Diradical Character of Neutral Heteroleptic Bis(1,2-dithiolene) Metal Complexes: Case Study of [Pd(Me2timdt)(mnt)] (Me2timdt = 1,3-Dimethyl-2,4,5-trithioxoimidazolidine; mnt2– = 1,2-Dicyano-1,2-ethylenedithiolate)

The reaction of the bis(1,2-dithiolene) complex [Pd(Me2timdt)2] (1; Me2timdt•– = monoreduced 1,3-dimethyl-2,4,5-trithioxoimidazolidine) with Br2 yielded the complex [Pd(Me2timdt)Br2] (2), which was reacted with Na2mnt (mnt2– = 1,2-dicyano-1,2-ethylenedithiolate) to give the neutral mixed-ligand complex [Pd(Me2timdt)(mnt)] (3). Complex 3 shows an intense solvatochromic near-infrared (NIR) absorption band falling between 955 nm in DMF and 1060 nm in CHCl3 (ε = 10700 M–1 cm–1 in CHCl3). DFT calculations were used to elucidate the electronic structure of complex 3 and to compare it with those of the corresponding homoleptic complexes 1 and [Pd(mnt)2] (4). An in-depth comparison of calculated and experimental structural and vis–NIR spectroscopic properties, supported by IEF-PCM TD-DFT and NBO calculations, clearly points to a description of 3 as a dithione-dithiolato complex. For the first time, a broken-symmetry (BS) procedure for the evaluation of the singlet diradical character (DC) of heteroleptic bis(1,2-dithiolene) complexes has been developed and applied to complex 3. The DC, predominant for 1 (nDC = 55.4%), provides a remarkable contribution to the electronic structures of the ground states of both 3 and 4, showing a diradicaloid nature (nDC = 24.9% and 27.5%, respectively). The computational approach developed here clearly shows that a rational design of the DC of bis(1,2-ditiolene) metal complexes, and hence their linear and nonlinear optical properties, can be achieved by a proper choice of the 1,2-dithiolene ligands based on their electronic structure.


■ INTRODUCTION
The interest of the scientific community toward bis(1,2dithiolene) metal complexes has been continuously increasing during the past few decades, 1−6 accompanied by a growing number of applications relying on the superconducting, 7−12 photoconducting, 13−17 magnetic, and linear and nonlinear optical properties 18−22 of this class of compounds. Bis(1,2dithiolene) complexes [M(R 2 C 2 S 2 ) 2 ] q− of d 8 metal ions M x+ , such as Ni II , Pd II , Pt II , and Au III , feature peculiar properties, 5,23 such as molecular planarity and the ability to exist in welldefined oxidation states q typically ranging between x − 4 and x − 2, 24−26 also assuming fractional charges in nonintegral oxidation state (NIOS) salts. 9,12 The redox noninnocence of the 1,2-dithiolene ligands (Scheme 1) renders it difficult to partition the charge of the complexes between the ligands L and the central metal ion M x+ . 27,28 The typical redox steps accessible to bis(1,2-dithiolene) complexes of group 10 metals (M = Ni, Pd, Pt) are summarized in Scheme 2. Dianionic bis(1,2-dithiolene) complexes [ML 2 ] 2− are diamagnetic species, which can be isolated as stable anions in salts such as (Ph 4 P) 2 [Ni(mnt) 2 ] (mnt 2− = maleonitrile-1,2-dithiolate, 1,2-dicyano-1,2-ethylenedithiolate). 29 27 In diamagnetic neutral complexes [ML 2 ], the central metal ion can carry formal charges varying between 0 and +4, while the ligands can assume a neutral, monoanionic, or dianionic charge (Scheme 2), indicating a large degree of π-electron delocalization involving the metal as well as the L ligands (metalloaromaticity). 32 Spectroscopic and theoretical results suggest that the complexes are better described as formed by the metal dication M II , whatever the charge on the complex. 27,33 Therefore, the oxidation/reduction steps leading from [ML 2 ] 2− to [ML 2 ] are mainly located on the ligands, 33−35 analogously to what has been reported for [Au III (Ar-edt) 2 ] 0/− complexes (Ar-edt 2− = arylethylene-1,2dithiolate; Ar = phenyl, 2-naphthyl, 2-pyrenyl). 36 Hence, the neutral M II complexes can be described as diamagnetic singlet species formed by two antiferromagnetically coupled monoanionic radical ligands, [M II (L •− ) 2 ]. 33,37 Indeed, neither the closed-shell (CS) restricted delocalized nor the localized singlet diradical description represents reliably the ground state (GS) of neutral bis(1,2-dithiolene) complexes, so that an index n DC of the diradical character (DC) can be calculated to evaluate the relative weight of the diradical singlet description. 37−39 Notably, different optical properties in the visible−near-infrared (vis−NIR) region are associated with the differently charged forms of bis(1,2-dithiolene) complexes (electrochromism). 16,40,56 Neutral complexes [ML 2 ] show a peculiar intense absorption in the region above 800 nm. 2,5,30 This band, attributed to a π−π* HOMO → LUMO (H → L) one-electron excitation, 5,6 is shifted to lower energies and lowered in intensity in the corresponding monoreduced forms [ML 2 ] − , 41 while the dianions [ML 2 ] 2− do not show any vis− NIR absorption. In this context, for a few decades, some authors have been investigating the [M(R′ 2 timdt) 2 ] q− class of photoconducting 42−44 complexes (R′ 2 timdt •− = monoreduced 1,3-disubstituted imidazoline-2,4,5-trithione; M = Ni, Pd, Pt; q = 0, 1, 2; Chart S1). 