Spin-state energetics and spin-crossover behavior of pseudotetrahedral cobalt(III)-imido complexes. The role of the tripodal supporting ligand

DFT calculations have underscored the importance of the tripodal supporting ligand in tuning the spin-state energetics of pseudotetrahedral transition metal imido complexes. In particular, we have focused on Co(III)-imido complexes, where our best estimate (OLYP) of the singlet-triplet splitting varies from 0.75 eV for a trisphosphine complex (1) and 0.3 eV for a tris(N-heteroyclic-carbene) complex (2) to essentially 0.0 eV for a hydrotris(pyrazolyl)borate (3) complex. The experimentally studied analogues of 1, 2, and 3 all exhibit S = 0 ground states; however, the experimental analogue of 3 exhibits spin-crossover behavior due to a low-lying S = 1 state. Interestingly, whereas all the pure functionals examined successfully predict nearly equienergetic singlet end triplet states for 3, the hybrid functionals B3LYP and O3LYP exhibit a clear (and incorrect) preference for the S = 2 state. In addition, we have also carried out an exploratory survey of Cr(III), Mn(III), and Fe(III) imido complexes with trisphosphine and hydrotris(pyrazolyl)borate (Tp) supporting ligands. Among the more interesting predictions of this study is that an FeIII(Tp)(imido) species should exhibit a high-spin S = 5/2 ground state, which would be unique for an iron-imido complex.     

Calibration of DFT Functionals for the Prediction of Fe Mössbauer Spectral Parameters in Iron-Nitrosyl and Iron-Sulfur Complexes: Accurate Geometries Prove Essential

Six popular density functionals in conjunction with the conductor-like screening (COSMO) solvation model have been used to obtain linear M?ssbauer isomer shift (IS) and quadrupole splitting (QS) parameters for a test set of 20 complexes (with 24 sites) comprised of nonheme nitrosyls (Fe-NO) and non-nitrosyl (Fe-S) complexes. For the first time in an IS analysis, the Fe electron density was calculated both directly at the nucleus, ρ(0)(N), which is the typical procedure, and on a small sphere surrounding the nucleus, ρ(0)(S), which is the new standard algorithm implemented in the ADF software package. We find that both methods yield (near) identical slopes from each linear regression analysis but are shifted with respect to ρ(0) along the x-axis. Therefore, the calculation of the Fe electron density with either method gives calibration fits with equal predictive value. Calibration parameters obtained from the complete test set for OLYP, OPBE, PW91, and BP86 yield correlation coefficients (r(2)) of approximately 0.90, indicating that the calibration fit is of good quality. However, fits obtained from B3LYP and B3LYP* with both Slater-type and Gaussian-type orbitals are generally found to be of poorer quality. For several of the complexes examined in this study, we find that B3LYP and B3LYP* give geometries that possess significantly larger deviations from the experimental structures than OLYP, OPBE, PW91 or BP86. This phenomenon is particularly true for the di- and tetranuclear Fe complexes examined in this study. Previous M?ssbauer calibration fit studies using these functionals have usually included mononuclear Fe complexes alone, where these discrepancies are less pronounced. An examination of spin expectation values reveals B3LYP and B3LYP* approach the weak-coupling limit more closely than the GGA exchange-correlation functionals. The high degree of variability in our calculated S(2) values for the Fe-NO complexes highlights their challenging electronic structure. Significant improvements to the isomer shift calibrations are obtained for B3LYP and B3LYP* when geometries obtained with the OLYP functional are used. In addition, greatly improved performance of these functionals is found if the complete test set is grouped separately into Fe-NO and Fe-S complexes. Calibration fits including only Fe-NO complexes are found to be excellent, while those containing the non-nitrosyl Fe-S complexes alone are found to demonstrate less accurate correlations. Similar trends are also found with OLYP, OPBE, PW91, and BP86. Correlations between experimental and calculated QSs were also investigated. Generally, universal and separate Fe-NO and Fe-S fit parameters obtained to determine QSs are found to be of good to excellent quality for every density functional examined, especially if [Fe(4)(NO)(4)(μ(3)-S)(4)](-) is removed from the test set.     

