Aromatic Lateral Substituents Influence the Excitation Energies of

Article pubs.acs.org/JPCA

Aromatic Lateral Substituents Influence the Excitation Energies of Hexaaza Lanthanide Macrocyclic Complexes: A Wave Function Theory and Density Functional Study Walter A. Rabanal-León,*,†,§ Juliana A. Murillo-López,‡,§ Dayán Páez-Hernández,†,§ and Ramiro Arratia-Pérez*,†,§ †

Downloaded by UNIV OF MANITOBA on September 11, 2015 | http://pubs.acs.org Publication Date (Web): September 10, 2015 | doi: 10.1021/acs.jpca.5b07202

Facultad de Ciencias Exactas, Ph.D. Program in Molecular Physical Chemistry, Relativistic Molecular Physics (ReMoPh) Group, Universidad Andrés Bello, Santiago 8370146, Chile ‡ Facultad de Ingeniería, Centro de Bioinformática y Simulación Molecular (CBSM), Universidad de Talca, 2 Norte 685, Casilla 721, Talca, Chile S Supporting Information *

ABSTRACT: The high interest in lanthanide chemistry, and particularly in their luminescence, has been encouraged by the need of understanding the lanthanide chemical coordination and how the design of new luminescent materials can be affected by this. This work is focused on the understanding of the electronic structure, bonding nature, and optical properties of a set of lanthanide hexaaza macrocyclic complexes, which can lead to potential optical applications. Here we found that the DFT ground state of the open-shell complexes are mainly characterized by the manifold of low lying f states, having small HOMO−LUMO energy gaps. The results obtained from the wave function theory calculations (SO-RASSI) put on evidence the multiconfigurational character of their ground state and it is observed that the large spin− orbit coupling and the weak crystal field produce a strong mix of the ground and the excited states. The electron localization function (ELF) and the energy decomposition analysis (EDA) support the idea of a dative interaction between the macrocyclic ligand and the lanthanide center for all the studied systems; noting that, this interaction has a covalent character, where the d-orbital participation is evidenced from NBO analysis, leaving the f shell completely noninteracting in the chemical bonding. From the optical part we observed in all cases the characteristic intraligand (IL) (π−π*) and ligand to metal charge-transfer (LMCT) bands that are present in the ultraviolet and visible regions, and for the open-shell complexes we found the inherent f−f electronic transitions on the visible and near-infrared region.

■

INTRODUCTION From 1960 to today, the advances made on the inorganic, bioinorganic, and supramolecular chemistry are oriented to understand chemical reactivity, photophysics, and the magnetic behavior of macrocyclic and metal−macrocyclic systems. Particularly, lanthanide macrocyclic complexes formed by condensation of Schiff bases have had a significant repercussion on bioinorganic and supramolecular chemistry because they can be used as models for the study of more intricated biological macrocyclic systems as metalloporphyrins (hemoglobin, myoglobin, cytochromes, chlorophylls), corrins (vitamin B12), and antibiotics (valinomycin, nonactin). These systems not only are appealing from the biological point of view but also are used as chemical models to promote the study of metal− macrocyclic interactions, which subsequently became the first step for the elaboration of a more sophisticated and highefficient near-infrared (NIR) technologies, devices based on single molecule magnets (SMM), medical applications, etc.1−6 Additionally, “rare-earth” metal ions have been found to be very efficient metal templates in the synthesis of complexes of © XXXX American Chemical Society

this type of macrocyclic complex, where the lanthanide ions can be allocated via stereochemical constraints inside of the macrocyclic host during the synthetic template process.6−11 Furthermore, the lanthanide complexes of these macrocyclic ligands were remarkable for their exceptional inertness toward metal release in solution, a feature that contrasted with the common behavior of the labile transition metal ions. The issues mentioned before made possible a detailed study of the photophysical properties of a set of trivalent lanthanide cations in aqueous solution, where their high stability also allows the analysis of the bonding interaction between the macrocyclic ring and the lanthanide center.5 All the above works as a motivation for us to gain insight on the study of polyaza macrocyclic systems coordinated to lanthanide ions. To do so, we gave special attention to the 18membered hexaaza lanthanide macrocyclic complexes syntheReceived: July 24, 2015 Revised: August 31, 2015

A

DOI: 10.1021/acs.jpca.5b07202 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article


The Journal of Physical Chemistry A sized by Radecka-Paryzek on the 1980s.7,8 This trivalent lanthanide (Ln = La, Ce, Pr, Nd) macrocyclic system was shown to be air and thermally stable, and the spectral and analytical data support the cyclization and the formation of the macrocyclic ring. Additionally, electronic spectra of the solution complexes in acetonitrile evidence π−π* and ligand to metal charge-transfer (LMCT) bands in a range around 200−650 nm, but no more information in the NIR region is reported. Unfortunately, due to the amount of time and the complexity of modeling lanthanide (or actinide) macrocyclic compounds, there are few computational studies reported. One of these is presented by Schreckenbach,12 who analyzed the dioxoactinide (uranyl, plutonyl, and neptunyl ions) with Schiff base macrocyclic ligands; another one is a previous work reported by Arratia-Pérez and co-workers,13 where analogous hexaaza macrocyclic systems with aliphatic lateral units coordinated to lanthanide centers were studied. In both cases, the importance of considering relativistic effects on modeling their structures and properties was pointed out; what is more, the results of the time-dependent analysis suggest the possibility of using these kinds of macrocyclic ligands as antenna chromophores. For that reason, the present contribution is based on the study of a set of metal macrocyclic complexes with aromatic lateral units and the three lighter lanthanide ions (La3+, Ce3+, and Pr3+). We pursue the understanding of the electronic structure, the bonding interactions that govern the stability of these kind of systems, and moreover a detailed description of the excitation energies from a quantum relativistic point of view. This research deals with the possibility of using macrocyclic rings with aromatic lateral units as antenna to sensitize and maximize NIR-luminescence of some lanthanide ions.

