Bonding Nature and Electron Delocalization of An(COT)2, An = Th, Pa

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Bonding Nature and Electron Delocalization of An(COT)2, An = Th, Pa, U Day
an P
aez-Hern
andez,* Juliana A. Murillo-L
opez, and Ramiro Arratia-P
erez* Departamento de Ciencias Químicas, Facultad de Ciencias Exactas, Universidad Andr
es Bello, Rep
ublica 275, Santiago, Chile

bS Supporting Information ABSTRACT: A systematic study of a series of An(COT)2 compounds, where An = Th, Pa, U, and COT represents cyclooctatetraene, has been performed using relativistic density functional theory. The ZORA Hamiltonian was applied for the inclusion of relativistic effects, taking into account all of the electrons for the optimization and explicitly including spin
orbit coupling effects. Time-dependent density functional theory (TDDFT) was used to calculate the excitation energies with the GGA SAOP functional, and the electronic transitions were analyzed using double group irreducible representations. The calculated excitation energies are in perfect correlation with the increment of the ring delocalization as it increases along the actinide series. These results are sufficient to ensure that, for these complexes, the increment in delocalization, as indicated by ELF bifurcation and NICS analysis, leads to a shift in the maximum wavelength of absorption in the visible region. Also, delocalization in the COT ring increases along the actinide series, so the systems become more aromatic because of a modulation induced by the actinides.

’ INTRODUCTION In 1968, the first 5f aromatic system was synthesized, uranium(IV) bis(cyclooctatetraene), U(COT)2, by Streitwieser and M€uller-Westerhoff.1
4 Since then, U(COT)2 and its 5f analogues have been extensively studied, and bis(cyclooctatetraene) derivatives of the AnIV elements are now also known for Th, Pa, Np, and Pu.3 A qualitative discussion of the electronic structure of these compounds was given in the original report, in which the electronic structure was supposed to be similar to that of the bis(cyclopentadienyl) iron series, except that the orbitals of the rings and of the metal involved in bonding had one additional node in going around the main symmetry axis of the molecule.2 The principal 5f orbital
π ligand interaction was considered to be between the ligand e2u combination and the fxyz and fz(x2
y2) (fz) orbitals of the metal, this being similar in character to the well-known e1g ligand
dxz, dyz metal interaction in the lighter metallocenes.3 The actinide elements have special properties because of the 5f orbital participation in their complexes. For instance, uranocene is extremely air-sensitive, enflaming in air, so that it is essential to exclude all traces of air during all operations with it. It is rapidly decomposed by aqueous bases and strong acids, but it is slowly hydrolyzed in neutral water, because, in its bonding scheme, both the highest occupied and lowest unoccupied orbitals are predominantly 5f uranium orbitals. Thus, reactions with many reagents will occur at the metal, resulting in the cleavage of the metal
ligand bonds.4 Because of the experimental difficulties inherent in the study of An(COT)2 compounds,1,5 high-quality theoretical methods can play an important role in elucidating the molecular properties of these compounds. Crystallographic studies have shown that uranocene has D8h symmetry, and this point group has been used to propose the symmetry of other actinocenes. The f n (n = 0, 1, r 2011 American Chemical Society

2) electron configurations and high symmetry of these complexes simplify the theoretical interpretation of their bonding, electronic, and spectral properties, thus providing the opportunity to carry out benchmarking theoretical studies.2,6,7 An aspect of relevance in the theoretical treatment of these compounds is the spin
orbit coupling that affects their electronic structure, absorption spectrum selection rules, and magnetic properties, which has been related to the existence of multiconfigurational ground states. Despite the good agreement between theoretical and experimental studies concerning metal
ligand bonding, there is no clear experimental determination of the 5f-level ordering and the amount of interaction between fσ, fπ, and fj atomic orbitals and ligand orbitals. This is because spin
orbit interactions and electron
electron repulsion considerably complicate the upper part of the energy level scheme of actinocenes.2,6,7 The metal
ligand bonding can be characterized by electronicdensity-based techniques. In the present contribution, two approaches are used to discuss the chemical bonding. The first is the electron localization function (ELF) approach of Becke and Edgecombe8,9 that can be defined in terms of the excess of local kinetic energy density due to the Pauli exclusion principle, T(F(r)), and the Thomas
Fermi kinetic energy density, which can be regarded as a “renormalization” factor, Th(F(r)), and is written in the Lorentzian form as "




ELF ¼ 1 þ

TðrÞ Th ðrÞ

2 #


Received: April 25, 2011 Revised: July 7, 2011 Published: July 14, 2011 8997

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Figure 1. Actinide complex configuration with D8h symmetry.

