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Article

Ab Initio Computations of O and AO as well as ReO2, WO2 and BO2-Terminated ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 (001) Surfaces

by
Roberts I. Eglitis
1,*,
Juris Purans
1,
Anatoli I. Popov
1,
Dmitry Bocharov
1,
Anastasiia Chekhovska
1 and
Ran Jia
1,2,*
1
Institute of Solid State Physics, University of Latvia, 8 Kengaraga Street, LV1063 Riga, Latvia
2
Laboratory of Theoretical and Computation Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, China
*
Authors to whom correspondence should be addressed.
Symmetry 2022, 14(5), 1050; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14051050
Submission received: 15 April 2022 / Revised: 10 May 2022 / Accepted: 17 May 2022 / Published: 20 May 2022
(This article belongs to the Special Issue Applied Surface Science)
Browse Figures
Versions Notes

Abstract

:
We present and discuss the results of surface relaxation and rumpling computations for ReO3, WO3, SrTiO3, BaTiO3 and BaZrO3 (001) surfaces employing a hybrid B3LYP or B3PW description of exchange and correlation. In particular, we perform the first B3LYP computations for O-terminated ReO3 and WO3 (001) surfaces. In most cases, according to our B3LYP or B3PW computations for both surface terminations BO2- and O, AO-terminated ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 (001) surface upper layer atoms shift downwards, towards the bulk, the second layer atoms shift upwards and the third layer atoms, again, shift downwards. Our ab initio computes that ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 (001) surface Γ-Γ bandgaps are always smaller than their respective bulk Γ-Γ bandgaps. Our first principles compute that B-O atom chemical bond populations in the BaTiO3, SrTiO3 and BaZrO3 perovskite bulk are always smaller than near their BO2-terminated (001) surfaces. Just opposite, the Re-O and W-O chemical bond populations in the ReO3 (0.212e) and WO3 (0.142e) bulk are slightly larger than near the ReO2 and WO2-terminated ReO3 as well as WO3 (001) surfaces (0.170e and 0.108e, respectively).

