J. Phys. Chem. B 1998, 102, 10789-10798
10789
Theoretical Study of the Structure and Spectroscopic Properties of Cobalt(II) Coordinated to Six-Rings in Zeolites Kristine Pierloot,* Annelies Delabie, and Carl Ribbing Department of Chemistry, UniVersity of LeuVen, Celestijnenlaan 200F, B-3001 HeVerlee-LeuVen, Belgium
An A. Verberckmoes and Robert A. Schoonheydt Center for Surface Chemistry and Catalysis, UniVersity of LeuVen, K. Mercierlaan 92, B-3001 HeVerlee-LeuVen, Belgium ReceiVed: April 17, 1998; In Final Form: July 27, 1998
The structure of the local Co(II) six-ring oxygen environment in zeolite A and the corresponding ligand field spectrum have been studied using large cluster models, including all six surrounding Si or Al tetrahedra terminated by either H or OH groups. Structures were optimized by means of density functional theory (DFT), using a nonlocal (BP86) approach and keeping the orientation of all dangling bonds frozen at the X-ray diffraction (XRD) positions. Electronic spectra were calculated using multiconfigurational perturbation theory based on a CASSCF wave function (CASPT2). It is shown that, in all cases, the presence of the Co(II) ion induces a local distortion of the zeolite surface, resulting in an oxygen coordination number of 3, 4, or 5, depending on the Si/Al ratio. This distortion is reflected in the calculated electronic spectra, showing an increased splitting of the Co2+ free-ion 4F and 4P states as compared to the (average) XRD structures. A new general assignment of the spectrum is proposed, different from earlier assignments based on ligand field theory. The calculated excitation energies of the optimized structures are in excellent agreement with the experimental band positions, thus proving the strength of the present combined DFT-CASPT2 approach. Our results further suggest that the experimentally observed splitting of the main band in the spectrum is due to the presence of asymmetric coordination sites, rather than to Jahn-Teller effects or spin-orbit coupling. The latter may, however, at least partly be responsible for the splitting of the weak feature at 25 000 cm-1.
1. Introduction Zeolites are inorganic crystalline substances, built from an infinitely extending three-dimensional network of SiO4 and AlO4 tetrahedra, linked by sharing all the oxygens.1 The presence of Al3+ instead of Si4+ creates a negative charge, which is compensated by exchangeable cations (e.g. H+, Na+, Ca2+). These cations can be exchanged by transition metal ions which, after dehydration, may occupy different sites. The sites can be given in the notation of Mortier2 (capital letters), as shown in Figure 1A for zeolite A, or in the notation of Smith3 (Roman numbers). Both notations are given in Figure 1B for faujasitetype zeolites X and Y. The transition metal ions are distributed over the available sites, such that an optimum coordination with the structural oxygens and a minimal energy are established. However, in the absence of adsorbed molecules, the resulting transition metal coordination environment is still unsaturated. This makes the transition metal sites interesting centers for adsorption and opens the possibility for catalysis. A crucial step in the investigation of the catalytic potential of these transition metal centers is the study of the different coordination possibilities of the metal in the zeolite and its accompanying electronic structure. One way to study the coordination of transition metal ions in zeolites is by X-ray diffraction (XRD). Table 1 shows the Co-O distances and angles subtended at Co obtained from XRD on cobalt-containing zeolite A (CoA) and zeolite Y (CoY), * Corresponding author. E-mail:
[email protected].
respectively. The crystal structure of dehydrated partially Co(II)-exchanged zeolite A (CoNaA) was determined some time ago by Riley and Seff.4,5 A cubic crystal structure (space group Pm3m) was determined, with the Co(II) ion found at only one site, e.g. on the unit cell 3-fold axis (site A in Figure 1), surrounded by a six-ring of oxygens. The transition metal is situated slightly (0.34 Å) above the plane of three equivalent oxygens at 2.06-2.08 Å (denoted as O(3)), with a second shell of three oxygens (O(2)) at a distance of 2.94-3.04 Å, thus giving it a C3V site symmetry. The O(3)-Co-O(3) angle of 117.4-119.4° indicates an almost trigonal planar coordination with the three close oxygens. For CoY, two partially exchanged CoY powder samples were analyzed by XRD;6 the distances and angles of Co(II) at site I′ (Figure 1B) are given in Table 1. The Co-O(3) and Co-O(2) distances of the Co19Y sample are close to the distances in Co4A. However, the O(3)-Co-O(3) angle is distinctly lower, indicating that at site I′ Co(II) is lifted out of the plane of the O(3) oxygens, toward the cuboctahedra (see Figure 1B). It must, however, be emphasized that these highly symmetrical XRD structures represent an average situation, as no distinction is made between Si4+ and Al3+. In reality, the presence of different Si/Al ratios in the six-ring surrounding the Co2+ ion may induce local distortions of this ring and hence influence the coordination of the different oxygen ligands. An alternative way of obtaining information about the coordination environment of transition metal ions in zeolites is provided by electronic spectroscopy. With a partially occupied 3d shell in an ionic coordination environment, the lowest
10.1021/jp9819036 CCC: $15.00 © 1998 American Chemical Society Published on Web 12/08/1998
10790 J. Phys. Chem. B, Vol. 102, No. 52, 1998
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Figure 2. Diffuse reflectance spectrum of Co1.32A, dehydrated at 400 °C.9
Figure 3. Diffuse reflectance spectra of Co5.9X and Co8.2Y, dehydrated at 400 °C.14
Figure 1. Structures of zeolite A (A) and faujasite-type zeolites X and Y (B), with indication of cation sites.