Second is the nucleus-independent chemical shift (NICS), which is a useful index for analyzing electronic delocalization.10
15 The NICS is a generalization of the chemical shift into an induced scalar field, where the nuclear shielding tensor is well-defined in all points of space, not only at the positions of the nuclei.10 Our aim was to perform a systematic study of a series of compounds of the form An(COT)2, where An = Th, Pa, U. Herein, we present the optimized geometrical parameters, bonding nature, electronic density properties, and absorption spectra for these complexes. All results are based on scalar and spin
orbit relativistic calculations, as implemented in the ADF code. Electron delocalization was studied through the calculation of NICS indexes and the ELF.

’ THEORETICAL MODEL AND COMPUTATIONAL DETAILS To study the fn systems interacting with a COT2 ligand in a D8h environment (Figure 1), we considered taking into account relativistic effects in the electronic structure and spectroscopic properties of two sets of models with different An oxidation states. One set contains early actinides with maximum oxidation states, namely, Th(IV), Pa(V), and U(VI), and the other set considers the f0, f1, and f2 configurations corresponding to Th(IV), Pa(IV), and U(IV), respectively. All structural and electronic properties were obtained using the Amsterdam Density Functional (ADF) code,16 where the relativistic scalar and spin
orbit effects were incorporated by the zeroth-order regular approximation (ZORA Hamiltonian). All molecular structures were fully optimized by an analytical energy gradient method as implemented by Verluis and Ziegler, using the local density approximation (LDA) within the Vosko
Wilk
Nusair parametrization for local exchange correlations.17
19 The Perdew
Burke
Ernzerhof (PBE) generalized gradient approximation exchange-correlation functional was used.20 Geometry optimizations were calculated by a standard Slater-type-orbital (STO) basis set with triple-ζ quality double plus polarization functions (TZ2P) for all atoms.21 Calculations on open-shell systems were performed using spin-unrestricted methods. In all cases, frequency analyses were performed after the geometry optimization, in which we obtained only positive frequencies, thus verifying local minima. Two different population analysis algorithms were applied for the calculation of the charge distribution: Hirshfeld and Voronoi cells (VDD).16,22,23 These methods are based on the electronic density analysis and do

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not explicitly use the basis functions for the charge distribution calculation. They proved to be numerically very similar and to yield chemically meaningful charges.22,23 Time-dependent density functional theory (TDDFT) was employed to calculate the excitation energies.24,25 We also used the GGA SAOP (statistical average of orbitals exchange correlation potential) functional that was specially designed for the calculation of optical properties.26,27 In this case, the excitation energies were estimated by spin
orbit time-dependent perturbation density functional theory. Calculations of the electron localization function (ELF) were performed with the DGrid 4.4 program,28 and the results were visualized with MOLEKEL 5.4 software.29 As noted above, the Lorentzian form of the ELF confines its values within the [0,1] interval, thereby facilitating its analysis and interpretation. A region of space with a high value of the ELF corresponds to a region where it is more probable to localize an electron or a pair of electrons. In this case, the Pauli principle has little influence on their behavior, and the excess local kinetic energy has a low value. In contrast, at the boundaries between such regions, the probability of repulsion of the electrons is rather high, the excess local kinetic energy has a high value, and the ELF has its minimum. To better understand the aromaticity, the electron delocalization can be obtained through the ELF bifurcation analysis.30 The bifurcation points have been interpreted as a measure of interaction among the different basins and, chemically, as a measure of electron delocalization.31 On the other hand, Nucleus-independent chemical shifts (NICS) were obtained by calculating NMR shielding values with the gauge-independent atomic orbital (GIAO)32
34 method using the generalized gradient approximation OPBE35 functional, which was specially designed for the calculation of chemical shifts. These calculations were performed at the plane of the ring, NICS(0); at a distance of 1.0 Å above the perpendicular plane of the ring toward the actinide metal, NICS (1); and at a distance of 1.0 Å above the ring away from the metal, NICS (
1). Negative NICS values indicate the presence of diatropic rings currents, which is interpreted as aromaticity, whereas positive values denote paratropic ring current, which is interpreted as antiaromaticity.10
15,36 In addition to the shielding tensor isotropic value, the σzz component was determined. This value gives a measure of the electronic currents around the principal axes of the molecule.