1. Introduction

Advanced (001) surfaces and interfaces in the ReO3, WO3 complex oxides as well as BaTiO3, SrTiO3 and BaZrO3 perovskites are of paramount importance due to the numerous technological applications and great potential for fundamental research caused by their phase transitions [1,2,3,4,5,6,7,8,9,10]. Over the course of the last 25 years, the (001) surfaces of ReO3 and WO3, as well as BaTiO3, SrTiO3 and BaZrO3 perovskites, have been broadly explored worldwide both from the theory and experimental sides [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26]. All our ab initio computed BaTiO3, SrTiO3 and BaZrO3 complex oxides belong to the commonly named ABO3 perovskites. In our case, A is equal to Ba or Sr, whereas B denotes the Ti or Zr atoms [27]. Our computed materials ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 have a huge number of applications in new and emerging technologies. For example, the novel trioxo-rhenium complex [ReO3(phen)(H2PO4)]·H2O has important antibacterial properties [28]. Tungsten oxide nanodots (WO3−x) exhibit remarkable antibacterial capabilities [29]. Tungsten oxide and graphene oxide (WO3-GO) nanocomposite is an excellent antibacterial as well as an anticancer agent [30]. BaTiO3 may be used as an electrical insulator and a piezoelectric substance in different kinds of microphones as well as other transducers [31]. SrTiO3 is an outstanding photocatalyst for the extremely important water splitting process [32,33]. BaZrO3-based ceramic substances are widely used in protonic fuel cell applications [34,35,36,37,38] as well as in hydrogen separation membranes [39,40].
Along with its great technological potential [31,41], BaTiO3 is also a marvellous material for fundamental research since it exhibits several phase transitions [42]. Namely, BaTiO3 exists as one of four polymorphs [43,44] as a function of temperature. As the temperature lowers from high temperature to low temperature [43,44], the crystal symmetries of these four BaTiO3 polymorphs are the cubic BaTiO3 phase, tetragonal BaTiO3 phase, orthorhombic BaTiO3 phase and, finally, the rhombohedral BaTiO3 phase [43,44]. Three of these four BaTiO3 phases, tetragonal, orthorhombic and rhombohedral [43,44], display the ferroelectric effect [43,44]. It is worth noting that recently, the ab initio computations of the temperature effects on the structural, energetic, electronic as well as vibrational properties of four BaTiO3 polymorphs by means of the quasi-harmonic approximations were carried out by Oliveira et al. [45]. The ab initio study of the stability between these four BaTiO3 phases, performed by Oliveira et al. [45], breaks out into several contributions arising from the vibration of the lattice, electronic structure as well as volume expansion/contraction. This novel study by Oliveira et al. [45] was helpful in order to confirm the sequence of the BaTiO3 phase transitions as cubic → tetragonal → orthorhombic → rhombohedral [45] and also its transition temperatures. In contrast to BaTiO3, the SrTiO3 and BaTiO3 perovskites are so-called incipient ferroelectrics, and they exist only in their high symmetry cubic structure [46,47].
In our ab initio computations, we employed the standard cubic unit cells of BaTiO3, SrTiO3 and BaZrO3 crystals containing five atoms [46,47]. The A-type ABO3 perovskite atom in the cubic structure was positioned at the corner of the cube position. The ABO3 perovskite A atom had the following fractional coordinates (0, 0, 0). The B-type ABO3 perovskite atom in the cubic structure was positioned at the cube body center position. The B atom had the following fractional coordinates (½, ½, ½). Lastly, at the ABO3 perovskite, cubic phase face center positions were filled with three cubic ABO3 perovskite O atoms. The three ABO3 perovskite O atoms had the following fractional coordinates (½, ½, 0), (½, 0, ½) and (0, ½, ½) [48,49,50,51]. All three of our ab initio computed cubic ABO3 perovskites (BaTiO3, SrTiO3 and BaZrO3) had the P m 3 ¯ m space group with the space group number 221. Additionally, the ReO3 and WO3 crystals at their cubic symmetry structure had exactly the same space group P m 3 ¯ m with the same space group number 221. The only paramount difference between the BaTiO3, SrTiO3 and BaZrO3 ABO3 perovskites as well as ReO3 and WO3 crystals, which had exactly the same cubic symmetry structure, the same space group P m 3 ¯ m and even the same space group number 221, was missing an A-type atom in the ReO3 and WO3 materials.
To the best of our knowledge, only a few ab initio computations up to now exist in the world of science, dealing with the ReO2 or WO2-terminated polar ReO3 and WO3 (001) surfaces [52,53,54]. It is worth noting that up to now there have been no ab initio computations performed in the world dealing with O-terminated polar ReO3 or WO3 (001) surfaces. For our ab initio computations, relevant experimental data [46,55,56,57,58,59,60,61,62,63,64,65] dealing with ReO3, WO3, BaTiO3, SrTiO3 and PbTiO3 bulk crystals are collected in Table 1.
The perfect cubic structure for the ReO3 conducting oxide [55] is stable at all temperature ranges starting from room temperature. The crystal structure of tungsten trioxide (WO3) [56] depends on the temperature. WO3 has tetragonal symmetry if the temperature is above 740 °C. WO3 is orthorhombic [56] at the temperature range from 330 °C to 740 °C. WO3 is monoclinic [56] at the temperature range from 17 °C to 330 °C. Finally, WO3 is triclinic [56] at the temperature range from −50 °C to 17 °C. It is worth noting that the most common structure for WO3 is monoclinic. The space group for the WO3 monoclinic structure is P21/n. The experimentally measured WO3 (Γ-Γ) bandgap is equal to 3.74 eV [57]. In the BaTiO3 perovskite matrix, according to the experimental measurements performed by Wemple, the room temperature (RT) bandgaps are equal to 3.38 eV and 3.27 eV [58] for the light polarized parallel and perpendicular to the ferroelectric axis c. The experimental SrTiO3 Γ-Γ bandgap, according to measurements by Benthem et al. [59], is equal to 3.75 eV (Table 1). Finally, the experimental BaZrO3 Γ-Γ bandgap, according to experiments performed by Robertson, is equal to 5.3 eV [60] (Table 1). ReO3 is cubic at all temperatures, starting from liquid helium temperature to 673 K. The experimentally measured ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 bulk lattice constants in cubic crystal structures are listed by us in Table 1. The objective of our contribution was to carry out the first ab initio computations for polar O-terminated ReO3 and WO3 (001) surfaces. We compared our ab initio computation results for polar ReO3 and WO3 as well as neutral BaTiO3, SrTiO3 and BaZrO3 perovskite (001) surfaces and pointed out systematic tendencies in our performed computations in a way that is comfortably approachable for a broad audience of readers worldwide.