45−52 Neutral [M(R′ 2 timdt) 2 ] complexes show a strikingly intense absorption at about 1000 nm (molar extinction coefficient ε as large as 120000 M −1 cm −1 in toluene), 48 whose energy can be fine-tuned by a proper choice of the metal M and the substituents R′. 46,48 The corresponding reduced forms show a NIR absorption falling at about 1450 nm for M = Ni, Pt and at about 1700 nm for M = Pd. 51 Mixed-ligand bis(1,2-dithiolene) complexes [M(L)(L′)] have been much less investigated than homoleptic complexes 48,53 and are often prepared by metathesis reactions. 54 −56 The synthetic way of obtaining [M(L)(L′)] complexes by replacement of halides in MLX 2 complexes has been previously reported in a few cases. 48 In these complexes, most often containing a Ni II ion, 31,57−61 the most electron withdrawing "pull" ligand L tends to assume the ene-1,2-dithiolate form L 2− (d in Scheme 1), with shorter C−C and longer C−S bond distances, while the other "push" ligand (L′) assumes a 1,2dithione form (b in Scheme 1), with longer C−C and shorter C−S distances, so that the complex is generally described as the dithione-dithiolato species [M II (L 2− )(L′)]. The electronic structure of these complexes in their neutral state, reminiscent of that of diimine-dichalcogenolato complexes, 62−64 shows the HOMO featuring a larger contribution from the "pull" ligand L 2− and the LUMO from the "push" ligand L′. The peculiar visible−near-IR (vis−NIR) electron transition of the neutral species assumes a partial charge-transfer (CT) character from the 1,2-dithiolato L 2− ligand to the 1,2-dithione L′ (LL′CT), testified by a remarkable negative solvatochromism of the resulting absorption band. 54 In comparison to homoleptic complexes, the DC of heteroleptic bis(1,2-dithiolene) complexes has not been investigated, implicitly accepting that the GS configuration of these complexes is fully defined by the dithione-dithiolato CS description. 48 Nevertheless, it is conceivable that a continuous variation from ideally pure open-shell singlet diradicals [M II (L •− )(L′ •− )] to CS dithionedithiolato complexes [M II (L)(L′ 2− )] occurs as the difference in the donor properties of the L and L′ ligands increases. Therefore, we have considered as a case study the mixed-ligand 1,2-dithiolene Pd II complex featuring the well-known mnt "pull" ligand coupled to the "push" ligand Me 2 timdt. Herein, we report an experimental and theoretical investigation on the resulting complex [Pd(Me 2 timdt)(mnt)], in comparison with the relevant parent complexes [Pd(Me 2 timdt) 2 ] and [Pd-(mnt) 2 ], aimed at evaluating the role of the electronic structure of the ligands in tailoring the DC in homoleptic and heteroleptic bis(1,2-dithiolene) palladium complexes.
For all compounds, tight SCF convergence criteria and fine numerical integration grids (grid = ultrafine) were used. In order to evaluate the singlet diradical contribution to the GS in the BS approach, the differences between the total electronic energy of the singlet state (ε S ), the BS-singlet state (ε BS ), and the triplet (ε T ) states were considered: 38,91,92 The effective electron exchange integrals J ab 93 were calculated as follows: where ⟨S 2 ⟩ T and ⟨S 2 ⟩ BS represent the spin expectation values 94,95 determined at the optimized geometry for the triplet and brokensymmetry GSs, respectively, after verification of the wave function stability (stable = opt). The singlet−triplet energy gap Δε ST SC = ε S SC − ε T , accounting for the effect of spin contamination to the energy of the singlet GS, 95 corresponding to a mixing of the singlet and triple state, was calculated as

BS
Therefore, the ε S SC value was obtained: The diradical character index n DC can be directly calculated from ⟨S 2 ⟩ BS : 17,37 A complete natural population analysis (NPA) was carried out with a natural bonding orbital (NBO) 96 partitioning scheme (pop = nboread, with boao and bndidx keywords in the NBO section of the input file) in order to investigate the charge distributions and Wiberg bond indexes. 97 Absorption vertical transition energies and oscillator strengths were calculated at the time-dependent (TD) DFT level. 98,99 TD-DFT calculations were carried out at the optimized geometry in the gas phase and in a selection of solvents (CHCl 3 , CH 2 Cl 2 , DMF, THF, acetonitrile), implicitly taken into account by means of the polarizable continuum model in its integral equation formalism (IEF-PCM), 100 describing the cavity of the complexes within the reaction field (SCRF) through a set of overlapping spheres.
