Excitation energies of some d1systems calculated using time-dependent density functional theory: an implementation of open-shell TDDFT theory for doublet–doublet excitations

Characterization of "Free Base" and Metal Complex Thioalkyl Porphyrazines by Magnetic Circular Dichroism and TDDFT Calculations

UV–vis absorption and magnetic circular dichroism (MCD) spectra of octakis thioethyl “free base” porphyrazine H₂OESPz and its metal complexes MOESPz (M = Mg, Zn, Ni, Pd, Cu), as well as of [MnOESPz(SH)] were recorded. In the last case, MCD proved to have quite good sensitivity to the coordination of this complex with 1-methylimidazole (1-mim) in benzene. Time-dependent density functional theory (TDDFT) calculations were carried out for the considered porphyrazine complexes and showed good performance on comparing with MCD and UV–vis experimental spectra, even in the open-shell Cu and Mn cases. Calculations accounted for the red shift observed in the thioalkyl compounds and allowed us to reveal the role of sulfur atoms in spectroscopically relevant molecular orbitals and to highlight the importance of the conformations of the thioethyl external groups. Calculated MCD spectra of [MnOESPz(SH)] confirm the Mn(III) → Mn(II) redox process, which leads to the [Mn(OESPz)(1-mim)₂] species, and the relevance of the spin state for MCD is revealed.

Generalized single excitation configuration interaction: an investigation into the impact of the inclusion of non-orthogonality on the calculation of core-excited states

In this paper, we investigate different non-orthogonal generalizations of the configuration interaction with single substitutions (CIS) method and their impact on the calculation of core-excited states.

Vibrational coherence transfer in the ultrafast intersystem crossing of a diplatinum complex in solution

We investigate the ultrafast transient absorption response of tetrakis(μ-pyrophosphito)diplatinate(II), [Pt₂(μ-P₂O₅H₂)₄]^4- [hereafter abbreviated Pt(pop)], in acetonitrile upon excitation of its lowest singlet ¹A_2u state. Compared with previously reported solvents [van der Veen RM, Cannizzo A, van Mourik F, Vlček A, Jr, Chergui M (2011) J Am Chem Soc 133:305-315], a significant shortening of the intersystem crossing (ISC) time (<1 ps) from the lowest singlet to the lowest triplet state is found, allowing for a transfer of vibrational coherence, observed in the course of an ISC in a polyatomic molecule in solution. Density functional theory (DFT) quantum mechanical/molecular mechanical (QM/MM) simulations of Pt(pop) in acetonitrile and ethanol show that high-lying, mostly triplet, states are strongly mixed and shifted to lower energies due to interactions with the solvent, providing an intermediate state (or manifold of states) for the ISC. This suggests that the larger the solvation energies of the intermediate state(s), the shorter the ISC time. Because the latter is smaller than the pure dephasing time of the vibrational wave packet, coherence is conserved during the spin transition. These results underscore the crucial role of the solvent in directing pathways of intramolecular energy flow.

Relativistic DFT Calculations of Hyperfine Coupling Constants in 5d Hexafluorido Complexes: [ReF6 ]2- and [IrF6 ]2

The performance of relativistic density functional theory (DFT) methods has been investigated for the calculation of the recently measured hyperfine coupling constants of hexafluorido complexes [ReF6 ]2- and [IrF6 ]2- . Three relativistic methods were employed at the DFT level of theory: the 2-component zeroth-order regular approximation (ZORA) method, in which the spin-orbit coupling was treated either variationally (EV ZORA) or as a perturbation (LR ZORA), and the 4-component Dirac-Kohn-Sham (DKS) method. The dependence of the results on the basis set and the choice of exchange-correlation functional was studied. Furthermore, the effect of varying the amount of Hartree-Fock exchange in the hybrid functionals was investigated. The LR ZORA and DKS methods combined with DFT led to very similar deviations (about 20 %) from the experimental values for the coupling constant of complex [ReF6 ]2- by using hybrid functionals. However, none of the methods were able to reproduce the large anisotropy of the hyperfine coupling tensor of complex [ReF6 ]2- . For [IrF6 ]2- , the EV ZORA and DKS methods reproduced the experimental tensor components with deviations of ≈10 and ≈5 % for the hybrid functionals, whereas the LR ZORA method predicted the coupling constant to be around one order of magnitude too large owing to the combination of large spin-orbit coupling and very low excitation energies.

