This paper presents an in-depth study of the performance of multiconfigurational second-order perturbation theory (CASPT2, NEVPT2) in describing spin state energetics in first-row transition metal (TM) systems, including bare TM ions, TM ions in a field of point charges (TM/PC), and an extensive series of TM complexes, where the main focus lies on the (3s3p) correlation contribution to the relative energies of different spin states. To the best of our knowledge, this is the first systematic NEVPT2 investigation of TM spin state energetics. CASPT2 has been employed in several previous studies but was regularly found to be biased toward high spin states. The bias was attributed to a too low value of the so-called IPEA shift ϵ, an empirical correction in the CASPT2 zeroth-order Hamiltonian with a standard value of 0.25 hartree. Based on comparisons with experiment (TM ions) and calculations with the multireference configuration interaction (TM ions and TM/PC systems) and coupled-cluster (TM complexes) methods, we demonstrate in this work that standard CASPT2 works well for valence correlation and that its bias toward high-spin states is caused by an erratic description of (3s3p) correlation effects. The latter problem only occurs for spin transitions involving a ligand field (de)excitation, not in bare TM ions. At the same time the (3s3p) correlation contribution also becomes strongly ϵ dependent. The error can be reduced by increasing ϵ but only at the expense of deteriorating the CASPT2 description of valence correlation in the TM complexes. The alternative NEVPT2 method works well for bare TM and TM/PC systems, but its results for the TM complexes are disappointing, with large errors both for the valence and (3s3p) correlation contributions to the relative energies of different spin states.

Important electromeric states in manganese-oxo porphyrins MnO(P)+ and MnO(PF4)+ (porphyrinato or meso-tetrafluoroporphyrinato) have been investigated with correlated ab initio methods (CASPT2, RASPT2), focusing on their possible role in multistate reactivity patterns in oxygen transfer (OAT) reactions. Due to the lack of oxyl character, the MnV singlet ground state is kinetically inert. OAT reactions should therefore rather proceed through thermally accessible triplet and quintet states that have a more pronounced oxyl character. Two states have been identified as possible candidates: a MnV triplet state and a MnIVO(L•a2u)+ quintet state. The latter state is high-lying in MnO(P)+ but is stabilized by the substitutions of H by F at the meso carbons (where the a2u orbital has a significant amplitude). Oxyl character and Mn–O bond weakening in these two states stems from the fact that the Mn–O π* orbitals become singly (triplet) or doubly occupied (quintet). Moreover, an important role for the reactivity of the triplet state is also likely to be played by the π bond that has an empty π* orbital, because of the manifest diradical character of this π bond, revealed by the CASSCF wave function. Interestingly, the diradical character of this bond increases when the Mn–O bond is stretched, while the singly occupied π* orbital looses its oxygen radical contribution. The RASPT2 results were also used as a benchmark for the description of excited state energetics and Mn–O oxyl character with a wide range of pure and hybrid density functionals. With the latter functionals both the MnV → MnIV promotion energy and the diradical character of the π bond (with empty π*) are found to be extremely dependent on the contribution of exact exchange. For this reason, pure functionals are to be preferred.

The bond dissociation energy of a series of metallocenium ions, i.e., the energy difference of the reaction MCp2+ → MCp+ + Cp· (with M = Ti, V, Cr, Mn, Fe, Co, and Ni), was studied by means of multiconfigurational perturbation theory (CASPT2, RASPT2, NEVPT2) and restricted coupled cluster theory (CCSD(T)). From a comparison between the results obtained from these different methods, and a detailed analysis of their treatment of electron correlation effects, a set of MCp+–Cp binding energies are proposed with an accuracy of 5 kcal/mol. The computed results are in good agreement with the experimental data measured by threshold photoelectron photoion coincidence (TPEPICO) spectroscopy but disagree with the more recent threshold collision-induced dissociation (TCID) experiments.

