First-Principles Study on Electronic Properties and Optical Spectra of

Subscriber access provided by Temple University Libraries

Article

First-Principles Study on Electronic Properties and Optical Spectra of Ce-doped LaCaB O Crystal 2

10

19

Lixin Ning, Zongcui Wang, Yongfeng Wang, Junxian Liu, Shizhong Huang, Changkui Duan, Yong-Fan Zhang, and Hongbin Liang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp402706x • Publication Date (Web): 27 Jun 2013 Downloaded from http://pubs.acs.org on July 4, 2013

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

First-principles Study on Electronic Properties and Optical Spectra of Ce-doped La2CaB10O19 Crystal Lixin Ning,†,* Zongcui Wang,† Yongfeng Wang,† Junxian Liu,† Shizhong Huang,† Changkui Duan,‡ Yongfan Zhang,§ and Hongbin Liang||,* †

Department of Physics, Anhui Normal University, Wuhu, Anhui 241000, China Department of Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China § Department of Chemistry, Fuzhou University, Fuzhou, Fujian 350002, China || MOE Laboratory of Bioinorganic and Synthetic Chemistry, State Key Laboratory of Optoelectronic Materials and Technologies, School of Chemistry and Chemical Engineering, Sun Yat-sen University, Guangzhou 510275, China ‡

ABSTRACT: We report herein a first-principles investigation on electronic properties and 4f→5d transitions of Ce3+ substituted at La3+ and Ca2+ sites of La2CaB10O19 (LCB) crystal, using the hybrid density functional theory (DFT) and the wavefunction-based embedded cluster calculations, respectively. The hybrid DFT with PBE0 functional yields a band gap of 8.1 eV for LCB, in good agreement with the experimentally estimated value of ~8.3 eV. The energy gaps between the occupied Ce3+ 4f states and the valence band maximum of the host are predicted to be 1.93±0.12 eV, with slight dependence on the local environment. Based on the results of embedded cluster calculations at the CASSCF/CASPT2 level with the spin-orbit effect, the experimentally observed excitation bands are identified in association with the two cerium substitutions. The difference between the lowest 4f→5d transition energies of Ce3+ located at the two dopant sites are rationalized in terms of the variations in centroid energy and crystal-field splitting of 5d1 configuration with the local environment.

Keyword: La2CaB10O19 crystal; Ce3+ ion; band gap; 4f→5d transition; first-principles

1

ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 22

1. INTRODUCTION Borate compounds have been considered as suitable hosts for lanthanide ions for applications in vacuum discharge lamps and display screens, due to their good UV transparency, high optical damage threshold, and efficient luminescence.1,2 Among them, La2CaB10O19

(LCB) crystal has received attention

due

to its

large

effective

second-harmonic-generation (SHG) coefficient about two times greater than that of standard KH2PO4 (KDP) crystal.3 The material crystallizes in monoclinic symmetry with the space group C2, and is chemically stable, non-hygroscopic and easily grown from the melt. The crystal structure consists of infinite two-dimensional double-layers of B5O12 pentaborate groups (including three BO4 tetrahedra and two BO3 triangles) almost perpendicular to the c axis of the unit cell (Figure 1). The La3+ ions (site symmetry C1) are located within the double-layers and are each coordinated by ten oxygen ions, while the Ca2+ ions (site symmetry C2) are located between the double-layers and are each coordinated by eight oxygen ions. Li et al.4 have recently investigated optical properties of Ce-doped LCB crystal (or LCB:Ce3+), and have observed two-center luminescence of Ce3+ which was assigned to 5d→4f transitions of Ce3+ located at La3+ and Ca2+ sites, respectively, based on a correlation between the lowest 4f→5d transition energy and the local coordination structure. Since the 5d orbital is more extended than the 4f orbital, and thus its interactions with the lattice environment are much stronger. The 4f−5d transition bands consist of zero-phonon lines and broad vibronic progressions, and thus are usually difficult to analyze experimentally, especially when the site symmetry of the dopant ion is low. In this case, first-principles calculations are expected to be helpful, as they can in principle provide knowledge on geometries, and electronic states of the host and lanthanide impurity ions, which is a first requirement to understand the performance of materials in applications. In the present work, we have carried out first-principles calculations on LCB:Ce3+, and interpret quantitatively experimental optical spectra of Ce3+ in association with its local coordination structure. The compound prepared experimentally contains a mixture of isovalent (CeLa) and aliovalent (CeCa) substitutions, and is thus an interesting system to study with first-principles