TABLE 1: Co-O Distances and Angles Subtended at Cobalt, Obtained from X-ray Diffraction Studies on ConA and ConYa T (°C) R(Co-O3) (Å) R(Co-O2) (Å) O3-Co-O3 (deg) a
Co4A4
Co4A5
Co14Y6
Co19Y6
350 2.06 3.04 119.4
350 2.08 2.94 117.4
600 2.24 3.10 97
600 2.11 2.97 100
n denotes the number of Co(II) ions per unit cell.
excitations in the electronic spectra can be expected to originate from transitions within the 3d shell,7 with excitation energies depending on the ligand field (both the number and position of the coordinating oxygens) surrounding the transition metal ion. As such, these spectra provide a “fingerprint” of the specific transition metal environment in the considered zeolite, at least in cases where the metal ion only occupies one single coordination site. In case of multiple coordination sites, overlapping spectra are of course obtained. In such cases, chemometric techniques may be used for the further decomposition of the overall electronic spectrum into its individual components.8-10 The experimental ligand field spectrum of CoNaA, obtained by diffuse reflectance spectroscopy,9 is shown in Figure 2. The
d-d region of the spectrum consists of three main features: a broad band with a maximum at 7000 cm-1 (band I), a second broad band at 15 000-19 000 cm-1 (band II), and a weaker feature at 24 000-25 000 cm-1 (band III). However, all three features are split further by 1000-2000 cm-1. An interpretation of the spectrum, based on the six-ring coordination in the experimental crystal structure and making use of ligand field theory, was given by Klier.11-13 The transitions were labeled by the D3h group representation, even though the cobalt ions are not strictly in the plane of the three proximal oxygens. A weak-field scheme was used, in which the different D3h states are connected to their parent states, either 4F or 4P, in the free Co2+ ion. A 4E′′ (4F) ground state was found, and bands I and II in the spectrum were assigned as excitations within the 4F manifold: 4E′′ (4F) f 4E′ (4F) (band I) and 4E′′ (4F) f 4A1′′, 4A ′′ (4F) (band II), while the third band was assigned as the 2 transition from 4E′′ (4F) to 4E′′ (4P). According to this interpretation, band II corresponds to two different electronic states, which explains its splitting. The splittings of bands I and III, on the other hand, were attributed to Jahn-Teller effects. Klier did not extend his ligand field analysis to the six-ring in Co(II)exchanged faujasite-type zeolites. The experimental spectra of calcined CoX and CoY are shown in Figure 3.14 Multicomponent band systems are observed in the near-infrared and visible regions, which strongly resemble those of CoA. This suggests that the spectra of Co(II) in X and Y are both dominated by Co(II) coordinated to six-rings. In this work, we will present a thorough investigation of the coordination of Co(II) at oxygen six-rings in zeolites by means of ab initio methods. The most recent experimental crystal structure of CoNaA from Riley and Seff5 is used as a starting point for restricted geometry optimizations of the coordination environment of the Co(II) ion by means of density functional
Co(II) Coordinated to Six-Rings in Zeolites
Figure 4. Small Co(OA)3(OB)3Si6-xAlxH12(2-x)+ (A) and large Co(OA)3(OB)3Si6-xAlx(OCH)12(2-x)+ (B) (x ) 0-3) models used to describe the bonding of Co(II) to zeolite A.
theory (DFT). In these calculations, models with Al/Si ratios ranging between 0 and 1 are used. The electronic spectra of the different models are calculated with multiconfigurational secondorder perturbation theory (CASPT2),15 a method which is today firmly established as a powerful tool for the interpretation of electronic spectra, both for organic molecules16 and in different areas of transition metal chemistry.17,18 The sensitivity of the excitation energies to the structure of the Co(II) surroundings and the role played by the Al/Si ratio will be studied. 2. Theoretical Methods Calculations were performed on two different cluster models, with structural formulas CoO6Si6-xAlxH12(2-x)+ and CoO6Si6-xAlx(OH)12(2-x)+, (x ) 0-3), respectively. In the first model, which will be denoted as small in what follows, the dangling bonds of the silicon or aluminum atoms are terminated by H atoms, while in the so-called large models, OH groups are used instead. The Al/Si ratio was varied between 0 and 1, and the Al atoms were positioned such that they are always intervened by at least one Si (thus obeying Loewenstein’s rule19). A picture of the two models used is provided in Figure 4. In what follows, the different types of oxygens in the models will be denoted according to the labels given in this figure: OA and OB for the three close-lying and distant oxygens, respectively, in the sixring surrounding cobalt; OC for the oxygens belonging to the OH groups in the large models. Geometry optimizations were performed with density functional theory (DFT), using the Amsterdam density functional code, ADF.20 The gradient-corrected Becke exchange21 and Perdew correlation22 functionals, denoted as BP86, were used in all cases. The ADF code employs Slater-type basis functions for the expansion of the molecular orbitals and charge density. The basis sets used for Co, OA, and OB are triple-ζ with a polarization function, while for Si, Al, OC, and H, double-ζ basis sets were used. Atomic core orbitals, including the 1s, 2s, and 2p orbitals on Co, Si, and Al and the O 1s orbitals, were kept frozen in all calculations. The molecular grid used to perform numerical integration is controlled by an accuracy parameter, which was set to 4 during all calculations. The following convergence criteria were used in the geometry optimizations: 0.0005 hartree for the energy change, 0.0005 hartree/Bohr for the gradients, 0.001 Bohr for the changes in bond lengths, and 0.5° for the changes in bond angles. The spectra of all considered models were calculated using multiconfigurational perturbation theory based on a CASSCF wave function, i.e., the CASPT2 method.15 MOLCAS-4 software23 was used, and the basis sets employed are of the generally contracted ANO (atomic natural orbital) type24 (labeled as ANO-s in the MOLCAS basis set library). The starting primitive sets are (17s12p9d4f) for Co, (10s6p3d) for O,