Temperature- and excitation wavelength-dependent emission in a manganese(ii) complex

A mononuclear manganese(ii) complex with a chelating 4-(3,5-diphenyl-1H-pyrazol-1-yl)-6-(piperidin-1-yl)pyrimidine ligand (L), [MnL₂Cl₂]·H₂O, shows intriguing excitation wavelength-dependent emission. Depending on the excitation wavelength, the complex demonstrates three emission bands with the maxima at 380 nm, 440 nm and 495 nm. The 380 nm and 440 nm emissions originate from the π → π* and n → π* ligand-centered transitions. The long-wave 495 nm emission with microsecond lifetimes is related to the d-d transitions and/or metal-to-ligand and halogen-to-ligand charge transfer. The emission behavior of this complex is strongly temperature-dependent: upon cooling from 300 K down to 77 K, the intensity of emission considerably increases. The enhancement of the luminescence upon cooling is accompanied by the appearance of the vibrational structure. This complex is the first example of manganese(ii) complexes demonstrating excitation wavelength-dependent emission.

The electronic properties of three popular high spin complexes [TM(acac)3, TM = Cr, Mn, and Fe] revisited: an experimental and theoretical study

The occupied and unoccupied electronic structures of three high spin TM(acac)₃ (TM = Cr, Mn, and Fe) complexes (I, II, and III, respectively) were studied by revisiting their literature vapour-phase He(i) and, when available, He(ii) photoemission (PE) spectra and by means of original near-edge X-ray absorption fine structure (NEXAFS) spectroscopic data recorded at the O K-edge (^OK-edge) and TM L_2,3-edges (^TML_2,3-edges). The assignments of the vapour-phase He(i)/He(ii) PE spectra were guided by the results of spin-unrestricted non-relativistic Slater transition state calculations, while the ^OK-edge and ^TML_2,3-edge spectroscopic pieces of evidence were analysed by exploiting the results of spin-unrestricted scalar-relativistic time-dependent density functional theory (DFT) and DFT/ROCIS calculations, respectively. Although the actual symmetry (D₃, in the absence of any Jahn-Teller distortion) of the title molecules allowed an extensive mixing between TM t_2g-like and e_g-like atomic orbitals, the use of the Nalewajski-Mrozek TM-O bond multiplicity index combined with a thorough analysis of the ground state (GS) outcomes allowed the assessment of the TM-O bond weakening associated with the progressive TM 3d-based e_g-like orbital filling. The experimental information provided by ^OK-edge spectra was rather poor; nevertheless, the combined use of symmetry, orbitals and spectra allowed us (i) to rationalise minor differences characterizing spectral features along the series, (ii) to quantify the contribution provided by the ligand-to-metal-charge-transfer (LMCT) excitations to the different spectral features, and (iii) to recognize the t_2g-/e_g-like nature of the TM 3d-based orbitals involved in LMCT transitions. As far as the ^TML_2,3-edge spectra and the DFT/ROCIS results were concerned, the lowest lying I^,IIL₃ spectral features included states having either the GS spin multiplicity (S(I) = 3/2, S(II) = 2) or, at higher excitation energies (EEs), states with ΔS = ±1. In contrast to that, only states with ΔS = 0, -1 significantly contributed to the IIIL₃ spectral pattern. Along the whole series, the L₃ higher EE side was systematically characterized by states involving ^TM2p → π₄ MLCT excitations; as such, coupled-single excitations with ΔS = 0 were involved in I and II, while single MLCT ^TM2p → π₄ transitions with ΔS = -1 were involved in III.