Oscillator strength values calculated at the TD-DFT level along with experimental full width at half maximum (FWHM) values of the NIR band were used to evaluate the molar extinction coefficients ε. 101 Experimental FWHM values on an energy scale (eV) were evaluated from the corresponding values w determined in nm from the experimental NIR spectra: where m e and e are the mass and the charge of the electron, ν 0n is the frequency (s −1 ) of the transition between the states 0 and n, μ 0n is the transition dipole moment, and h is Planck's constant. f 0n is related to the experimental intensity of each absorption band: where ε is the molar extinction coefficient (M −1 cm −1 ) and ϖ is the frequency (cm −1 ). By adoption of Gaussian curve shapes for the absorption bands allows evaluating the molar extinction coefficients of the NIR transition at the TD-DFT level. Calculated molar extinction coefficients were scaled on experimental available data to give a corrected ε calc corr value. The nature of the minima of each structure optimized at the DFT and DFT-BS levels was verified by harmonic frequency calculations (f req = raman), including the determination of thermochemistry parameters (zero-point energy (ZPE) corrections and thermal corrections to enthalpy and Gibbs free energy) and the calculation of FT-Raman frequencies. Gibbs free energies were used to calculate absolute reduction potentials at 298 K (E Abs 298K ) according to the following equation: 103 where ΔG neutral 298K and ΔG anion 298K are the free energy values calculated at 298 K and ΔG e°/ F represents the potential of the free electron (−0.03766 eV at 298 K; ΔG neutral 298K is calculated on the most stable neutral form). 107 E Abs 298K values were also referenced to the Fc + /Fc couple, taken into account at the same level of theory.
The total static (i.e., under zero frequency) 108 second-order (quadratic) hyperpolarizability (the first hyperpolarizability) 109 β tot was calculated as previously described. 110 Throughout all this work, molecules in their optimized standard orientation were rotated in order to align the main symmetry axis (bisecting C−C 1,2-dithiolene bonds and passing through the central metal ion) with the z axis and lie on the yz plane. Molden 6.2 111 118 This suggests that the Me 2 timdt ligand in 3 should be considered to carry a partial negative charge and that the GS of 3 should include a partial DC. The unit cell contains pairs (Z = 2) of symmetry-related complex molecules, each forming slipped stacks along the a vector (Figures S1 and S2 in the Supporting Information) with an interplanar distance of 3.619 Å, very close to that featured by the stacks found in the crystal structure of [Pd(Et 2 timdt) 2 ] (3.6 Å). 45 Along the stacks, the terminal thione groups of the Me 2 timdt ligands weakly interact with the π-system of the imidazoline ring ( Figure S1). Weak contacts between the methyl substituents at the Me 2 timdt ligands and the terminal N atoms of the mnt ligands (H(3A)···N(5) iv 2.644 Å; (iv) −1 + x, y, 1 + z) are responsible for the interactions between adjacent stacks aligned along the c direction. Notably, the crystal packing is sensibly different from that found in [Pd(Et 2 timdt)(mnt)], where the complex molecules are stacked in an alternate head-to-tail disposition, allowing for shorter interplanar distances (3.570 Å). 48 Absorption Spectroscopy. Neutral [Pd(R′ 2 timdt) 2 ] bis-(1,2-dithiolene) complexes featuring alkyl R substituents show a peculiar, intense NIR absorption falling at about 1010 nm, with molar extinction coefficients ε as high as 70000 M −1 cm −1 in CH 2 Cl 2 . 45,46 The UV−vis−NIR absorption spectrum of a CH 2 Cl 2 solution of 1 shows a NIR absorption maximum falling at 1008 nm (full width at half-maximum (FWHM) w = 131 nm; Figure S3). Notably, the NIR peak shows at least three Gaussian components (λ 1 = 1004.8 nm, w 1 = 121.9 nm, integral ratio 74.5%; λ 2 = 890.3 nm, w 2 = 93.5 nm, 6.6%; λ 3 = 1120.2 nm, w 3 = 155.4 nm, 18.9%; Figure S3), 65 in agreement with the spectral decomposition reported for [Pd-(2,4-t Bu 2 C 6 H 2 S 2 ) 2 ], for which a series of d−d transitions with different spin couplings to the open-shell ligands were envisaged. 33 Complex 3 shows a well-defined intense NIR peak at 1060 nm in CHCl 3 (ε = 10700 M −1 cm −1 ; Figure 2), in perfect agreement with the spectral features shown by [Pd(Et 2 timdt)(mnt)] in the same solvent (λ max = 1061 nm, ε = 12500 M −1 cm −1 ). 48 The NIR band can be decomposed into two main peaks, each accounting for about half the area of the band (λ 1 = 1066.2 nm, w 1 = 140.6 nm, 51.6%; λ 2 = 1025.1 nm, w 2 = 249.5 nm, 48.4% in CHCl 3 ; Figures S4 and S5). The NIR band displays a remarkable negative solvatochromism, with absorption maxima wavelengths ranging between 955 nm in DMF and 1060 nm in CHCl 3 (Table 1). When the solvent polarity is increased, the change in the experimental spectral shapes ( Figure S6) suggests that the relative weight and the energy difference between the red component and the main peak of the solvatochromic NIR band increases, so that a greater polar nature should be attributed to the higher energy peak as compared to the main peak.
