DFT Investigation of the Molecular Properties of the Dimethylglyoximato Complexes [M(Hdmg)2] (M = Ni, Pd, Pt)

Important applications of the NiII, PdII and PtII complexes [M(Hdmg)2] (H2dmg = dimethylglyoxime) stem from their metal...metal stacked virtually insoluble aggregates. Given the virtual insolubility of the materials, we postulated that the rare reports on dissolved species in solution do not represent monomolecular species but oligomers. We thus studied the structural and spectral properties of the monomolecular entities of these compounds using density functional theory (DFT) and time-dependent DFT computations in dimethyl sulfoxide (DMSO) as a solvent. The molecular geometries, IR and UV-vis spectra, and frontier orbitals properties were computed using LANL2DZ ecp and def2TZVP as basis sets and M06-2X as the functional. The results are compared with the available experimental and other calculated data. The optimised molecular geometries proved the asymmetric character of the two formed O–H . . . O bonds which connect the two Hdmgligands in the completely planar molecules. Calculated UV-vis spectra revealed the presence of three absorptions in the range 180 to 350 nm that are red-shifted along the series Ni–Pd–Pt. They were assigned to essentially ligand-centred π−π* transitions in part with metal(d) to ligand(π*) charge transfer (MLCT) contributions. The notorious d-p transitions dominating the colour and electronics of the compounds in the solid-state and oligomeric stacks are negligible in our monomolecular models strongly supporting the idea that the previously reported spectroscopic observations or biological effects in solutions are not due to monomolecular complexes but rather to oligomeric

On the other hand, some applications as the analytical photometric determination of traces of Ni, Pd or Pt [32,35,52] or their use in (medical) coordination chemistry [52][53][54][55][56] seem to make use of the properties of the molecular units and UV-vis absorption spectra of [Ni(Hdmg)2] in solution have been discussed as to stem from monomolecular units [15,16,46,57]. However, other spectroscopic data from species in solution is not reported and the frequently reported virtual insolubility of the materials sheds doubts on the question of the monomolecular species cause the absorptions of [Ni(Hdmg)2] [15,16,52,57] and are responsible for the biological effects of [Ni(Hdmg)2] [53] and [Pt(Hdmg)2] [54]. Recent quantum chemical calculations on [Ni(Hdmg)2] gave absorption bands at 180, 220, 248sh, and 359 nm for the monomer and marked shifted bands (183, 218, 254sh, 368 nm) for the dimer in the gas phase letting us assume that the reported solution spectra represent dissolved, but very probably oligomeric species.
We thus embarked on a study of the three complexes [M(Hdmg)2] (M = Ni, Pd, Pt) using density functional theory (DFT). Starting from the results of the previous DFT study on the [Ni(Hdmg)2] complex, which used the range-separated hybrid functional ωB97X-D, augmented with dispersion correction and split-valence LANL2DZ effective core potentials (ecp) for Ni and 6-31G (d,p) basis set for all non-metallic elements [1], we chose the M06-2X as nonlocal functional without any symmetry constraint and split-valence LANL2DZ ecp (all metals) and def2TZVP (other atoms) basis sets. In contrast to the previous calculation that was carried out in the gas-phase, we applied the conductor-like polarizable continuum model (CPCM) for DMSO as a solvent to study the effect of this very polar solvent in comparison to the non-polar gas-phase study. The def2TZVP basis set instead of the more sophisticated 6-31G (d,p) was chosen to save computational time. For the same reason, we used the Hay and Wadt effective core potentials for the metal atoms. We thus calculated molecular structures, IR data, frontier orbital compositions, and UVvis absorption spectra. We compared our calculated results with available experimental data and results from similar DFT studies with different functionals and basis sets and thus also provide an overview of the present state of knowledge. Pressure experiments have shown that the M ... M interactions account also for the compressibility of these structures and the pressure-dependent changes of colour and electronic properties [3,4,8,12,[26][27][28][29][30][31]. These virtually insoluble metal ... metal stacked solids are the basis for applications of the three compounds [M(Hdmg) 2 ] (M = Pt, Pd, Ni) for the extraction or removal of these elements [32][33][34][35], as components of solid catalysts [36][37][38][39][40], as solid but easily evaporable precursors [37][38][39][40][41][42][43][44][45][46][47], and in optical devices (e.g., pressure calibrants/indicators) [3,4,12,[26][27][28][29][30][31][48][49][50][51].