’ RESULTS AND DISCUSSION Geometry and Electronic Structure. The geometries calculated using both functionals were in agreement with experimental results. These geometries are reported in Tables 1 and 2 for closed- and open-shell complexes, respectively, where d(M
COT) is the distance from the metal to the COT centroid. Although the experimental geometry of Pa(COT)2 is unavailable for comparison, the d(Pa
COT) value obtained in our calculations lies between the experimental d(An
COT) distances of Th(COT)2 (2.004 Å) and U(COT)2 (1.923 Å), which augurs well for the validity of this methodology. In general, the d(An
COT) values from the LDA are, as is typical, too short. By using the average geometric parameters of Th(COT)2 and U(COT)2 as a gauge, the PBE exchange-correlation functional seems to be the best choice for the Pa(COT)2 system. Comparing Tables 1 and 2, it can be seen that the distance d(An
COT) in closed-shell complexes is shorter than that in open-shell complexes because of the lower electronic density 8998

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Table 1. Structural Parameter Optimization of Closed-Shell Systems system Th(COT)2 LDA

d(M
COT)

d[M
C(COT)]

d(COT
COT)

(Å)

(Å)

(Å)

4.003

2.001

2.716

PBE

2.048

2.761

4.096

expt5

2.004

2.701

4.007

LDA

1.886

2.629

3.772

PBE

1.934

2.675

3.867

1.819 1.891

2.583 2.645

3.638 3.782

Pa(COT)2+

U(COT)22+ LDA PBE

Table 2. Structural Parameter Optimization of Open-Shell Systems system

d(M
COT) (Å) d[M
C(COT)] (Å) d(COT
COT) (Å)

Pa(COT)2 LDA

1.921

2.637

3.842

PBE

1.983

2.711

3.966

expta

1.964

2.674

LDA PBE

1.945 1.957

2.694 2.683

3.890 3.922

expt5

1.924

2.647

3.847

U(COT)2

a

Average value between the distances reported for Th and U.

Table 3. Charge Transfer (CT) Obtained from All Actinide Complexesa complex

a

Hirshfeld

Voronoi

Th
IV

3.37

3.72

Pa
IV

3.30

3.59

U
IV Pa
V

3.36 4.20

3.62 4.48

U
VI

5.22

5.50

CT = qM(free)
qM(complex).

repulsion between the metal and the ring. This fact can be analyzed in terms of the metal
ring charge transfer. As can be seen in Table 3, a greater transfer of electronic density occurs in the closed-shell systems than in the openshell systems. In the first set of complexes, which contains all of the actinides in the same oxidation state, it can be shown that the charge transfer is almost the same; even the geometries do not vary very much. However, if the same actinides with different oxidation states are compared, namely, PaIV with Pa V or UIV with UVI and so on, an increment of charge transfer can be observed that is related to the possibility of back-donation in open-shell complexes from the metal to the ring. Previous studies have shown and explained the 5f orbital participation in the metal
ligand bonding in actinocenes, AnIV(COT)2 (An = Th
Pu).7 In particular, it is well-recognized that the actinide

Figure 2. Molecular orbital diagram for ThIV(COT)2 complex with the inclusion of scalar relativistic (SR) effects under D8h symmetry and spin
orbit (SO) effects under D8h* symmetry.

fδ orbitals (fz, fxyz) interact with the filled e200 molecular orbitals (MOs) of C8H8 rings, whereas the other orbitals fσ (fz3), fπ (fxz2, fyz2) and fj [fx(x2
3y2) (fx), fy(3x2
y2) (fy)] are localized and considered as nonbonding. In this context, the fδ orbitals are antibonding.7 This hypothesis was corroborated in the present work because the contribution of the 5f orbitals can be observed in the highest occupied molecular orbital (HOMO) in both sets of systems. 8999