Ligand-field and charge-transfer spectra of N-heterocyclic pentacyanoferrate(II) complexes [Fe(CN)5L]n− were investigated using multiconfigurational perturbation theory. The spectrum of [Fe(CN)5(py)]3– was studied in detail under vacuum and in the following polarizable continuum model (PCM) simulated solvents: acetone, acetonitrile, dimethylsulfoxide (DMSO), ethanol, methanol, and water. The ligand-field states proved to be rather insensitive to the solvent environment, whereas much stronger solvent effects were observed for the charge-transfer (CT) transitions. The nature of the intense band was confirmed as a metal-to-ligand charge transfer originating from a 3dxz → πb1* (L)-orbital transition. The difference between the calculated and experimental transition energy of this CT transition is minimal for aprotic solvents, but increases strongly with the solvent proton donor ability in the protic solvents. In an attempt to improve the description of this CT state, up to 14 solvent molecules were explicitly included in the quantum model. In DMSO, the spectra of complexes with ligands L (where L is pyridine, 4-picoline, 4-acetylpyridine, 4-cyanopyridine, pyrazine, and N-methylpyrazinium) correlate very well with the experiment.

Reaction of NO with amorphous Mn(TPP) layers gives two Mn(TPP)(NO) isomers with linear and bent Mn–N–O geometries that reversibly interconvert with changes in temperature. DFT computations predict that the linear complex is the singlet ground state while the bent structure is a triplet state.

Manganese(V)–oxo corrole and corrolazine have been studied with ab initio multiconfiguration reference methods (CASPT2 and RASPT2) and large atomic natural orbital (ANO) basis sets. The calculations confirm the expected singlet dδ2 ground states for both complexes and rule out excited states within 0.5 eV of the ground states. The lowest excited states are a pair of Mn(V) triplet states with dδ1dπ1 configurations 0.5–0.75 eV above the ground state. Manganese(IV)–oxo macrocycle radical states are much higher in energy, ≥1.0 eV relative to the ground state. The macrocyclic ligands in the ground states of the complexes are thus unambiguously ‘innocent’. The approximate similarity of the spin state energetics of the corrole and corrolazine complexes suggests that the latter macrocycle on its own does not afford any special stabilization for the MnVO center. The remarkable stability of an MnVO octaarylcorrolazine thus appears to be ascribable to the steric protection afforded by the β-aryl groups.

A series of model transition-metal complexes, CrF6, ferrocene, Cr(CO)6, ferrous porphin, cobalt corrole, and FeO/FeO–, have been studied using second-order perturbation theory based on a restricted active space self-consistent field reference wave function (RASPT2). Several important properties (structures, relative energies of different structural minima, binding energies, spin state energetics, and electronic excitation energies) were investigated. A systematic investigation was performed on the effect of: (a) the size and composition of the global RAS space, (b) different (RAS1/RAS2/RAS3) subpartitions of the global RAS space, and (c) different excitation levels (out of RAS1/into RAS3) within the RAS space. Calculations with active spaces, including up to 35 orbitals, are presented. The results obtained with smaller active spaces (up to 16 orbitals) were compared to previous and current results obtained with a complete active space self-consistent field reference wave function (CASPT2). Higly accurate RASPT2 results were obtained for the heterolytic binding energy of ferrocene and for the electronic spectrum of Cr(CO)6, with errors within chemical accuracy. For ferrous porphyrin the intermediate spin 3A2g ground state is (for the first time with a wave function-based method) correctly predicted, while its high magnetic moment (4.4 μB) is attributed to spin–orbit coupling with very close-lying 5A1g and 3Eg states. The toughest case met in this work is cobalt corrole, for which we studied the relative energy of several low-lying Co(II)–corrole π radical states with respect to the Co(III) ground state. Very large RAS spaces (25–33 orbitals) are required for this system, making compromises on the size of RAS2 and/or the excitation level unavoidable, thus increasing the uncertainty of the RASPT2 results by 0.1–0.2 eV. Still, also for this system, the RASPT2 method is shown to provide distinct improvements over CASPT2, by overcoming the strict limitations in the size of the active space inherent to the latter method.