Structural Characterization of Thermochromic and Spin Equilibria in Solid-State Ni(detu)4Cl2 (detu = N,N'-Diethylthiourea)

Consecutive thermochromic lattice distortional and spin crossover equilibria in solid-state Ni(detu)4Cl2 (detu = N,N'-diethylthiourea) are investigated by variable-temperature X-ray crystallography (173-333 K), DFT calculations, and differential scanning calorimetry. Thermochromism and anomalous magnetism were reported previously (S. L. Holt, Jr., et al. J. Am. Chem. Soc. 1964, 86, 519-520); the latter was attributed to equilibration of a singlet ground state and a thermally accessible triplet state, but structural data were not obtained. A crystal structure at 173(2) K revealed [Ni(detu)4](2+) centers with distorted planar ligation of nickel(II) to the four sulfur atoms, with an average Ni-S bond length of 2.226(3) Å. The nickel ion was displaced out-of-plane by 0.334 Å toward a proximal apical chloride at a nonbonding distance of 3.134(1) Å. Asymmetry in the trans S-Ni-S angles was coupled to a monoclinic ↔ tetragonal lattice distortion (T(1/2) = 254 ± 11 K), resulting in thermochromism. Spin crossover occurs by tetragonal modulation of nickel(II) with approach of the proximal chloride at higher temperatures (T(1/2) = 383 ± 18 K), which is consistent with a contraction of -0.096(4) Å in the Ni···Cl separation observed at 293 K. A high-spin (S = 1) square-pyramidal [Ni(dmtu)4Cl](+) model (dmtu = N,N'-dimethylthiourea) was optimized by DFT calculations, which estimated limiting equatorial Ni-S bond lengths of 2.45 Å and an apical Ni-Cl bond of 2.43 Å. Electronic spectra of the spin isomers were calculated by TD-DFT methods. Assignment of the FTIR spectrum was assisted by frequency calculations and isotope substitution.

An experimental NEXAFS and computational TDDFT and ΔDFT study of the gas-phase core excitation spectra of nitroxide free radical TEMPO and its analogues

Core excitation (NEXAFS) C 1s, N 1s, and O 1s gas-phase spectra of stable nitroxide free radical TEMPO and two of its amide-substituted analogues are assigned from the onset of the absorptions to the vicinity of the core-ionization thresholds using the theoretical TDDFT and ΔDFT methods.

Electronic structure of CuTPP and CuTPP(F) complexes: a combined experimental and theoretical study II

CuTPP and CuTPP(F) thick films deposited on Au(111) have been studied by coupling NEXAFS spectroscopy at the ^C/N/FK-edges and ^CuL_2,3-edges and spin-unrestricted TD-DFT calculations.

The role of the metal ion in the photophysical behavior of Co(II), Ni(II), and Cu(II) octabutoxynaphthalocyanines: insights from ultra-fast time-resolved spectroscopy and DFT/TDDFT calculations

The photo-deactivation mechanism of the MNc(OBu)8 (M = Co, Ni, Cu) series of complexes is reviewed, with special emphasis on the role played by the central metal. Ultra-fast transient absorption experiments and Density Functional Theory and time-dependent Density Functional Theory calculations consistently show that the central metal modifies the photo-deactivation mechanism of the investigated complexes by inducing substantial changes in the nature and energy of the excited states lying between the photo-generated state and the ground state.

Understanding the electronic structure of 4d metal complexes: from molecular spinors to L-edge spectra of a di-Ru catalyst