Figure 1. Selected molecular structure for all lanthanide hexaaza macrocyclic complexes with aromatic lateral units [LnIIIHAMBz]3+ (LnIII = La3+, Ce3+, Pr3+; HAMBz = C30H26N6).

potential energy surfaces because they only present positive frequencies. Particularly, the spin−orbit effects for open-shell molecules were calculated using the ZORA Hamiltonian with the noncollinear approximation. Additionally to this, Dirac− Hartree−Fock (DHF) four-component electronic structure calculations for the complex with the lanthanum center were performed with the fully relativistic code DIRAC 13.0,19 considering Dyall’s triple-ζ quality basis set20 for the lanthanide and Dunning’s basis set21 for light atoms. To study the stability and the bonding nature of these systems, we looked for a methodology to quantify the lanthanide−macrocycle interactions. Therefore, an analysis of bonding energetics was performed by combining a fragment approach to the molecular structure of a chemical system with the decomposition of the total bonding energy (EBE), according to Morokuma−Ziegler energy partitioning scheme,22 as

■

COMPUTATIONAL DETAILS 1. Density Functional Theory (DFT) Calculations. The proposal of the present work is to perform a conscientious theoretical study of the [LnIIIHAMBz]3+ complexes based on the detailed description of the electronic structure of these complexes and the bonding interaction between the trivalent lanthanide center (La3+, Ce3+, and Pr3+), and the neutral hexaaza macrocyclic ligand C30H26N6 (HAMBz), with the aim to describe and compare the molecular electronic structures and their relative stabilities. All this work was developed on the framework of the relativistic density functional theory (R-DFT) by using the Amsterdam Density Functional (ADF 2012.01)14 code, where the scalar (SR) and spin−orbit (SO) relativistic effects were incorporated by means of a two-component Hamiltonian with the zeroth-order regular approximation (ZORA)15 considering the noncollinear approximation.16 All the molecular structures presented above were fully optimized via the analytical energy gradient method implemented within the generalized gradient approximation (GGA) employing the nonlocal correction proposed by Perdew, Burke, and Erzenhof (PBE).17 Furthermore, uncontracted triple-ζ quality Slater-type orbital (STO) basis sets, augmented with two sets of polarization functions (TZ2P), were used for all atoms.18 The complete set of geometry optimizations were done under a C2v symmetry constraint, according to the experimental results reported by Radecka-Paryzek7,8 (Figure 1). After all geometry optimizations, a frequency analysis was performed by using the analytical second derivative method implemented in ADF code; the results allow us to confirm that the optimized structures are minima on their respective

E BE = E Pauli + Eelestat + Eorb

(1)

where EPauli, Eelestat, and Eorb are the Pauli repulsion, electrostatic interaction, and orbital-mixing terms, respectively. In this way, the electrostatic component is calculated from the superposition of the unperturbed fragment densities at the molecular geometry and corresponds to the classical electrostatic effects associated with Coulombic attraction and repulsion. The electrostatic contribution is most commonly dominated by the nucleus−electron attraction and therefore has a stabilizing influence. The Pauli term is obtained by requiring that the electronic antisymmetry conditions be satisfied and has a destabilizing character, whereas the orbital-mixing component represents a stabilizing factor originating from the relaxation of the molecular system due to the mixing of occupied and unoccupied orbitals and can involve electron pair bonding, charge-transfer, or donor−acceptor interactions, and polarization. Additionally to this, and in a qualitative way, the topological analysis of the electron localization function (ELF)23 was used to define localized attractors corresponding to the core, bonding, and nonbonding electron pairs and their spatial arrangement.24 The ELF was computed with the DGRID 4.6 program25 and further analysis was visualized with the MOLEKEL 5.4 software.26 Moreover, the net charge analysis B


Article

The Journal of Physical Chemistry A Table 1. Experimental and Calculated Geometrical Parametersa

d Ln−Npyr d Ln−Nimine ∠Npyr−Ln−Npyr ∠Npyr−Ln−NimineI ∠NimineI−Ln−NimineII ∠Ringpyr−Ringpyr

[LaHAMBz]3+

[CeHAMBz]3+

[PrHAMBz]3+

calc

calc

calc

expb

2.631 2.589 121.6 60.6 60.6 121.0

2.583 2.554 121.4 61.2 60.9 121.4

2.591 2.549 121.8 61.1 61.4 103.6

2.651(4) 2.657(4) 60.5(1) 60.7(1) 110.3(1)

a


Bond lengths (Å) and angles and dihedral angles (deg) for the ground state of the [LnIIIHAMBz]3+ systems under a C2v symmetry point group at the scalar relativistic level. Experimental esd’s are in parentheses. bExperimental data reported in ref 11.

Figure 2. Molecular orbital (MO) energy diagram for all [LnIIIHAMBz]3+ systems at nonrelativistic (NR), scalar relativistic (SR), and spin−orbit (SO) levels. The green dashed line separates occupied from virtual orbitals/spinors.

into account by means of the Douglas−Kroll−Hess transformation,36 and the spin−orbit integrals are calculated using the atomic mean field integrlas (AMFI) method.37 In all cases the all-electron ANO-RCC basis set with TZP quality is employed as follows: Ce and Pr, 8s7p4d3f2g1h; N, 4s3p2d1f. The other atoms in the structure were treated at the DZP level.38 The active spaces selected for both complexes have proven to be correct in the description of the electronic structure of these complexes;13,39 in the case of the Ce3+ complex seven doublets were calculated and for the Pr3+ complex 20 one triplet and 50 singlets were considered. For the analysis of the 4f orbitals and their states, the following nomenclature was adopted:

of the metal center and charge-transfer phenomena were evaluated using different population analysis schemes like multipole derived charge (MDC),27 Voronoi (VDD),28 and natural bonding orbital (NBO).29 Excitation energies and absorption spectra were calculated using the time-dependent density functional theory (TDDFT)30,31 at scalar relativistic level for both closed- and open-shell systems. The excitation energies were calculated using the statistical average of orbital exchange−correlation model potential (SAOP),32 which was specially designed for the response property calculations. On this part, we have a special interest in electronic transitions lying in the near-infrared (NIR) region, because these transitions have significant importance in several technological applications specially in the field of optics. 2. Wave Function Theory (WFT) Calculations. WFT calculations have been performed using the MOLCAS 7.833 suite of programs without any symmetry constraint. The active space consist in one electron in the seven f orbitals for the Ce3+ complex and two electrons in the same seven orbitals for the Pr3+ complex. First, the complete active space self-consistent field (CASSCF)34 calculation is performed to obtain a highquality wave function and then the spin−orbit interaction is evaluated by states interaction between the CASSCF wave function by the restricted active space states interaction (RASSI) method.35 The scalar relativistic effects are taken

fσ = f0 = {fz3

⎧ f + f−1 = fz 2x ⎪ +1 fδ = f±1 = ⎨ ⎪f ⎩ +1 − f−1 = fz 2y

fπ = f±2 C

⎧ f + f−2 = fz ⎪ +2 =⎨ ⎪f ⎩ +2 − f−2 = fxyz DOI: 10.1021/acs.jpca.5b07202 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A fϕ = f±3

