Quan Manh Phung

A Multiconfigurational Perturbation Theory and Density Functional Theory Study on the Heterolytic Dissociation Enthalpy of First-Row Metallocenes.

The heterolytic dissociation enthalpy of a series of first-row metallocenes M(C5H5)2, M = V, Mn, Fe, and Ni, was studied by (restricted) multiconfigurational perturbation theory and density functional theory. The results were compared directly to the experimental values, taking into account all necessary contributions to the relative energy. Of the tested functionals, B3LYP performs best in reproducing the binding energy, while the PBE0 functional gives the best structures. High quality multiconfigurational perturbation calculations were also carried out, demonstrating the superior performance of a larger, restricted active space. The spin crossover behavior of manganocene is correctly predicted by multiconfigurational perturbation theory as opposed to the three functionals B3LYP, PBE0, and M06, which (severely) overstabilize the high-spin with respect to the low-spin state.

Spin State Energetics in First-Row Transition Metal Complexes: Contribution of (3s3p) Correlation and Its Description by Second-Order Perturbation Theory

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.

Cumulant Approximated Second-Order Perturbation Theory Based on the Density Matrix Renormalization Group for Transition Metal Complexes: A Benchmark Study

The complete active space second order perturbation theory (CASPT2) can be extended to larger active spaces by using the density matrix renormalization group (DMRG) as solver. Two variants are commonly used: the costly DMRG-CASPT2 with exact 4-particle reduced density matrix (4-RDM) and the cheaper DMRG-cu(4)-CASPT2 in which the 4-cumulant is discarded. To assess the accuracy and limitations of the latter variant DMRG-cu(4)-CASPT2 we study the spin state energetics of iron porphyrin Fe(P) and its model compound FeL2, a model for the active center of NiFe hydrogenase, and manganese-oxo porphyrin MnO(P)(+); a series of excited states of chromium hexacarbonyl Cr(CO)6; and the interconversion of two Cu2O2(2+) isomers. Our results clearly show that PT2 on top of DMRG is essential in order to obtain quantitative results for transition metal complexes. Good results were obtained with DMRG-cu(4)-CASPT2 as compared to full CASPT2 and DMRG-CASPT2 in calculations with small- and medium-sized active spaces. In calculations with large-sized active spaces (∼30 active orbitals), the performance of DMRG-cu(4)-CASPT2 is less impressive due to the errors originating from both the finite number of renormalized states m and the 4-RDM approximation.

Spin State Energetics and Oxyl Character of Mn-Oxo Porphyrins by Multiconfigurational ab Initio Calculations: Implications on Reactivity

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.

Theoretical Study of the Dissociation Energy of First-Row Metallocenium Ions

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.

Toward Highly Accurate Spin State Energetics in First-Row Transition Metal Complexes: A Combined CASPT2/CC Approach

In previous work on the performance of multiconfigurational second-order perturbation theory (CASPT2) in describing spin state energetics in first-row transition metal systems [ Pierloot et al. J. Chem. Theory Comput. 2017 , 13 , 537 - 553 ], we showed that standard CASPT2 works well for valence correlation but does not describe the metal semicore (3s3p) correlation effects accurately. This failure is partially responsible for the well-known bias toward high-spin states of CASPT2. In this paper, we expand our previous work and show that this bias could be partly removed with a combined CASPT2/CC approach: using high-quality CASPT2 with extensive correlation-consistent basis sets for valence correlation and low-cost CCSD(T) calculations with minimal basis sets for the metal semicore (3s3p) correlation effects. We demonstrate that this approach is efficient by studying the spin state energetics of a series of iron complexes modeling important intermediates in oxidative catalytic processes in chemistry and biochemistry. On the basis of a comparison with bare CCSD(T) results from this and previous work, the average error of the CASPT2/CC approach is estimated at around 2 kcal mol-1 in favor of high spin states.

Dinuclear Iron(II) Spin‐Crossover Compounds: A Theoretical Study

The structures and spin-state energetics of two di-iron(II) complexes based on thiadiazole and oxadiazole ligands in different crystals were studied by using density functional theory and second-order perturbation theory based on the density matrix renormalization group approach (DMRG-CASPT2). When taking into account all different contributions to the relative energy, our theoretical approach is capable of providing results that are in excellent agreement with established experimental data. In all cases, we correctly describe the ground state of the complexes as well as predict their spin-crossover behavior. A comparison between the two complexes in the gas phase and in different crystals shows how the structures change by moving from the gas phase to different crystals and reveals a large impact of the crystal stabilization on the relative spin-state energy. This theoretical work also demonstrates the applicability of the DMRG-CASPT2 approach to quantitatively study the spin-state energetics of multinuclear transition-metal complexes.