J. Phys. Chem. B, Vol. 102, No. 52, 1998 10791 (13s10p) for Si and Al, and (7s) for H. They were contracted to the following final structure: [6s4p3d1f] for Co, [3s2p1d] for OA and OB, [4s3p] for Si and Al. In the small models, a [2s] basis set was used for H, while in the large models, [2s1p] and [1s] basis sets were used for OC and H, respectively (for the labeling of the different oxygen atoms, see Figure 4). The CASSCF/CASPT2 calculations consist of two major steps. In the first step, a CASSCF wave function is built by distributing 13 electrons in an active space consisting of 8 orbitals with predominantly cobalt 3p and 3d character. Remaining correlation effects are dealt with in the second, CASPT2 step, where the CASSCF wave function is the reference function. In the CASPT2 step, all electrons originating from the Co 3p and 3d, Si and Al 3s and 3p, O 2s and 2p, and H 1s orbitals are correlated. This means that, for the small models, 87 electrons are included in the correlation treatment, while for the large models, the total number of correlated electrons is 159. The correlation of the distant electrons (e.g. on the Si, Al, and the terminating H or OH groups) is not expected to significantly influence the results but cannot be avoided in a molecular orbital scheme, with the molecular orbitals delocalized over the entire molecule. Actually, the presence of such a large number of electrons in the correlation treatment causes a problem in the perturbation treatment in that it is responsible for the appearance of so-called intruder states. To deal with the intruder states, a level-shift technique, together with a back-correction,25 was employed. The value of the applied level-shift was 0.3 hartree. It was shown recently26 that a level-shift of this magnitude does not significantly alter the calculated excitation energies in other transition metal systems with a similar intruder state problem. The choice of the CASSCF active space deserves some attention. To describe the different states in the ligand field spectrum, the minimal active space that can be used consists of the five orbitals with predominantly cobalt 3d character. These five orbitals are for CoO6Si3Al3H12- (but very similar orbitals are obtained for all other models) shown in Figure 5. As one can see, all five orbitals involved in the different excited states are indeed mainly Co 3d, with a small contribution from the nearby OA oxygens. As such, the calculated excited states in the spectrum can indeed be characterized as genuine ligand field states. Apart from these five orbitals, additional orbitals from the manifold of ligand valence orbitals may, in principle, be included in the active space. In fact, in transition metal complexes with strongly covalent bonds, the addition of these orbitals is crucial to describe nondynamical correlation effects on the metal-ligand interaction.17 In the present case, however, ionic Co-O bonds are formed and the oxygen orbitals, when added to the active space, either keep an occupation number very close to 2 or are rotated into Co 3p orbitals. The latter is an indication of the importance of the Co 3p orbitals in the correlation treatment. It has been shown17,27 that 3p-3d intershell correlation effects play a crucial role in the description of the relative energy of the different terms originating from 3dn configurations in transition metal ions and their complexes. The effect may essentially be described by including the 3p electrons in the CASPT2 correlation treatment. However, it was also shown27 that slightly better results are obtained when the 3p orbitals are already included in the CASSCF step. This is also the case here. However, test calculations with and without Co 3p orbitals in the CASSCF active space gave differences which were never larger than a few hundred reciprocal centimeters. In view of the fact that the latter calculations are not considerably more computationally demanding, the eightorbital active space was preferred in all calculations.
10792 J. Phys. Chem. B, Vol. 102, No. 52, 1998
Pierloot et al. The present procedure to calculate the spin-orbit couplings requires the use of one set of orbitals to describe all states. This orbital set was constructed from a weighted average of the density matrixes resulting from the CASSCF calculations on the quartet states. The different states between which the spinorbit coupling was calculated were then constructed from a full CI expansion in this orbital set, using the active space (13 electrons in 8 orbitals) described above. The corresponding wave functions were used to construct the off-diagonal elements of the spin-orbit matrix. For the diagonal elements, CASPT2 energies were used, obtained from CASPT2 calculations where the same wave functions constituted the reference. 3. Results and Discussion
Figure 5. The five CASSCF active orbitals involved in the different ligand field states calculated in this work. The plotted orbitals are from the CoO6Si3Al3H12- model (step 5 structure).
The full point group symmetry of the different CoO6Si6-xAlxE12(2-x)+ (E ) H or OH) models considered in this work is either C3V (x ) 0), C3 (x ) 3), Cs (x ) 2), or C1 (x ) 1 or 2). Since only Abelian point groups are accepted by the MOLCAS code, the CASSCF/CASPT2 calculations on the C3V models were performed using Cs symmetry, while for the C3 models, no symmetry was used. However, in both cases, additional symmetry restrictions were imposed (by making use of the SUPSYM option) to prevent mixing between orbitals belonging to different representations in the parent symmetry groups. In all but one test case, state-average CASSCF calculations were performed, including all states belonging to a given symmetry representation (e.g. A in C1 and A′ or A′′ in Cs), and followed by a CASPT2 calculation on each state. To check the validity of this approach, a second set of CASPT2 calculations on the CoO6Si6H12 model were performed, making use of individually optimized CASSCF orbitals for each of the states included (see further in Table 2). For all model compounds, CASSCF/CASPT2 calculations were performed on all states corresponding to the 4F ground state and the 4P first excited state of the free Co(II) ion. For the inclusion of spin-orbit coupling, additional CASPT2 calculations were also performed in one case (e.g. on the CoO6Si4Al2H12 model with Cs symmetry) on the doublet states corresponding to the lowest free-ion 2G, 2P, 2H, and 2D states. The calculation of the spin-orbit couplings was performed by means of an effective one-electron operator28
R2 H ˆ so ) Zeff 2
∑i (1/r3)lˆi‚sˆi
(1)
where Zeff is an effective charge and R the fine structure constant. A value of Zeff ) 15.2 (in atomic units of charge) was obtained from a set of test calculations on the free Co2+ ion, where the effective charge was scaled until optimum accordance with the experimental spectrum29 was obtained.