⎧ f + f−3 = fx ⎪ +3 =⎨ ⎪f ⎩ +3 − f−3 = f y

For the open-shell complexes, the 4f shell is occupied; then the nature of the frontier orbitals changed with respect to the lanthanum complex with the consequent reduction of the H−L gap as a result of the low-lying 4f states. For that reason, the lanthanum complex should be considered as a reference to evaluate the crystal field ligand effect over the electronic structure of the f-electrons. The correct description of this inherent behavior of the f shell orbital energies shows the importance of considering relativistic effects. A change on the energetics for both systems can be seen from Figure 2, where an increment of the H−L gap is observed when scalar and spin−orbit effects are taken into account. Although, there is a change on the frontier orbital/spinor energy levels, this change continues, giving small H−L gaps for both systems, 0.32 and 0.59 eV for cerium and praseodymium complexes, respectively. In addition, it is well-known that the scaled ZORA spinor energies are exactly equal to the Dirac energies for hydrogenlike systems; when the systems become heavier, some differences appear but remain close in energy compared to other regular approximations, even the unscaled ZORA. When molecular orbital energy levels for a heavy-element-containing system are studied, there are some differences that are important to analyze, where the Dirac spinor energy levels can be considered as a benchmark for these systems (Figure ESI-S1). The population analysis is depicted in Table 2, the results show that in all cases the systems exhibit a charge transfer from


■

RESULTS AND DISCUSSION 1. Geometrical Parameters. The lanthanum, cerium, and praseodymium trivalent cations have been found to be effective in the template synthesis of conjugated 18-membered hexaaza macrocyclic ligand. References to the known structures of the related complexes and the examination of molecular structural parameters reveals that their cavity would have a diameter of roughly 5.4 Å;7,8 this value is quite close with the calculated cavity of the macrocycle host, which has a value between 5.1 and 5.2 Å (taken in consideration the distances between the lanthanide and the pyridine or imine nitrogen atoms). Therefore, these lanthanide ions with a six-coordinate ionic diameter between 2.00 and 2.34 Å40 are sufficiently large to be effectively bounded to all six nitrogen donor atoms of this quasi-planar macrocycle. For describing the coordination mode of the lanthanide ion, we mention that there are four imine nitrogens almost in the same plane with the lanthanide, and the two pyridine nitrogens coordinated out of this plane, conferring to the molecule a vshape. The coordination polyhedra of the microsymmetry formed by the six nitrogen atoms could be approximated to a cis-distorted trigonal prism. The calculated ground-state geometries for all [LnIIIHAMBz]3+ are in good agreement with experimental Xray diffraction data first reported by Radecka-Paryzek8 and confirmed by Benetollo et al.;11 the results of the geometry optimizations were summarized in Table 1. The geometrical conformation achieved by the HAMBz macrocyclic ligand is symmetrical and it is characterized by a dihedral angle of 103.6° between the planes of the two pyridine rings (with respect to the experimental value of 110.3°), this bending of the pyridine rings over the o-phenylene rings breaks the π- conjugation among all the four aromatic units on the macrocycle. 2. Electronic Structure. From the molecular orbital energy diagram depicted in Figure 2, it is observed how the spherical distribution of the charge splits by the crystal field. In the [LaHAMBz]3+ system, we have a 4f0 electronic configuration on the valence region for the lanthanide center, where the symmetric distribution of the electronic charge confers a high stability to the different occupied energy levels, which are mainly characterized as groups of π (pz) orbitals that come from the four aromatic units on the macrocycle, whereas the lowest unoccupied orbitals are strongly composed of d and f atomic orbitals from the lanthanum ion. This has as a consequence the biggest HOMO−LUMO (H−L) gap (≈1.85 eV) for the studied series. On the electronic structures of the lanthanum complex there are differences with respect to the analogous aliphatic complexes reported in a previous work;13 looking at the lanthanum case, we observed a significant reduction on the HOMO−LUMO gap of ≈1.2 eV, which could be directly related to the change on the conformational distribution of the macrocycle generated by the electrostatic, steric, and orbital interactions between the ring and the lanthanide center; this conformational change on the macrocyclic ring with aromatic lateral units produces lost conjugation by destabilizing the π (pz) occupied orbitals in the frontier region.

Table 2. Multipole Derived Charge (MDC-q), Voronoi (VDD), and Natural Bond Orbital (NBO) Population Analysis over the Lanthanide Center and Nitrogen Atoms for all [LnIIIHAMBz]3+ Complexes at the Scalar Relativistic Level NBO MDC-q La Npyr Nimine Ce Npyr Nimine Pr Npyr Nimine

VDD

NACa

NECb

[LaHAMBz]3+ 2.234

2.653

2.408

−0.816 −0.877

−0.449 −0.458

[core] 6s(0.06)4f(0.17)5d(0.53) [core]2s(1.36)2p(4.13) [core]2s(1.34)2p(4.15)

−0.453 −0.455


−0.446 −0.440


2.632 −0.605 −0.675 2.464 −0.804 −0.869

−0.507 −0.520 [CeHAMBz]3+ 2.386 2.185 (0.94)c

−0.505 −0.512 [PrHAMBz]3+ 2.300 2.168 (2.07)c −0.501 −0.512

a c

NAC: natural atomic charge. bNEC: natural electronic configuration. Spin density value.

the nitrogen atoms on the macrocyclic ligand toward the lanthanide center, the charge transfer from the imine being slightly bigger than that from the pyridine nitrogens. Furthermore, spin density analysis of the open-shell molecules evidences that the electronic density is centered over f orbitals on the cerium (0.94) and praseodymium (2.07) ions, these, in addition to the results obtained from natural electronic configuration (NEC), could confirm a 3+ oxidation state for all the lanthanide ions on the studied series. D