2


Page 3 of 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


methods. The results may provide background information for other materials with similar substitutions, e.g., Ca3La3(BO3)5:Ce3+ crystal.5 Hybrid DFT-based supercell model calculations were performed to obtain the optimized atomic and electronic structures of LCB:Ce3+. The hybrid DFT methods have been shown to improve results on defect physics in wide band-gap oxides,6,7 when compared with the standard DFT methods, due to the partial recovered discontinuity in the exchange-correlation potential by mixing with the Fock exchange. Based on the optimized supercell structures, Ce-centered embedded clusters were constructed with their embedding environments represented

by ab initio model potentials (AIMPs), and wave function-based

CASSCF/CASPT2 calculations with the spin-orbit effect were performed to obtain the 4f1 and 5d1 energy levels of Ce3+, which were then compared with experimental excitation spectra. This work is the first systematic investigation on electronic and optical properties of Ce-doped LCB crystal based on first-principles calculations. The paper is organized as follows. The details of computation are described in Methodology. The results for structural and electronic properties and 4f→5d transitions are presented and discussed in Results and Discussion, with the final conclusions collected in Conclusion.

2. METHODOLOGY

The CeLa-doped LCB crystal was modeled using a 1×2×1 supercell containing 128 atoms, in which one of the eight La3+ ions was substituted with a Ce3+ ion, corresponding to the chemical formula La2-xCexCaB10O19 (x=0.25). For CeCa substitution, a supercell of the same size was employed, in which one of the four Ca2+ ions were replaced by a Ce3+ and another by a Na+ which was used for charge compensation according to experiments4. In this case, the chemical formula is La2Ca1-2xCexNaxB10O19 (x=0.25). The nearest Ce3+-Ce3+ distance in the present CeLa- and CeCa-doped LCB supercell models is around 9.2 Å. Such a distance, if in experiments, would imply energy transfer between Ce3+ ions resulting in concentration quenching of the emission but, in theoretical studies of localized electronic states of individual Ce3+ ions, this distance is large enough to neglect their mutual influence. 3



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The atomic coordinates and lattice parameters of the supercells were optimized by periodic DFT calculations using the hybrid PBE0 functional8 as implemented in VASP.9,10 The La (5s25p65d16s2), Ca (3p64s2), Na (2p63s1), B (2s22p1), O (2s22p4), and Ce (5s25p64f15d16s2) were treated as valence electrons, and their interactions with the respective cores were described by the projected augmented wave (PAW) method.11 The geometry optimizations were performed until the total energies and the Hellmann-Feynman forces on the atoms were converged to 10−6 eV and 0.01 eV Å−1, respectively. For comparison, the geometry optimizations were also performed with the standard PBE12,13 and the hybrid HSE0614,15 functionals. The electronic properties were then studied using the optimized geometries. In PBE0 and HSE06, 25% of the Fock exchange is mixed with 75% of the PBE exchange and, besides, in HSE06 the long-range part of the Fock exchange is replaced by the corresponding PBE counterpart with the range separation controlled by a screening parameter (0.2 Å−1). Due to the large size of the supercells and the high computational cost of the hybrid DFT with plane wave basis sets, only one k-point Г was used to sample the Brillouin zone, with the cutoff energy of the plane wave basis set to 550 eV. On the basis of the DFT-optimized supercell geometries, the cerium-centered (Ce17− LaO10)

and (CeCaO8)13− clusters were constructed, with their immediate surroundings

within the spheres of a radius 10.0 Å represented by 687-682 AIMP embedding potentials at lattice sites, to account for the electrostatic, exchange, and Pauli interactions of the clusters with their environments. The remaining portions of the surroundings were simulated by 92584-91993 point charges at lattice sites, which were generated by the method of Lepetit16 and produced the same electrostatic potentials as the method of Ewald.17 For these embedded clusters, wavefunction-based CASSCF/CASPT2 calculations with the spin-orbit effect were carried out to obtain the 4f1 and 5d1 energy levels of Ce3+, using the program MOLCAS.18 Due to the many electrons involved in the CASSCF calculations, a [4f, 5d, 6s] complete active space has been adopted. The bonding, static and dynamic correlation effects of the Ce3+ 5s, 5p, 4f and 5d electrons and the O2− 2s, 2p electrons have been taken into account. More details on the calculation may be found in ref 19. No symmetry (C1 point group) was used in the calculations, and the 4f1 and 5d1 energy levels of Ce3+ will be labeled by 4f1-7 and 5d1-5, respectively, in order of increasing energy. We used a relativistic effective core potential ([Kr] core) with a (14s10p10d8f3g)/[6s5p6d4f1g] Gaussian valence basis set from ref 20 for cerium, and a [He] core effective core potential with a (5s6p1d)/[2s4p1d] valence basis set from ref 21 for oxygen. These basis sets were further augmented by the respective

4


Page 4 of 22

Page 5 of 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


auxiliary spin-orbit basis sets for a proper description of the inner core region in the spin-orbit calculations. In addition, we added extra basis set (9s)/[1s] to the B atoms closest to the embedded clusters in order to improve the orthogonality between the orbitals of the clusters and their embedding environments.