On the other hand, some applications as the analytical photometric determination of traces of Ni, Pd or Pt [32,35,52] or their use in (medical) coordination chemistry [52][53][54][55][56] seem to make use of the properties of the molecular units and UV-vis absorption spectra of [Ni(Hdmg) 2 ] in solution have been discussed as to stem from monomolecular units [15,16,46,57]. However, other spectroscopic data from species in solution is not reported and the frequently reported virtual insolubility of the materials sheds doubts on the question of the monomolecular species cause the absorptions of [Ni(Hdmg) 2 ] [15,16,52,57] and are responsible for the biological effects of [Ni(Hdmg) 2 ] [53] and [Pt(Hdmg) 2 ] [54]. Recent quantum chemical calculations on [Ni(Hdmg) 2 ] gave absorption bands at 180, 220, 248sh, and 359 nm for the monomer and marked shifted bands (183, 218, 254sh, 368 nm) for the dimer in the gas phase letting us assume that the reported solution spectra represent dissolved, but very probably oligomeric species.
We thus embarked on a study of the three complexes [M(Hdmg) 2 ] (M = Ni, Pd, Pt) using density functional theory (DFT). Starting from the results of the previous DFT study on the [Ni(Hdmg) 2 ] complex, which used the range-separated hybrid functional ωB97X-D, augmented with dispersion correction and split-valence LANL2DZ effective core potentials (ecp) for Ni and 6-31G (d,p) basis set for all non-metallic elements [1], we chose the M06-2X as nonlocal functional without any symmetry constraint and split-valence LANL2DZ ecp (all metals) and def2TZVP (other atoms) basis sets. In contrast to the previous calculation that was carried out in the gas-phase, we applied the conductor-like polarizable continuum model (CPCM) for DMSO as a solvent to study the effect of this very polar solvent in comparison to the non-polar gas-phase study. The def2TZVP basis set instead of the more sophisticated 6-31G (d,p) was chosen to save computational time. For the same reason, we used the Hay and Wadt effective core potentials for the metal atoms. We thus calculated molecular structures, IR data, frontier orbital compositions, and UV-vis absorption spectra. We compared our calculated results with available experimental data and results from similar DFT studies with different functionals and basis sets and thus also provide an overview of the present state of knowledge.
Recently reported DFT and TD-DFT calculations on the molecular and electronic structures of planar d 8 configured Ni II , Pd II , and Pt II complexes have shown that the reliability of calculated data with experimental data [58][59][60][61][62][63][64][65][66] is very much dependent on functionals and basis sets. Furthermore, comparative DFT and experimental studies for these three metals were recently reported [62][63][64][65][66][67] allowing to gauge for the differences of these three metals.

Experimental Section
Computational Methods. All calculations were performed using the Gaussian 09 suite of programs [68]. Geometry optimisations and calculations of all complexes were carried out in DMSO as solvent using density functional theory (DFT) employing the conductorlike polarizable continuum model (CPCM) [69,70]. The functional for this study is M06-2X [71] as nonlocal functional, which is applied without any symmetry constraint. We used split-valence basis sets def2TZVP [72] for all non-metallic elements and LANL2DZ [73] for metals (M = Ni, Pd, and Pt) the latter applying the effective core potentials ecp(10/18) for Ni, ecp(28/18) for Pd, and ecp(60/18)for Pt by Hay and Wadt [74][75][76]. TD-DFT calculations for UV-vis transitions were run at the same level of theory and basis sets with DMSO as a solvent model for 45 singlet excited states.

