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Orbital entanglement and CASSCF analysis of the Ru-NO bond in a Ruthenium nitrosyl complex.

Freitag L, Knecht S, Keller SF, Delcey MG, Aquilante F, Pedersen TB, Lindh R, Reiher M, González L - Phys Chem Chem Phys (2015)

Bottom Line: Based on the configurations and orbital occupation numbers obtained for the CASSCF wavefunction and on the orbital entropy measurements evaluated for the DMRG wavefunction, we unravel electron correlation effects in the Ru coordination sphere of the complex.The electron configuration of Ru is an equally weighted superposition of Ru(II) and Ru(III) configurations, with the Ru(III) configuration originating from charge donation mostly from Cl ligands.However, and contrary to what is typically assumed, the electronic configuration of the NO ligand is best described as electroneutral.

View Article: PubMed Central - PubMed

Affiliation: Institut für theoretische Chemie, Universität Wien, Währinger Str. 17, 1090 Vienna, Austria. leticia.gonzalez@univie.ac.at.

ABSTRACT
Complete active space self-consistent field (CASSCF) wavefunctions and an orbital entanglement analysis obtained from a density-matrix renormalisation group (DMRG) calculation are used to understand the electronic structure, and, in particular, the Ru-NO bond of a Ru nitrosyl complex. Based on the configurations and orbital occupation numbers obtained for the CASSCF wavefunction and on the orbital entropy measurements evaluated for the DMRG wavefunction, we unravel electron correlation effects in the Ru coordination sphere of the complex. It is shown that Ru-NO π bonds show static and dynamic correlation, while other Ru-ligand bonds feature predominantly dynamic correlation. The presence of static correlation requires the use of multiconfigurational methods to describe the Ru-NO bond. Subsequently, the CASSCF wavefunction is analysed in terms of configuration state functions based on localised orbitals. The analysis of the wavefunctions in the electronic singlet ground state and the first triplet state provides a picture of the Ru-NO moiety beyond the standard representation based on formal oxidation states. A distinct description of the Ru and NO fragments is advocated. The electron configuration of Ru is an equally weighted superposition of Ru(II) and Ru(III) configurations, with the Ru(III) configuration originating from charge donation mostly from Cl ligands. However, and contrary to what is typically assumed, the electronic configuration of the NO ligand is best described as electroneutral.

No MeSH data available.


Active space orbitals and their respective occupation numbers used in the optimization of the S0 (a) and T1 (b) electronic states using CASSCF calculations. Panel (c) shows the additional orbitals used in the DMRG(18,18)[512]-SCF calculation. Double-shell d orbitals are indicated with a prime. The remaining orbitals correspond to those in column (a).
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fig1: Active space orbitals and their respective occupation numbers used in the optimization of the S0 (a) and T1 (b) electronic states using CASSCF calculations. Panel (c) shows the additional orbitals used in the DMRG(18,18)[512]-SCF calculation. Double-shell d orbitals are indicated with a prime. The remaining orbitals correspond to those in column (a).

Mentions: The choice of the CASSCF active space is motivated by its feasibility for a configuration analysis of the Ru coordination sphere. Accordingly, all Ru 4d orbitals and the ligand orbitals interacting with them must be included, resulting in a total active space of 13 orbitals with 16 electrons (denoted (16,13)), including the five Ru 4d orbitals, two pairs of NO π and π* orbitals, one pair of indazole π and π* orbitals, one combination of p orbitals on the Cl atoms (denoted σCl) as well as the NO σ orbital. The last two orbitals are particularly important because they participate in the covalent bond formed between the metal and the NO and Cl ligands, respectively; accordingly, each of them mixes with the dz2 and the dx2–y2 orbitals of the Ru atom, respectively. A fair comparison of the CASSCF wavefunction analyses on the S0 and T1 geometry should be done using the same active spaces in both calculations. For RuHIndNO, this can be only achieved in the S0 calculation by a state-average (SA)-CASSCF calculation over the lowest three singlet states. Thus, the T1 calculation was similarly averaged over three states, to ensure that the deterioration of the wavefuction quality due to state averaging is similar in both spin states. The resulting orbitals and corresponding natural orbital occupation numbers of the optimised S0 and T1 geometries are collected in Fig. 1a and b, respectively.