3.1. Electronic Spectra Obtained Using the CoNaA Crystal Structure. To check as to how far the electronic structure of the Co(II) ion in zeolite A may be explained by a highsymmetrical coordination environment, a first series of CASPT2 calculations were performed on the electronic spectra of the small CoO6Si6-xAlxH12(2-x)+ models with x ) 0-3, using the CoNaA crystal structure with three close-lying oxygens at 2.08 Å and three distant oxygens at 2.94 Å. The results are shown in Table 2. The leftmost column of the table shows the experimental 4P-4F splitting29 in the free Co(II) ion (14 561 cm-1). In the CoO6Si6H122+ model with C3V symmetry, both terms split as follows: 4F f 2 × 4E + 4A1 + 2 × 4A2; 4P f 4E + 4A . In CoO Si Al H -, the Si and Al atoms are at 2 6 3 3 12 alternating positions and the symmetry is reduced from C3V to C3, with the following correspondences: E f E; A1, A2 f A. In CoO6Si4Al2H12, the two aluminums are positioned such that they are mirrored by one of the C3V symmetry planes. Within Cs symmetry, the C3V representations are reduced as follows: E f A′ + A′′; A1 f A′; A2 f A′′. Finally, with only one aluminum in the ring, no symmetry is retained. Note, however, that the lowering of the symmetry with respect to C3V is merely due to the substitution of Si by Al, the geometry of the models being frozen at the XRD (average) crystal structure in all cases. For CoO6Si6H122+, two different sets of results are included in Table 2. Column A represents the results obtained by using individually optimized CASSCF orbitals for each of the states, while the results presented in column B were obtained with one state-average set of CASSCF orbitals per symmetry representation (within Cs symmetry; see also section 2). The difference between both sets of results increases with the calculated excitation energy; the largest difference (1700 cm-1) is found for the c4A2 excited state. This difference should be considered as an upper bound of the accuracy that can be expected from the present CASPT2 results. Only CASPT2 results using stateaverage CASSCF orbitals were obtained for all other models; these results should therefore be compared to the results in column B for CoO6Si6H122+. From the calculated excitation energies, we find a splitting of the 4F state by at most 3500 cm-1 in the different models, while the states originating from 4P are found around 15 500 and 21 000 cm-1, respectively. These results put serious doubts on the ligand field interpretation given by Klier13 of the different bands in the CoNaA spectrum (Figure 2). Even if the results in Table 2 are not yet the final answer, it is unlikely that local distortions of the oxygen coordination sphere may increase the calculated splittings to such an extent that, for example, the band at 16 000 cm-1 could actually correspond to one of the 4F states. A reassignment of the spectrum is therefore proposed, according to which only band I belongs to the free Co(II) 4F state, while bands II and III are due to the splitting of the 4P state. We also
Co(II) Coordinated to Six-Rings in Zeolites
J. Phys. Chem. B, Vol. 102, No. 52, 1998 10793
TABLE 2: CASPT2 Spectral Data (cm-1) for the CoO6Si6-xAlxH12(2-x)+ Models, Obtained at the CoNaA Crystal Structure Co2+ exp29 0
14561
a
Si6 (C3V) energy Ba
state
0 273
0 313
X4A2 a4E
1580 2793
2063 3286
a4A1 b4E
2734 14840
3457 15906
b4A2 c4E
20044
21777
c4A2
Aa 4F
4
P
Si5Al (C1) energy Ba 0 36 71 2004 2639 3024 3495 15858 16039 22129
Si4Al2 (Cs)
Si3Al3 (C3)
state
energy Ba
state
X4A b4A c4A d4A e4A f4A g4A h4A i4A j4A
0 140 574 2326 3204 3451 3486 15240 15981 22411
X4A′′ b4A′′ a4A′ b4A′ c4A′ c4A′′ d4A′′ e4A′′ d4A′ f4A′′
energy Ba
state
0 63
X4A a4E
2260 3235
a4A b4E
3523 15719
b4A c4E
22793
c4A
A: using individually optimized CASSCF orbitals. B: using average CASSCF orbitals.
