; Vance, F. W.; Hupp, J. T.; LeCours, S. M.; Therien, M. J. J. Am. Chem. Soc. 1998, 120, 2606–2611. (9) Zhang, T. G.; Zhao, Y. X.; Asselberghs, I.; Persoons, A.; Clays, K.; Therien, M. J. J. Am. Chem. Soc. 2005, 127, 9710–9720. (10) Uyeda, H. T.; Zhao, Y. X.; Wostyn, K.; Asselberghs, I.; Clays, K.; Persoons, A.; Therien, M. J. J. Am. Chem. Soc. 2002, 124, 13806–13813. (11) Nakamura, T.; Underhill, A. E.; Coomber, A. T.; Friend, R. H.; Tajima, H.; Kobayashi, H. Inorg. Chem. 1995, 34, 870–876. (12) Aragoni, M. C.; Arca, M.; Demartin, F.; Devillanova, F. A.; Garau, A.; Isaia, F.; Lelj, F.; Lippolis, V.; Verani, G. J. Am. Chem. Soc. 1999, 121, 7098–7107. (13) Williams, R.; Billing, E.; Waters, J. H.; Gray, H. B. J. Am. Chem. Soc. 1966, 88, 43–50. (14) Ferraro, J. R.; Williams, J. M. Introduction to Synthetic Electrical Conductors; Academic: New York, 1987. (15) Cassoux, P.; Valade, L.; Kobayashi, H.; Kobayashi, A.; Clark, R. A.; Underhill, A. E. Coord. Chem. ReV. 1991, 110, 115–160. (16) Pomare´de, B.; Garreau, B.; Malfante, I.; Valade, L.; Cassoux, P.; Legros, J. P.; Audouard, A.; Brossard, L; Ulmet, J. P.; Doublet, M. L.; Canadell, E. Inorg. Chem., 1994, 33, 3401–3414. (17) Sun, S.; Wu, P.; Zhu, D.; Ma, Z.; Shi, N. Inorg. Chim. Acta 1998, 268, 103–107. (18) Sato, A.; Kobayashi, H.; Naito, T.; Sakai, F.; Kobayashi, A. Inorg. Chem. 1997, 36, 5262–5269. (19) Kochurani; Singh, H. B.; Jasinski, J. P.; Paight, E. S.; Butcher, R. J. Polyhedron 1997, 16, 3505–3510. (20) Matsubayashi, G.; Natsuaki, K.; Nakano, M.; Tamura, H.; Arakow, R. Inorg. Chim. Acta 1997, 262, 103–107. (21) Veldhuizen, Y.; Veldman, N.; Lakin, M. T.; Spek, A. L.; Paulus, P. M.; Faulmann, C.; Haasnoot, J. G.; Maaskant, M. J. A.; Reedijk, J. Inorg. Chim. Acta 1996, 245, 27–34. (22) Fujiwara, H.; Arai, E.; Kobayashi, H. Chem. Commun. 1997, 9, 837–838. (23) Romaniello, P.; Aragoni, M. C.; Arca, M.; Cassano, T; Denotti, C.; Devillanova, F. A.; Isaia, F.; Lelj, F.; Lippolis, V.; Tommasi, R. J. Phys. Chem. A 2003, 107, 9679–9687. (24) Sato, I.; Saito, Y., Patent JP 2005099755, 2005. (25) Romaniello, P.; Lelj, F. J. Mol. Struct. 2003, 636, 23–37. (26) Cassano, T.; Tommasi, R.; Nitti, L.; Aragoni, M. C.; Arca, M.; Denotti, C.; Devillanova, F. A.; Isaia, F.; Lippolis, V.; Lelj, F.; Romaniello, P. J. Chem. Phys. 2003, 118, 5995–6002. (27) Curreli, S.; Deplano, P.; Faulmann, C.; Ienco, A.; Mealli, C.; Mercuri, M. L.; Pilia, L.; Pintus, G.; Serpe, A.; Trogu, E. F. Inorg. Chem. 2004, 43, 5069–5079. (28) Oudar, J. L. J. Chem. Phys. 1977, 67, 446–457. Oudar, J. L; Chemla, D. S. J. Chem. Phys. 1977, 66, 2664–2668. (29) Romaniello, P.; Lelj, F. Chem. Phys. Lett. 2003, 372, 51–58. (30) Lange, S. J.; Nie, H.; Stern, C. L.; Barrett, A. G. M.; Hoffman, B. M. Inorg. Chem. 1998, 37, 6435–6443.
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