Binding of CO, NO, and O2 to heme by density functional and multireference ab initio calculations

Using the CASSCF/CASPT2 approach, along with several DFT methods (PBE0, B3LYP, BP86, OLYP), we have investigated the bonding of CO, NO, and O2 molecules to two model heme systems: an iron(II) porphyrin with and without an axial imidazole ligand. The experimentally available binding energies are best reproduced by the CASPT2 method and with the OLYP functional. The other functionals considered perform much worse, either severely overbinding (BP86) or underbinding (B3LYP, PBE0). Significant discrepancies between the different density functionals are observed, not only for the energetics but sometimes also for structure predictions. This confirms our viewpoint that a balanced treatment of the electronic exchange and correlation is vital to describe the weak metal-ligand bond between heme and CO, NO, or O2. The binding energies DeltaEb were split into two contributions: the so-called spin-pairing energy DeltaE sp and the "inherent" binding energy DeltaEb0, and both contributions were analyzed in terms of method and basis set effects. We have also investigated the spin density distributions resulting from the bonding of the NO molecule (a noninnocent ligand) to heme. Our analysis at the DFT and CASSCF level shows that, while various density functionals predict qualitatively very different spin distributions, the CASSCF spin populations most closely correspond to the results obtained with the pure BP86 or OLYP rather than with the hybrid functionals.     

Broken symmetry density functional study of a mixed‐valence unsymmetrical dinuclear iron complex

Density functional theory (DFT) calculations with different exchange‐correlation functionals were performed for a mixed valence Fe(II)/Fe(III) binuclear complex with μ‐methoxo and two μ‐carboxylate bridging ligands, (1) with geometry optimizations being performed for all possible spin multiplicities (M_S = 2, 4, 6, 8, and 10). Within the exchange‐correlation functionals studied, only the hybrid GGA functionals B3P and B3LYP and also the pure GGA functional RPBE, predicts the geometry with high spin (S = 9/2) to be more stable than the geometry with low spin state (S = 1/2) by 20 kcal/mol, in agreement with the experimental findings. These functionals also predict the same stability order for the different spin states, being M_S = 10>8>6>2>4. The meta‐GGA functionals TPSS and TPSSh and also the pure GGA functionals BLYP and BP86 predict different stability orders. The computed average EPR g‐tensor, g_av, of 2.03, at the B3LYP level, is in good agreement with the experimental findings. Heisenberg exchange coupling constants, J, were calculated within the broken‐symmetry formalism, at the B3LYP level, showing that the two iron centers are antiferromagnetic coupling, with a very weak coupling constant of about ?7 cm^?1, in good agreement with the experimental value. Additionally, the effect of using different multiplicities of the reference geometries on the computed J value is discussed. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Density functional theory study of trans-dioxo complexes of iron, ruthenium, and osmium with saturated amine ligands, trans-[M(O)2(NH3)2(NMeH2)2]2+ (M=Fe, Ru, Os), and detection of [Fe(qpy)(O)2]n+ (n=1, 2) by high-resolution ESI mass spectrometry

Density functional theory (DFT) calculations on trans-dioxo metal complexes containing saturated amine ligands, trans-[M(O)2(NH3)2(NMeH2)2]2+ (M=Fe, Ru, Os), were performed with different types of density functionals (DFs): 1) pure generalized gradient approximations (pure GGAs): PW91, BP86, and OLYP; 2) meta-GGAs: VSXC and HCTH407; and 3) hybrid DFs: B3LYP and PBE1PBE. With pure GGAs and meta-GGAs, a singlet d2 ground state for trans-[Fe(O)2(NH3)2(NMeH2)2]2+ was obtained, but a quintet ground state was predicted by the hybrid DFs B3LYP and PBE1PBE. The lowest transition energies in water were calculated to be at lambda approximately 509 and 515 nm in the respective ground-state geometries from PW91 and B3LYP calculations. The nature of this transition is dependent on the DFs used: a ligand-to-metal charge-transfer (LMCT) transition with PW91, but a pi(Fe-O)-->pi*(Fe-O) transition with B3LYP, in which pi and pi* are the bonding and antibonding combinations between the dpi(Fe) and ppi(O(2-)) orbitals. The FeVI/V reduction potential of trans-[Fe(O)2(NH3)2NMeH2)2]2+ was estimated to be +1.30 V versus NHE based on PW91 results. The [Fe(qpy)(O)2](n+) (qpy=2,2':6',2':6',2':6',2'-quinquepyridine; n=1 and 2) ions, tentatively assigned to dioxo iron(V) and dioxo iron(VI), respectively, were detected in the gas phase by high-resolution ESI-MS spectroscopy.     