3. RESULTS AND DISCUSSION 3.1 Structural and Electronic Properties of Undoped LCB

The structure of undoped LCB was first optimized with the DFT-PBE0 method. The calculated (experimental) values of the lattice parameters are: a=11.050 (11.043) Å, b= 6.572 (6.563) Å, c = 9.108 (9.129), and β = 91.575 (91.470) deg, with the deviations no larger than 0.25%. Table 1 lists the calculated internal parameters of the atoms, which shows a good agreement with the experimental values. In Tables S1 and S2 of the Supporting Information, the lattice and internal parameters obtained by DFT with the PBE, HSE06, and PBE0 functionals are compared, showing that the results with PBE0 give the best overall agreement with the experimental data. Figures 2(a)-2(c) depict the total and orbital projected densities of states (DOS) for LCB, calculated using DFT with the pure PBE, and the hybrid HSE06 and PBE0 functionals, based on the respectively optimized atomic structures. A comparison of the figures shows immediately that the hybrid DFT gives a much larger band gap than the pure DFT, and the value (8.1 eV) with PBE0 is close to the experimental value of ~8.3 eV, as estimated from the peak position of excitonic absorption band plus the electron-hole binding energy of the exciton.4 The widening of the band gap from the pure to hybrid DFT occurs with an upward shift of the empty La 4f bands relative to the valence band maximum. This is consistent with the expectation that, the effects of correction for the self-interaction errors as implemented in the hybrid DFT, is especially pronounced for localized electronic states, such as shifting upwards and downwards the empty and occupied 4f bands, respectively. The orbital projected DOS obtained with PBE0 [Figure 2(c)] shows that the top of the valence band is formed by O 2p states with a dispersion of about 9.8 eV, and the bottom of the conduction band is predominantly derived from the localized La 4f states with a band width of around 1.2 eV. It is noted that, with the three DFT functionals, the calculated orbital characters for the valence and conduction band edge states are basically the same, although their energy 5



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

positions relative to the Fermi level (EF) are different. The above results indicate that the PBE0 functional is more suitable for the calculation of the electronic structure of undoped LCB, which provides a good starting point for the following investigations of LCB:Ce3+.

3.2 Structural and Electronic Properties of Ce-doped LCB

Table 2 gives the calculated lattice parameters for CeLa- and CeCa-doped LCB supercells with the DFT-PBE0 method, along with the results of undoped LCB for comparison. There are two symmetrically inequivalent Ca-Ca combinations (with the distances of 6.428 and 6.572 Å) within the optimized LCB supercell for the charge-compensated CeCa-NaCa substitution, which are hereafter denoted as CeCa1 and CeCa2, respectively. We can see from the table that the CeLa substitution produces a negligible decrease (by −0.173%) of the supercell volume, while the CeCa1 and CeCa2 substitutions induce small expansions (by 0.422% and 0.409%, respectively). In addition, the CeLa substitution slightly distorts the monoclinic phase of undoped LCB into a triclinic one, but with the deviations of the angles less than ±0.035o, whereas the CeCa1 and CeCa2 substitutions do not affect the monoclinic phase of the supercell. Thus, the DFT-PBE0 calculations predict a negligible deformation of the crystallographic phase when Ce3+ is substituted at the La3+ site or the Ca2+ site with a Na+ for charge compensation, in agreement with experimental XRD results.4 In Table S3 of the Supporting Information, we listed the lattice parameters for CeLa- and CeCa-doped LCB supercells calculated using DFT with the pure PBE functional, the deviations of which with respect to those with PBE0 (Table 2) are no larger than 1%. Table 3 lists the PBE0 values of the bond distances from Ce3+ to the coordinating oxygen ions in the optimized CeLa-, CeCa1-, and CeCa2-doped LCB supercells. Compared with the undoped system, the changes in the M−O bond lengths are small for the CeLa substitution, with a maximum deviation of 0.030 Å and an average decrease of 0.009 Å. This is consistent with the similar ionic radii of Ce3+ (1.25 Å) and La3+ (1.27 Å) in the 10-fold coordination.22 In the cases of CeCa substitution, the deformations of the local geometry are more substantial and anisotropic. For the nearest six O atoms (O2a,b−O4a,b), the M−O bond lengths are increased by 0.023−0.055 Å, whereas for the farthest two O atoms (O1a,b), the bond lengths 6