DFT-Optimised Molecular Geometries
The DFT-calculated geometries show centrosymmetric planar molecules with two identical O-H . . . O bonds ( Figure 1). In contrast to earlier reports [4,5,12,15,18] we did not find different torsion angles of the four CH 3 groups. In a recent experimental diffraction study using high-quality single crystals of [Ni(Hdmg) 2 ] up to pressures of 5 GPa [4] interactions with the two different oxime O atoms on one Hdmgligand led to different torsion angles of the two CH 3 groups. We suppose that our calculations underestimate these small torsional energies [4].
Recently reported DFT and TD-DFT calculations on the molecular and electronic structures of planar d 8 configured Ni II , Pd II , and Pt II complexes have shown that the reliability of calculated data with experimental data [58][59][60][61][62][63][64][65][66] is very much dependent on functionals and basis sets. Furthermore, comparative DFT and experimental studies for these three metals were recently reported [62][63][64][65][66][67] allowing to gauge for the differences of these three metals.

Experimental Section
Computational Methods. All calculations were performed using the Gaussian 09 suite of programs [68]. Geometry optimisations and calculations of all complexes were carried out in DMSO as solvent using density functional theory (DFT) employing the conductor-like polarizable continuum model (CPCM) [69,70]. The functional for this study is M06-2X [71] as nonlocal functional, which is applied without any symmetry constraint. We used split-valence basis sets def2TZVP [72] for all non-metallic elements and LANL2DZ [73] for metals (M = Ni, Pd, and Pt) the latter applying the effective core potentials ecp(10/18) for Ni, ecp(28/18) for Pd, and ecp(60/18)for Pt by Hay and Wadt [74][75][76]. TD-DFT calculations for UV-vis transitions were run at the same level of theory and basis sets with DMSO as a solvent model for 45 singlet excited states.

DFT-Optimised Molecular Geometries
The DFT-calculated geometries show centrosymmetric planar molecules with two identical O-H … O bonds ( Figure 1). In contrast to earlier reports [4,5,12,15,18] we did not find different torsion angles of the four CH3 groups. In a recent experimental diffraction study using high-quality single crystals of [Ni(Hdmg)2] up to pressures of 5 GPa [4] interactions with the two different oxime O atoms on one Hdmgligand led to different torsion angles of the two CH3 groups. We suppose that our calculations underestimate these small torsional energies [4]. The calculated M-N bond lengths increase from 1.912 to 2.015 Å along the series Ni << Pt < Pd which reflects the size of the central atom (Tables S2-S4, Supplementary). In many experimental and theoretical studies, Pd II has been found slightly larger than Pt II [63][64][65][66][77][78][79][80][81], in keeping with the effects of the lanthanide contraction [82]. While for the Ni complex (Table S2) the two calculated M-N bonds show identical length, for Pd the M-N6(oximate) bond is slightly shorter than M-N3(oxime) ( Table S3). For Pt M-N3 is markedly shorter than M-N6 (Table S4). Experimentally M-N6 is found slightly shorter than M-N3 for both Pt and Pd, while for Ni the experimental data is ambiguous. A shorter The calculated M-N bond lengths increase from 1.912 to 2.015 Å along the series Ni << Pt < Pd which reflects the size of the central atom (Tables S2-S4, Supplementary). In many experimental and theoretical studies, Pd II has been found slightly larger than Pt II [63][64][65][66][77][78][79][80][81], in keeping with the effects of the lanthanide contraction [82]. While for the Ni complex (Table S2) the two calculated M-N bonds show identical length, for Pd the M-N6(oximate) bond is slightly shorter than M-N3(oxime) ( Table S3). For Pt M-N3 is markedly shorter than M-N6 (Table S4). Experimentally M-N6 is found slightly shorter than M-N3 for both Pt and Pd, while for Ni the experimental data is ambiguous. A shorter M-N6 bond compared to the M-N3 bond is in line with a Coulombic contribution to the M-L bond which is probably not correctly reproduced by the DFT calculations which usually overestimate the covalent character of a bond.