Relative energy of the high-(5T2g) and low-(1A1g) spin states of the ferrous complexes [Fe(L)(NHS4)]: CASPT2 versus density functional theory

High-level ab initio calculations using multiconfigurational perturbation theory [complete active space with second-order perturbation theory (CASPT2)] were performed on the transition energy between the lowest high-spin (corresponding to (5T2g) in Oh) and low-spin (corresponding to 1A1g in Oh) states in the series of six-coordinated Fe(II) molecules [Fe(L)(NHS4)], where NHS4 is 2,2'-bis(2-mercaptophenylthio)diethylamine dianion and L=NH3, N2H4, PMe3, CO, and NO+. The results are compared to (previous and presently obtained) results from density functional theory (DFT) calculations with four functionals, which were already shown previously by Casida and co-workers [Fouqueau et al., J. Chem. Phys. 120, 9473 (2004); Ganzenmuller et al., ibid. 122, 234321 (2005); Fouqueau et al., ibid. 122, 044110 (2005); Lawson Daku et al., ChemPhysChem 6, 1393 (2005)] to perform well for the spin-pairing problem in these and other Fe(II) complexes, i.e., OLYP, PBE0, B3LYP, and B3LYP*. Very extended basis sets were used both for the DFT and CASPT2 calculations and were shown to be necessary to obtain quantitative results with both types of method. This work presents a sequel to a previous DFT/CASPT2 study of the same property in the complexes [Fe(H2O)6]2+, [Fe(NH3)6]2+, and [Fe(bpy)3]2+ [Pierloot et al., J. Chem. Phys. 125, 124303 (2006)]. The latter work was extended with new results obtained with larger basis sets and including the OLYP functional. For all considered complexes, the CASPT2 method predicts the correct ground state spin multiplicity. Since experimental data for the actual quintet-singlet (free) energy differences are not available, the performance of the different DFT functionals was judged based on the comparison between the DFT and CASPT2 results. From this, it was concluded that the generalized gradient OLYP functional performs remarkably well for the present series of ferrous compounds, whereas the success of the three hybrid functionals varies from case to case.     

Evaluation of exchange‐correlation functionals in comparison to B3LYP for the description of silicon and Cu‐doped silicon clusters

Several developed exchange‐correlation functionals in density functional theory have been systematically applied to describe the geometries and electronic properties of small silicon (Si_n+1, n < 5) and doped silicon (CuSi_n) clusters. The performance of the various approaches is done with their critical comparison with B3LYP and available high level wave function methods. Our calculations indicate that all functional give reasonable results. Further, OLYP/6‐311+G* approach generally agrees with B3LYP results. The good performance of OLYP is of significant interest knowing that the hybrid functionals are computationally more demanding than nonhybrid schemes. So, we recommend OLYP/6‐311+G* approach for studying the doped silicon clusters and understanding the electronic properties of silicon by the presence of doped metal impurities. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Comparison of density functionals for the study of the high spin low spin gap in Fe(III) spin crossover complexes

A detailed investigation of the accuracy of different quantum mechanical methods for the study of iron(III) spin crossover complexes is presented. The energy spin state gap between the high and low spin states; ΔE (HS‐LS) of nine iron(III) quinolylsalicylaldiminate complexes were calculated with nine different DFT functionals, then compared. DFT functionals: B3LYP, B3LYP‐D3, B3LYP*, BH&HLYP, BP86, OLYP, OPBE, M06L, and TPSSh were tested with six basis sets: 3‐21G*, dgdzvp, 6‐31G**, cc‐pVDZ, Def2TZVP, and cc‐pVTZ. The cations from the X‐ray crystal structures of [Fe(qsal‐OMe)₂]Cl·MeCN·H₂O, [Fe(qsal‐OMe)₂]Cl·2MeOH·0.5H₂O, [Fe(qsal‐OMe)₂]BF₄·MeOH, [Fe(qsal‐OMe)₂]NCS·CH₂Cl₂, [Fe(qsal‐F)₂]NCS, [Fe(qsal‐Cl)₂]NCS·MeOH, [Fe(qsal‐Br)₂]NCS·MeOH, [Fe(qsal‐I)₂]OTf·MeOH, and [Fe(qsal)₂]NCS?CH₂Cl₂ were used as starting structures. The results show that B3LYP, B3LYP‐D3, OLYP, and OPBE with a 6‐31G**, Def2TZVP, and cc‐pVTZ basis set give reasonable results of ΔE (HS‐LS) compared with the experimental data. The enthalpy of [Fe(qsal‐I)₂]⁺ calculated with an OLYP functional and cc‐pVTZ basis set (1.48 kcal/mol) most closely matches the experimental data (1.34 kcal/mol). B3LYP* yields an enthalpy of 5.92 kcal/mol suggesting it may be unsuitable for these Fe(III) complexes, mirroring recent results by Kepp (Inorg . Chem ., 2016, 55 , 2717–2727).     