note that, according to our results, the ground state of Co(II) in zeolite A is nondegenerate in all calculated models, as opposed to the 4E′′ (D3h) ground state proposed by Klier.13 We do, however, find a low-lying 4E state in both CoO6Si6H12 (313 cm-1) and CoO6Si3Al3H12 (63 cm-1). With our new assignment, the splitting of both Co(II) freeion states is seriously underestimated by the CASPT2 results. The calculated splitting of 3500 cm-1 for the 4F state corresponds to only half of the experimental band maximum of band I. The calculated splitting of the 4P state, 5000-7000 cm-1, is closer to the experimental splitting of bands II and III by around 8000 cm-1. The calculated excitation energy of the c4E state in CoO6Si6H122+ and CoO6Si3Al3H12- and the corresponding states in the models with lower symmetry, 15 000-16 000 cm-1, nicely corresponds to the experimental band maximum of band II. However, the calculated result for the second state, 21 70022 700 cm-1, is definitely too low when compared to band III. It is also clear that, as long as the structures are kept frozen, substituting Si by Al does not have a profound effect on the calculated excitation energies. The largest effect is found for the highest state in the spectrum, which is raised by 1000 cm-1 when the Al/Si ratio is altered from 0 to 1. The other states are affected by 200 cm-1 or less. 3.2. Structures Obtained at Different Levels of Optimization. As a next step in our investigation, we decided to examine how the combined presence of Co(II) and Al instead of Si in the six-ring may affect the local structure of the oxygens and, in turn, the cobalt-oxygen coordination properties. To do so, a series of restricted geometry optimizations was performed on the models CoO6Si6E122+ (C3V) and CoO6Si4Al2E12 (Cs), with E ) H or OH. The optimizations were performed in several steps, in each step allowing a next layer of cobalt-surrounding atoms to relax their positions with respect to the CoNaA crystal structure. However, in all cases, the position and orientation of the dangling bonds (Si-H or Al-H in the small models, O-H in the large models) were kept fixed at the crystal values. In this way, we hoped to obtain a realistic picture of the local distortions caused by the presence of Co(II) and Al in an otherwise rigid crystal. Thus, the following geometry optimization steps were performed. Step 1: Small models were used, and the entire O6Si6-xAlxH12 frame was kept fixed, except for the Si-H and Al-H bond distances, which were optimized (note, however, that the orientation of the hydrogens was kept fixed toward the next layer of oxygens in the crystal). The Co(II) ion was allowed to move freely in the ring.
TABLE 3: Structure of the CoO6Si6E122+ and CoO6Si4Al2E12 Models (E ) H or OH), Obtained at the Different (BP86) Optimization Steps CoNaA5
step 1
step 2
step 3
step 4
R(Co-OA) (Å) R(Co-OB) (Å) OA-Co-OA (deg) OB-Co-OB (deg)
CoO6Si6E122+ 2.08 2.08 2.94 2.94 117.5 117.6 120.0 120.0
2.01 2.79 112.4 119.9
2.00 2.79 115.6 120.0
2.02 2.80 115.4 120.0
R(Co-OA1) (Å) R(Co-OA2) (Å) R(Co-OA) (Å)
CoO6Si4Al2E12 2.08 2.12 2.08 2.06 2.08 2.08
2.06 1.98 2.01
2.02 1.98 2.00
2.02 1.98 2.00
R(Co-OB1) (Å) R(Co-OB2) (Å) R(Co-OB) (Å)
2.94 2.94 2.94
2.90 2.97 2.95
3.28 2.59 2.82
3.21 2.65 2.84
3.47 2.52 2.84
OA1-Co-OA2 (deg) OA2-Co-OA2 (deg) OA-Co-OA (deg)
117.5 117.5 117.5
116.6 119.6 117.6
117.7 104.3 113.2
121.0 107.1 116.4
124.1 98.7 115.6
OB1-Co-OB2 (deg) OB2-Co-OB2 (deg) OB-Co-OB (deg)
120.0 120.0 120.0
120.7 118.5 120.0
119.3 119.5 119.4
119.8 119.4 119.7
118.4 122.2 120.0
Step 2: Small models were used, and the same procedure as before was followed, except that now only the Si6-xAlxH12 frame was kept fixed, while the CoO6 cluster was allowed to relax. Step 3: Large models were used. The Si6-xAlx(OH)12 frame was fixed, except for the O-H distances, which were optimized (but oriented toward the next layer of Si,Al in the crystal). Step 4: Large models were used. Now only the (OH)12 frame was kept fixed (distances were optimized), while the entire CoO6Si6-xAlx cluster was allowed to relax. Step 5: Starting from the structures obtained at level 4, the dangling OH groups were replaced by H, and only the Si,Al-H bond distances were reoptimized. No additional information concerning the structures is obtained in this last step. The idea is merely to check whether the presence of OH groups is important for the description of the electronic spectra of the model compounds. The resulting geometries are shown in Table 3. Only the Co-O bond distances and the angles subtended at Co have been included in this table. More details of the structures may be obtained from the Supporting Information. The positions of the two aluminums in CoO6Si4Al2E12 and the labeling of the different oxygen types in Table 3 are as shown in Figure 6. First of all, it is noteworthy that the symmetries obtained for the two models, C3V for CoO6Si6E122+ and Cs for CoO6Si4Al2E12, really represent minima on the potential surface, not saddle points with one or more negative Hessian eigenvalues. Since the size of the models under consideration is too large to actually
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Figure 6. Labeling of the OA and OB oxygens (used in Table 3) in the CoO6Si4Al2E12 (E ) H, OH) model with Cs symmetry. Only the central CoO6Si4Al2 cluster is shown.