Ligands. The relative stability of the variously charged forms of 1,2-dithiolene ligands (Scheme 1) depends on the nature of the R substituents. The mnt ligand is generally encountered in its 1,2-dithiolate form, and the corresponding neutral species is unreported. In fact, neutral 1,2-dithiolene species are generally unstable, 6 but depending on the R substituents they can be found as either 1,2-dithiones (Scheme 1, b), for instance embedded in 1,2-dithioxamides, 119 or stabilized as 1,2-dithietes (Scheme 1, a). 120−122 Since vicinal dithioxamides in five-membered rings are reportedly unstable, 123 R′ 2 timdt ligands cannot be isolated as neutral 2,4,5trithiones and the sulfuration of disubstituted 2-thioxomidazolidine-4,5-diones leads to tetrasubstituted 4,5,6,7tetrathiocino[1,2-b:3,4-b′]diimidazolyl-2,9-dithione or 4,5,9,10-tetrathiocino[1,2-b:5,6-b′]-2,7-dithione (a and b in Chart S4 in the Supporting Information, respectively), the latter type of compounds being the final product of the Br 2 oxidation of [Pd(R′ 2 timdt) 2 ] complexes (R′ = Et). 124 The only example of an authentic radical monoanion R″ 2 timdt •− has been isolated in compound 5. 72 Neutral 1,2-dithiolene ligands stabilized in the form of 3,4-disubstituted 1,2-dithietes have been characterized in few cases (R = CF 3 , 120 COOCH 3 , 121 1adamantyl 122 ). An examination of the ZPE-corrected total electronic energies ε ZPE 0 of the neutral 1,2-dithiolene ligands in the dithione and dithiete forms ( Table 2) shows that the dithiete form is more favored for the mnt ligand in comparison to the Me 2 timdt ligand (ε ZPE 0 = 16.28 and −42.58 kcal/mol, respectively). A comparison of the C−C bond distances calculated for Me 2 timdt q− (d C−C = 1.500, 1.434, and 1.394 Å for q = 0, 1, and 2, respectively; Table 2) can be made with the corresponding bond distances determined structurally in [Pd(Et 2 timdt)Br 2 ] (average d C−C value 1.47(1) Å; q = 0; Chart S2), 5 (d C−C = 1.417(4) Å, q = 1; Chart S2), 48 [6· 2Br] 2+ (Br 2 ) 2 (Br 2 ) 3 (6 = 4,5,9,10-tetrathiocino[1,2-b:5,6-b′]-1,3,6,8-tetraethyldiimidazolyl-2,7-dithione; d C−C = 1.37(2) Å, q = 2; Chart S2), and 1,3-dimethyl-4,5-bis(phenylsulfanyl)-1,3dihydro-2H-imidazole-2-thione (7, d C−C = 1.361(6) Å, q = 2; Chart S2). 74 As expected, on passing from dianions to the corresponding neutral species the C−C bond lengths increase Diradical Character (DC) in Bis(1,2-dithiolene) Complexes. The ground state (GS) of neutral bis(1,2-dithiolene) complexes is characterized by a significant degree of DC, 33−37 due to the very narrow HOMO−LUMO energy gap ΔE H−L that renders the singlet and triplet GSs very close in energy. In a pure diradical the nonbonding molecular orbitals (NBMOs) ψ a and ψ b hosting the two electrons at the highest energy are degenerate, being localized on the two different ligands in bis(1,2-dithiolene) metal complexes, 127 and they have consequently a negligible overlap integral S ab = ⟨ψ a |ψ b ⟩. Under these conditions, the two possible spin states, i.e. singlet (2S + 1 = 1) and triplet (2S + 1 = 3), are degenerate, their energy difference Δε ST = ε S − ε T being related to the exchange interaction J = 1/2(ε S − ε T ) = 1/2Δε ST . 91 When S ab is not negligible and the two NBMOs are quasi-degenerate, the triplet configuration is the most stable (ε S > ε T ) and J assumes positive values in the so-called diradicaloids or diradical-like compounds. Wirz proposed discriminating between diradicals and diradicaloids depending on the singlet−triplet energy gaps (Δε ST ≤ 10 and 100 kJ mol −1 for diradicals and diradicaloids, respectively). 128 When the energy difference between the two involved MOs is larger and a significant gap exists, the energy stabilization competes with the electron−electron exchange interaction, and the CS singlet GS becomes progressively more stable. The theoretical evaluation of the GS in diradical and diradicaloid species is a challenging task, which requires the evaluation of the stability of the triplet and singlet GSs of the investigated compound. The triplet GS can generally be calculated by theoretical methods with unrestricted wave functions, such an unrestricted HF (UHF) or density functional theory (UDFT). The modeling of open-shell singlet diradicals requires multireference approaches: for instance, multireference coupled-cluster calculations, such as Mk-CCSD(T), 129 complete active-space self-consistent field (CASSCF), 94 or the complete-active-space second-order perturbation theory (CASPT2). 