Assessment of the OLYP and O3LYP density functionals for first-row transition metals

We have investigated the performance of the OLYP and O3LYP density functionals for predicting atomic excitation energies and ionization potentials, and bond dissociation energies, geometries, and vibrational frequencies for selected first-row transition metal compounds, including hydrides (MH) and singly charged methylene and methyl cations. The OLYP and O3LYP functionals are similar to the well-known BLYP and B3LYP functionals, respectively, but use a new optimized exchange functional (OPTX) developed by Handy and Cohen (Mol Phys 2001, 99, 403) in place of the standard B88 exchange. A previous study by us on organic reactions (J Chem Phys 2002, 117, 1331) indicated that both OLYP and O3LYP gave results for heats of reaction and barrier heights that were overall superior to those using the popular B3LYP functional. For transition metals, however, although OLYP is overall superior to BLYP for molecular calculations, it is inferior to B3LYP. O3LYP provides results for molecules of about the same quality as B3LYP. For atomic excitation and 4s ionization energies, unless relativistic effects are included, OLYP and O3LYP are clearly worse than both BLYP and B3LYP. There is thus no real incentive to use either OLYP or O3LYP in place of B3LYP for calculations involving first-row transition metals.     

Assessment of density functionals for the high-spin/low-spin energy difference in the low-spin iron(II) tris(2,2'-bipyridine) complex.

In the iron(II) low-spin complex [Fe(bpy)3]2+, the zero-point energy difference between the 5T2g(t4(2g)e2g) high-spin and the 1A(1g)(t(6)2g) low-spin states, Delta(E)0HL, is estimated to lie in the range of 2500-5000 cm(-1). This estimate is based on the low-temperature dynamics of the high-spin-->low-spin relaxation following the light-induced population of the high-spin state and on the assumption that the bond-length difference between the two states Delta(r)HL is equal to the average value of approximately 0.2 A, as found experimentally for the spin-crossover system. Calculations based on density functional theory (DFT) validate the structural assumption insofar as the low-spin-state optimised geometries are found to be in very good agreement with the experimental X-ray structure of the complex and the predicted high-spin geometries are all very close to one another for a whole series of common GGA (PB86, PW91, PBE, RPBE) and hybrid (B3LYP, B3LYP*, PBE1PBE) functionals. This confirmation of the structural assumption underlying the estimation of Delta(E)0HL from experimental relaxation rate constants permits us to use this value to assess the ability of the density functionals for the calculation of the energy difference between the HS and LS states. Since the different functionals give values from -1000 to 12000 cm(-1), the comparison of the calculated values with the experimental estimate thus provides a stringent criterion for the performance of a given functional. Based on this comparison the RPBE and B3LYP* functionals give the best agreement with experiment.     

Computational study of iron bis(dithiolene) complexes: redox non-innocent ligands and antiferromagnetic coupling