Page 6 of 22

Page 7 of 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


are decreased by 0.098−0.137 Å. The average changes of the M−O bond lengths are, however, very small, by −0.005 and 0.001 Å for the CeCa1- and CeCa2- substitutions, respectively. Such anisotropic deformation of the local geometry is usually difficult to detect by classical investigation techniques, making it necessary to employ first-principles calculations. The values of M−O bond lengths obtained with the DFT-PBE method are listed in Table S4 of the Supporting Information, and are larger than the corresponding PBE0 values by 0.004−0.035 Å. Figures 3(a)-3(c) show the total and orbital projected DOS for the ground states of CeLa-, Ceca1-, and CeCa2-doped LCB supercells, calculated with the hybrid DFT-PBE0 method. One observes that, for all the three substitutions, the incorporation of Ce into LCB leads to formation of 4f electronic states in the band gap. The single peak at EF corresponds to the state filled by a lone 4f electron, indicating the +3 oxidation state of the dopant. The empty Ce3+ 4f states constitute the conduction band minima, and are split due to the interaction with the crystalline environment. Compare to those of undoped LCB [Figure 2(c)], the shape of the valence DOS for CeLa-doped LCB [Figure 3 (a)] is almost identical, while for CeCa1- and CeCa2-doped LCB [Figures 3(b) and 3(c)], the shapes are a little more dispersive. These are consistent with the fact that CeLa substitution causes negligible structural relaxations of the LCB supercell, whereas the relaxations are more substantial for CeCa1 or CeCa2 substitutions, inducing changes in chemical bonding. In Figure 3, we also indicate the values for the gaps (∆E4f) between the occupied Ce3+ 4f band and the top of the host valence band within the single-electron picture, which are inherently difficult to measure experimentally.23 The variation of the values (1.81−2.05 eV) reflects the dependence of ∆E4f on the local environment of Ce3+, as in other Ce-doped oxides.24

3.3 4f→5d Transition Energies of Ce3+

On the basis of the PBE0-optimized supercell geometries, the Ce-centered embedded clusters, (CeLaO10)17−, (CeCa1O8)13−, and (CeCa2O8)13−, were constructed with their surroundings represented by AIMPs and point charges at lattice sites. For brevity, these

7



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

clusters will be denoted as CeLa, CeCa1, and CeCa2 clusters, respectively. Wave function-based CASSCF/CASPT2 calculations with the effect of spin-orbit coupling were performed to derive the Ce3+ 4f1 and 5d1 energy levels, and the results are shown in Table 4. We first note the close proximity of the energy levels between CeCa1 and CeCa2 clusters, with the average deviations in absolute value of 36 cm−1 and 226 cm−1 for the 4f1 and 5d1 levels, respectively. This indicates that the slight differences in the local geometries of CeCa1 and CeCa2 clusters have negligible effects on the splittings of 4f1 and 5d1 levels, and hence these two clusters will be referred to as CeCa without distinction in the following discussion. For all the clusters, the calculated 4f1 levels falls into two groups (i.e. 4f1-3 and 4f4-7 levels), which are linked to the 2F5/2 and 2F7/2 multiplet terms of Ce3+, respectively, with a splitting of 2359−2564 cm−1 by the spin-obit interaction. When comparing the calculated 4f→5d transition energies with those estimated from experimental excitation band maxima [Figure 4 (a)], the lowest band at ~32050 cm−1 (band K) can be assigned to the lowest 4f1→5d1 transition of Ceca with a deviation of about 1058 cm−1, while the band higher at ~36765 cm−1 (band J) are mainly due to the 4f1→5d1 transition of CeLa with an deviation of 143 cm−1. These assignments are consistent with excitation spectral measurements, and are also in support of the conclusions made earlier based on qualitative analyses of 5d1 centroid shift and crystal-field splitting in relation with the local environment. The excitations bands G, F, and E may have contributions from 4f1→5d2-4 transitions of CeLa and the 4f1→5d2-5 transitions of CeCa. The band D at around 52100 cm−1 can be assigned to the single 4f1→5d5 transition of CeLa with a deviation of 1547 cm−1. The band H has been identified as the excitonic transition of the LCB host.4 A schematic representation of 4f1→5di transitions is shown in Figures 4(b) and 4(c) for CeLa and CeCa clusters, respectively, with the relative intensities within each cluster calculated using the wavefunctions and energies at the spin-orbit level. The lowest 4f1→5d1 transition of Ce3+ at the Ca2+ site is redshifted by ~5916 cm−1 from that at the La3+ site, which can be explained quantitatively by using the calculated energy-level data in Table 4. The transition energy can be decomposed as ∆E(4f1→5d1) = ∆Ece(4f1→5d1) − ∆Ecfs(5d1), where ∆Ece(4f1→5d1) denotes the energy difference between the