TABLE 4: CASPT2 Spectral Data (cm-1) for the CoO6Si6E122+ and CoO6Si4Al2E12 Models (E ) H or OH), Obtained at the Different (BP86) Optimization Steps state
crystal
step 4
step 5
a4E a4A1 b4E b4A2 c4E c4A2
CoO6Si6E122+ (C3V4A2 Ground State) 313 312 704 662 584 2063 2065 3052 2982 2856 3286 3290 3979 4085 3914 3457 3440 5272 5376 5191 15906 15903 16718 16407 16414 21777 21788 22550 22994 22839
step 1
step 2
step 3
461 2800 3686 5109 16247 22737
b4A′′ a4A′ b4A′ c4A′ c4A′′ d4A′′ e4A′′ d4A′ f4A′′
CoO6Si4Al2E12 (Cs4A′′ Ground State) 140 84 767 779 923 574 664 992 862 908 2326 2294 3181 3148 3125 3204 3205 3833 3772 4236 3451 3403 4788 4684 4660 3486 3468 6600 6583 6397 15240 14940 16563 16135 16171 15981 16288 16323 16206 16755 22411 22419 24053 24396 25187
772 798 2927 4145 4624 6197 16025 16563 25076
perform the calculation of the Hessian, a number of test calculations were instead performed using lower symmetries and starting from structures that were severely distorted from C3V and Cs, respectively. In all cases, the final structures obtained showed no significant differences from the structures reported in Table 3. At least in case of CoO6Si6E122+, this observation was not to be expected a priori. Indeed, although our calculations predict a nondegenerate 4A2 ground state for the C3V models (see Table 2 and also further in Table 4), the lowest excited state a4E is calculated close in energy and may be expected to be Jahn-Teller unstable. This excited-state Jahn-Teller effect, if large enough to overcome the a 4E-X4A2 energy difference, might in principle have led to a ground-state geometrical distortion from C3V to Cs symmetry. Our calculations have proven this not to be the case. For CoO6Si6E122+, no drastic structural changes are found at the different optimization steps. The structure obtained in step 1 (with only Co2+ allowed to move) is not significantly different from the crystal structure. Larger changes are observed in step 2, in that all six oxygens move closer to the central Co(II) ion. The distance with the close-lying oxygens (OA) is reduced by 0.07 Å, while for the three distant oxygens, a slightly larger reduction, 0.14 Å, is calculated. Replacing the H groups by OH (step 3) and also relaxing the Si-Al atoms (step 4) do not affect the geometry of the central CoO6 cluster to any large extent. The difference between the optimized Co-O distances in CoO6Si6E122+ and the experimental values reported for CoNaA may actually reflect an uncertainty in the latter values, caused by the facts that in the zeolite only part of the Na+ ions are substituted by Co2+ and that the conformational differences between the Co2+-centered and the Na+-centered six-windows cannot be taken into account by the XRD measurements. As reported by the authors of ref 5, it is reasonable to expect that
the true Co-O distances are slightly less than the reported XRD values, while the Na-O distances are moderately larger. We now turn to CoO6Si4Al2E12. As indicated in Figure 6 four distinct oxygen types are found in this case: OA1 and OB1 are the oxygens situated in the symmetry plane, while the two OA2 or OB2 oxygens are mirrored by this plane. In Table 3, OA and OB denote the average results obtained for the three short-lying and distant oxygens, respectively. As one can see, these average results are in fact very similar to the results obtained for CoO6Si6E122+, with distances differing by less than 0.05 Å and angles by less than 0.5°. As such, they also show similar deviations from the average trigonal structures obtained from the XRD measurements. However, the individual results obtained for the different oxygen types clearly reveal considerable distortions from this average trigonal symmetry. The distances with the close-lying oxygens are the least distorted. As from step 1, the central Co(II) moves in the symmetry plane away from OA1, so that two shorter bonds (Co-OA2) and one longer bond (CoOA1) are formed. The difference, 0.06 Å, is rather small, and this difference is not significantly altered during subsequent optimization steps. On the other hand, as from step 2, important changes are found for the distances between Co and the three distant oxygens. The two OB2 oxygens strongly move toward the central Co(II), while the third OB1 oxygen is moved away. The difference between the two distances, 0.69 Å at step 2, is slightly decreased to 0.56 Å in step 3, when the H groups are replaced by OH. However, after optimization of the Si and Al positions in step 4, a final difference in Co-OB bond lengths of close to 1 Å is found. The structure presented in Figure 6 is the one obtained from this final step, and one can clearly see how the two OB2 oxygens are bent inward in the ring, while OB1 is bent outward. The final result obtained for the two CoOB2 distances, 2.52 Å, points to the formation of two weak bonds, which, in addition to the three strong bonds already present, give the Co(II) ion a five- instead of a three-coordinated environment. To make room for the two additional bonds, the angles between the OA oxygens also undergo thorough changes. As shown by Table 3, the two OA1-Co-OA2 angles open to a value of 124.1°, leaving only 98.7° for the OA2-Co-OA2 angle (step 4). 3.3. Electronic Spectra at the Different Optimization Levels. From the results reported in the previous section, it may already be anticipated that the electronic spectra calculated using optimized structures should show larger splittings of both the free-ion 4F and 4P states as compared to the results obtained in the CoNaA crystal structure (Table 2). Indeed, both the general shortening of the Co-OA bonds and the formation of additional Co-O bonds in the presence of two aluminums may be expected to generate an increased oxygen ligand field strength. This expectation is corroborated by Table 4, showing the CASPT2 excitation energies obtained at the different steps in the optimization of CoO6Si6E122+ and CoO6Si4Al2E12. Looking first at the results obtained for CoO6Si6E122+, we note a large change of the excitation energies at step 2, which is also the step at which the largest structural effects were obtained (Table 3). The splitting of the 4F state is increased by almost 2000 cm-1 as compared to the crystal structure results, while both states originating from 4P are calculated about 1000 cm-1 higher in energy. No significant changes in the excitation energies are found at further optimization steps, in accordance with the fact that the structural changes found at these steps are also small.