The molecular and electronic structure of monomeric ([Fe(S2C2H2)2](z), [Fe(S2C2(C6H4-p-OCH3)2)2](z)) and dimeric ([{Fe(S2C2H2)2}2](z)) iron bis(dithiolene) complexes, and of their phosphine adducts ([(PH3)Fe(S2C2H2)2](z), [(P(C6H5)3)Fe(S2C2H2)2](z), [(PH3)Fe(S2C2(C6H4-p-OCH3)2)2](z)), carrying various charges (z = 0, 1-, 2-), have been investigated by density functional theory (DFT). Net total spin polarization values S of zero, two, and four have been considered for all neutral model compounds and their dianions, whereas all monoanions have been examined with net total spin polarization values S of one, three, and five. The DFT calculations utilized the pure functional BP86, as well as the hybrid functionals B3LYP and B3LYP*. For the monomers, the calculations reveal the presence of redox non-innocent dithiolene ligands and antiferromagnetic coupling between the ligands and the metal center. For the dimers, complexes with antiferromagnetically coupled iron centers have been found to represent structures of low energy, if not lowest energy structures. The spin-coupling constant of [{Fe(S2C2H2)2}2](2-) is calculated as J = -230 cm(-1). On the basis of the computational results, a model for reversible, electrochemically controlled binding and release of phosphine ligands to iron bis(dithiolene) complexes is proposed. Only BP86 and B3LYP* results, but not those of B3LYP calculations, are in qualitative agreement with experimental findings. BP86 calculations provide the best quantitative match in comparison with the experiment.     

(57)Fe Mössbauer isomer shifts of heme protein model systems: electronic structure calculations

We report the results of density functional theory (DFT) calculations of the (57)Fe M?ssbauer isomer shifts (delta(Fe)) for a series of 24 inorganic, organometallic, and metalloprotein/metalloporphyrin model systems in S = 0, (1)/(2), 1, (3)/(2), 2, and (5)/(2) spin states. We find an excellent correlation between calculation and experiment over the entire 2.34 mm s(-1) range of isomer shifts: a 0.07-0.08 mm s(-1) rms deviation between calculation and experiment (corresponding to 3-4% of the total delta(Fe) range, depending on the functionals used) with R(2) values of 0.973 and 0.981 (p < 0.0001). The best results are obtained by using the hybrid exchange-correlation functional B3LYP, used previously for (57)Fe M?ssbauer quadrupole splittings and (57)Fe NMR chemical shifts and chemical shielding anisotropies. The relativistically corrected value of alpha, alpha(rel), converges with the large basis set used in this work, but the exact values vary somewhat with the methods used: -0.253 a(0)(3) mm s(-1) (Hartree-Fock; HF); -0.316 a(0)(3) mm s(-1) (hybrid HF-DFT; B3LYP), or -0.367 a(0)(3) mm s(-1) (pure DFT; BPW91). Both normal and intermediate spin state isomer shifts are well reproduced by the calculations, as is the broad range of delta(Fe) values: from [Fe(VI)O(4)](2-) (-0.90 mm s(-1) expt; -1.01 mm s(-1) calc) to KFe(II)F(3) (1.44 mm s(-1) expt; 1.46 mm s(-1) calc). Molecular orbital analyses of all inorganic solids as well as all organometallic and metalloporphyrin systems studied reveal that there are three major core MO contributions to rho(tot)(0), the total charge density at the iron nucleus (and hence delta(Fe)), that do not vary with changes in chemistry, while the valence MO contributions are highly correlated with delta(Fe) (R(2) = 0.915-0.938, depending on the functionals used), and the correlation between the valence MO contributions and the total MO contribution is even better (R(2) = 0.965-0.976, depending on the functionals used). These results are of general interest since they demonstrate that DFT methods now enable the accurate prediction of delta(Fe) values in inorganic, organometallic, and metalloporphyrin systems in all spin states and over a very wide range of delta(Fe) values with a very small rms error.     

Theoretical study of the Fe(phen)(2)(NCS)(2) spin-crossover complex with reparametrized density functionals

The theoretical study of spin-crossover compounds is very challenging as those parts of the experimental findings that concern the electronic structure of these compounds can currently hardly be reproduced because of either technical limitations of highly accurate ab initio methods or because of inaccuracies of density functional methods in the prediction of low-spin/high-spin energy splitting. However, calculations with reparametrized density functionals on molecules of the thermal spin-crossover type can give improved results when compared with experiment for close-lying states of different spin and are therefore important for, e.g., transition metal catalysis. A classification of transition metal compounds within hybrid density functional theory is given to distinguish standard, critical, and complicated cases. From the class of complicated cases we choose the prominent spin-crossover compound Fe(phen)(2)(NCS)(2) and show in a first step how the electronic contribution to the energy splitting can be calculated. In a second step, the vibrational effects on the spin flip are investigated within the harmonic force-field approximation of the isolated-molecule approach. A main result of the study is the necessity of exact-exchange reduction in hybrid density functionals to arrive at reasonable electronic energy splittings. The study resolves problems that originated from the use of standard density functionals, which are not able to reproduce the electronic contribution to the low-spin/high-spin splitting correctly, and demonstrates to which extent reparametrized density functionals can be used for the prediction of the spin-crossover effect.     