L(2,3)-edge X-ray absorption spectroscopy (XAS) has demonstrated unique capabilities for the analysis of the electronic structure of di-Ru complexes such as the blue dimer cis,cis-[Ru(III)(2)O(H(2)O)(2)(bpy)(4)](4+) water oxidation catalyst. Spectra of the blue dimer and the monomeric [Ru(NH(3))(6)](3+) model complex show considerably different splitting of the Ru L(2,3) absorption edge, which reflects changes in the relative energies of the Ru 4d orbitals caused by hybridization with a bridging ligand and spin-orbit coupling effects. To aid the interpretation of spectroscopic data, we developed a new approach, which computes L(2,3)-edges XAS spectra as dipole transitions between molecular spinors of 4d transition metal complexes. This allows for careful inclusion of the spin-orbit coupling effects and the hybridization of the Ru 4d and ligand orbitals. The obtained theoretical Ru L(2,3)-edge spectra are in close agreement with experiment. Critically, existing single-electron methods (FEFF, FDMNES) broadly used to simulate XAS could not reproduce the experimental Ru L-edge spectra for the [Ru(NH(3))(6)](3+) model complex nor for the blue dimer, while charge transfer multiplet (CTM) calculations were not applicable due to the complexity and low symmetry of the blue dimer water oxidation catalyst. We demonstrated that L-edge spectroscopy is informative for analysis of bridging metal complexes. The developed computational approach enhances L-edge spectroscopy as a tool for analysis of the electronic structures of complexes, materials, catalysts, and reactive intermediates with 4d transition metals.

A time-dependent density functional theory (TDDFT) interpretation of the optical spectra of zinc phthalocyanine π-cation and π-anion radicals

The UV–visible and near-IR spectra of the zinc phthalocyanine π-cation and π-anion radicals, [ZnPc(–1)]•+ and [ZnPc(–3)]•–, are investigated by time-dependent density functional theory (TDDFT) calculations using the pure, asymptotically correct, statistical average of (model) orbital potentials (SAOP) functional. The nature and intensity of the main spectral features are highlighted and interpreted on the basis of the ground-state electronic structure of the complexes. Similarities and differences with previous TDDFT/B3LYP results are discussed. TDDFT/SAOP results for the π-anion radical prove to be in excellent agreement with the solution spectra and generally in line with deconvolution analyses of solution absorption and magnetic circular dichroism (MCD) spectra. On the basis of these results a novel interpretation of the Q-band system is proposed. For the π-cation radical TDDFT/SAOP calculations provide a satisfactory description of the UV region of the spectrum. However, they do not reproduce accurately the energy and intensity of the Q band observed at 825 nm. The description of the Q-band region appears to be complicated by the presence of spurious non-Gouterman transitions. Furthermore, the calculations, either in the gas phase or in solution, do not account for the broad absorption near 500 nm that has been suggested to arise from a nondegenerate, z-polarized 2A2g excited state. Theory and experiment can be reconciled if the presence of an axial ligand such as CN– is explicitly considered in the calculations. TDDFT/SAOP results for the axially ligated [ZnPc(–1)(CN)]• species indicate that the 500 nm feature is related to the axial ligation induced symmetry lowering of the π-cation radical and this band is assigned to a z-polarized transition associated with the hole in the 2a1u.

Metal–Metal Electronic Coupling insyn andanti Stereoisomers of Mixed-Valent (FeCp)2-, (RhL2)2-, and (FeCp)(RhL2)-as-Indacenediide Ions

The extent of metal-metal electronic coupling was quantified for a series of syn and anti stereoisomers of (FeCp)(2)-, (RhL(2))(2)- and (FeCp)(RhL(2))- (L(2)=1,5-cyclooctadiene (cod), L=CO) as-indacenediide mixed-valent ions by spectroelectrochemical and DFT studies. The effect of the syn/anti orientation of the metal units with respect to the planar aromatic ligand indicates that electron transfer occurs through the bridge rather than through space. The nature of the metal was found to be crucial: while homobimetallic diiron species are localised valence-trapped ions (Class II), the dirhodium analogues are almost delocalised mixed-valent ions (borderline and Class III). Finally, despite their redox asymmetry, even in the heterobimetallic iron-rhodium as-indacenediide complexes, strong metal-metal coupling is present. In fact, oxidation of the iron centre is accompanied by electron transfer from rhodium to iron and formation of a reactive 17-electron rhodium site. syn and anti Fe-Rh as-indacenediide complexes are rare examples of heterobimetallic systems which can be classified as borderline Class II/Class III species.

