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 Mn(V) 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 Mn(V) triplet state and a Mn(IV)O(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 Mn(V) → Mn(IV) 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.

Investigation of the excited-state decay dynamics of transition-metal systems is a crucial step for the development of photoswitchable molecular based materials with applications in growing fields as energy conversion, data storage, or molecular devices. The photophysics of these systems is an entangled problem arising from the interplay of electronic and geometrical rearrangements that take place on a short time scale. Several factors play a role in the process: various electronic states of different spin and chemical character are involved, the system undergoes important structural variations and several nonradiative processes can occur. Computational chemistry is a useful tool to get insight into the microscopic description of the photophysics of these materials, since it provides unique information about the character of the electronic spin states involved, the energetics and time evolution of the system. In this review article, we present an overview of the state of the art methodologies available to address the several aspects that have to be incorporated to properly describe the deactivation of excited states in transition-metal complexes. The most recent developments in theoretical methods are discussed and illustrated with examples.

Spin-orbit couplings have been calculated in twenty snapshots of a molecular dynamics trajectory of [Fe(bpy)] to address the importance of geometrical distortions and second-order spin-orbit coupling on the intersystem crossing rate constants in the light-induced spin crossover process. It was found that the effective spin-orbit coupling between the MLCT andT state is much larger than the direct coupling in the symmetric structure, which opens the possibility of a direct MLCT-T deactivation without the intervention of triplet metal-centered states. Based on the calculated deactivation times, we conclude that both the direct pathway and the one involving intermediate triplet states are active in the ultrafast population of the metastable HS state, bringing in agreement two experimental observations that advocate for either deactivation mechanism. This resolves a long-standing dispute about the deactivation mechanism of Fe(ii)-polypyridyl complexes in particular, and about light-induced magnetism in transition metal complexes in general.

ABSTRACT:The relative stability of high-spin and low-spin states has been studied in a series of Fe(II) complexes with model ligands of different σ donation strength. The natural (delocalized) orbitals are transformed to atomic-like orbitals to analyze the multiconfigurational wave function in a valence bond picture. This analysis reveals a direct relation between the stabilization of the low-spin state and the importance of the ligand-to-metal charge transfer in the σ orbitals. The multiconfigurational second-order perturbation theory (CASPT2) energy dependence of the low-spin state as function of the Fe-ligand distance deviates significantly from coupled cluster (CCSD(T)) calculations. This is ascribed to the intrinsic multiconfigurational character of the wave function of the low-spin state, invalidating the use of the simple closed-shell reference in the coupled cluster calculations.

A computational strategy is presented to describe excited states, involving the transfer of an electron from one metallic site to a neighboring metal center, the so-called metal-to-metal charge-transfer (MMCT) states. An accurate ab initio treatment of these states in transition metal compounds is intrinsically difficult for both time-dependent density functional and wave function-based methods. The rather large dependence of the MMCT energies on the applied functional makes difficult to extract reliable estimates from density functional theory, while the standard multiconfigurational approach (complete active space SCF + second-order perturbation theory) leads to severe intruder state problems and unrealistic, negative energies. The analysis of the failure of the multiconfigurational approach shows that the state-average orbitals are biased toward the ground state and strongly deficient to describe the MMCT state. We propose a method to improve the orbitals by gradually approaching as much as possible the state-specific description of the MMCT state in the reference wave function for the second-order perturbation treatment of the dynamic electron correlation

Accurate electronic structure calculations of the lowest excited states have been performed on twenty snapshots of a molecular dynamics simulation of [Fe(bpy)3](2+) dissolved in water. The thermal motion distorts the structure of the complex from its average D3 symmetry, causing the localization on one bipyridine ligand of the excited electron in the metal-to-ligand charge transfer (MLCT) state. The excitation energy is about 0.25 eV lower than that for the delocalized description of the MLCT state and is in good agreement with experiments. The composition of the MLCT band is carefully analyzed and the effect of thermal motion on the mechanism of light-induced spin crossover is discussed.

We developed a procedure that combines three complementary computational methodologies to improve the theoretical description of the electronic structure of nickel oxide. The starting point is a Car-Parrinello molecular dynamics simulation to incorporate vibrorotational degrees of freedom into the material model. By means of complete active space self-consistent field second-order perturbation theory (CASPT2) calculations on embedded clusters extracted from the resulting trajectory, we describe localized spectroscopic phenomena on NiO with an efficient treatment of electron correlation. The inclusion of thermal motion into the theoretical description allows us to study electronic transitions that, otherwise, would be dipole forbidden in the ideal structure and results in a natural reproduction of the band broadening. Moreover, we improved the embedded cluster model by incorporating self-consistently at the complete active space self-consistent field (CASSCF) level a discrete (or direct) reaction field (DRF) in the cluster surroundings. The DRF approach offers an efficient treatment of electric response effects of the crystalline embedding to the electronic transitions localized in the cluster. We offer accurate theoretical estimates of the absorption spectrum and the density of states around the Fermi level of NiO, and a comprehensive explanation of the source of the broadening and the relaxation of the charge transfer states due to the adaptation of the environment.