香豆素衍生物的荧光发射能计算及XC泛函的合理选择

采用含时密度泛函理论(TDDFT)与单激发组态相互作用(CIS)处理相结合的计算方案对香豆素系列15种已知荧光化合物的发射能进行了系统考察. 结果表明, 发射能与吸收能一样, 其计算值主要取决于交换-相关(XC)泛函的选择. 只要泛函选用得当, 在使用较小基组的TDDFT/6-31G(d)//CIS/3-21G(d)理论水平上即可使绝大部分化合物的实验发射能在精度达0.16 eV以内得以重现. 与吸收能计算不同的是, 无法选用单一的一种泛函来对全系列化合物的发射能作出满意的理论预测. 激发态无明显电荷转移的、7位上有氨(或胺)基取代或有氮原子相连的化合物, 其适用泛函为不含Hartree-Fock(HF)交换能的纯泛函OLYP和BLYP. 而激发态发生较大程度电荷转移的、3 位上有共轭取代基的衍生物, 其适用泛函则为含20%的HF交换成分的混合泛函B3LYP. 因此, 发射能计算中的XC泛函选择, 应同时考虑取代基团效应以及激发态的电子结构特征. 其中, 发射能计算值受XC泛函中HF交换能比例的影响十分敏感. 文中还对激发能计算中的溶剂效应校正方案和激发态几何优化精度的影响进行了讨论.     

Mössbauer quadrupole splittings and electronic structure in heme proteins and model systems: a density functional theory investigation

We report the results of a series of density functional theory (DFT) calculations aimed at predicting the (57)Fe M?ssbauer electric field gradient (EFG) tensors (quadrupole splittings and asymmetry parameters) and their orientations in S = 0, (1)/(2), 1, (3)/(2), 2, and (5)/(2) metalloproteins and/or model systems. Excellent results were found by using a Wachter's all electron basis set for iron, 6-311G for other heavy atoms, and 6-31G for hydrogen atoms, BPW91 and B3LYP exchange-correlation functionals, and spin-unrestricted methods for the paramagnetic systems. For the theory versus experiment correlation, we found R(2) = 0.975, slope = 0.99, intercept = -0.08 mm sec(-)(1), rmsd = 0.30 mm sec(-)(1) (N = 23 points) covering a DeltaE(Q) range of 5.63 mm s(-)(1) when using the BPW91 functional and R(2) = 0.978, slope = 1.12, intercept = -0.26 mm sec(-)(1), rmsd = 0.31 mm sec(-)(1) when using the B3LYP functional. DeltaE(Q) values in the following systems were successfully predicted: (1) ferric low-spin (S = (1)/(2)) systems, including one iron porphyrin with the usual (d(xy))(2)(d(xz)d(yz))(3) electronic configuration and two iron porphyrins with the more unusual (d(xz)d(yz))(4)(d(xy))(1) electronic configuration; (2) ferrous NO-heme model compounds (S = (1)/(2)); (3) ferrous intermediate spin (S = 1) tetraphenylporphinato iron(II); (4) a ferric intermediate spin (S = (3)/(2)) iron porphyrin; (5) ferrous high-spin (S = 2) deoxymyoglobin and deoxyhemoglobin; and (6) ferric high spin (S = (5)/(2)) metmyoglobin plus two five-coordinate and one six-coordinate iron porphyrins. In addition, seven diamagnetic (S = 0, d(6) and d(8)) systems studied previously were reinvestigated using the same functionals and basis set scheme as used for the paramagnetic systems. All computed asymmetry parameters were found to be in good agreement with the available experimental data as were the electric field gradient tensor orientations. In addition, we investigated the electronic structures of several systems, including the (d(xy))(2)(d(xz),d(yz))(3) and (d(xz),d(yz))(4)(d(xy))(1) [Fe(III)/porphyrinate](+) cations as well as the NO adduct of Fe(II)(octaethylporphinate), where interesting information on the spin density distributions can be readily obtained from the computed wave functions.     