Ligand field photofragmentation spectroscopy of [Ag(L)N]2+ complexes in the gas phase: Experiment and theory

Experiments have been undertaken to record photofragmentation spectra from a series of [Ag(L)N]2+ complexes in the gas phase. Spectra have been obtained for silver(II) complexed with the ligands (L): acetone, 2-pentanone, methyl-vinyl ketone, pyridine, and 4-methyl pyridine (4-picoline) with N in the range of 4-7. A second series of experiments using 1,1,1,3-fluoroacetone, acetonitrile, and CO2 as ligands failed to show any evidence of photofragmentation. Interpretation of the experimental data has come from time-dependent density functional theory (TDDFT), which very successfully accounts for trends in the spectra in terms of subtle differences in the properties of the ligands. Taking a sample of three ligands, acetone, pyridine, and acetonitrile, the calculations show all the spectral transitions to involve ligand-to-metal charge transfer, and that wavelength differences (or lack of spectra) arise from small changes in the energies of the molecular orbitals concerned. The calculations account for an absence in the spectra of any effects due to Jahn-Teller distortion, and they also reveal structural differences between complexes where the coordinating atom is either oxygen or nitrogen that have implications for the stability of silver(II) compounds. Where possible, comparisons have also been made with the physical properties of condensed phase silver(II) complexes.

Time-dependent density functional theory/discrete reaction field spectra of open shell systems: The visual spectrum of [FeIII(PyPepS)2]− in aqueous solution

We report the calculated visible spectrum of [FeIII(PyPepS)2]- in aqueous solution. From all-classical molecular dynamics simulations on the solute and 200 water molecules with a polarizable force field, 25 solute/solvent configurations were chosen at random from a 50 ps production run and subjected the systems to calculations using time-dependent density functional theory (TD-DFT) for the solute, combined with a solvation model in which the water molecules carry charges and polarizabilities. In each calculation the first 60 excited states were collected in order to span the experimental spectrum. Since the solute has a doublet ground state several excitations to states are of type "three electrons in three orbitals," each of which gives rise to a manifold of a quartet and two doublet states which cannot properly be represented by single Slater determinants. We applied a tentative scheme to analyze this type of spin contamination in terms of Delta and Delta transitions between the same orbital pairs. Assuming the associated states as pure single determinants obtained from restricted calculations, we construct conformation state functions (CFSs), i.e., eigenfunctions of the Hamiltonian Sz and S2, for the two doublets and the quartet for each Delta,Delta pair, the necessary parameters coming from regular and spin-flip calculations. It appears that the lower final states remain where they were originally calculated, while the higher states move up by some tenths of an eV. In this case filtering out these higher states gives a spectrum that compares very well with experiment, but nevertheless we suggest investigating a possible (re)formulation of TD-DFT in terms of CFSs rather than determinants.

Synthesis, molecular and electronic structure, and TDDFT and TDDFT-PCM study of the solvatochromic properties of (Me2Pipdt)Mo(CO)4 complex (Me2Pipdt = N,N'-dimethylpiperazine-2,3-dithione)

The synthesis, spectroscopic, and structural characterization of the (Me2Pipdt)Mo(CO)4 complex (Me2Pipdt = N,N'-piperazine-2,3-dithione) are presented in this paper. The title complex crystallizes in the P2(1)/n space group with a = 25.541(3) A, b = 10.3936(14) A, c = 10.9012(12) A, beta = 92.261(9) degrees , V = 2891.6(6) A(3), and Z = 8. Gas- and solution-phase structural and electronic features of (Me2Pipdt)Mo(CO)4 and Me2Pipdt have been investigated using density functional theory. The molecular structure underscores the flexibility of the NC(S)C(S)N fragment in both the free ligand and the metal complex. On the basis of structural, spectroscopic, and theoretical results, the bidentate ligand in (Me2Pipdt)Mo(CO)4 is considered to be in the dithione, not dithiolate, form. Time-dependent density functional theory has been used for the investigation of the excited states and solvatochromic properties of (Me2Pipdt)Mo(CO)4. The calculated vertical excitation energies in solution are consistent with the experimental data, showing that the metal-to-ligand charge-transfer transitions, in both the visible and UV regions, dominate over the ligand-based pi-pi transitions.