2. Computation Methods and Materials

We performed our forefront ab initio computations for the ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 bulk and their (001) surfaces by means of the hybrid B3PW [66,67] or B3LYP [68] exchange-correlation functionals. Both these B3PW [66,67] as well as B3LYP [68] hybrid exchange-correlation functionals are implemented into the very famous, world-class computational package CRYSTAL [69], developed by Torino University, Italy. The computational package CRYSTAL [69] utilizes 2-D isolated slab representation for the (001) surface structure first principles computations. We performed the reciprocal space integration in our first principles computations for ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 matrixes. Namely, we integrated the Brillouin zone employing the 8 × 8 × 8 times expanded Pack–Monkhorst [70] net for the bulk ab initio computations as well as 8 × 8 × 1 times enlargement for the (001) surface ab initio computations of these materials. In order to achieve the high accuracy of our computations, sufficiently large tolerances of 7, 8, 7, 7 and 14 were used by us for the Coulomb overlap, Coulomb penetration, exchange overlap, the first exchange pseudo-overlap as well as for the second exchange pseudo-overlap, respectively. With the goal of detecting the performance of various non-identical methods, we computed the bulk Γ-Γ bandgaps for ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 matrixes (Table 2 and Figure 1) and compared our ab initio computation results with the available experimental data [14,59,60,71,72,73,74,75,76].
As it is possible to see from Table 2 and Figure 1, the Hartree–Fock (HF) [77,78] method always, for all computed materials, significantly overestimates the Γ-Γ bandgap. For example, our ab initio computed BaTiO3 (Γ-Γ) bulk bandgap is overestimated by 3.67 times with respect to the experimental BaTiO3 bulk Γ-Γ bandgap values (Table 2). Additionally, our ab initio computed SrTiO3 bulk Γ-Γ bandgap is overestimated by 3.29 times regarding the experimental SrTiO3 bulk Γ-Γ bandgap value (Table 2). In our density functional theory (DFT) computations, we used the local density approximation (LDA) with the Dirac–Slater exchange [79] as well as the Vosko–Wilk–Nusair correlation [80] energy functionals and a set of GGA exchange and correlation functionals as suggested by Perdew and Wang (PWGGA) [66,67]. On another side, the ab initio computed Γ-Γ bulk bandgaps for all five materials using the PWGGA are always considerably underestimated with respect to the experimental bulk Γ-Γ bandgap values (Table 2 and Figure 1). For example, our ab initio PWGGA computed MgF2 bulk Γ-Γ bandgap value (6.94 eV) is 1.97 times underestimated with respect to the experimental MgF2 Γ-Γ bulk bandgap value equal to (13.0 eV) [76] (Figure 1 and Table 2). As we can see from Table 2 and Figure 1, the hybrid exchange-correlation functionals B3PW and B3LYP always allow us to achieve the best possible agreement between the ab initio computed as well as experimental bulk Γ-Γ bandgaps for all five of our first principles computed materials BaTiO3, SrTiO3, BaZrO3, MgF2 as well as CaF2. The main reason for such a good agreement is that the hybrid B3LYP and B3PW functionals include a portion of exact exchange energy density from the HF theory (20%), while the rest of the exchange-correlation part is a mixture of various approaches (both exchange and correlation). This is the key reason why we performed all our future bulk as well as (001) surface ab initio computations by means of the B3PW or B3LYP hybrid exchange-correlation functionals (Table 2 and Figure 1).