Article

The Journal of Physical Chemistry A


The small H−L energy gap values added to the low-lying inherent behavior of the 4f shell and the low crystal-field effect suggest the possibility of a significant mixing between the ground and the excited states having as a consequence a change or effect on their properties. Because of this, it is important to evaluate the effect of the crystal field and the spin−orbit coupling, as well as the electronic correlation, using a higher level of theory. In this context, the wave function theory, by means of CASSCF calculations, was used to get improved information about their electronic structure; here it is possible to evaluate the correlation between the spin-free (SF) states and the results when the spin−orbit coupling (SOC) is considered. For the [CeHAMBz]3+ system, the SF states are issued from the ground SF ion term 2F and are ordered, at the SF-CASSCF level of calculations, according to the splitting of a L = 3 manifold by a C2 crystal field environment; this allows us to identify seven Krammer’s doublets, as can be seen on the first part of Table 3. Table 3. Spin-Free (SF) and Spin−Orbit (SO) States, Ground-State Total Energies (au), Relative-State Energies (cm−1) (Values in eV in Parentheses), and Their Respective Wave Functions for the [CeHAMBz]3+ Complex Calculated at a CAS(1,7)SCF Active Spacea state 2

B(1) 2 B(2) 2 B(3) 2 A(1) 2 B(4) 2 A(2) 2 A(3) state 2

E1/2(1) E1/2(2) 1 E1/2(3) 2 E1/2(4) 2 E1/2(5) 1 E1/2(6) 1 E1/2(7) 2

SF-CAS(1,7) SCF 0 (0.0) 80 (0.0099) 460 (0.0570) 501 (0.0621) 616 (0.0764) 1384 (0.1716) 2869 (0.3557) SO-CAS(1,7) SCF 0 338 1386 2342 2647 3053 4627

(0.0) (0.0419) (0.1718) (0.2904) (0.3282) (0.3785) (0.5737)

wave function (CF) −0.956|f0⟩ + 0.281|f+2 ⟩ −0.892|f−1⟩ + 0.329|f−3⟩ − 0.155|f+3⟩ 0.934|f+1⟩ − 0.251|f−2⟩ −0.890|f−2⟩ + 0.354|f−3⟩ − 0.202|f+3⟩+ 0.117|f0⟩ 0.328|f+1⟩ + 0.262|f+2⟩ − 0.166|f−2⟩ + 0.136|f0⟩ 0.706|f−2⟩ + 0.329|f+2⟩ − 0.155|f0⟩ −0.921|f−3⟩ − 0.337|f−1⟩

Figure 3. Spin-free (SF) and spin−orbit (SO) energy-state diagram for [CeHAMBz]3+ in a CAS(1,7) active space.

wave function (CF+SO) 42% 43% 65% 48% 54% 60% 70%

2

B(1) + 36% 2B(2) + 22% 2B(3) B(1) + 30% 2B(2) + 20% 2B(3) + 8% 2B(4) 2 B(1) + 20% 2B(3) + 15% 2B(4) 2 A(1) + 35% 2A(2) + 17% 2A(3) 2 B(4) + 30% 2B(3) + 16% 2B(2) 2 A(2) + 25% 2A(1) + 15% 2A(3) 2 A(3) + 30% 2A(2)

complex the first 11 low lying triplet and singlet states are presented in Table 4. These triplet states come from the free ion ground state 3H4, and the first singlet excited state appears relatively high in energy at 7000 cm−1 and contributes only with the 0.1% of the energy stabilization to the ground state when the SO interaction is considered. Because of that, the variation in the relative energies is minimal, when the full calculation (considering both triplet and singlet states) is compared with the only triplet state interaction calculation. Comparing the total energy of the ground state when the triplet-only and the triplet−singlet state interaction are considered, producing a decrease of roughly 200 cm−1 in the total energy, gives evidence of the lower contribution of the singlet states to the wave function of the ground state, which is 91.73% |T⟩ + 8.27% |S⟩. 3. Bonding Nature. The results presented in Table 5 evidence that the metal−ligand interaction has a covalent character for all the complexes, because there is a higher contribution from the orbital interaction energy in comparison with the electrostatic one, whereas the sterical contribution represented by the Pauli’s term is almost constant in all cases. When we evaluated the decomposition of the orbital interaction in terms of irreducible representations (irrep’s), they can be characterized as combination of dxy/dyz orbitals for the lanthanide center and px/py for the macrocyclic ligand; this suggests a stronger interaction between the lanthanide ion and the four imine nitrogen atoms over the interaction with the two

2

For spin−orbit states: 1E1/2 = A ⊗ Γspin=1/2 and 2E1/2 = B ⊗ Γspin=1/2. The SF-ground-state (2B(1)) and the SO-ground-state (2E1/2(1)) total energies are −331.01520698 au (−9007.3869 eV) and −331.02072792 au (−9007.5371 eV), respectively. a

As expected, the wave function for the ground state (2B1), under a C2 symmetry constraint, has a strong f0 character, although the first excited state 2B2 appears only at 80 cm−1 and its wave function is the result of the lineal combination among the f−1 and f±3 orbital functions. When SOC is included (last part of the Table 3), we have as a consequence a strong mixing between the SF states due to the spin−orbit interaction, and also to the crystal field of the system. The ground state 2E1/2(1) is the result of the interaction of the three first spin-free states and the same strong mixing occurs for the other six Kramer’s states; this can be observed in Figure 3. The energy difference due to this splitting is around 338 cm−1. The situation is similar for the [PrHAMBz]3+ complex, where it is necessary to consider two different multiplicities for a better description of the ground state. For the [PrHAMBz]3+ E


Article


electrons, as a consequence of the electron donation from the nitrogen atoms to the lanthanide center for all the studied complexes. The electron localization function (ELF) shows the interaction among the imine and pyridine nitrogen atoms with the lanthanide ion (Figure 4a,b), but these are not governed strictly by the presence of disynaptic basins among the nitrogens and the lanthanide center; however, a lone pair monosynaptic basins well-oriented to the lanthanide center is clearly observed on the three-dimensional topological representation of the ELF (Figure 4c), suggesting an electron polarization among σ-lone pairs from the nitrogen atoms to the 5d orbitals in the lanthanide center. This can be translated as a dative interaction that serves as a justification of the 5d occupation and the covalent behavior shown by the NBO and the energy decomposition analysis. 4. Optical Properties. The electronic spectra of the studied series of lanthanide hexaaza macrocyclic complexes presented here are characterized in all cases by two types of bands: (i) The intraligand (IL) bands, which have the highest oscillator strength value (the most intense bands), are exhibited on the ultraviolet and visible region of the spectra. (ii) The following and less intense bands are those characterized as ligand to metal charge transfer (LMCT) and localized on the visible region. Additionally to this and only for the open-shell complexes, another set of purely f−f electronic transitions is present in the NIR region. Going deep on the description of the electronic transitions, we found that for the [LaHAMBz]3+ the calculated excitation energies were reproduced in good agreement the experimental data previously reported by Radecka-Paryzek7 for the π−π* electronic transitions; these bands experimentally are around 225 [228.1], 245 [246.4], 278 [285.8], and 358 [344.6] nm (in square brackets are the calculated results of the present work). Furthermore, LMCT bands from the π orbitals of the macrocyclic ligand to the empty f orbitals (fσ and fϕx) on the lanthanum center are observed. (See Table 6 and Figure 5.) With respect to the open-shell systems, there are no experimental results about the electronic spectra; however, the accurate results obtained with the same methodology in analogous systems reported in previous work support the robustness of the calculations.13 For cerium and praseodymium complexes, we found the IL bands are slightly shifted to the visible region. This shift made, in the case of the praseodymium complex, the IL and LMCT start to mix; nevertheless, the nature of the orbitals involved in the electronic transitions is still π−π* from the macrocyclic ring and π−fδ, σ, ϕx at 536.5,