8


Page 8 of 22

Page 9 of 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


ground 4f1 level and the 5d1 centroid, and ∆Ecfs(5d1) (i.e., the crystal field stabilization energy) refers to the relative energy of the 5d1 level with respect to the 5d1 centroid. From Table 4, the values of ∆Ece (∆Ecfs) are 42882 cm−1 (5974 cm−1) and 42197 cm−1 (11205 cm−1) for CeLa and CeCa clusters, respectively. For ∆Ece, the decrease by 685 cm−1 from CeLa to CeCa can be rationalized as a consequence of two competing effects. According to the Judd-Morrison model,25,26 ∆Ece is decreased with the shortening of the average Ce−O bond lengths (from 2.64 to 2.47 Å), but it is increased with the reduction of the coordination number (from ten to eight). For ∆Ecfs, the increase by 5231 cm−1 from CeLa to CeCa is consistent with the expectation that the 5d1 crystal field splitting should increase with the size reduction of the coordination polyhedron, and this effect dominates the large redshift of the 4f1→5d1 transition from CeLa to CeCa. It was established from empirical regularity that the lowest 4f1→5d1 transition energy of Ce3+ in a host lattice is lower by 12240 ± 750 cm−1 than the lowest 4f2 → 4f15d1 transition of Pr3+ with the same lattice environment.27 Thus, for the ground state geometries, the lowest 4f15d1 energy levels of Pr3+ at La3+ and Ca2+ sites of LCB are estimated to be at 49148 ± 750 cm−1 and 43232 ± 750 cm−1, respectively, and are close to those (~ 49020 and ~ 44640 cm−1, respectively) measured from excitation band maxima of Pr3+ in LCB.28 These energies are to be compared with the energy of the 4f2 1S0 level, which is usually in the range 46500−47000 cm-1 for Pr3+ in oxides and is not very sensitive to the coordination environment. From the comparisons, we expect that photon cascade emission initiated from the 1S0 level might be possible for Pr3+ at La3+ site, but not for Pr3+ at Ca2+ site where only 4f15d1→4f2 emission is possible, taking into account the Stokes shift due to lattice relaxation in the lowest 4f15d1 state. This is in agreement with experimental observations on LCB:Pr3+.28

4. CONCLUSIONS

The electronic properties and 4f→5d transitions of the dopant Ce3+ located at La3+ and Ca2+ sites of LCB crystal have been investigated using the hybrid DFT calculations with the supercell model and the wavefunction-based CASSCF/CASPT2 calculations with the 9



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

embedded cluster model, respectively. It was found that the hybrid PBE0 functional is more suitable for the calculations of electronic structures of the system, when compared with the pure PBE and the hybrid HSE06 functionals, in view of the close agreement between the calculated and experimental band-gap values for the host. The locations of Ce3+ 4f1 ground state levels have been predicted to be 1.93±0.12 eV above the top of the host valence bands with the DFT-PBE0 method. Based on the DFT-optimized supercell geometries, the Ce-centered embedded clusters were constructed, and the CASSCF/CASPT2 calculations including the spin-orbit effect were performed to derive the 4f1 and 5d1 energy levels of Ce3+ at the La3+ and Ca2+ sites. From comparison of calculated and experimental 4f→5d transition energies, the experimental excitation bands were identified in association with the site occupations. Finally, the decrease of the lowest 4f→5d transition energy from CeLa to CeCa substitution was analyzed in terms of centroid energy and crystal-field splitting of 5d1 configuration. The present work demonstrates that a combination of the hybrid DFT with appropriate functionals and the wavefunction-based methods may be of use in determining the 4f1 ground state level of Ce3+ relative to valence or conduction band states of the host and elucidating 4f−5d transition properties of the impurity ion in connection with its local coordination structure in cerium-doped optical materials.

AUTHOR INFORMATION Corresponding author * E-mail: [email protected]; [email protected] Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS We thank Professor Luis Seijo for the help with the program MOLCAS. This work has been supported by the National Science Foundation of China (Grant nos 11174005, 21171176, 11074315, 21073035, and U1232108).

10


Page 10 of 22

Page 11 of 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


ASSOCIATED CONTENT Supporting Information Calculated lattice parameters (Table S1) and internal parameters (Table S2) for undoped LCB using DFT with the PBE, HSE06, and PBE0 functionals, and calculated lattice parameters (Table S3) and local structural data (Table S4) for CeLa- and CeCa-doped LCB supercells using DFT with the PBE functional. This material is available free of charge via the Internet at http://pubs.acs.org.