The oxime/oximato N3-O2/N6-O7 bonds are calculated in excellent agreement with the experimental values showing a markedly shorter N6-O7 bonds in all cases. Also the chelate N3-M-N6 angles about 82 • for the Ni complex and~79 • for the Pt and Pd derivatives agree very well with the experimental data. The same is true for the N6-M-N10 angles (~97 • for Ni;~100 for Pd and Pt) which, together with the size of the metal set the stage for the O-H ... O hydrogen bond ( Figure 1).
In agreement with the experimental data, the computations reproduced the strong asymmetric O-H . . . O hydrogen bonds [83]. Most of our calculated geometries of these H bonds agree very well with the experimental data. The maximum differences between recent X-ray data [4,11] [16,20,24,84,85], suggested a symmetric H bond in which the H atoms occupies a central position between the two O atoms and a very recent theoretical study found a symmetric relaxed potential energy curve (PEC) [1]. However, the same DFT study could show that the rigid PEC exhibits asymmetric double-well potentials with two clear minima [1] in keeping with other experimental work from 1959 to date [11,19,28,[86][87][88][89][90], and further theoretical studies [3,5] The authors of this study report that the values calculated with the B3LYP functional gave lower agreement with experimental data. However, the main problem is that experimental data is only available for the stacked molecules in the solid making comparison with data calculated in the gas phase [5] or in solution (our study) impossible. In a very recent study on [M(Hdmg) 2 ] (M = Ni, Cu), the range-separated hybrid functional ωB97X-D, augmented with dispersion correction, was used alongside with splitvalence 6-31G (d,p) basis set for all non-metallic elements and LANL2DZ ecp for Ni and Cu [1]. The geometry of the [Ni(Hdmg) 2 ] complex does not vary largely from ours. This method allowed also to calculate the Ni ... Ni distances to 3.17 Å, which is markedly shorter than the reported experimental values of about 3.24 Å (Table S1) [1]. In a similar way, the Pt derivative [Pt(Hdmg) 2 ] was geometry-optimised using the mPW1PW91 functional with 6-31G(d,p) and LANL2DZ basis sets, again with very similar molecular geometries [3]. The Pt ... Pt distance at ambient pressure was calculated to 3.3 Å which compares reasonably well with about 3.25 Å found in experimental structures (Table S1). Our spectral assignments (Tables 1-3) are in keeping with an early detailed report on the IR spectra of Ni-, Pd-, Pt-and Cu-dimethylglyoximate complexes, including deuteration experiments [21], DFT-calculated and experimental data on [Ni(Hdmg) 2 ] [87], and recent DFT-calculated IR spectra for [Ni(Hdmg) 2 ] [1]. The marked deviation of the calculated values from experimental data is very probably because all these experiments have been carried out on solid samples. Thus, the experimental data represents the molecular stacks and not isolated molecules. Therefore, instead of comparing our calculated data with experimental data, we use it solely for benchmarking our computational method.

Infrared (IR) Spectroscopy
Compared with the recently applied range-separated hybrid functional ωB97X-D, augmented with dispersion correction and split-valence 6-31G (d,p) basis set for all nonmetallic elements and LANL2DZ ecp [1], our results for the N-O stretching vibration of the [Ni(Hdmg) 2 ] gave markedly lower values, while the C=N stretch are quite similar and the O-H bending is calculated at far higher energy (Table 1). Compared with the results from early calculations using the B3LYP functional and 6-311+(+)G**basis set for all atoms [87] our introduction of split basis had only a small impact on the N-O stretching and O-H bending energies, while for the C=N stretch our values lie markedly higher. Compared with the experimental data from solid samples, our calculated values and those of the recent DFT study using also split basis sets [1] are much higher. We tentatively ascribe this to the more sophisticated modelling of the metal atoms using split basis sets and believe that values of about 1650 cm -1 represent the C=N stretch in isolated molecules, while the stacking in the solid reduces the energy of this resonance markedly. Our spectral assignments (Tables 1-3) are in keeping with an early detailed report on the IR spectra of Ni-, Pd-, Pt-and Cu-dimethylglyoximate complexes, including deuteration experiments [21], DFT-calculated and experimental data on [Ni(Hdmg)2] [87], and recent DFT-calculated IR spectra for [Ni(Hdmg)2] [1]. The marked deviation of the calculated values from experimental data is very probably because all these experiments have been carried out on solid samples. Thus, the experimental data represents the molecular stacks and not isolated molecules. Therefore, instead of comparing our calculated data with experimental data, we use it solely for benchmarking our computational method.     Three transitions in the calculated spectra can be assigned to N-O stretching. They show very different intensities for the three complexes, while the energies are rather invariable (Figure 2, Tables 1-3).