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Table 4. Group Compatibility Relations (Γ X E1/2 = Γ*) for the Single D8h and Double D8h* Point Groups D8h

Table 6. Calculated NICS Values (in ppm) at Selected Positions, with Values of NICSzz in Parentheses

D8h*

system
2

a1g,u

e1/2g,u

a2g,u b1g,u

e1/2g,u e3/2g,u

b2g,u

e3/2g,u

e1g,u

e1/2g,u x e3/2g,u

e2g,u

e3/2g,u x e5/2g,u

e3g,u

e5/2g,u x e7/2g,u

NICS(0)

NICS(1)

NICS(
1)

COT


11.63


13.52




Th(COT)2

(
39.40)
16.40

(
39.31)
47.43



27.89

(
43.40)

(
139.01)

(
56.61)


49.98


94.28


23.29

(
56.39)

(
147.39)

(
41.85)


119.36


271.84


45.49

(
52.80)

(
136.06)

(
39.40)

Pa(COT)2+ U(COT)22+

Table 5. HOMO Energies Obtained by SR and SO Calculations and Orbital Splittings Due to the SO Effect EHOMO (eV) system

scalar

SO

Δ(SO
scalar)
3

ΔEso

Th(IV) Pa(V)


4.644
9.033


4.639
9.011

5.0  10 2.2  10
2

0.16 0.19

U(VI)


13.544


13.385

1.6  10
1

0.27

Pa(IV)


2.632


2.928

3.0  10
1

0.12

U(IV)


3.234


3.406

1.4  10
1

0.03

We show the metal 6d- and 5f-orbital contributions to the set of molecular orbitals from HOMO
6 through LUMO + 3 (where the LUMO is the lowest unoccupied molecular orbital) in Tables S1 and S2 of the Supporting Information. An increment of fz and fxyz orbital contributions is noticed in both sets as one moves along the actinide series. For the closed-shell compounds, these orbitals make a significant contribution to the HOMO, whereas the other 5f orbitals are destabilized by the ligand field interaction. On the other hand, for the open-shell compounds, these orbitals (fz, fxyz) are more internal, whereas the fx and fy orbitals, which contribute to the HOMO, are localized in the metal center and are considered as nonbonding. Figure 2 shows a qualitative diagram representation of the molecular orbitals for Th(COT)2; it compares a scalar relativistic model and a spin
orbit model and illustrates the relationships between single and double group irreducible representations. Table 4 reports the compatibility relations between the irreducible representations of single D8h and double D8h* groups. The relationships given in Table 4 are useful for interpreting the energy level diagram shown in Figure 2. This figure also shows a slight destabilization in the HOMO that has a small increment in the other complexes, where U(COT)22+ has the greatest destabilization with an approximate value of 0.2 eV in the closed-shell case (see Table 5). This behavior can be explained as being due to the spin
orbit effect on the 5f orbitals. In closedshell systems, the HOMO has significant contributions from fz and fxyz, which are strongly involved in the interaction with the ligand field; instead, the orbitals that contribute to the HOMO in the open-shell systems remain localized at the metal, and for that reason, they are stabilized. Table 5 also includes the spin
orbit splitting of the degenerate irreducible representations. To better understand the metal
ring interaction, it is convenient to study the possible electronic delocalization between the two structures and, in particular, the role of the metal in this delocalization. Aromaticity by NICS and ELF. The interaction between the metal center and the ring in these systems could lead to an

Figure 3. Spin magnetization density plots of highest occupied molecular spinor (E3/2u) and lowest unoccupied molecular spinor of U(COT)2.