REFERENCES (1) Blasse, G.; Grabmaier, B. C. Luminescent Materials: Berlin: Springer, 1994. (2) Yen, W. M.; Shionoya, A.; Yamamoto H. Phosphor Handbook (2nd edition); CRC Press: Boca Raton, 2007; Chap. 4–13. (3) Wu, Y.; Liu, J.; Fu, P.; Wang, J.; Zhou, H.; Wang, G.; Chen, C. A New Lanthanum and Calcium Borate La2CaB10O19. Chem. Mater. 2001, 13, 753–755. (4) Li, L.; Liang, H.; Tian, Z.; Lin, H.; Su, Q.; Zhang, G. Luminescence of Ce3+ in Different Lattice Sites of La2CaB10O19. J. Phys. Chem. C 2008, 112, 13763–13768. (5) Liu, C.; Liang, H.; Kuang, X.; Zhong, J.; Sun, S.; Tao, Y. Structure Reﬁnement and Two-Center Luminescence of Ca3La3(BO3)5:Ce3+ under VUV−UV Excitation. Inorg. Chem. 2012, 51 8802–8809. (6) Oba, F.; Togo, A.; Tanaka, I.; Paier, J.; Kresse, G. Defect Energetics in ZnO: A Hybrid Hartree-Fock Density Functional Study. Phys. Rev. B 2008, 77, 245202. (7) Janotti, A.; Varley, J. B.; Rinke, P.; Umezawa, N.; Kresse, G.; Van de Walle, C. G. Hybrid Functional Studies of the Oxygen Vacancy in TiO2. Phys. Rev. B 2010, 81, 085212. (8) Perdew, J. P.; Ernzerhof, M.; Burke, K. Rationale for Mixing Exact Exchange with Density Functional Approximations. J. Chem. Phys. 1996, 105, 9982. (9) Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169–11186. (10) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B 1999, 59, 1758–1775. 11



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(11) Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B 1994, 50, 17953–17979. (12) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865–3868. (13) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1997, 78, 1396. (14) Heyd, J; Scuseria, G. E.; Ernzerhof, M. Hybrid Functionals Based on a Screened Coulomb Potential. J. Chem. Phys. 2003, 118, 8207. (15) Krukau, A. V.; Vydrov, O. A.; Izmaylov, A. F.; Scuseria, G. E. Influence of the Exchange Screening Parameter on the Performance of Screened Hybrid Functionals. J. Chem. Phys. 2006, 125, 224106. (16) Gellé, A.; Lepetit, M. Fast Calculation of the Electrostatic Potential in Ionic Crystals by Direct Summation Method. J. Chem. Phys. 2008, 128, 244716. (17) Ewald, P. P. The Computation of optical and Electrostatic Lattice Potentials. Ann. Phys.-Paris 1921, 64, 253–287. (18) Karlström, G.; Lindh, R.; Malmqvist, P-Å.; Roos, B. O.; Ryde, U.; Veryazov, V.; Widmark, P. O.; Cossi, M.; Schimmelpfennig, B.; Neogrady, P.; Seijo, L. Molcas: a Program Package for Computational Chemistry. Comput. Mater. Sci. 2003, 28, 222–239. (19) Muñoz-García, A. B.; Pascual, J. L.; Barandiarán, Z.; Seijo, L. Structural Effects and 4f-5d Transition Shifts Induced by La Codoping in Ce-Doped Yttrium Aluminum Garnet: First-Principles Study. Phys. Rev. B 2010, 82, 064114. (20) Seijo, L.; Barandiarán, Z.; Ordejón, B. Transferability of Core Potentials to f and d States of Lanthanide and Actinide Ions. Mol. Phys. 2003, 101, 73–80. (21) Barandiarán, Z.; Seijo, L. The Abinitio Model Potential Method. Cowan–Griffin Relativistic Core Potentials and Valence Basis Sets from Li (Z=3) to La (Z=57). Can. J. Chem. 1992, 70, 409–415. (22) Shannon, R. D. Revised Effective Ionic Radii and Systematic Studies of Interatomic Distances in Halides and Chalcogenides. Acta Cryst. A 1976, 32, 751–767. (23) van der Kolk, E.; Basun, S. A.; Imbusch, G. F.; Yen, W. M. Temperature Dependent

12


Page 12 of 22

Page 13 of 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Spectroscopic Studies of the Electron Delocalization Dynamics of Excited Ce Ions in the Wide Band Gap Insulator, Lu2SiO5. Appl. Phys. Lett. 2003, 83, 1740–1742. (24) Canning, A.; Chaudhry, A.; Boutchko, R.; Grønbech-Jensen, N. First-Principles Study of Luminescence in Ce-Doped Inorganic Scintillators. Phys. Rev. B 2011, 83 125115. (25) Judd, B. R. Correlation Crystal Fields for Lanthanide Ions. Phys. Rev. Lett. 1977, 39, 242–244. (26) Morrison, C. A. J. Host Dependence of the Rare-Earth Ion Energy Separation 4f N–4f N−1

nl. Chem. Phys. 1980, 72, 1001–1002.