Tuning the Electronic Communication in Heterobimetallic Mixed-Valence Ions of (1-Ferrocenyl)- and (2-Ferrocenyl)indenyl Rhodium Isomers

A series of heterobimetallic complexes of general structure [RhL(2){eta(5)-(2-ferrocenyl)indenyl}] (L(2)=cod, nbd, L=CO; cod=cyclooctadiene; nbd=norbornadiene) has been synthesised with the aim of tuning the metal-metal interaction in their mixed-valence ions generated both by chemical and electrochemical oxidation, and the results are compared with those obtained for [RhL(2){eta(5)-(1-ferrocenyl)indenyl}] isomers. Crystallographic studies and DFT calculations provide a detailed description of the structural and electronic features of these complexes evidencing a significant difference in the extent of planarity of the flexible bridging ligand between the 1- and 2-ferrocenyl isomers. Independent experimental probes, in particular the potential splitting in the cyclic voltammograms and the IT bands in the near-IR spectra, are rationalised in the framework of Marcus-Hush theory and at quantum chemistry level by DFT and TD-DFT methods. These methods allow us to establish a trend based on the magnitude of iron-rhodium electronic coupling H(ab) ranging from valence trapped to almost delocalised ions. The quasi planar bridge and the olefin ancillary ligands make [Rh(nbd){eta(5)-(2-ferrocenyl)indenyl}](+) and [Rh(cod){eta(5)-(2-ferrocenyl)indenyl}](+) rare examples of heterobimetallic systems which can be classified as borderline Class II/Class III species.

Electronic Transitions in [Re6S8X6]4- (X = Cl, Br, I): Results from Time-Dependent Density Functional Theory and Solid-State Calculations

Relativistic time-dependent density functional theory (TDDFT) calculations were performed on the excited states of the [Re6S8X6](4-) (X = Cl, Br, I) series. For all members of the series, the lowest excited states in the spectra do not correspond to a ligand-to-metal (or ligand-to-cluster) excitation but rather a cluster-cluster transition from the HOMO e(g) to antibonding t(1u) orbitals with only a modest admixture of Re-X sigma* character. These results lead to a re-evaluation of the role of the axial ligand in these compounds. The calculated excitation energies reproduce the experimental absorption and emission spectra. This work also confirms previous TDDFT calculations on the emission energies. Results for discrete cluster ions are compared with those obtained from calculations in the solid state in Cs4[Re6S8X6].CsX (X = Cl, Br) and Cs4[Re6S8I6].2CsI. Significant differences are seen in the relatively higher energies of the antibonding t(1u) orbital in the solid-state case, and an inversion in the orbital character of the two allowed absorptions is calculated. The e(g) (HOMO)-to-a(2g) (LUMO) orbital energy differences corresponding to the emission transition are quite comparable for the solid state and discrete cluster calculations, and both overestimate the observed emission energy by the same margin.

Calculation of excitation energies of open-shell molecules with spatially degenerate ground states. I. Transformed reference via an intermediate configuration Kohn-Sham density-functional theory and applications to d1 and d2 systems with octahedral and tetrahedral symmetries

A method for calculating the UV-vis spectra of molecules with spatially degenerate ground states using time-dependent density-functional theory (TDDFT) is proposed. The new transformed reference via an intermediate configuration Kohn-Sham TDDFT (TRICKS-TDDFT) method avoids the difficulties caused by the multireference nature of spatially degenerate states by rather than utilizing the ground state instead taking a nondegenerate excited state with desirable properties as the reference for the TDDFT calculation. The scope and practical application of the method are discussed. Like all open-shell TDDFT calculations this method at times suffers from the inability to produce transitions to states that are eigenfunctions of the total spin operator. A technique for alleviating this difficulty to some extent is proposed. The applicability and accuracy of the TRICKS-TDDFT method is demonstrated through example calculations of several d(1) and d(2) transition metal complexes with tetrahedral and octahedral symmetries. For the most part, the results of these calculations are similar in quality to to those obtained from standard TDDFT calculations.