electron delocalization that has been described as spatial aromaticity by some authors.37 This possible delocalization can be found by studying the behavior of the nuclear shielding tensor in the metal
ring half-space. This could show the possible changes in the well-known COT ring aromaticity and its modification by the metal. Table 6 reports the NICS values calculated at the same locations as mentioned before. The NICS values at the center of the ring in all complexes are larger than in the isolated COT ring; this fact shows a reinforcement of the ring delocalization that increase along the actinide series. In the same way, the values obtained at 1.0 Å over the ring indicate a diatropic current that is related to a reinforcement of the ring delocalization. More interesting results were obtained at a space between the metal and the ring, where the NICS values indicate an even greater electronic delocalization than the values at NICS(
1). This result indicates that, in addition to an increase in the ring π-aromaticity, a significant electronic delocalization could occur in the metallic center orbitals, mainly from the 5f orbitals, that increases the spatial aromaticity.37 Figure 3 depicts the highest occupied molecular spinor and the lowest unoccupied molecular spinor of U(COT)2, which clearly shows this delocalization. Because both frontier orbitals have large 5f-orbital contributions, one can be sure that the latter plays an important role in this delocalization. In addition to the chemical shift, other authors have employed the electronic localization function (ELF) to study the aromaticity and, in general, the electronic delocalization in different actinide systems.38,39 The most evident way to analyze the ELF is through its graphical representation, so Figure 4 shows a cutplane ELF representation in the same locations as the NICS indexes were calculated. Comparing this representation at the 9000

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Figure 4. Cut-plane ELF representation at selected positions.

plane of the ring of both isolated and complexated COT moieties, no difference can be observed, so a qualitative interpretation of the ELF at this point does not provide useful information; however, interesting results are obtained by the analysis of the representations 1.0 Å from the ring. In these representations, the core basins of carbon atoms cannot be observed, but the disynaptic basins associated with the C
C bonds in the COT ring are observed in all cases. As noted above, a high value of bifurcation implies that the minimum in the ELF is high, and the respective basins do not separate each other. Therefore, in this situation, the basins are correlated, and one can expect that the higher the bifurcation value, the more aromatic

the system. Comparing the ELF(
1) and ELF(1) representations in all actinide complexes evaluated, it can be observed that disynaptic basins in the former have higher ELF values than the other representations and the space between each basin decreases its ELF values rapidly to 0.50. This fact implies that the electrons are more localized in these basins, so these basins are less correlated and the aromaticity there is smaller than in the metal
ring space. This last result is in agreement with the NICS values obtained in these locations. Another interesting result is obtained when one compares the ELF representation at the same location for each actinide in the series. Comparing the ELF(1) among the actinide series, it can be observed that regions of space 9001

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Table 7. Characterization of Electronic Transitions for Open-Shell Systemsa system

f

λ (nm)

Th(COT)2 SAOP/ALDA/SO

3.0  10
1

202.2

origin 9e5/2u f 12e5/2g (52.24)

πfπ

9e5/2u f 13e5/2g (11.92) 8.3  10
2 3.5  10
2

15e3/2u f 15e3/2g (11.79) 277.7

10e5/2g f 11e5/2u (77.81)

πff

14e3/2g f 17e3/2u (16.78) 244.7

15e3/2u f 11e5/2g (34.97)

πfπ

9e5/2u f 7e7/2g (28.74) 2.7  10
2

Pa(COT)21+ SAOP/ALDA/SO

222.9

14e3/2g f 12e5/2u (20.49) 15e3/2u f 15e3/2g (70.74)

πfπ

15e3/2u f 16e3/2g (17.07)

7.5  10
2

365.4

14e3/2g f 16e3/2u (99.23)

πff

2.0  10
3

428.0

14e3/2g f 10e5/2u (47.68)

πff

14e3/2g f 21e1/2u (43.96)

1.5  10
3

454.7

10e5/2g f 10e5/2u (99.92)

πff

1.3  10
1

269.1

10e5/2g f 11e5/2u (67.50)

πff

355.4

14e3/2g f 17e3/2u (26.22) 10e5/2g f 16e3/2u (40.39)

πff

1.2  10
2

10e5/2g f 8e7/2u (37.00) 3.8  10
2

14e3/2g f 22e1/2u (14.38) 221.8

15e3/2u f 11e5/2g (37.21)

πfπ

9e5/2u f 7e7/2g (26.62) U(COT)22+ SAOP/ALDA/SO

a

3.3  10
1

14e3/2g f 12e5/2u (13.93) 335.1

10e5/2g f 11e5/2u (50.15)

πff

8.5  10
3

540.6

πff

1.5  10
3

14e3/2g f 17e3/2u (37.43) 14e3/2g f 16e3/2u (94.26)

738.3

14e3/2g f 10e5/2u (93.45)