The recently developed second-order perturbation theory restricted active space (RASPT2) method has been benchmarked versus the well-established complete active space (CASPT2) approach. Vertical excitation energies for valence and Rydberg excited states of different groups of organic (polyenes, acenes, heterocycles, azabenzenes, nucleobases, and free base porphin) and inorganic (nickel atom and copper tetrachloride dianion) molecules have been computed at the RASPT2 and multistate (MS) RASPT2 levels using different reference spaces and compared with CASPT2, CCSD, and experimental data in order to set the accuracy of the approach, which extends the applicability of multiconfigurational perturbation theory to much larger and complex systems than previously. Relevant aspects in multiconfigurational excited state quantum chemistry such as the valence−Rydberg mixing problem in organic molecules or the double d-shell effect for first-row transition metals have also been addressed.

The accuracy of the relative spin-state energetics of three small FeII or FeIII heme models from multiconfigurational perturbation theory (CASPT2) and density functional theory with selected functionals (including the recently developed M06 and M06-L functionals) was assessed by comparing with recently available coupled cluster results. While the CASPT2 calculations of spin-state energetics were found to be very accurate for the studied FeIII complexes (including FeP(SH), a model of the active site of cytochrome P450 in its resting state), there is a strong indication of a systematic error (around 5 kcal/mol) in favor of the high-spin state for the studied FeII complexes (including FeP(Im), a model of the active site of myoglobin). A larger overstabilization of the high-spin states was observed for the M06 and M06-L functionals, up to 22 and 11 kcal/mol, respectively. None of the tested density functionals consistently provides a better accuracy than CASPT2 for all model complexes.

In this paper, the results are presented from a comparative study of the electronic and geometric structure of copper correles 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 (C2v) and saddled (C2) 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 (C2) b type π orbital, and an unpaired CuII 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.

The structural, electronic and magnetic properties of two different models of the heterospin polymer chain complexes of Cu2+ hexafluoroacetylacetonate with two pyrazole-substituted nitronyl nitroxides Cu(hfac)2LR have been studied by means of multiconfigurational perturbation theory based on a CASSCF (complete active space self-consistent field) wave function, i.e. the CASPT2 method. Our calculations reveal the presence of two minima in the electronic energy curve along the Cu−OL bond, separated by only 6 kcal/mol, and corresponding to the X-ray structures of the CuO6 centers in Cu(hfac)2LPr at 115 and 293 K, respectively. The two energetic minima are characterized by a different electronic structure, thus giving rise to a different three-spin exchange coupling and explaining the thermally induced spin transitions in this family of compounds. The concomitant variations in the magnetic properties, i.e. g factors and magnetic moments μeff(T) were calculated and compared with the experimental data of Cu(hfac)2LPr. Even if the correspondence is only qualitative, our calculations provide a convincing explanation of the observed magnetic peculiarities. In particular, at low temperatures, the predicted ground-state is 2Au, well separated from the 2Ag, 4Au states and therefore exclusively populated. Its calculated g factors, g∥ = 1.848, g⊥ = 1.965, 1.974, qualitatively correspond to the observed g < 2 signals in the low-temperature EPR spectra. The previously assumed formal spin assignment >N−O•−Cu−•O−N< for these linear spin triads is challenged by our calculations, pointing instead to a more important role of the end-standing NO in the exchange interactions with Cu(II).

A theoretical study is presented of the electronic spectra of the complexes UO2Cl2ac4, UO2Cl2ac3, [UO2Cl3ac2]− and [UO2Cl3ac]− (ac = acetone) using perturbation theory based on a complete-active-space type wavefunction (CASSCF/CASPT2). Both scalar relativistic effects and spin–orbit coupling were included in the calculations. The calculated excitation energies and oscillator strength values have been compared to the experimental absorption spectrum for uranyl chloride complexes in acetone solution, for chloride-to-uranyl ratios between two and three. The main purpose of this work was to investigate the origin of the remarkable intensity increase observed in the lower part of the experimental absorption spectra, upon addition of chloride to uranyl complexes in acetone. The calculated excitation energies for the different complexes are similar and closely correspond to the experimental data. However, in none of the theoretical spectra, the high intensities observed in the lower part of the experimental spectrum are reproduced.

Reaction of NO with amorphous Mn(TPP) layers gives two Mn(TPP)(NO) isomers with linear and bent Mn–N–O geometries that reversibly interconvert with changes in temperature. DFT computations predict that the linear complex is the singlet ground state while the bent structure is a triplet state.