Table 4. Spin-Free (SF) and Spin−Orbit (SO) Relative State Energies in cm−1 (Values in eV in Parentheses) for the [PrAMBz]3+ Complex Calculated at a CAS(2,7)SCF Active Spacea


spin-free state

spin−orbit state

triplet-state

singlet-state

triplet-only

triplet & singlet

RE (cm−1)

RE (cm−1)

RE (cm−1)

RE (cm−1)

0 30 47 151 272 426 1096 1456 1475 1634 1690

(0.0) (0.0037) (0.0058) (0.0187) (0.0337) (0.0528) (0.1359) (0.1805) (0.1829) (0.2026) (0.2095)

7003 7041 7128 7233 7446 7647 8070 8213. 8273 20789 21162

(0.8683) (0.8729) (0.8837) (0.8968) (0.9232) (0.9481) (1.0006) (1.0183) (1.0257) (2.5775) (2.6238)

0 73 120 358 392 730 1288 1486 1514 2094 2100

(0.0) (0.0091) (0.0149) (0.0444) (0.0486) (0.0905) (0.1597) (0.1842) (0.1877) (0.2596) (0.2604)

0 69 130 360 417 750 1250 1472 1487 2304 2310

(0.0) (0.0086) (0.0161) (0.0446) (0.0517) (0.0930) (0.1550) (0.1825) (0.1844) (0.2857) (0.2864)

a

The total energies for the SF-triplet and the SF-singlet ground states are −707.46501873 au (−19251.1129 eV) and −707.43310970 au (−19250.2446 eV), respectively. The total energy for the SO ground state, considering only the SF-triplet states, is −707.47580422 au (−19251.4064 eV). The total energy for the SO ground state, considering the SF-triplet and the SF-singlet states, is −707.47681955 au (−19251.4340 eV).

Table 5. Morokuma−Ziegler Energy Decomposition Analysis (EDA) for the Ground State of the [LnIII HAMBz]3+ Systems, under a C2v Symmetry Point Group at the Relativistic Levela [LaHAMBz]3+

[CeHAMBz]3+

[PrHAMBz]3+

EPauli VElestat EOrb−a1

7.806 −12.566 −5.669

8.837 −12.962 −19.450

8.236 −12.874 5.063

EOrb−a2

−4.449

−2.060

0.928

EOrb−b1

−3.432

1.553

−12.912

EOrb−b2

−4.770

−0.244

−14.345

EOrb−total EBE % covalency

−18.320 −23.080 59.3

−20.201 −24.326 60.9

−21.266 −25.904 62.3

a

EPauli: Pauli repulsion. VElestat: electrostatic interaction. EOrb: orbital interaction. EBE: bonding energy

pyridine nitrogens. The “d”-covalent character is reflected by the increment of the 5d shell occupation in roughly 0.5

Figure 4. Topology of the ELF for [PrIIIHAMBz]3+ complex, where (a) shows the plane of two diimine groups with the lanthanide, (b) shows the plane of the pyridine group with the lanthanide, and (c) shows the three-dimensional plot of the electron pairs and their spatial arrangement. F


Article


Table 6. Excitation Energies (eV), Wavelengths (nm), Oscillator Strengths ( f), and Molecular Orbital Assignment calculated for the [LaHAMBz]3+ Complex at the Scalar Relativistic Level with the SAOP model Potential band

energy

λ

f (×10)

active MOs

%

assignment

a

c

5.436 5.223 5.032 4.338 4.310 4.149 3.598

228.1 237.4 246.4 285.8 287.7 298.8 344.6

0.6368 0.5121 0.5093 1.0227 0.3516 0.4081 0.2621

29a2(α,β) → 30a2(α,β) 38b2(α,β) → 37b1(α,β) 29a2(α,β) → 37b1(α,β) 36b1(α,β) → 30a2(α,β) 48a1(α,β) → 37b1(α,β) 36b1(α,β) → 37b1(α,β) 29a2(α,β) → 39b2(α,β)

81.2 85.7 87.4 81.7 83.3 72.9 90.7

d

3.064

404.6

0.1917

48a1(α,β) → 39b2(α,β)

91.7

e

2.773

447.1

0.2000

36b1(α,β) → 49a1(α,β)

95.0

π−π ILCT π−π ILCT π−π ILCT π−π ILCT π−π ILCT π−π ILCT π−π ILCT π−fϕx (La) π−π ILCT π−fϕx LMCT π−π ILCT π−fσ LMCT


b

In addition, a complementary assignment for the [PrHAMBz] absorption spectrum has been done using the information resulting from the SO-RASSI calculations. As can be seen in Table 9, the most important electronic transition in the near-IR region at SF and SO level is reported. As is possible to see, the energies for the |T⟩0 → |T⟩ and the spin- forbidden |T⟩0 → S⟩ transitions are similar in the region considered. This means that the molecule has a manifold of low-lying singlet and triplet states. However, an analysis of the final-state wave functions shows that the contribution of the singlet states is really lower as in the ground state, which allows us to assign the electronic transitions for this molecule like triplet−triplet. Comparing these results, obtained from SO-RASSI calculations, with the previously discussed DFT excitation energies, it is possible to observe a good correlation among the excitation energy values, and also the results represent a good description for the f−f electronic transitions, as is reported in previous theoretical and experimental work for other and analogous lanthanide complexes.13,41−43 To evaluate the functionality of these complexes to be used as a single antenna molecule, a comparison between the [CeHAMBz]3+ complex studied on this work and the previously reported lanthanide hexaaza macrocycle with aliphatic lateral units (diimine bridge) was done.13 In this context, we normalized the data related to the oscillator strength for both spectra with the aim to see the differences between the intensities of all the bands presented on these complexes. We found that not only were the IL and LMCT bands shifted to the visible region in the case of used the macrocycle with aromatic lateral units but also some bands increased their intensity, promoting a bigger absorption of radiation by the macrocyclic chromophore. Furthermore, something more

Figure 5. Absorption spectra for the [LaHAMBz]3+ complex calculated at the scalar relativistic level with the SAOP model potential.