With an aim to ab initio compute the TiO2-terminated BaTiO3, SrTiO3 and ZrO2-terminated BaZrO3 (001) surfaces, we selected nine-layer, mirror-symmetrical (001) slabs. They consisted of neutral and alternating TiO2(ZrO2) or AO layers (Figure 2). These slabs were positioned perpendicular to the axis z. Our generated nine-layer slab, used by us in ABO3 perovskite (001) surface ab initio computations, was terminated from both sides by the TiO2-terminated planes for BaTiO3 and SrTiO3 perovskites as well as by ZrO2-terminated planes for BaZrO3 perovskite (Figure 2). Accordingly, our in ab initio computations employed the (001) surface model for the BO2-terminated ABO3 perovskites and the nine-layer slab consisted of a 23-atom supercell. Our ab initio computed ABO3 perovskite BO2-terminated (001) slab was non-stoichiometric (Figure 2), and it had the following chemical equation A4B5O14. With the objective to directly compare the properties of three perovskites (BaTiO3, SrTiO3 and BaZrO3) as well as ReO3 and WO3 materials under the same conditions and, as much as possible, to reduce the computational time, we only investigated the high symmetry ( P m 3 ¯ m ) cubic phases of these five materials. In our surface structure B3LYP and B3PW first principles computations, we allowed the atoms of the upper two or three surface layers to only relax along the z-axis since the (001) surfaces of the perfect cubic crystals, due to symmetry restrictions, do not have any forces acting along the other x- or y-axes. We optimized the (001) surface atom atomic coordinated through the slab total energy minimization. For this purpose, we employed our own computer code, which implements [81] conjugated gradients optimization technique with numerical computation of derivatives [81].
Just opposite to our ab initio computed neutral BaTiO3, SrTiO3 and BaZrO3 (001) surfaces, which are built up from the neutral BO2 or AO layers (Figure 2), the WO2 or ReO2-terminated polar WO3 or ReO3 (001) surfaces were formed from charged (Figure 3) WO2 (ReO2) or O layers. This is much more demanding to compute at the ab initio level for the polar WO2 or ReO2-terminated WO3 or ReO3 (001) surfaces (Figure 3) than the neutral (Figure 2) ABO3 perovskite BO2-terminated (001) surfaces [8,52,82,83,84]. For example, in our ab initio computations, the ReO2-terminated polar ReO3 (001) surface consisted of nine alternating ReO2 or O layers (Figure 3). This means that this ReO2-terminated ReO3 polar (001) surface contained 19 atoms and had the chemical equation Re5O14.
In our ab initio computations, we employed the neutral atomic basis sets for all three atoms entering the WO3 and ReO3 crystals. Namely, we used the neutral W atom basis set from the reference [85] for the W atom. Additionally, for the Re atom, we used the neutral atom basis set from the reference [69]. Finally, for the O atom, again, we used the neutral O atom basis set, developed by Piskunov et al., from reference [71]. Using the neutral atomic basis sets for all three Re, W and O atoms, we determined in our ab initio computations that both ReO2 and WO2-terminated ReO3 and WO3 (001) surfaces have a total charge of our employed nine-layer slab equal to zero. In our ab initio computations, we utilized the well-known classical Mulliken population analysis for the description of the ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 effective atomic charges q and also their chemical bond populations P [86,87,88,89].
For our ab initio computations of AO-terminated BaTiO3, SrTiO3 and BaZrO3 (001) neutral surfaces, we used, from both sides, AO-terminated mirror-symmetrical slabs containing nine alternating AO and BO2 layers (Figure 4). These AO-terminated ABO3 perovskite (001) nine-layer slabs consisted of a supercell containing 22 atoms (Figure 4). They were non-stoichiometric, and they had the following unit cell equation A5B4O13 (Figure 4). The only striking difference between the AO-terminated BaTiO3, SrTiO3 and BaZrO3 (001) slabs (Figure 4) and O-terminated ReO3 and WO3 slabs was the missing O atom in the ReO3 and WO3 (001) slabs (Figure 5). Thereby, the O-terminated ReO3 and WO3 nine-layer (001) slabs consisted of alternating O-BO2-O-BO2-O-BO2-O-BO2-O layers (Figure 5). They contained 17 atoms and had the following unit cell equation B4O13 (Figure 5).