πff

1037.8

fff

933.5

fff

637.2

fff

629.6

fff

607.9

fff

471.2 441.4

fff fff

1236.0

fff

1090.9

fff

706.7

fff

697.4

fff

670.9

fff

508.2

fff

473.8

fff

Percentage contributions to f f f forbidden transition are included.

that previously bifurcate at ELF = 0.5, now separate at ELF = 0.75.30 As said before, this rise of the bifurcation value shows, as for the NICS results, that the electronic delocalization in the ring increases along the actinide series, so the systems become more aromatic because of the metal effect. Electronic Transitions. The electronic spectra of actinide compounds usually involve a combination of f f f, f f d, and charge-transfer transitions, not only because of the larger number of states derived from a single fn configuration, but also because of the splitting of these states by the ligand field and spin
orbit coupling. Because of the high symmetry of these systems, only a small number of electronic transition are dipole-allowed. First, because of the centrosymmetry of the molecule, an allowed

transition must involve a parity change. More specifically, in the D8h* double group, for an electronic-dipole-allowed transition from the E5/2u ground state (in closed-shell systems), the excited state has to be the E1/2g, E3/2g, E5/2g, or E7/2g state. As a consequence of this selection rule, all of the f f f transitions, which are predicted to occur in the IR or near-IR region, are forbidden because they do not involve a parity change. We include these transitions in Table 7 for open-shell systems and in Table S3 of the Supporting Information for closed-shell systems because of the possibility that they could gain some intensity through vibronic coupling. Our calculations indicate that the only allowed transitions that involve metal orbitals are f f d and f f π. In closed-shell systems, only π f f and intraligand 9002

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The Journal of Physical Chemistry A transitions appear; for uranium complexes, it is possible to predict also a series of f f f transitions between frontiers orbitals. In openshell complexes, the allowed f f d transition with lowest energy is predicted at 905 nm in Pa(COT)2 and 518 nm in U(COT)2; both transitions are in agreement with previously published values. In addition to the excitations due to 5f electrons discussed above, we also calculated the LMCT (ligand
metal charge-transfer) transitions from filled COT orbitals into empty metal-based orbitals. Table 7 lists the calculated transition energies for dipoleallowed electronic transitions from COT toward the 5f and 6d orbitals in the metal in open-shell systems; the corresponding list for closed-shell systems is in Table S3 (Supporting Information). For closed-shell complexes, we found that, for Th(COT)2, two transitions that should occur in the visible region; for Pa(COT)2+, these transition have a very low intensity; and for U(COT)22+, the two possible LMCT transitions occur at 541 and 738 nm. In the open-shell case, the situation is the same as for Pa(COT)2; that is, the LMCT transitions are characterized by very low intensity. For U(COT)2, the possible transition from ligand to metal d orbitals were found at 421 nm. An interesting result appears in the closed-shell case if the most intense transitions for Th, Pa, and U are compared, with wavelengths of 202, 269, and 335 nm, respectively. It can be observed that these values are in perfect correlation with the increment of the NICS value for this series. These results are sufficient to ensure that, for these complexes, the increment in delocalization leads to a shift in the maximum wavelength of absorption in the visible region.

’ CONCLUSIONS The actinide elements are very difficult to handle experimentally because of their radioactivity. Thus, reliable theoretical studies of such molecules can provide important guidance in the interpretation of the hard-to-obtain experimental data. Density functional calculations with spin
orbit effects are appropriate, because they provide good agreement with the available experimental data. The present contribution provides important information about the structure, bonding nature, and electronic properties of a series of actinocene complexes. Some ideas about the electronic delocalization and its influence on system stabilization and electronic transition are incorporated. Our future efforts will focus on the study of magnetic properties and their relationship to the properties predicted here. ’ ASSOCIATED CONTENT

bS

Supporting Information. Percentage contributions of d and f orbitals to frontier orbitals of closed-shell systems and of 6d and 5f orbitals to frontier orbitals of open-shell systems. Characterization of electronic transitions for closed-shell systems. This information is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] (D.P.-H.), [email protected] (R.A.-P.).

’ ACKNOWLEDGMENT We acknowledge funding from Grants Fondecyt 1110758, UNABDI-05-11/I, and UNAB-DI-17-11/R and an MECESUP fellowship.

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