642.9, and 737.8 nm for the cerium complex and π−fδ, σ, πx, ϕx at 382.0, 450.1, and 786.1 nm for the praseodymium system. The inherent f−f electronic transitions of the open-shell trivalent lanthanide ions, are localized on the NIR region predominantly from fπy,ϕy to fσ, δ in the case of the cerium ion and fσ, δ to fπx,ϕx for the praseodymium ion. The complete description of the excitations and their assignment are presented in Tables 7 and 8, whereas the calculated absorption spectra are depicted in Figures 6 and 7 for [CeHAMBz]3+ and [PrHAMBz]3+ complexes, respectively.

Table 7. Excitation Energies (eV), Wavelengths (nm), Oscillator Strengths ( f), and Molecular Orbital Assignment calculated for the [CeHAMBz]3+ Complex at the Scalar Relativistic Level with the SAOP model Potential band

energy

λ

f (×10)

active MOs

%

assignment

a b c d e f g h i

3.511 3.172 2.830 2.311 1.929 1.680 1.483 1.289 1.199

353.1 390.9 438.1 536.5 642.9 737.8 836.0 961.7 1034.0

0.2931 0.0964 0.1350 0.0173 0.0112 0.0133 0.0424 0.0097 0.0095

29a2(β) → 39b2(β) 29a2(α) → 50a1(α) 36b1(α,β) → 50a1(α,β) 36b1(β) → 49a1(β) 48a1(α) → 37b1(α) 36b1(α) → 49a1(α) 39b2(α) → 30a2(α) 39b2(α) → 51a1(α) 39b2(α) → 41b2(α)

81.9 83.8 90.4 98.1 99.6 99.7 99.1 97.0 91.0

π−π ILCT π−π ILCT π−π ILCT π−fδ,σ LMCT π−fπx,ϕx LMCT π−fδ,σ LMCT fπy,ϕy−fδ fπy,ϕy−fδ,σ fπy,ϕy−fϕy

G


Article



Table 8. Excitation Energies (eV), Wavelengths (nm), Oscillator Strengths ( f), and Molecular Orbital Assignment calculated for the [PrHAMBz]3+ Complex at the Scalar Relativistic Level with the SAOP model Potential band

energy

λ

a

3.437

360.7

0.1742

b

3.246

382.0

0.1554

c

2.755

450.1

0.1278

d e

2.118 1.577

585.4 786.1

0.0864 0.0464

f

1.461

848.6

0.0238

g

1.273

974.3

0.3544 × 10−2

h

1.139

1088.1

0.1332 × 10−3

i j

0.983 0.590

1261.6 2102.3

0.13316 × 10−3 0.2788 × 10−3

f (×10)

active MOs

%

assignment

29a2(β) → 39b2(β) 48a1(α) → 38b1(α) 36b1(β) → 30a2(β) 48a1(α) → 41b2(α) 36b1(α) → 50a1(α)

56.7 26.2 46.3 36.7 76.5

36b1(β) → 49a1(β) 29a2(α) → 42b2(α) 48a1(α) → 37b1(α) 49a1(α) → 38b1(α) 49a1(α) → 38b1(α) 48a1(α) → 37b1(α) 39b2(α) → 50a1(α)

21.9 98.2 66.3 14.9 40.1 32.5 53.2

39b2(α) → 51a1(α) 39b2(α) → 30a2(α) 49a1(α) → 38b1(α) 49a1(α) → 40b2(α) 49a1(α) → 37b1(α) 39b2(α) → 30a2(α)

44.7 45.6 42.5 98.2 75.1 23.7

π−π ILCT π−fπx,ϕx LMCT π−fδ LMCT π−π ILCT π−π ILCT π−fσ,δ LMCT π−π ILCT π−π ILCT π−fπx,ϕx LMCT fσ,δ−fπx,ϕx fσ,δ−fπx,ϕx π−fπx,ϕx LMCT fπy,ϕy−π fπy,ϕy−fσ,δ fπy,ϕy−fσ,δ fπy,ϕy−fδ fσ,δ−fπx,ϕx fσ,δ−fπy,ϕy fσ,δ−fπx,ϕx fπy,ϕy−fδ

Figure 7. Absorption spectra for the [PrHAMBz]3+ complex calculated at the scalar relativistic level with the SAOP model potential.

3+

Figure 6. Absorption spectra for the [CeHAMBz] complex calculated at the scalar relativistic level with the SAOP model potential.

Table 9. Spin-Free Triplet−Triplet, Triplet−Singlet, and Spin−Orbit Wavelengths (nm) of the Most Important Electronic Transitions in the near-IR Region for the [PrHAMBz]3+ Complex

interesting is the fact that also the intensities of f−f electronic transitions were increased in the case of the cerium complex with aromatic lateral units with respect to the complex with aliphatic lateral chains, where these transitions are imperceptible. This could suggest a more effective way to populate the lanthanide excited states and increase the luminescence of the lanthanide center (Figure 8).

■

CONCLUSIONS The results obtained in this work reproduce with accuracy the experimental data reported for these complexes (crystallographic and UV−vis spectra) and, from the point of view of the electronic structure, describe properly the trend of the f shell in the lanthanide series. Based on the symmetry of the orbital-term contribution to the bonding energy, the natural electronic configuration (NEC), and the topological analysis from the ELF, it is

|T⟩0 → |T⟩

|T⟩0 → |S⟩

from SOC

1482 1466 1449 1442 1439 1424

1428 1429 1402 1382 1342 1307

1372 1361 1304 1300 1299 1173

wave function final statea 96.55% 95.03% 96.74% 92.25% 91.78% 93.32%

|T⟩ |T⟩ |T⟩ |T⟩ |T⟩ |T⟩

+ + + + + +

3.45% 4.97% 3.26% 7.75% 8.22% 6.68%

|S⟩ |S⟩ |S⟩ |S⟩ |S⟩ |S⟩

The ground state for the [PrHAMBz]3+ system is 91.73% |T⟩ + 8.27% |S⟩. a

possible for us to suggest that the lanthanide−macrocycle bonding interaction is basically a dative interaction with certain covalent character, where the σ-lone pairs of nitrogen atoms H


Article

The Journal of Physical Chemistry A Author Contributions §

All the authors contribute equally to this work

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work has been supported by the Grant Millennium No. RC120001 and the Projects FONDECYT No. 1150629, FONDECYT No. 11140294 and the AKA-FINLAND-CONICYT-CHILE 2012. J.A.M.L. acknowledges CONICYT/Postdoctorado FONDECYT No. 3150041. W.A.R.L. acknowledges CONICYT/PCHA/Doctorado Nacional/2013 No. 63130118 for his Ph.D. fellowship.