(27) Dorenbos, P. The 4fn↔4fn-15d Transitions of the Trivalent Lanthanides in Halogenides and Chalcogenides. J. Lumin. 2000, 91, 91–106. (28) Chen, W.; Li, L.; Liang, H.; Tian, Z.; Su, Q.; Zhang, G. Luminescence of Pr3+ in La2CaB10O19: Simultaneous Observation PCE and f–d Emission in a Single Host. Opt. Mater. 2009, 32, 115–120.

13



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 22

Table 1. Calculated (calc.) internal parameters for the LCB crystal with the DFT-PBE0 method. The experimental (expt.) data from ref 3 are also listed for comparison

Atom

Site symmetry

La

C1

Ca

C2

O1

C2

O2

C1

O3

C1

O4

C1

O5

C1

O6

C1

O7

C1

O8

C1

O9

C1

O10

C1

B1

C1

B2

C1

B3

C1

B4

C1

B5

C1

Method Calc. Expt. Calc. Expt. Calc. Expt. Calc. Expt. Calc. Expt. Calc. Expt. Calc. Expt. Calc. Expt. Calc. Expt. Calc. Expt. Calc. Expt. Calc. Expt. Calc. Expt. Calc. Expt. Calc. Expt. Calc. Expt. Calc. Expt.

x

Y

0.1623 0.1624 0.0000 0.0000 0.0000 0.0000 0.3891 0.3884 0.3235 0.3218 −0.0707 −0.0714 0.2168 0.2158 0.0732 0.0722 0.0173 0.0157 0.1947 0.1939 −0.1489 −0.1482 0.1457 0.1456 0.4338 0.4326 −0.0385 −0.0397 0.3277 0.3272 0.1156 0.1142 0.2325 0.2327

−0.0026 0.0000 −0.1902 −0.1855 0.7645 0.7650 −0.0216 −0.0231 0.3126 0.3112 0.1244 0.1234 −0.3759 −0.3745 0.3545 0.3528 −0.2913 −0.2905 0.0012 −0.0004 −0.4456 −0.4464 0.9968 0.9992 0.1919 0.1919 0.3237 0.3219 −0.4879 −0.4884 −0.4404 −0.4406 0.0203 0.0212

14


z 0.1427 0.1405 0.5000 0.5000 0.0000 0.0000 0.1151 0.1124 0.1365 0.1359 0.1357 0.1319 0.1814 0.1790 0.2222 0.2213 0.2534 0.2537 0.3884 0.3903 0.5731 0.5732 0.6350 0.6372 0.1266 0.1249 0.1626 0.1608 0.2086 0.2072 0.2703 0.2688 0.5283 0.5289

Page 15 of 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 2. Calculated lattice parameters and volumes for the CeLa-, CeCa1, and CeCa2-doped LCB (1 × 2 × 1) supercells with the DFT-PBE0 method. The percent changes in parentheses were taken with respect to the volume of undoped LCB.

a (Å) 2b (Å) c (Å) α (deg) β (deg) γ (deg) Volume (Å3)

undoped 11.050 13.144 9.108 90.000 91.575 90.000 1322.295

CeLa CeCa1 CeCa2 11.044 11.082 11.079 13.138 13.139 13.140 9.101 9.124 9.124 90.031 90.000 90.000 91.594 91.629 91.611 89.998 90.000 90.000 1320.002 1327.870 1327.706 (−0.173%) (+0.422%) (+0.409%)

Table 3. Calculated distances (in Å) from the dopant site (M) to the atoms in the first coordination shell before and after the CeLa and CeCa substitutions in LCB with the DFT-PBE0 method. The values in parentheses are the differences taken with respect to the data before substitution. See Figure 1 for the definition of atomic labels. M = La M−O1 M−O2 M−O3 M−O4 M−O5 M−O6 M−O7 M−O8 M−O9 M−O10

