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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.


Single-orbital entropy, s(1), and mutual information, I, in the DMRG(16,13)[1000] (equivalent to the CASSCF) wavefunction of RuHIndNO. The size of the red circles next to the orbitals correlates with the magnitude of the corresponding single-orbital entropy. The lines connecting the dots represent the mutual information: solid lines indicate strong entanglement (I > 0.1), dashed grey lines stand for middle entanglement (0.01 > I > 0.1) and dotted green lines indicate weak entanglement (0.001 > I > 0.01). The line width is also proportional to the absolute value of I.
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fig4: Single-orbital entropy, s(1), and mutual information, I, in the DMRG(16,13)[1000] (equivalent to the CASSCF) wavefunction of RuHIndNO. The size of the red circles next to the orbitals correlates with the magnitude of the corresponding single-orbital entropy. The lines connecting the dots represent the mutual information: solid lines indicate strong entanglement (I > 0.1), dashed grey lines stand for middle entanglement (0.01 > I > 0.1) and dotted green lines indicate weak entanglement (0.001 > I > 0.01). The line width is also proportional to the absolute value of I.

Mentions: Fig. 4 shows the single-orbital entropies and mutual information for the S0 structure, as defined in eqn (1)–(3), as obtained from the DMRG(16,13)[1000] calculation. One can immediately recognise that orbitals 4, 5, 9 and 10 (corresponding to the dxz,yz ± πx,y* orbitals) have the largest single-orbital entropy (as indicated by the size of the corresponding red circles in Fig. 4), while e.g. orbital 3 (dxy) shows very low entropy. Orbitals 4, 5, 9 and 10 also show high entanglement with each other, and additionally 9 and 10 are also entangled with the πx,y orbitals, labelled 1 and 2. Large single-orbital entropies and strong entanglement with more than one orbital are a signature of static correlation. In contrast, small single-orbital entropies combined with weak entanglement among many orbitals or strong entanglement between two orbitals only is an indication of dynamic correlation. Accordingly, the πx,y – dxz,yz – πx,y* orbitals (1, 2, 4, 5, 9, 10), corresponding to two Ru–NO π bonds, are strongly entangled (i.e. interact strongly) and are responsible for static correlation. The entanglement of the orbitals 1 with 9 and 2 with 10 is due to dynamic correlation, as expected from ππ* pairs. One can distinguish other orbital pairs which show largely dynamic correlation, i.e. have smaller single-orbital entropy and are strongly entangled only with each other, but not with other orbitals of the active space, such as orbitals 7 and 11 (πInd and πInd*, which are again a textbook example of dynamic correlation), 6 and 12 (dx2–y2 ± σCl) and 8 and 13 (dz2 ± σ). The latter two orbital pairs correspond to Ru bonds with chlorido ligands and the Ru–NO σ bond. The single-orbital entropy values correlate well with the deviation of the occupation numbers from 2 or 0 (recall Fig. 1a). The orbitals with the largest deviation (4, 5, 9, 10) show both static and dynamic correlation, whereas orbitals with smaller deviations (7 and 11, 6 and 12, 8 and 13) show mostly dynamic correlation.


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)

Single-orbital entropy, s(1), and mutual information, I, in the DMRG(16,13)[1000] (equivalent to the CASSCF) wavefunction of RuHIndNO. The size of the red circles next to the orbitals correlates with the magnitude of the corresponding single-orbital entropy. The lines connecting the dots represent the mutual information: solid lines indicate strong entanglement (I > 0.1), dashed grey lines stand for middle entanglement (0.01 > I > 0.1) and dotted green lines indicate weak entanglement (0.001 > I > 0.01). The line width is also proportional to the absolute value of I.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig4: Single-orbital entropy, s(1), and mutual information, I, in the DMRG(16,13)[1000] (equivalent to the CASSCF) wavefunction of RuHIndNO. The size of the red circles next to the orbitals correlates with the magnitude of the corresponding single-orbital entropy. The lines connecting the dots represent the mutual information: solid lines indicate strong entanglement (I > 0.1), dashed grey lines stand for middle entanglement (0.01 > I > 0.1) and dotted green lines indicate weak entanglement (0.001 > I > 0.01). The line width is also proportional to the absolute value of I.
Mentions: Fig. 4 shows the single-orbital entropies and mutual information for the S0 structure, as defined in eqn (1)–(3), as obtained from the DMRG(16,13)[1000] calculation. One can immediately recognise that orbitals 4, 5, 9 and 10 (corresponding to the dxz,yz ± πx,y* orbitals) have the largest single-orbital entropy (as indicated by the size of the corresponding red circles in Fig. 4), while e.g. orbital 3 (dxy) shows very low entropy. Orbitals 4, 5, 9 and 10 also show high entanglement with each other, and additionally 9 and 10 are also entangled with the πx,y orbitals, labelled 1 and 2. Large single-orbital entropies and strong entanglement with more than one orbital are a signature of static correlation. In contrast, small single-orbital entropies combined with weak entanglement among many orbitals or strong entanglement between two orbitals only is an indication of dynamic correlation. Accordingly, the πx,y – dxz,yz – πx,y* orbitals (1, 2, 4, 5, 9, 10), corresponding to two Ru–NO π bonds, are strongly entangled (i.e. interact strongly) and are responsible for static correlation. The entanglement of the orbitals 1 with 9 and 2 with 10 is due to dynamic correlation, as expected from ππ* pairs. One can distinguish other orbital pairs which show largely dynamic correlation, i.e. have smaller single-orbital entropy and are strongly entangled only with each other, but not with other orbitals of the active space, such as orbitals 7 and 11 (πInd and πInd*, which are again a textbook example of dynamic correlation), 6 and 12 (dx2–y2 ± σCl) and 8 and 13 (dz2 ± σ). The latter two orbital pairs correspond to Ru bonds with chlorido ligands and the Ru–NO σ bond. The single-orbital entropy values correlate well with the deviation of the occupation numbers from 2 or 0 (recall Fig. 1a). The orbitals with the largest deviation (4, 5, 9, 10) show both static and dynamic correlation, whereas orbitals with smaller deviations (7 and 11, 6 and 12, 8 and 13) show mostly dynamic correlation.

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.