130 137 Accordingly, 1 is calculated to be sensibly more stable to reduction in the gas phase and in CH 2 Cl 2 than 4 (E Abs 298K = 3.057 and 4.349 eV for complex 1 and 4.786 and 5.752 eV for complex 4, in the gas phase and in CH 2 Cl 2 , respectively). In Table 3, the metric parameters optimized for the bis(1,2dithiolene) complexes 1 q− and 4 q− (q = 0, 1, 2) are summarized. In the case of neutral complexes (q = 0), the geometry was optimized (i) for the singlet CS (RDFT), (ii) for the triplet open-shell (UDFT), and (iii) for the singlet diradical (DFT-BS) GS configurations. The total electronic energy ε T of the 3 B 1u triplet state is calculated to be lower by about 2.4 kcal mol −1 (10 kJ mol −1 ) in comparison to that (ε S ) of the uncorrected singlet 1 A g GS (ε 2 < 0, eq 2), thus classifying 1 as a diradical species. 128 In fact, the DFT-BS GS of 1 shows a large ⟨S 2 ⟩ BS value (0.80, Table 4), indicating a considerable spin contamination from the triplet state. 94 An evaluation of the total electronic energy of the BS GS shows that it is the most stable configuration in comparison to both the triplet and CS-singlet configurations (eq 1), reflected by the diradical character n DC = 55.4% (Table 4, eq 5). The singlet GS calculated for 4 is sensibly lower in energy in comparison to the relevant triplet state (Table 4), indicating a diradicaloid character. Accordingly, the singlet diradical configuration is only slightly more stable than the uncorrected CS singlet state and has an ⟨S 2 ⟩ BS value smaller than 0.5. In fact, the spin-contamination corrected state (eq 4) was found to be the most stable state with only a partial diradical character (n DC = 27.5%, Table 4 Table 3) are very close to those calculated for the hypothetical free Me 2 timdt •− and mnt •− radical anions (1.681 and 1.675 Å, respectively) but remarkably different from those calculated for the relevant 1,2-dithiones and 1,2-dithiolates ( Table 2). This supports the description of neutral homoleptic complexes as [Pd(L •− ) 2 ] for both classes of complexes. Although the agreement between structural and optimized C−C distances is less accurate in comparison to C−S bond lengths, the former values are affected very greatly by the charge on the ligands. In Figure 3, the optimized C−C distances and the corresponding Wiberg bond indices (WBIs) 97 are compared for a variety of R′ 2 timdt derivatives showing a CC double bond, as in 4,5,9,10-tetrathiocino[1,2b:5,6-b′]diimidazolyl-1,3,6,8-tetramethyl-2,7-dithione (Me 2 timdt) 2 and compound 7, 74 or a single bond, as in the neutral complex 2 and in compound 5 (Chart S2). 72,73 For these compounds, a clear correlation (R 2 = 0.99) holds between the optimized C−C bond distance d C−C within the R 2 timdt ring and the corresponding WBI C−C values. This clearly shows that WBIs calculated at the optimized distances   (Figure 4a and Figure S8). In fact, the b 3u KS-HOMO (MO 107 according to a progressive labeling based on an energy scale) is mainly made up of the four 3p x AOs of the four donor S atoms, perpendicular to the molecular yz plane, and the four C 2p x AOs taken with opposite phases. The terminal S atoms also participate in this MO, while the contribution from the central Pd ion is very poor (4%). The 108 b 2g KS-LUMO involves the same atomic species as the HOMO with a larger contribution from the bonding sulfur atoms, but the contributions from the two ligands are opposite in phase. In the KS-LUMO, the metal ion is only marginally involved (5%) as well through its 3d yz AOs. In the singlet diradical DFT-BS GS configuration, the αand β-HOMOs show the same composition as the HOMOs of the constituent 1,2-dithiolene Me 2 timdt •− ligands, analogously to what was previously reported for different Ni and Pt bis(1,2-dithiolene) metal complexes, 52 the central Pd ion participating to both α and β MOs (3%). Notably, the DFT-BS approach results in a stabilization of the KS-HOMO and destabilization of the KS-LUMO with respect to the restricted CS solution, thus increasing the ΔE H−L gap ( Figure 5, top). The CS description of complex 1 features a single allowed NIR one-electron excitation calculated at the TD-DFT level. This corresponds to the 1 A g → 1 B 1u transition, involving almost exclusively (97%) the one-electron HOMO−LUMO (H → L) excitation. This is calculated to fall at 963.0 nm (oscillator strength f = 0.436) in the gas phase and 1068.3 nm (f = 0.581) in CH 2 Cl 2 . The oscillator strength calculated at the TD-DFT level along with the experimental FWHM value of the NIR band were used to evaluate the molar extinction coefficient ε for 1 (eq 6). 