For the C=N stretching modes the calculated spectra show two transitions for Ni (Table 1) and Pd (Table 2) and two merged bands for Pt (Table 3). They have similar intensities and similar energies for Pd and Pt but far higher values for Ni. We ascribe the energy differences between the metals to higher metal d to π* CN backbonding for Pt and Pd compared to Ni, in keeping with the larger 5d and 4d orbitals compared with 3d.  [86]. Akin to a recent theoretical study [1], we also found that the asymmetric O-H stretching vibration in comparison with the symmetric stretching is very intense. This is in line with the bigger change of molecular dipole moment for the asymmetric O-H stretching mode.

Energies and Compositions of the Frontier Orbitals
The energies and compositions of the lowest unoccupied molecular orbital (LUMO) and highest occupied molecular orbitals (HOMO) were calculated for the three complexes based on the S 0 and T 1 geometry-optimised structures ( Figures S1-S3 and Tables S5-S7 in the Supplementary Materials). In the electronic S 0 ground state, most of the frontier orbitals including HOMO-3 to LUMO+3 differ from the Ni complex to the Pd and Pt derivatives, with the exception of the LUMOs which are highly similar in all three complexes with large coefficients on the metal-ligand bonds and the dmg π system (Figure 3 and Figure S2). The HOMO for the Ni complex is essentially centred on the ligands (100%) and has high similarities with the HOMO-1 for Pt (Figure 3), while the HOMO for the Pt complex obtains some metal d contributions (18%). For Pd these two orbitals are almost degenerate and the HOMO also obtains some metal contributions (8%). All three HOMO-3 orbitals have predominant metal d z 2 character with the d z 2 character getting more and more dominant along the series Ni << Pd < Pt. For all three complexes, the LUMO and LUMO+1 have small to negligible metal contributions. The LUMO+2 for Pt and the LUMO+3 for Pd resemble the essentially metal-centred LUMO+3 of the Ni complex ( Figure S2) and clearly represent the metal p z orbital. derivatives, with the exception of the LUMOs which are highly similar in all three complexes with large coefficients on the metal-ligand bonds and the dmg π system (Figures 3  and S2). The HOMO for the Ni complex is essentially centred on the ligands (100%) and has high similarities with the HOMO-1 for Pt (Figure 3), while the HOMO for the Pt complex obtains some metal d contributions (18%). For Pd these two orbitals are almost degenerate and the HOMO also obtains some metal contributions (8%). All three HOMO-3 orbitals have predominant metal dz 2 character with the dz 2 character getting more and more dominant along the series Ni << Pd < Pt. For all three complexes, the LUMO and LUMO+1 have small to negligible metal contributions. The LUMO+2 for Pt and the LUMO+3 for Pd resemble the essentially metal-centred LUMO+3 of the Ni complex (Figure S2) and clearly represent the metal pz orbital. The calculated HOMO-LUMO energy gaps are 6.302 and 6.413 eV for the Ni and Pd complexes, respectively and reduced to 6.062 eV for the Pt complex, which is caused by a marked stabilisation of the LUMO (Figure 3). This series Pd > Ni > Pt agrees quite well with the experimental binding energies and electrochemical or optical HOMO-LUMO gaps of comparable series of Pt, Pd, and Ni complexes [63][64][65]67,77].
The XPS determined Ni 2p binding energies for [Ni(Hdmg)2] are reported at about 853 (2p3/2) to 870 (2p1/2) eV [38] while for the ligands N(1s) and O(1s) binding energies the sequence is Pt ~ Pd > Ni [91] which is in keeping with the size of the metal valence orbitals for the π-backbonding.