3. Ab Initio Computation Results for ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 Bulk Properties

As an opening of our first principles computations, by means of the B3LYP or B3PW hybrid exchange-correlation functionals, we computed the ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 bulk lattice constants [52,53,54,90,91,92,93]. It is worth noting that we performed all our ab initio computations by B3LYP hybrid exchange-correlation functional B3LYP for ReO3 and WO3 matrixes as well as by B3PW hybrid exchange-correlation functional for BaTiO3, SrTiO3 and BaZrO3 perovskites. Our ab initio computed bulk lattice constants for ReO3 (3.758 Å), WO3 (3.775 Å), BaTiO3 (4.008 Å), SrTiO3 (3.904 Å) and BaZrO3 (4.234 Å) perovskites are in a fine agreement with the obtained experimental measurements (Table 1). For example, our ab initio B3LYP computed ReO3 bulk lattice constant (3.758 Å) is only overestimated by approximately 0.29% with respect to the experimental ReO3 bulk lattice constant equal to 3.747 Å (Table 1). Additionally, our ab initio B3PW computed BaTiO3 bulk lattice constant (4.008 Å) is almost in a perfect agreement with the experimentally measured BaTiO3 bulk lattice constant (4.004 Å) (Table 1).
As we can see from Table 3, our ab initio computed atomic charges for all atoms are considerably smaller than the generally accepted classical ionic charges in ABO3 perovskites for Ba or Sr atoms (+2e), for Ti or Zr atoms (+4e), or for O atoms (−2e). Additionally, our ab initio computed Re and W atom effective charges in ReO3 or WO3 materials (+2.382e or +3.095e, respectively) are considerably smaller than the Re or W classical ionic charges equal to (+6e). It is worth noting that the absolute values of O atom charges in the ABO3 perovskites BaTiO3, SrTiO3 and BaZrO3 (−1.388e, −1.407e, and −1.316e, respectively) are always larger than the absolute values of O atom charges in the ReO3 or WO3 crystals (−0.794e or −1.032e, respectively). Just opposite, our ab initio computed chemical bond populations between the Re and O as well as W and O atoms in the ReO3 and WO3 materials (Table 3) (+0.212e and +0.142e, respectively) are always considerably larger than the respective B-O atom chemical bond populations in the BaTiO3, SrTiO3 and BaZrO3 perovskites (+0.098e, +0.088e and +0.108e, respectively).
As a next step, by means of B3LYP or B3PW (Table 4 and Figure 6) hybrid exchange-correlation functionals, at the ab initio level, we computed the ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 bulk Γ-Γ bandgaps. As we can see from Table 4 and Figure 6, our B3LYP computed ReO3 bulk Γ-Γ bandgap is equal to 5.76 eV. This is a theoretical prediction since, to the best of our knowledge, there is no experimental bandgap yet detected for the ReO3 matrix at Γ-point. Our computed WO3 bulk Γ-Γ bandgap (4.95 eV) by 1.21 eV exceeds the WO3 experimentally detected [56] bulk Γ-Γ bandgap (Table 4). Determined by means of the B3PW hybrid exchange-correlation functional ab initio, our computed BaTiO3 (3.55 eV), SrTiO3 (3.96 eV) and BaZrO3 (4.93 eV) bulk Γ-Γ bandgaps are in a fair agreement with the experimentally measured bulk Γ-Γ bandgaps for BaTiO3, SrTiO3 and BaZrO3 perovskites (3.2 eV, 3.75 eV and 5.3 eV, respectively) (Table 4 and Figure 6).

4. Ab Initio Computation Results for the BO2 and O-Terminated ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 (001) Surfaces