101 The symmetric and antisymmetric combinations of the α-107 → α-108 and β-107 → β-108 excitations (H,H → L,L double exciton states) are calculated as BS-GS → ES 1 and BS-GS → ES 2 transitions. Double exciton states have been reported for conjugated chromophores with open-shell diradical character, 127 such as polyenes 138,139 and quinoidal oligothiophenes. 140 The double exciton state is one-photon forbidden, and it has been observed as a weak band at lower energies in comparison to the main absorption band due to the onephoton allowed single exciton state. 127 The symmetry-allowed transition BS-GS → ES 2 falls at wavelength values lower (E = 1.487 eV, λ max = 833.6 nm, f = 0.310) than those predicted for the singlet GS (see above). The complex envelope of the NIR absorption band of neutral [M(R,R′timdt) 2 ] bis(1,2-dithiolene) complexes can be attributed to the contribution of doubly excited states to the main single exciton states, thus possibly accounting for the unusually high molar extinction coefficients observed for the NIR absorption in this class of bis(1,2-dithiolene) complexes. 46,49 The forbidden BS-GS → ES 1 transition (1.142 eV, λ max = 1085.6 nm) may provide a low-energy weak contribution 138 to the NIR absorption due to the vibronic coupling with the B 1u antisymmetric combination of the stretching Pd−S vibrations, calculated at 294.1 and 293.2 cm −1 at the RDFT and DFT-BS levels, respectively.   (Table 4). 91,128 While the 3 B 1 state is sensibly less stable than the singlet state, the singlet diradical BS (⟨S 2 ⟩ BS = 0.436) and the 1 B 1 CS singlet configurations differ by less than 1 kcal mol −1 ( Table 4). The singlet configurations calculated at the RDFT and DFT-BS levels show very close optimized Pd− S, C−C, and C−S bond distances, only very slightly overestimated (by less than 0.03 Å) in comparison to the relevant structural distances ( Table 3). The difference Δd C−C between the C−C bond distances d C−C of the two 1,2dithiolene ligands (corresponding to the C(1)−C(1) i and C(4)−C(4) i structural bond lengths in Figure 1 for the Me 2 timdt and mnt ligands, respectively) is evaluated correctly (C(1)−C(1) i > C(4)−C(4) i ), but it is slightly underestimated, so that the calculated dithione-dithiolato character is less pronounced than expected on the basis of the structural data ( Table 3). The DFT-BS description of the GS provides a lower Δd C−C value in comparison to the CS description. Accordingly, while the charge Q Pd on the central Pd ion in the CS and in the singlet diradical GSs is essentially unchanged (ΔQ Pd = 0.024 | e|), the difference in the charges calculated on the two 1,2dithiolene ligands at the NBO level is sensibly larger in the former (0.514 and 0.390 |e|, respectively). In the RDFT approach, the optimized values for the C−C distances of the Me 2 timdt and mnt ligands correspond to noticeably different WBIs (1.168 and 1.417 in the 1 B 1 CS GS) and clearly fall in different regions of the d C−C vs WBI C−C correlation ( Figure 3). Therefore, a comparison between structural and DFToptimized data indicates that the CS description is more suitable than the singlet diradical description in modeling the GS of the mixed-ligand complex 3. Notably, the value of the C−C bond lengths within the mnt ligand in 3 (1.393 Å, Table  3) is even shorter than the value calculated for the free mnt 2− ligand (1.406 Å, Table 2). On passing from 3 to the radical anion 3 •− and the dianion 3 2− , only minor differences (lower than 0.02 Å) are observed on the mnt ligand, while the Me 2 timdt ligand is more greatly affected, the d C−C distance being progressively shortened (d C−C = 1.428, 1.397, and 1.364 Å within the Me 2 timdt ligand for 3, 3 − , and 3 2− , respectively; Table 3). In summary, a comparison between calculated and experimental data supports the hypothesis that the GS of 3 can be better described as a dithione-dithiolato [Pd II (Me 2 timdt)-(mnt 2− )] complex with a minor contribution from the singlet diradical [Pd II (Me 2 timdt •− )(mnt •− )] description. Accordingly, the diradical character n DC = 24.9% (eq 5) is calculated for complex 3 (Table 4). 