Gas-phase DFT calculations of [Ni(Hdmg)2] gave a value of 7.32 eV decreasing to 6.97 eV upon dimerisation [1] and very similar HOMO and LUMO compositions. Adding one or two H2O or NH3 molecules as additional axial ligand increased the value for the monomer and also changed the orbital composition of HOMO and LUMO [1].
The frontier orbitals of the T1 excited state (LSOMO: Lowest Singly Occupied Molecular Orbital, and HSOMO: Highest Singly Occupied Molecular Orbital) showed predominant contributions of the ligand to the HSOMO and HSOMO+1, while the metal participation increases in the LSOMO and LSOMO-1 for Pd and Pt complexes ( Figure S3 and Table S7, Supplementary). So, again the Ni complex differs from the Pd and Pt derivatives. The calculated HOMO-LUMO energy gaps are 6.302 and 6.413 eV for the Ni and Pd complexes, respectively and reduced to 6.062 eV for the Pt complex, which is caused by a marked stabilisation of the LUMO (Figure 3). This series Pd > Ni > Pt agrees quite well with the experimental binding energies and electrochemical or optical HOMO-LUMO gaps of comparable series of Pt, Pd, and Ni complexes [63][64][65]67,77].
Gas-phase DFT calculations of [Ni(Hdmg) 2 ] gave a value of 7.32 eV decreasing to 6.97 eV upon dimerisation [1] and very similar HOMO and LUMO compositions. Adding one or two H 2 O or NH 3 molecules as additional axial ligand increased the value for the monomer and also changed the orbital composition of HOMO and LUMO [1].
The frontier orbitals of the T 1 excited state (LSOMO: Lowest Singly Occupied Molecular Orbital, and HSOMO: Highest Singly Occupied Molecular Orbital) showed predominant contributions of the ligand to the HSOMO and HSOMO+1, while the metal participation increases in the LSOMO and LSOMO-1 for Pd and Pt complexes ( Figure S3 and Table S7, Supplementary). So, again the Ni complex differs from the Pd and Pt derivatives. The HSOMO and LSOMO are mostly located in the ligand for Ni complex and metal contribution increases in the HSOMO+2 and HSOMO+3.
When comparing the HOMO-LUMO (S 0 ) and LSOMO-HSOMO (T 1 ) energy level diagrams for the three complexes ( Figure S4, Supplementary) a significant stabilisation in the energy of the HSOMO compared with the LUMO is found, while the LSOMO for the T 1 state remained close to the HOMO of the S 0 state in all three cases.

UV-vis Absorption Spectroscopy
TD-DFT calculated absorption bands are very similar for all three complexes and show three main band systems containing several transitions (Figure 4). A closer look shows that the intense bands in the range 150-180 nm are very similar with maxima at 170, 171 and 176 nm for Ni(II), Pd(II), and Pt(II), respectively. The band system ranging from 180 to 280 nm shows more pronounced differences in energy (211, 231 and 250 nm) and band shape. The long-wavelength envelopes found from 270 to 400 nm are very similar for Ni and Pd, with maxima at 310 and 312 nm, respectively. For the Pt complex, the long-wavelength absorption is markedly red-shifted to the range 307-440 nm with a maximum of 350 nm. The intensity of these maxima decreases along the series from 6178 (Ni) to 4016 (Pd) and 2835 ε/M -1 cm -1 (Pt) ( Table 4).
The HSOMO and LSOMO are mostly located in the ligand for Ni complex and metal con-tribution increases in the HSOMO+2 and HSOMO+3.
When comparing the HOMO−LUMO (S0) and LSOMO−HSOMO (T1) energy level diagrams for the three complexes ( Figure S4, Supplementary) a significant stabilisation in the energy of the HSOMO compared with the LUMO is found, while the LSOMO for the T1 state remained close to the HOMO of the S0 state in all three cases.