As we can see from our ab initio computation results for ReO2 and WO2-terminated ReO3 and WO3, as well as BO2-terminated BaTiO3, SrTiO3 and BaZrO3 (001) surfaces, collected in Table 5, for all five our computed materials ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3, the upper layer atoms relax inwards, in the direction towards the bulk (Table 5). The only exception from this systematic trend is the upward shift of the WO2-terminated WO3 (001) surface upper layer O atom by 0.42% of a0 (Table 5). Just opposite, all second layer atoms relax upwards, with the single exception of the ReO2-terminated ReO3 (001) surface second layer O atom, which relaxes inwards by 0.32% of the ReO3 cubic lattice constant a0 (Table 5). Again, all third layer ReO2 and WO2-terminated ReO3 and WO3, as well as ZrO2-terminated BaZrO3 (001) surface atoms, relax inwards (Table 5). It is worth noting that for all our calculated ReO2 and WO2-terminated ReO3 and WO3 as well as BO2-terminated BaTiO3, SrTiO3 and BaZrO3 perovskite (001) surfaces, in all three layers the metal atom displacement magnitudes are always larger than the O atom displacements (Table 5).
It is worth noting that we are the first in the world to perform ab initio computations for O-terminated ReO3 and WO3 (001) surfaces (Table 6). As we can see from our ab initio computation results for O-terminated ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 (001) surfaces, all upper-layer atoms relax inwards (Table 6). The only single exception from this systematic trend is the upwards relaxation of the SrO-terminated SrTiO3 (001) surface upper layer O atom by +0.84% (Table 6) of the SrTiO3 bulk lattice constant a0. In contrast, almost all second layer atoms relax upwards. The only two exceptions are the inward relaxation of O-terminated ReO3 and WO3 (001) second layer O atoms by (−0.53 and −0.11% of a0, respectively) (Table 6). Finally, all our ab initio calculated third layer atoms relax inwards, towards the bulk. It is worth noting that for both upper O-terminated ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 (001) surface layers, the metal atom displacement magnitudes are always larger than the O atom relaxation shifts (Table 6).
Comparison of our ab initio calculation results with other calculations as well as available experimental data for SrO-terminated SrTiO3 (001) surface [94,95,96,97,98] are listed in Table 7. As we can see from Table 7, our ab initio B3PW computed surface rumpling amplitudes s for SrO-terminated SrTiO3 (001) surfaces (+5.66% of a0) are in a qualitative agreement with other computation results ranging from (+5.8% of a0) to (+8.2% of a0) as well as in a qualitative agreement with available experimental data (Table 7). Additionally, our ab initio investigation calculated that changes in the interlayer distances Δd12 and Δd23 are in qualitative agreement with other calculation results and most experiments (Table 7). Unfortunately, our computed changes in interlayer distances Δd12 disagree with the RHEED experiment (Table 7), but our computed changes in interlayer distance Δd23 disagree with the SXRD experiment (Table 7). Nevertheless, since the LEED, RHEED and SXRD experiments do not always agree with each other, even with respect to signs, we can not take these LEED, RHEED and SXRD experiments (Table 7) too seriously.
Our ab initio computed that B-O atom chemical bond populations in the BaTiO3, SrTiO3 and BaZrO3 perovskite bulk (Table 8 and Figure 7) are always smaller than near their BO2-terminated (001) surfaces. Just opposite, the Re-O and W-O chemical bond populations in the ReO3 (0.212e) and WO3 (0.142e) bulk (Table 8 and Figure 7) are slightly larger than near the ReO2 and WO2-terminated ReO3 as well as WO3 (001) surfaces (0.170e and 0.108e, respectively) (Table 8 and Figure 7). Nevertheless, the largest chemical bond populations in the ReO3 and WO3 matrixes are among the upper layer Re atom and the second layer O atom (0.262e) as well as among the upper layer W atom and the second layer O atom (0.278e).
According to our ab initio computations, the Γ-Γ bandgaps near the BO2, AO, or O-terminated ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 (001) surfaces are always reduced with respect to their relevant bulk Γ-Γ bandgaps (Table 9 and Figure 8). Experimental data, where available, for the bulk Γ-Γ bandgaps are listed for comparison purposes (Figure 8 and Table 9). As we can see from Table 9 and Figure 8, for ReO3 and WO3 crystals, our ab initio computed Γ-Γ bandgaps near their O and especially ReO2 and WO2-terminated (001) surfaces are much more strongly reduced with respect to their bulk Γ-Γ bandgap values, than near the BO2 and AO-terminated BaTiO3, SrTiO3 and BaZrO3 perovskite (001) surfaces. For example, TiO2 (3.95 eV) and SrO-terminated (3.72 eV) SrTiO3 (001) surface Γ-Γ bandgaps are reduced only by (0.01 and 0.24 eV, respectively) regarding their bulk Γ-Γ bandgap value of 3.96 eV (Table 9 and Figure 8).

5. Conclusions

According to our ab initio computation results for BO2, AO and O-terminated ReO3, WO3, SrTiO3, BaTiO3 and BaZrO3 (001) surfaces, in most cases, the upper surface layer atoms relax inwards towards the bulk. The second surface layer atoms, again, in most cases, relax upwards, while the third layer atoms, again, relax inwards.
Our ab initio computation results for SrO-terminated SrTiO3 (001) in most cases are in a fair agreement with previous calculation results and available experimental data. It is worth noting that our ab initio calculated interlayer distance Δd12 disagrees with the RHEED experiment (Table 7) with respect to the sign. Nevertheless, since the RHEED experiment also disagrees with the LEED and SXRD experiments, we can probably not take this available RHEED experiment [97] too seriously (Table 7).
According to our ab initio computations, the Γ-Γ bandgaps near the BO2, AO or O-terminated ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 (001) surfaces are always reduced with respect to their relevant bulk Γ-Γ bandgaps.
Our ab initio computed B-O atom chemical bond populations in the BaTiO3, SrTiO3 and BaZrO3 perovskite bulk are always smaller than near their BO2-terminated (001) surfaces. Just opposite, the Re-O and W-O chemical bond populations in the ReO3 (0.212e) and WO3 (0.142e) bulk are slightly larger than near the ReO2 and WO2-terminated ReO3 as well as WO3 (001) surfaces (0.170e and 0.108e, respectively). Nevertheless, the largest chemical bond populations in the ReO3 and WO3 matrixes are among the upper layer Re atom and the second layer O atom (0.262e) as well as among the upper layer W atom and the second layer O atom (0.278e).