141 The KS-HOMO and KS-LUMO in the CS description (MOs 93 and 94, respectively) are π-innature MOs mainly located on the mnt (61%) and Me 2 timdt (70%) ligands, respectively, with only minor contributions from the 4d xz AO of the Pd central atom (6% and 8%, respectively; Table S7). Hence, KS-HOMO and KS-LUMO in the heteroleptic complex can be considered as being derived from the in-phase and out-of-phase combinations of the SOMOs of the constituent ligands mnt •− and Me 2 timdt •− (Figure 4b and Figures S7 and S8). The former ("pull" electron-withdrawing ligand, HOMO at lower energy) contributes mostly to the KS-HOMO of 3 and assumes a larger character of 1,2-dithiolate, while the latter ("push" ligand, HOMO at higher energy) contributes mostly to the KS-LUMO of 3 and assumes a larger character of 1,2-dithione, in agreement with the structural data discussed above. In the DFT-BS description, the eigenvalues of the corresponding αand β-MOs are remarkably unequal, reflecting their different compositions ( Figure 5 (bottom) and Figure S9). In particular, the α-MO 93 is located on the mnt ligand (76% ; Table S8 and (a) in Figure S9), while the β-MO 93 is less stable and is located largely on the Me 2 timdt ligand (63% ; Table S8 and (c) in Figure S9). Conversely, the α-MO 94 is located almost entirely on the Me 2 timdt ligand (91% ; Table S8 and (b) in Figure S9), while the β-MO 94 shows contributions from both ligands (mnt 54%, Me 2 timdt 36%; Table S8 and (d) in Figure  S9). Therefore, both the RDFT and DFT-BS approaches agree in attributing an LL′CT character to the lowest energy transition, from the mnt "pull" ligand to the Me 2 timdt "push" ligand. TD-RDFT calculations show, in excellent agreement with experimental data (Figure 2 and Figure S3 in the Supporting Information), three main spectral regions, namely (i) an overlap of intense transitions in the UV region (λ < 280 nm), (ii) a band in the visible region (300 ≤ λ ≤ 500 nm), and (iii) a single very intense NIR transition (λ > 800 nm). In Figure 6, the UV−vis−NIR spectrum of 3 in CHCl 3 solution, simulated on the basis of singlet IEF-PCM TD-RDFT calculations (Table 5) Figure S10). Both in the gas phase and in the solvents considered at the IEF-PCM level, the NIR transition is attributed exclusively to the H → L one-electron excitation. Accordingly, a linear correlation holds between the calculated transition energies in the NIR region and the ΔE H−L energy gap evaluated in each of the examined solvents (Table  1; R 2 = 0.92). Along the series CHCl 3 , CH 2 Cl 2 , THF, CH 3 CN, and DMF the contribution of the mnt fragment to KS-HOMO and KS-LUMO slightly increases (68% to 70%) and decreases (16% to 13%), respectively (Table S7). The contribution of the Me 2 timdt fragment to the KS-HOMO and to the KS-LUMO decreases (23% to 20%) and increases (78% to 82%), respectively. Therefore, on passing to CHCl 3 to DMF, the NIR transition assumes a larger LL′CT character, and the ΔE H−L energy gap increases from 1.68 eV in CHCl 3 to 1.77 eV in DMF and CH 3 CN, in agreement with the experimental trend of NIR absorption energies (Table 1). Calculated oscillator strengths f fall between 0.356 and 0.385 in DMF and CHCl 3 , respectively (Table S9). Oscillator strength values calculated at the TD-DFT level have been used along with experimental full widths at half-maximum (FWHM, w) to evaluate the ratio between the extinction coefficient in each solvent and that in CHCl 3 solution. The resulting scaled calculated extinction coefficients ε calc corr (Table 1) progressively decrease with an increase in the transition energies. TD-DFT calculations were carried out on 3 in the singlet diradical electron configuration. Since the two α-93 → α-94 and β-93 → β-94 (H → L) excitations are not degenerate ( Figure 5, bottom), the αexcitation contributes mainly (58.1%) to the symmetryallowed transition at higher energy (0.853(α-93 → α-94) − 0.464(β-93 → β-94); E = 1.629 eV, λ = 761 nm, f = 0.267 in the gas phase), while the β-excitation contributes to the transition at lower energy (0.486(α-93 → α-94) + 0.881(β-93 → β-94); E = 0.746 eV, λ = 1663 nm, f = 0.033), forbidden in the C 2v point group. Although the contribution of the singlet diradical description to the GS of 3 is limited, it is conceivable that the former transition, corresponding to a double exciton state, can provide a high-energy component to the NIR transition. Notably, due to its nature, the double exciton transition is predicted to show remarkable solvatochromic effects, thus accounting for the different spectral shapes observed on varying the solvent (Table 1 and Figure S6).