Orbital entanglement and CASSCF analysis of the Ru-NO bond in a Ruthenium nitrosyl complex.

Freitag L, Knecht S, Keller SF, Delcey MG, Aquilante F, Pedersen TB, Lindh R, Reiher M, González L - Phys Chem Chem Phys (2015)

Active space orbitals and their respective occupation numbers used in the optimization of the S0 (a) and T1 (b) electronic states using CASSCF calculations. Panel (c) shows the additional orbitals used in the DMRG(18,18)[512]-SCF calculation. Double-shell d orbitals are indicated with a prime. The remaining orbitals correspond to those in column (a).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4447059&req=5

fig1: Active space orbitals and their respective occupation numbers used in the optimization of the S0 (a) and T1 (b) electronic states using CASSCF calculations. Panel (c) shows the additional orbitals used in the DMRG(18,18)[512]-SCF calculation. Double-shell d orbitals are indicated with a prime. The remaining orbitals correspond to those in column (a).
Mentions: The choice of the CASSCF active space is motivated by its feasibility for a configuration analysis of the Ru coordination sphere. Accordingly, all Ru 4d orbitals and the ligand orbitals interacting with them must be included, resulting in a total active space of 13 orbitals with 16 electrons (denoted (16,13)), including the five Ru 4d orbitals, two pairs of NO π and π* orbitals, one pair of indazole π and π* orbitals, one combination of p orbitals on the Cl atoms (denoted σCl) as well as the NO σ orbital. The last two orbitals are particularly important because they participate in the covalent bond formed between the metal and the NO and Cl ligands, respectively; accordingly, each of them mixes with the dz2 and the dx2–y2 orbitals of the Ru atom, respectively. A fair comparison of the CASSCF wavefunction analyses on the S0 and T1 geometry should be done using the same active spaces in both calculations. For RuHIndNO, this can be only achieved in the S0 calculation by a state-average (SA)-CASSCF calculation over the lowest three singlet states. Thus, the T1 calculation was similarly averaged over three states, to ensure that the deterioration of the wavefuction quality due to state averaging is similar in both spin states. The resulting orbitals and corresponding natural orbital occupation numbers of the optimised S0 and T1 geometries are collected in Fig. 1a and b, respectively.

Bottom Line: Based on the configurations and orbital occupation numbers obtained for the CASSCF wavefunction and on the orbital entropy measurements evaluated for the DMRG wavefunction, we unravel electron correlation effects in the Ru coordination sphere of the complex.The electron configuration of Ru is an equally weighted superposition of Ru(II) and Ru(III) configurations, with the Ru(III) configuration originating from charge donation mostly from Cl ligands.However, and contrary to what is typically assumed, the electronic configuration of the NO ligand is best described as electroneutral.

View Article: PubMed Central - PubMed

Affiliation: Institut für theoretische Chemie, Universität Wien, Währinger Str. 17, 1090 Vienna, Austria. leticia.gonzalez@univie.ac.at.

ABSTRACT
Complete active space self-consistent field (CASSCF) wavefunctions and an orbital entanglement analysis obtained from a density-matrix renormalisation group (DMRG) calculation are used to understand the electronic structure, and, in particular, the Ru-NO bond of a Ru nitrosyl complex. Based on the configurations and orbital occupation numbers obtained for the CASSCF wavefunction and on the orbital entropy measurements evaluated for the DMRG wavefunction, we unravel electron correlation effects in the Ru coordination sphere of the complex. It is shown that Ru-NO π bonds show static and dynamic correlation, while other Ru-ligand bonds feature predominantly dynamic correlation. The presence of static correlation requires the use of multiconfigurational methods to describe the Ru-NO bond. Subsequently, the CASSCF wavefunction is analysed in terms of configuration state functions based on localised orbitals. The analysis of the wavefunctions in the electronic singlet ground state and the first triplet state provides a picture of the Ru-NO moiety beyond the standard representation based on formal oxidation states. A distinct description of the Ru and NO fragments is advocated. The electron configuration of Ru is an equally weighted superposition of Ru(II) and Ru(III) configurations, with the Ru(III) configuration originating from charge donation mostly from Cl ligands. However, and contrary to what is typically assumed, the electronic configuration of the NO ligand is best described as electroneutral.

No MeSH data available.