Co(II) Coordinated to Six-Rings in Zeolites
J. Phys. Chem. B, Vol. 102, No. 52, 1998 10795
TABLE 5: Effect of Spin-Orbit Coupling for CoO6Si4Al2H12 (Step 5) state
no SOC
X4A′′
0
a4A′
690
b4A′′
753
b4A′
2 871
c4A′
4 030
c4A′′
4 690
d4A′′
6 187
e4A′′
16 062
d 4A′
16 585
a2A′′ b2A′′ a2A′ b2A′ c2A′ c2A′′ d2A′′ d2A′′ e2A′ e2A′′ f2A′ f2A′′ g2A′ g2A′′ h2A′′ f4A′′
16 877 17 237 17 375 17 396 17 541 18 670 19 070 19 092 19 577 20 170 21 662 21 822 22 939 23 818 24 327 25 139
h2A′ i2A′′ i2A′ j2A′′ j2A′ k2A′ k2A′′ l2A′′ l2A′ m2A′′ m2A′ n2A′ n2A′′
25 129 25 441 25 587 26 105 26 268 26 503 27 007 27 312 28 269 28 401 28 508 29 228 29 294
with SOC -464 -302 459 708 780 1 111 2 757 2 944 3 806 3 945 4 641 4 913 6 281 6 402 15 909 15 934 16 387 16 562 16 683 16 946 17 183 17 546 17 925 18 650 18 984 19 126 19 649 20 238 21 733 21 862 22 925 23 851 24 247 24 858 24 969 25 275 25 453 25 840 26 026 26 302 26 520 27 225 27 522 28 231 28 604 28 755 29 202 29 536
73% X4A′′ + 15% a4A′ + 12% b4A′′ 77% X4A′′ + 11% a4A′ + 11% b4A′′ 1% X4A′′ + 54% a4A′ + 39% b4A′′ + 4% b4A′ 3% X4A′′ + 47% a4A′ + 47% b4A′′ + 2% b4A′ 19% X4A′′ + 35% a4A′ + 43% b4A′′ + 2% b4A′ 25% X4A′′ + 32% a4A′ + 41% b4A′′ + 2% b4A′ 2% a4A′ + 1% b4A′′ + 87% b4A′ + 2% c4A′ + 7% c4A′′ 3% a4A′ + 3% b4A′′ + 90% b4A′ + 2% c4A′ + 1% c4A′′ 1% b4A′′ + 2% b4A′ + 84% c4A′ + 7% c4A′′ + 5% d4A′′ 4% b4A′ + 87% c4A′ + 6% c4A′′ + 2% d4A′′ 2% b4A′ + 2% c4A′ + 89% c4A′′ + 6% d4A′′ 4% b4A′ + 13% c4A′ + 80% c4A′′ + 2% d4A′′ 1% c4A′ + 3% c4A′′ + 94% d4A′′ 7% c4A′ + 4% c4A′′ + 88% d4A′′ 92% e4A′′ + 1% b2A′ + 5% d4A′ 89% e4A′′ + 1% b2A′ + 8% d4A′ 3% e4A′′ + 73% d4A′ + 15% a2A′′ + 3% b2A′′ + 1% a2A′ + 2% c2A′ 9% e4A′′ + 79% d4A′ + 6% a2A′′ + 2% b2A′′ + 2% c2A′ 1% e4A′′ + 24% d4A′ + 53% a2A′′ + 2% b2A′′ + 12% a2A′ + 1% b2A′ + 4% c2A′ 2% e4A′′ + 4% d4A′ + 2% a2A′′ + 15% b2A′′ + 13% a2A′ + 38% b2A′ + 24% c2A′ 1% e4A′′ + 2% d4A′ + 1% a2A′′ + 65% b2A′′ + 11% a2A′ + 11% b2A′ + 3% c2A′ + 2% c2A′′ 1% e4A′′ + 1% d4A′ + 15% a2A′′ + 2% b2A′′ + 55% a2A′ + 14% b2A′ + 9% c2A′ + 2% c2A′′ 6% a2A′′ + 7% b2A′′ + 2% a2A′ + 28% b2A′ + 52% c2A′ + 2% d2A′′ 3% a2A′ + 77% c2A′′ + 13% d2A′ + 2% d2A′′ + 1% e2A′ 1% b2A′ + 3% c2A′′ + 21% d2A′ + 55% d2A′′ + 16% e2A′ + 2% e2A′′ 13% c2A′′ + 60% d2A′ + 23% d2A′′ + 2% e2A′ 3% d2A′ + 15% d2A′′ + 73% e2A′ + 4% e2A′′ + 1% f2A′ 1% d4A′ + 1% b2A′ + 6% e2A′ + 84% e2A′′ + 5% f2A′ 4% e2A′′ + 68% f2A′ + 22% f2A′′ 1% e2A′′ + 21% f2A′ + 69% f2A′′ + 4% g2A′ + 1% h2A′ 1% f2A′ + 2% f2A′′ + 85% g2A′ + 9% g2A′′ + 1% h2A′ 8% g2A′ + 83% g2A′′ + 5% h2A′ 89% h2A′′ + 1% h2A′ + 2% f4A′′ + 5% i2A′ 2% g2A′′ + 1% h2A′′ + 74% f4A′′ + 3% h2A′ + 11% i2A′ + 3% j2A′′ + 3% k2A′′ + 1% l2A′ 2% h2A′′ + 74% f4A′′ + 12% h2A′ + 2% i2A′′ + 2% i2A′ + 2% j2A′′ + 3% k2A′′ 3% f4A′′ + 24% h2A′ + 49% i2A′′ + 16% i2A′ + 1% j2A′′ + 4% j2A′ 1% g2A′ + 3% g2A′′ + 15% f4A′′ + 43% h2A′ + 30% i2A′′ + 1% i2A′ + 4% j2A′ 4% h2A′′ + 14% f4A′′ + 6% h2A′ + 9% i2A′′ + 48% i2A′ +14% j2A′′ + 1% j2A′ + 2% k2A′′ 4% f4A′′ + 2% i2A′′ + 10% i2A′ + 59% j2A′′ + 21% k2A′ 1% f4A′′ + 4% i2A′′ + 2% i2A′ + 80% j2A′ + 1% k2A′ + 1% k2A′′ + 7% l2A′′ 3% f4A′′ + 3% i2A′ + 10% j2A′′ + 4% j2A′ + 58% k2A′ +15% k2A′′ +3% l2A′′ +1% l2A′ 3% f4A′′ + 3% j2A′′ + 2% j2A′ + 5% k2A′ + 57% k2A′′ +19% l2A′′ +9% l2A′ 1% f4A′′ + 2% i2A′′ + 1% j2A′′ + 4% j2A′ + 4% k2A′ +9% k2A′′ +67% l2A′′ +7% l2A′ + 4% m2A′ 8% l2A′ + 57% m2A′′ + 32% m2A′ + 1% n2A′ + 1% n2A′′ 1% j2A′′ + 1% k2A′ + 3% k2A′′ + 32% l2A′ + 23% m2A′′ + 30% m2A′ + 4% n2A′ + 4% n2A′′ 2% f4A′′ + 3% j2A′′ + 4% k2A′ + 3% k2A′′ + 39% l2A′ + 13% m2A′′ + 27% m2A′ + 4% n2A′ + 3% n2A′′ 1% l2A′ + 4% m2A′′ + 7% m2A′ + 50% n2A′ + 36% n2A′′ 2% m2A′′ + 1% m2A′ + 40% n2A′ + 56% n2A′′