Finally, the lack of an inversion center in the title complexes suggests a possible application of heteroleptic bis(1,2-dithiolene) complexes as second-order nonlinear optical (SONLO) materials. Prompted by the results obtained at TD-DFT level, since small geometrical differences can determine large differences in NLO properties, 38,39 we calculated static dipole moments (μ) and static first (quadratic) hyperpolarizabilities (β tot ) for 3 in the gas phase and in CH 2 Cl 2 and CHCl 3 solutions (Table S10). 109 Calculations were also carried out at the DFT-BS level (Table S10) in the gas phase. For the sake of comparison, the same calculations were also undertaken, at the same level of theory, on [Pt(phen)(tdt)] (phen = 1,10-phenanthroline; tdt 2− = 3,4-toluenedithiolate; Chart S2), a neutral diimine-dithiolate Pt complex showing a very large hyperpolarizability value among those investigated experimentally by means of EFISH measurements (λ max = 583 nm; β μ = −28 × 10 −30 esu with ω = 1.569 × 10 11 GHz; zero-frequency β 0 = −16 × 10 −30 esu). 71 In agreement with the charge distribution within complex 3, the μ vector lies along the molecular z axis and β shows only tensor z components. As previously observed for different heteroleptic metal complexes containing 1,2-dithiolato ligands, 62 a dramatic increase in β tot was calculated when solvation is taken into account (|β tot | = 37.6 × 10 −30 , 475.6 × 10 −30 , and 330.5 × 10 −30 esu in the gas phase, CH 2 Cl 2 , and CHCl 3 , respectively). In addition, when the diradical character of 3 is evaluated at the DFT-BS level, the β tot value dramatically increases (177.4 × 10 −30 esu in the gas phase), reaching the same order of magnitude computed for [Pt(phen)(tdt)].

■ CONCLUSIONS
DFT calculations have been exploited to investigate the structural and spectroscopic features of the heteroleptic mixedligand neutral complex Pd II bis(1,2-dithiolene) 3, to highlight the differences between the homoleptic related complexes 1 and 4 and to develop sound structure−property relationships. The closed-shell (CS) description is only partially suitable to describe the electronic structure of bis(1,2-dithiolene) complexes, andwhatever the nature of the ligandsthe singlet diradical character (DC) must be taken into account. The broken-symmetry (BS) approach within DFT, although itself a dramatic approximation underestimating the DC of bis(1,2-dithiolene) metal complexes, is a useful tool in supplementing the description of the ground state (GS). A few general conclusions can be drawn (1) The nature of the 1,2-dithiolene ligand is responsible for the relevance of diradical character (DC) in the GS of 1,2-dithiolene complexes. In homoleptic neutral bis(1,2dithiolene) complexes, on passing from complex 4 to complex 1, the n DC index is roughly doubled. This can  Inorganic Chemistry pubs.acs.org/IC Article be related to the capability of the ligands mnt •− and Me 2 timdt •− , respectively, to stabilize the unpaired electron. In heteroleptic mixed-ligand complexes, the absolute one-electron-reduction potentials E Abs 298K calculated for the L/L •− and L′/L′ •− couples can be used to evaluate the nature of the [Pd II (L)(L′)] complex. The 1,2-dithiolene ligand displaying the largest reduction potential ("pull" ligand) features its π-NBMO at lower energy and contributes largely to the KS-HOMO of the heteroleptic complex, while that with the lowest potential ("pull" ligand) contributes to the KS-LUMO. As a consequence, it is conceivable that the difference ΔE Abs 298K in the absolute reduction potentials of the ligands L and L′ can be adopted as a useful parameter to estimate the push−pull nature of the resulting heteroleptic neutral complexes [Pd II (L)(L′)] and the different localizations of the KS-HOMO and KS-LUMO. A larger push−pull character points to a larger dithione-dithiolato nature and a lower DC of the complex. This implies that the DC is the largest in homoleptic bis(1,2-dithiolene) complexes [Pd II (L) 2 ] with ligands L featuring low values of E Abs 298K , such as Me 2 timdt, and decreases in heteroleptic complexes [Pd II (L)(L′)] in dependence on ΔE Abs 298K .
(2) Several authors have observed that metal−sulfur bond lengths optimized at the DFT level are slightly overestimated in comparison to structural bond distances. This can be attributed to the use of RDFT calculations in complexes featuring a significant DC. The DFT-BS approach leads to bond distances closer to the structural distances. It can be deduced that, in the case of complexes with a large DC, such as complex 1, the difference between CS-optimized distances and the relevant experimental metric parameters increases with the DC of the complex. Summarily, this investigation shows that the DC of bis(1,2dithiolene) metal complexes can be extensively modulated by means of the choice of the substituents R at the 1,2-dithiolene core, allowing for the rational design of the linear and nonlinear optical properties of the resulting complexes and hence the possibility of applying them in fields as varied as nonlinear optics, photoconductivity, and electrochromism.
Further studies are ongoing in our laboratory to investigate in detail the role of the central metal ion and to generalize the limited findings described here for the Pd II complexes with the mnt and Me 2 timdt ligands to other homoleptic and heteroleptic bis(1,2-dithiolene) complexes differing in the nature of the central metal ions and 1,2-dithiolene ligands.

Accession Codes
CCDC 2027023 contains the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing data_request@ccdc.cam.ac.uk, or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.