Author Contributions

All authors, R.I.E., J.P., A.I.P., D.B., A.C. and R.J. contributed equally to the writing of the manuscript and the performance of ab initio computations. All authors have read and agreed to the published version of the manuscript.

Funding

This research received funding from the Latvian-Ukraine cooperation Project No. LV/UA-2021/5. The Institute of Solid State Physics, University of Latvia (Latvia), as the Centre of Excellence, has received funding from the European Unions Horizon 2020 Framework Programme H2020-WIDESPREAD01-2016-2017-Teaming Phase2 under Grant Agreement No. 739508, project CAMART2.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

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Symmetry 14 01050 g001 550
Figure 1. Ab initio computed and experimentally studied bulk Γ-Γ bandgaps (in eV) for BaTiO3, SrTiO3, BaZrO3, MgF2 and CaF2 crystals obtained by means of different methods: (1) PWGGA; (2) B3LYP; (3) B3PW; (4) Experiment; (5) HF.
Figure 1. Ab initio computed and experimentally studied bulk Γ-Γ bandgaps (in eV) for BaTiO3, SrTiO3, BaZrO3, MgF2 and CaF2 crystals obtained by means of different methods: (1) PWGGA; (2) B3LYP; (3) B3PW; (4) Experiment; (5) HF.
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Figure 2. Side view of the BO2-terminated ABO3 perovskite (001) surface slab containing 9 layers as well as the definitions of the surface rumpling s and the near-surface interplane distances Δdij.
Figure 2. Side view of the BO2-terminated ABO3 perovskite (001) surface slab containing 9 layers as well as the definitions of the surface rumpling s and the near-surface interplane distances Δdij.
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Figure 3. Side view of the BO2-terminated ReO3 or WO3 (001) surface slab containing 9 layers as well as the definitions of the surface rumpling s and the near-surface interplane distances Δdij.
Figure 3. Side view of the BO2-terminated ReO3 or WO3 (001) surface slab containing 9 layers as well as the definitions of the surface rumpling s and the near-surface interplane distances Δdij.
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Figure 4. Side view of the AO-terminated ABO3 perovskite 9 layers containing (001) surface.
Figure 4. Side view of the AO-terminated ABO3 perovskite 9 layers containing (001) surface.
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Figure 5. Side view of the O-terminated ReO3 and WO3 (001) surface containing nine-layer slabs.
Figure 5. Side view of the O-terminated ReO3 and WO3 (001) surface containing nine-layer slabs.
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Figure 6. Ab initio computed (1) as well as experimentally measured (2) bulk Γ-Γ bandgaps (in eV) for ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3.
Figure 6. Ab initio computed (1) as well as experimentally measured (2) bulk Γ-Γ bandgaps (in eV) for ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3.
Symmetry 14 01050 g006
Symmetry 14 01050 g007 550
Figure 7. Our ab initio computed Re-O, W-O and B-O chemical bond populations (in e) for the ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 crystal bulk (line 1) as well as their ReO2-, WO2- and BO2-terminated ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 (001) surfaces (line 2).
Figure 7. Our ab initio computed Re-O, W-O and B-O chemical bond populations (in e) for the ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 crystal bulk (line 1) as well as their ReO2-, WO2- and BO2-terminated ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 (001) surfaces (line 2).
Symmetry 14 01050 g007
Symmetry 14 01050 g008 550
Figure 8. Our ab initio computed ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 bulk Γ-Γ bandgaps (in eV) (line 4), experimental bulk Γ-Γ bandgaps (line 3), AO-terminated (001) surface bandgaps at Γ-point (line 2) as well as BO2-terminated (001) surface bandgaps at Γ-point (line 1).