UV-vis Absorption Spectroscopy
TD-DFT calculated absorption bands are very similar for all three complexes and show three main band systems containing several transitions (Figure 4). A closer look shows that the intense bands in the range 150−180 nm are very similar with maxima at 170, 171 and 176 nm for Ni(II), Pd(II), and Pt(II), respectively. The band system ranging from 180 to 280 nm shows more pronounced differences in energy (211, 231 and 250 nm) and band shape. The long-wavelength envelopes found from 270 to 400 nm are very similar for Ni and Pd, with maxima at 310 and 312 nm, respectively. For the Pt complex, the long-wavelength absorption is markedly red-shifted to the range 307−440 nm with a maximum of 350 nm. The intensity of these maxima decreases along the series from 6178 (Ni) to 4016 (Pd) and 2835 ε/M -1 cm -1 (Pt) ( Table 4).    The broad long-wavelength absorption band for [Ni(Hdmg) 2 ] is essentially composed of the HOMO-1→LUMO (79%) and HOMO→LUMO+1 (12%) transitions (Table S8, Supplementary). The same band for the Pd complex correspond to a mixture of the HOMO-1→LUMO (48%) and HOMO→LUMO (35%) transitions (Table S9). Visual plots of the molecular orbitals ( Figure S1, SI) show that both bonds have almost pure π−π* character. For the Pt complex, this band is essentially described by the HOMO→LUMO (90%) tran-sition (Table S10) with has essentially ligand-centred π−π* character, but with a marked metal-to-ligand charge transfer (MLCT) contribution ( Figure S1).
Further absorption bands at higher energy have predominant π−π* character which is in line with most of the states being essentially ligand centred ( Figure S1 and Tables S6 and S7). Marked MLCT contributions for the Ni complex are found for transitions from HOMO-8 and HOMO-9 to the LUMO (Table S8). Corresponding transitions from the Pd and Pt derivatives include the HOMO-7 and HOMO-6 states, respectively (Tables S9 and S10). This is in line with the increasing ligand field energy and π-backbonding in the series Ni-Pd-Pt leading to a de-stabilisation of the low-lying dπ orbitals. No transitions with pronounced ligand field (d-d*) character were found for the three complexes. However for Pd and Pt transitions with marked d-p character (HOMO-3→LUMO+3 (Pd) or HOMO-3→LUMO+2 (Pt)) were found at quite high energies corresponding to 167 and 181 nm for Pd and Pt, respectively. The p-type HOMO+3 orbital for Ni is less involved in electronic transitions.
The recently calculated absorption spectra of monomeric and dimeric (Ni ... Ni stacked) [Ni(Hdmg) 2 ] are on first view similar to our spectrum absorption maxima [1]. A closer look shows that the energies of the two UV bands with maxima at 180 and 220 nm do not differ much between monomer and dimer. The calculated energies of these gasphase calculations using the range-separated hybrid functional ωB97X-D, augmented with dispersion correction and split-valence 6-31G (d,p) basis set for all non-metallic elements and LANL2DZ ecp for Ni are only slightly lower than our numbers (Table 4). However, for the long-wavelength bands, this method gave a very different band maximum of 359 nm compared with 310 nm from our calculations in DMSO solvent and dimerisation shifted the band to 368 nm [1]. In the same study the long-wavelength band is described to have d-p character although their main contributions come from the HOMO-1→LUMO and HOMO-2→LUMO transitions [1] and their HOMO-1, HOMO-2 and LUMO show higher metal contributions than those calculated in our study.
In summary, contrasting to previous assignments of the absorption bands ranging from 200 to 450 nm to essentially MLCT with some π-π* character we found a predominant π-π* character for all these bands. In contrast to previous studies, we also found that admixture of metal contributions of MLCT or d-p type occurs rather for transitions at higher energies, while the long-wavelength bands retain rather pure π-π* character. However, this picture rapidly changes when axial ligands were added or dimers were formed [1,2]. Then metal-contributions both of MLCT and d-p type get more pronounced for the longwavelength absorptions of the monomeric species and dominate for the stacked molecules in the solid the visible spectral range with the typical d-p transitions (mixed with MLCT type of transition) [1][2][3]6,15,46,[48][49][50][51][52]. In our calculations, we used the conductor-like polarizable continuum model (CPCM) for the inclusion of polarisation effects from the solvent (here: DMSO). However, this method does not include real solvent molecules which are potentially coordinating but provides a polarisable surrounding (continuum). Compared with calculations on monomers in the gas phase [1] our calculation might thus overestimate delocalisation effects. However, our model definitely seems to be able to circumvent the dramatic impact of any species (ligands, other complexes) in the axial positions of the planar complexes on the d z 2 and p z orbitals leading to massive metal contributions to optical transitions.