For CoO6Si4Al2E12, the largest changes in the excitation energies are also found at optimization step 2. Compared to that of the crystal structure, the splitting of the 4F state is almost doubled, from 3500 to 6600 cm-1. We also note the considerable increase in excitation energy of the highest, f4A′′, state, from 22 400 to 24 000 cm-1. Any further optimization steps leave the 4F splitting invariant. However, a further increase of the 4P splitting is found at optimization step 4, with the f4A′′ state now calculated at 25 187 cm-1, more than 2000 cm-1 higher than that of the corresponding c4A2 state in CoO6Si6E122+. It is clear that the difference between the calculated spectra for both models should be traced back to the stronger oxygen ligand field in CoO6Si4Al2E12, with five instead of three close-lying oxygens. The fact that the largest changes in the spectrum of this model are found at optimization steps 2 and 4 is again in accordance with the results for the structures in Table 3, with the largest changes in the Co-OB2 distances calculated at these steps. It should also be noted that, for both models, the changes of the calculated excitation energies between optimization steps 4 and 5 are limited, with differences of less than 250 cm-1.
Obviously, given the same structure for the central CoO6Si6-xAlx cluster (as is the case for steps 4 and 5; see previous section), the presence of either H or OH as terminating group does not affect the spectral characteristics of the central cobalt ion to any significant extent. Looking again at Figure 5, this is of course not surprising: the different orbitals involved in the calculated excited states are completely localized on the central Co(II) and its surrounding oxygens, with no contribution to the terminating groups or even to Si and Al. The present results thus clearly indicate that the spectral properties of transition metal ions coordinated in zeolites are determined solely by their immediate surroundings and can as such be accurately described by the cluster models used in the present work. The fact that hydrogen groups are sufficient to describe the spectra is also important from a computational point of view, since the present CASPT2 calculations on the small model systems are considerably less demanding than when large models have to be used. When comparing the calculated excitation energies for the final structures (step 4 or 5) to the experimental CoNaA spectrum (Figure 2), we find a close correspondence between the results obtained for CoO6Si4Al2E12 and the experimental
10796 J. Phys. Chem. B, Vol. 102, No. 52, 1998
Pierloot et al.
TABLE 6: Structure Obtained at (BP86) Optimization Steps 4 and 5 for Different CoO6Si6-xAlxE12(2-x)+ (E ) H or OH) Models, with x ) 0-3 Si6 Si3Al3 Si4Al2 Si4Al2 Si5Al1 CoNaA5 (C3V) (C3) (Cs) (C1) (C1) R(Co-OA) (Å) average
2.08
2.02 2.02 2.02 2.02
1.95 1.95 1.95 1.95
2.02 1.98 1.98 2.00
2.18 1.88 1.96 2.03
2.22 1.90 1.98 2.03
2.94
2.80 2.80 2.80 2.80
2.98 2.98 2.98 2.98
3.47 2.52 2.52 2.84
3.41 2.48 2.65 2.85
3.33 3.17 2.13 2.88
117.5
115.4 115.4 115.4 115.4
114.0 114.0 114.0 114.0
124.1 124.1 98.7 115.6
118.5 100.4 126.9 115.3
103.1 107.6 140.2 117.0
120.0
120.0 120.0 120.0 120.0
119.8 119.8 119.8 119.8
118.4 118.4 122.2 119.6
120.2 111.3 127.2 119.6
109.8 126.4 123.3 119.8
R(Co-OB) (Å) average OA-Co-OA (deg) average OB-Co-OB (deg) average
band maxima at 16 000 and 25 000 cm-1, respectively, confirming our assignment of these two bands as belonging to the freeion 4P state (see also section 3.1). The calculated 4F splitting is now 6200 cm-1, considerably larger than the splitting found when the crystal structure is used but still slightly below the maximum of the first broad band in the experimental spectrum. We do, however, not find any indication from these calculations of an appreciable splitting of the bands at 16 000 and 25 000 cm-1. Only one, nondegenerate, state (f4A′′) is calculated at 25 000 cm-1, while the two states (e4A′′, d4A′) calculated around 16 000 cm-1 are found to be split by only 500 cm-1, which is considerably less than the experimental band splitting of several thousand reciprocal centimeters. At this point, we decided to check as to how far the observed optical band splitting may be explained by spin-orbit coupling. Calculations including spin-orbit coupling were performed on the step 5 structure of CoO6Si4Al2H12, as described in section 2. The results are shown in Table 5. The leftmost column shows the CASPT2 results obtained for the different quartet and doublet states without spin-orbit coupling. The quartet states are found at slightly different (