Copper corroles: the question of noninnocence

In this paper, the results are presented from a comparative study of the electronic and geometric structure of copper corroles by means of either density functional theory (DFT, using both pure and hybrid functionals) and multiconfigurational ab initio methods, starting from either a complete active space (CASSCF) or restricted active space (RASSCF) reference wave function and including dynamic correlation by means of second-order perturbation theory (CASPT2/RASPT2). DFT geometry optimizations were performed for the lowest singlet and triplet states of copper corrole, both unsubstituted and meso-substituted with three phenyl groups. The effect of saddling on the electronic structure was investigated by comparing the results obtained for planar (C(2v)) and saddled (C(2)) structures. With DFT, the origin of the saddling distortion is found to be dependent on the applied functional: covalent Cu 3d-corrole π interactions with pure functionals (BP86, OLYP), antiferromagnetic exchange coupling between an electron in the corrolate (C(2)) b type π orbital, and an unpaired Cu(II) 3d electron with hybrid functionals (B3LYP, PBE0). The CASPT2 results essentially confirm the suggestion from the hybrid functionals that copper corroles are noninnocent, although the contribution of diradical character to the copper-corrole bond is found to be limited to 50% or less. The lowest triplet state is calculated at 0-10 kcal/mol and conform with the experimental observation (variable temperature NMR) that this state should be thermally accessible.     

Proper Choice of XC Functionals and Calculations of Fluorescence-Emitting Energies for Coumarin Derivatives

A scheme of time-dependent density functional theory (TDDFT) combined with single-excitation configuration interaction (CIS) approach was employed to make a detailed investigation of the emitting energy for fifteen well-known coumarin derivatives. The results showed that the predicted emitting energies as well as the absorption ones were dominated mainly by the exchange-correlation (XC) functional to be used. So long as a functional is properly chosen, the experimental emitting energy of most derivatives can be accurately reproduced within 0.16 eV by a calculation at the TDDFT/6-31G(d)//CIS/3-21G(d) theoretical level. It was found that, nevertheless, the hybrid functional, B3LYP, well predicted the absorption energies for all the fifteen coumarin derivatives but none of the functionals could work equally well for the emitting energy calculations. Two pure functionals, OLYP and BLYP, yield good emitting energies for the 7-aminocoumarins or derivatives with a N atom connected to 7-position, which exhibit inconspicuous charge transfer (CT) in their excited states, whereas the B3LYP hybrid functional, with 20% Hartree-Fock (HF) exchange energy, performs significantly better than OLYP and BLYP for those 3-substituted coumarins with larger CT in excited states. Thus, in comparison with the absorption energies, the selection of proper functionals for the emitting energy calculations becomes more complex. In all probability, it is effective and doable to choose an XC-functional with alterable fraction of HF exchange energy according to the composition and structure characteristics of molecule.     

Mapping the d-d excited-state manifolds of transition metal beta-diiminato-imido complexes. Comparison of density functional theory and CASPT2 energetics

Trigonal-planar, middle transition metal diiminato-imido complexes do not exhibit high-spin states, as might be naively expected on the basis of their low coordination numbers. Instead, the known Fe(III), Co(III), and Ni(III) complexes exhibit S = 3/2, S = 0, and S = 1/2 ground states, respectively. Kohn-Sham DFT calculations have provided a basic molecular orbital picture of these compounds as well as a qualitative rationale for the observed spin states. Reported herein are ab initio multiconfiguration second-order perturbation theory (CASPT2) calculations, which provide a relatively detailed picture of the d-d excited-state manifolds of these complexes. Thus, for a C(2v) Fe(III)(diiminato)(NPh) model complex, two near-degenerate states ((4)B(2) and (4)B(1)) compete as contenders for the ground state. Moreover, the high-spin sextet, two additional quartets and even a low-spin doublet all occur at <0.5 eV, relative to the ground state. For the Co(III) system, although CASPT2 reproduces an S = 0 ground state, as observed experimentally for a related complex, the calculations also predict two exceedingly low-energy triplet states; there are, however, no other particularly low-energy d-d excited states. In contrast to the Fe(III) and Co(III) cases, the Ni(III) complex has a clearly nondegenerate (2)B(2) ground state. The CASPT2 energetics provide benchmarks against which we can evaluate the performance of several common DFT methods. Although none of the functionals examined perform entirely satisfactorily, the B3LYP hybrid functional provides the best overall spin-state energetics.