Conclusions
We have studied the three Ni II , Pd II and Pt II complexes [M(Hdmg) 2 ] (H 2 dmg = dimethylglyoxime) by density functional DFT and TD-DFT methods to explore the structural and IR and UV-vis absorption spectroscopic properties of the molecular species of these complexes. The three compounds have a very high tendency to form metal ... metal directed stacks and thus aggregate rapidly in solution. This has previously hampered spectroscopic characterisation of these complexes in solution and most of the studies, including theoretical studies, and most reported applications have been focussing on the solid-state. Still, some applications such as catalysis, trace element detection and biomedicine might be based on monomolecular species. Studies reporting spectroscopic properties of the complexes in solution are rare and mainly restricted to UV-vis absorption spectra. These studies reported bands in the visible range (>400 nm), but recent quantum chemical calculations did not agree with these observations and we supposed that instead of monomolecular species these solutions represent monomolecular together with oligomeric species. Thus, spectroscopic data of the monomolecular species is probably not reported yet. Thus, we computed the molecular geometries, IR spectra, frontier orbital compositions and energy together with UV-vis spectra using the M06-2X functional and LANL2DZ ecp (metals) and def2TZVP (other atoms) as basis sets. DMSO as solvent was included employing the conductor-like polarizable continuum model (CPCM). The optimised molecular geometries proved the asymmetric character of the two formed O-H . . . O bonds in the compounds, which connect the adjacent Hdmgligands in the completely planar complexes. IR frequencies of the O-H bond were higher in the Pd II and Pt II complexes than the Ni II derivative in line with weaker H . . . O interactions. Comparison of calculated data of [M(Hdmg) 2 ] from three DFT studies showed that the use of split-valence basis sets is superior to the previously reported use of one type of basis sets for the metals and the light atoms (B3LYP functional and 6-311+(+)G**basis set). Calculated compositions of frontier orbitals gave essentially ligand-centred lowest unoccupied molecular orbitals (LUMOs) and highest occupied molecular orbitals (HOMO) except for the LUMO+3 (Ni, Pd) or LUMO+2 (Pt) with clear metal p z and the HOMO-3 orbitals with predominant metal d z 2 character. Calculated UV-vis spectra gave three bands in the range 180 to 350 nm. These bands are similar for all three complexes but show a marked red-shift in the series going from Ni to Pt. We assign them to predominantly ligand-centred π-π* transitions, in contrast to previous assignments to mainly metal(d) to ligand(π*) charge transfer (MLCT) transitions. For our calculations metal contributions to the π-π* transitions occur only at higher energies for the monomolecular species, while the long-wavelength bands have almost pure π-π* character. These metal contributions comprise MLCT and also the notorious so-called d-p transitions that dominate the visible spectral range and the colours and other opto-electronic properties of the three compounds in the solid. Although, these d-p transitions have previously been assigned to absorption bands in the UV to vis range (200-450 nm) for the isolated molecules in solution, we found significant d-p contributions only for bands at around 180 for Pt and Pd and none for Ni. Other calculations on monomers, dimers and oligomers showed that further ligands added to the two axial positions, dimerisation or oligomerisation has a strong impact on both the 3d z 2 and the 4p z orbitals dramatically increasing their contributions to the electronic transitions. Together with these calculations, our results support our idea that spectroscopic data of these three complexes does not represent the isolated molecules but a mixture of monomeric and oligomeric species. In a way, we looked for the first time at the isolated molecules in a surrounding-isolating solvent model.