2.256 2.653 2.733 2.706 2.830 2.826 2.669 2.528 2.548 2.697

M−O1a,b M−O2a,b M−O3a,b M−O4a,b

M = Ca 2.714 2.346 2.355 2.455

M = CeLa 2.226 (−0.030) 2.648 (−0.005) 2.739 (+0.006) 2.701 (−0.005) 2.839 (+0.009) 2.832 (+0.006) 2.653 (−0.016) 2.520 (−0.008) 2.527 (−0.021) 2.677 (−0.020) M = CeCa1 2.577 (−0.137) 2.369 (+0.023) 2.395 (+0.040) 2.510 (+0.055)

M = CeCa2 2.616 (−0.098) 2.377 (+0.031) 2.388 (+0.033) 2.492 (+0.037)

15



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table 4. Calculated energy levels of 4f1 and 5d1 configurations for the (CeLaO10)17−, (CeCa1O8)13−, and (CeCa2O8)13− embedded clusters in LCB, using the CASSCF/CASPT2 method with the effect of spin-orbit coupling.

4f1 4f2 4f3 4f4 4f5 4f6 4f7

CeLa 0 538 725 2199 2771 2998 3151

CeCa1 0 397 752 2445 2634 3129 3579

CeCa2 0 423 721 2431 2593 3095 3473

5d1 5d2 5d3 5d4 5d5

36908 38948 40910 43996 53647

30916 40508 42638 46910 49707

31068 40906 42378 47110 49829

16


Page 16 of 22

Page 17 of 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure captions Figure 1 Schematic representations of the geometrical structure of the LCB crystal and the local coordination structures of La and Ca atoms in the crystal.

Figure 2 Total and orbital-projected DOS for the LCB crystal calculated using DFT with the PBE, HSE06, and PBE0 functionals. The derived band-gap energies (Egap) are indicated in the legends. The Fermi level is set at zero energy.

Figure 3 Total and orbital-projected DOS for the CeLa-, CeCa1-, and CeCa2-doped LCB crystals using DFT with the PBE0 functional. The energies of the occupied Ce3+ 4f bands with respect to the valence band maximum of the host are indicated in the legends. The Fermi levels are indicated by the dash lines.

Figure 4 Schematic diagram for the calculated energies and relative oscillator strengths of the 4f1→5di (i = 1-5) transitions in CeLa- and CeCa-doped LCB crystal. The experimental excitation spectrum is also included for comparison.

17



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 22

Figure 1

1

9

10

2 8 La

B5O3 B4O4 B3O4 B2O3 B1O4

4

3

7 6

5 3a

4a

c

2a 1a

Ca

b

4b

2b 1b 3b

18


Page 19 of 22

Figure 2

DOS (States/eV)

120

Total La f La d Ca d

(a) PBE

100

Egap=4.1 eV

80

Op Bs Bp

60 40 20 0 -8

-6

-4

-2

0

2

4

6

8

8

10

120

(b) HSE06

DOS (States/eV)

100 80

Egap=7.3 eV

60 40 20 0

-10 120

DOS (States/eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-8

-6

-4

-2

0

2

4

6

(c) PBE0

100

Egap=8.1 eV

80 60 40 20 0

-10

-8

-6

-4

-2

0

2

4

Energy (eV)

19


6

8

10


DOS (States/eV)

Figure 3

40

(a) LCB:CeLa

DOS (States/eV)

Total Ce f Ce d La f La d

1.84 eV

20 0

Ca d Op Bs Bp

-20 -40 -10 40

-8

-6

-4

-2

0

2

4

6

8

10

2

4

6

8

10

2

4

6

8

10

(b) LCB:CeCa1 2.05 eV

20 0 -20 -40 -10

DOS (States/eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 22

40

-8

-6

-4

-2

0

(c) LCB:CeCa2 1.81 eV

20 0 -20 -40 -10

-8

-6

-4

-2

0

Energy (eV)

20


Page 21 of 22

Figure 4

(a)

Relative intensities (arb. units)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


K

J

G

F

Expt. E H

D

(b)

5d1

Calc. CeLa

5d2

(c)

5d3 5d 4

5d5

5d1

Calc. CeCa 5d2

30

35

40

5d3

5d5 5d4 45

50

55 3

-1

60

Energies ( 10 cm )

21


65

70


TOC Graphic

K

J

G

F

3+

E

Expt. LCB:Ce

H

D

Relative intensities (arb. units)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 22

5d1

Calc. (CeLaO10)+17

5d2 5d5

5d3 5d 4 5d1

Calc. (CeCaO8)+13 5d2

30

35

40

5d3

5d5 5d4 45

50

55 3

-1

60

65

Energies ( 10 cm )

22


70

First-Principles Study on Electronic Properties and Optical Spectra of

Recommend Documents