■

Figure 8. Comparison between the normalized absorption spectra of the cerium hexaaza macrocycles with aromatic (red) and aliphatic (black) lateral units.

and the d shell of the lanthanide center are involved through a charge-transfer phenomena. The electronic structure of the lanthanide open-shell complexes, characterized by the two-component DFT calculations, show a manifold of low-lying f states; the poor description of the ground and excited states of the singledeterminant DFT calculations were improved by means of the SF and SO-RASSI results, where the multideterminant character of the CAS calculations shows a strong mixing between the SF ground and excited states when the spin−orbit coupling is considered. The analysis of the f−f electronic transitions from the DFT and the SO-RASSI calculations has a good correspondence among them and also reproduces in good agreement the f−f electronic transitions reported in other theoretical works; this points out the importance of the electronic correlation and the spin−orbit coupling interaction for a proper description of the ground and excited states, as well as for a correct assignment of the electronic transitions. In addition, these complexes exhibit great features to be used as antenna molecules to autosensitize the lanthanide emissive states. Because the complexes presented here have high absorption by the macrocyclic ring and increased intensities, especially of f−f transitions, that could lead to a more efficient populations of the lanthanide excited states. Here, it is clearly shown that the aromatic substituent sensitizes efficiently the lanthanide ions.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b07202. Two-component ZORA and four-component Dirac− Hartree−Fock (DHF) molecular orbital/spinor energy diagram and Cartesian coordinates (PDF)

■

REFERENCES

(1) Stotz, R. W.; Stoufer, R. C. A Novel Macrocyclic Binuclear Copper(II) Complex Exhibiting A Metal-Metal Interaction. J. Chem. Soc. D 1970, 1682−1683. (2) Drew, M. G. B.; Cabral, J.; Cabral, M. F.; Ésho, F. S.; Nelson, S. M. Alkaline Earth, Lead(II), And Cadmium(II) Complexes Of A Nitrogen Analogue Of [18] Annulene; X-Ray Crystal Structure Of The Lead And Cadmium Complexes. J. Chem. Soc., Chem. Commun. 1979, 1033−1035. (3) Gray, C. J.; Hart, F. A. Syntheses And Properties Of Complexes Of A Conjugated Macrocyclic Hexamine With Lanthanide Nitrates. J. Chem. Soc., Dalton Trans. 1987, 2289−2290. (4) Bünzli, J.-C. G.; Piguet, C. Taking Advantage Of Luminescent Lanthanide Ions. Chem. Soc. Rev. 2005, 34, 1048−1077. (5) Eliseeva, S. V.; Bünzli, J.-C. G. Lanthanide Luminescence For Functional Materials And Bio-Sciences. Chem. Soc. Rev. 2010, 39, 189−227. (6) Vigato, P. A.; Tamburini, S.; Bertolo, L. The Development Of Compartmental Macrocyclic Schiff Bases And Related Polyamine Derivatives. Coord. Chem. Rev. 2007, 251, 1311−1492. (7) Radecka-Paryzek, W. Preparation And Characterization Of Lanthanum(III) Complex Of The Hexadentate Macrocyclic Ligand 2, 7, 13, 18 - Tetramethyl - 4, 5:15, 16 Dibenzo - 3, 6, 14, 17, 23, 24 Hexaazatricyclo [17.3.1.18,12] - Tetrakoza - 1(23), 2, 4, 6, 8, 10, 12(24), 13, 15, 17, 19, 21 - Dodecaene. Inorg. Chim. Acta 1981, 54, L251− L253. (8) Radecka-Paryzek, W. The Template Synthesis And Characterization Of Hexaaza 18-Membered Macrocyclic Complexes Of Cerium(III), Praseodymium(III) And Neodymium- (III) Nitrates. Inorg. Chim. Acta 1985, 109, L21−L23. (9) Radecka-Paryzek, W.; Patroniak, V.; Lisowski, J. Metal Complexes Of Polyaza And Polyoxaaza Schiff Base Macrocycles. Coord. Chem. Rev. 2005, 249, 2156−2175. (10) Bombieri, G. New Trends In The Structural Chemistry Of Actinide And Lanthanide Coordination Compounds. Inorg. Chim. Acta 1987, 139, 21−32. (11) Benetollo, F.; Bombieri, G.; de Cola, L.; Polo, A.; Smailes, D. L.; Vallarino, L. M. Six-Nitrogen Macrocyclic Complexes Of The Dioxouranium(VI) And Praseodymium(III) Ions. Inorg. Chem. 1989, 28, 3447−3452. (12) Shamov, G. A.; Schreckenbach, G. Relativistic Density Functional Theory Study Of Dioxoactinide(VI) and -(V) Complexation With Alaskaphyrin And Related Schiff-Base Macrocyclic Ligands. J. Phys. Chem. A 2006, 110, 9486−9499. (13) Rabanal-León, W. A.; Páez-Hernández, D.; Arratia-Pérez, R. Covalent Lanthanide (III) Macrocyclic Complexes: The Bonding Nature And Optical Properties Of A Promising Single Antenna Molecule. Phys. Chem. Chem. Phys. 2014, 16, 25978−25988. (14) Te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Fonseca Guerra, C.; van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T. Amsterdam Density Functional (ADF) Program DFT for molecules, 2012. (15) Lenthe, E. v.; Baerends, E. J.; Snijders, J. G. Relativistic Regular Two-Component Hamiltonians. J. Chem. Phys. 1993, 99, 4597−4610.

AUTHOR INFORMATION

Corresponding Authors

*W. A. Rabanal-León. Phone: +56-2-2770-3352. Fax: +56-22770-3352. E-mail: [email protected]. *R. Arratia-Pérez. Phone: +56-2-2770-3352. Fax: +56-2-27703352. E-mail: [email protected]. I


Article



(39) Gendron, F.; Páez-Hernández, D.; Notter, F.-P.; Pritchard, B.; Bolvin, H.; Autschbach, J. Magnetic Properties And Electronic Structure Of Neptunyl (VI) Complexes: Wavefcuntions, Orbitals And Crystal-Field Models. Chem. - Eur. J. 2014, 20, 7994−8011. (40) Shannon, R. D. Revised Effective Ionic Radii And Systematic Studies Of Interatomic Distances In Halides And Chalcogenides. Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr. 1976, 32, 751−767. (41) Binnemans, K.; van Deun, R.; Gorller-Walrand, C.; Adam, J. L. Spectroscopic Properties Of Trivalent Lanthanide Ions In Fluorophosphate Glasses. J. Non-Cryst. Solids 1998, 238, 11−29. (42) Richardson, F. S. Selection Rules For Lanthanide Optical Activity. Inorg. Chem. 1980, 19, 2806−2812. (43) Ferraro, F.; Aparecida Barboza, C.; Arratia-Pérez, R. A Relativistic Study Of The Electronic And Magnetic Properties Of Cerocene And Thorocene And Its Anions. J. Phys. Chem. A 2012, 116, 4170−4175.

(16) Anton, J.; Fricke, B.; Engel, E. Noncollinear And Collinear Relativistic Density-Functional Program For Electric And Magnetic Properties Of Molecules. Phys. Rev. A: At., Mol., Opt. Phys. 2004, 69, 012505. (17) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (18) Van Lenthe, E.; Baerends, E. J. Optimized Slater-Type Basis Sets For The Elements 1−118. J. Comput. Chem. 2003, 24, 1142−1156. (19) Visscher, L.; Jensen, H. J. Aa.; Bast, R.; Saue, T.; et al. DIRAC, a relativistic ab initio electronic structure program, Release DIRAC13; 2013 (http://www.diracprogram.org). (20) Gomes, A. S. P.; Dyall, K. G.; Visscher, L. Relativistic DoubleZeta, Triple-Zeta, And Quadruple-Zeta Basis Sets For The Lanthanides La-Lu. Theor. Chem. Acc. 2010, 127, 369−381. (21) Dunning, T. H., Jr. Gaussian Basis Set For Use In Correlated Molecular Calculations. I. The Atoms Boron Through Neon And Hydrogen. J. Chem. Phys. 1989, 90, 1007−1023. (22) Kitaura, K.; Morokuma, K. A New Energy Decomposition Scheme For Molecular Interactions Within The Hartree-Fock Approximation. Int. J. Quantum Chem. 1976, 10, 325−340. (23) Becke, A. D.; Edgecombe, K. E. A Simple Measure Of Electron Localization In Atomic And Molecular Systems. J. Chem. Phys. 1990, 92, 5397−5403. (24) Savin, A.; Nesper, R.; Wengert, S.; Fässler, T. F. ELF: The Electron Localization Function. Angew. Chem., Int. Ed. Engl. 1997, 36, 1808−1832. (25) Kohout, M. DGrid Version 4.6; Radebeul, 2011. (26) Varetto, U. MOLEKEL, Version 5.4; Swiss National Supercomputing Centre: Lugano, Switzerland, 2012. (27) Swart, M.; van Duijnen, P. T.; Snijders, J. G. A Charge Analysis Derived From An Atomic Multipole Expansion. J. Comput. Chem. 2001, 22, 79−88. (28) Fonseca Guerra, C.; Handgraaf, J.-W.; Baerends, E. J.; Bickelhaupt, F. M. Voronoi Deformation Density (VDD) Charges: Assessment Of The Mulliken, Bader, Hirshfeld, Weinhold, And VDD Methods For Charge Analysis. J. Comput. Chem. 2004, 25, 189−210. (29) Reed, A. E.; Weinstock, R. B.; Weinhold, F. Natural Population Analysis. J. Chem. Phys. 1985, 83, 735−746. (30) Marques, M. A. L.; Gross, E. K. U. Time-Dependent Density Functional Theory. Annu. Rev. Phys. Chem. 2004, 55, 427−455. (31) van Gisbergen, S. J. A.; Snijders, J. G.; Baerends, E. J. Implementation Of Time-Dependent Density Functional Response Equations. Comput. Phys. Commun. 1999, 118, 119−138. (32) Gritsenko, O. V.; Schipper, P. R. T.; Baerends, E. J. Approximation Of The Exchange-Correlation Kohn-Sham Potential With A Statistical Average Of Different Orbital Model Potentials. Chem. Phys. Lett. 1999, 302, 199−207. (33) Aquilante, F.; De Vico, L.; Ferré, N.; Ghigo, G.; Å Malqvist, P.; Neogrády, P.; Pedersen, T. B.; Pitonak, M.; Roos, B. O.; SerranoAndrés, M.; Urban, M.; Veryazov, Y.; Lindh, R. MOLCAS 7: The Next Generation. J. Comput. Chem. 2010, 31, 224−247. (34) Roos, B. O.; Taylor, P. R. A Complete Active Space SCF Method (CASSCF) Using A Density Matrix Formulated Super-CI Approach. Chem. Phys. 1980, 48, 157−173. (35) Malmqvist, P.-A.; Roos, B. O.; Schimmelpfenning, B. The Restricted Active Space (RAS) State Interaction Approach With SpinOrbit Coupling. Chem. Phys. Lett. 2002, 357, 230−240. (36) Hess, B. A. Relativistic Electronic-Structure Calculations Employing A Two-component No-Pair Formalism With ExternalField Projection Operators. Phys. Rev. A: At., Mol., Opt. Phys. 1986, 33, 3742−3748. (37) Hess, B. A.; Marian, C. M.; Wahlgren, U.; Gropen, O. A MeanField Spin-Orbit Method Applicable To Correlated Wavefunctions. Chem. Phys. Lett. 1996, 251, 365−371. (38) Roos, B. O.; Lindh, R.; Malmqvist, P.; Veryazov, V.; Widmark, P. O. New Relativistic Atomic Natural Orbital Basis Sets For Lanthanide Atoms With Applications To The Ce Diatom And LuF3. J. Phys. Chem. A 2008, 112, 11431−11435. J


Aromatic Lateral Substituents Influence the Excitation Energies of

Recommend Documents