Figure 8. Our ab initio computed ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 bulk Γ-Γ bandgaps (in eV) (line 4), experimental bulk Γ-Γ bandgaps (line 3), AO-terminated (001) surface bandgaps at Γ-point (line 2) as well as BO2-terminated (001) surface bandgaps at Γ-point (line 1).
Symmetry 14 01050 g008
Table
Table 1. Experimental details for ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 crystals relevant to our ab initio computations. The experimental data include the crystal structure at room temperature (RT), bandgap values at RT, transition temperatures to cubic phase, as well as experimental lattice constants at cubic phase.
Table 1. Experimental details for ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 crystals relevant to our ab initio computations. The experimental data include the crystal structure at room temperature (RT), bandgap values at RT, transition temperatures to cubic phase, as well as experimental lattice constants at cubic phase.
CrystalSymmetry in RTBandGap (Γ-Γ) (eV)
in RT		Trans. T (K) to
Cubic Phase		Exp. Latt. Con. (Å), Cubic Ph.
ReO3Cubic [55]UnknownCubic from liquid helium T till 673 K3.747 Å [61]
WO3Monoclinic [56]3.74 eV [57]Unknown3.71–3.75 Å [62]
BaTiO3Tetragonal ↔ orthorhombic (278 K)3.38 eV (∥ c);
3.27 eV (⟂ c) [58]		403 K [45]4.004 Å—474 K [63]
SrTiO3Cubic3.75 eV [59]110 K [45]3.898 Å—110 K [64]
BaZrO3Cubic5.3 eV [60]Cubic, all T4.199 Å RT [65]
Table
Table 2. BaTiO3, SrTiO3, BaZrO3, MgF2 as well as CaF2 (Γ-Γ) bulk bandgaps (in eV) ab initio computed by means of various methods [14,71,72,73,74]. Available experimental data for bulk (Γ-Γ) bandgaps (in eV) are listed for comparison purpose [59,60,72,75,76].
Table 2. BaTiO3, SrTiO3, BaZrO3, MgF2 as well as CaF2 (Γ-Γ) bulk bandgaps (in eV) ab initio computed by means of various methods [14,71,72,73,74]. Available experimental data for bulk (Γ-Γ) bandgaps (in eV) are listed for comparison purpose [59,60,72,75,76].
ApproachBaTiO3SrTiO3BaZrO3MgF2CaF2
HF11.7312.3312.9619.6520.77
B3PW3.553.964.939.4810.96
B3LYP3.493.894.799.4210.85
PWGGA1.972.313.246.948.51
Experiment3.2 [72]3.75 [59]5.3 [60]13.0 [76]12.1 [75]
Table
Table 3. Our ab initio B3LYP or B3PW computed ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 bulk crystal effective atomic charges Q (in e) as well as bond populations P (in e) between the atoms.
Table 3. Our ab initio B3LYP or B3PW computed ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 bulk crystal effective atomic charges Q (in e) as well as bond populations P (in e) between the atoms.
CrystalReO3WO3BaTiO3SrTiO3BaZrO3
AtomPropertyB3LYPB3LYPB3PWB3PWB3PW
AQ--+1.797+1.871+1.815
P--−0.034−0.010−0.012
OQ−0.794−1.032−1.388−1.407−1.316
P+0.212+0.142+0.098+0.088+0.108
BQ+2.382+3.095+2.367+2.351+2.134
Table
Table 4. Our ab initio B3LYP or B3PW computed ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 bulk Γ-Γ bandgaps (in eV). Experimentally measured Γ-Γ bulk bandgaps (in eV) are listed for comparison purposes.
Table 4. Our ab initio B3LYP or B3PW computed ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 bulk Γ-Γ bandgaps (in eV). Experimentally measured Γ-Γ bulk bandgaps (in eV) are listed for comparison purposes.
MaterialTheoretical Γ-Γ Bulk Gap (eV)Experimental Γ-Γ Bulk Gap (eV)
ReO3 5.76 eV (B3LYP)Unknown
WO34.95 eV (B3LYP)3.74 eV [57]
BaTiO33.55 eV (B3PW)3.2 eV [72]
SrTiO33.96 eV (B3PW)3.75 eV [59]
BaZrO34.93 eV (B3PW)5.3 eV [60]
Table
Table 5. ReO2 and WO2-terminated ReO3 and WO3 as well as BO2-terminated BaTiO3, SrTiO3 and BaZrO3 perovskite (001) surface upper three-layer atom shifts (in % of the bulk lattice constant a0).
Table 5. ReO2 and WO2-terminated ReO3 and WO3 as well as BO2-terminated BaTiO3, SrTiO3 and BaZrO3 perovskite (001) surface upper three-layer atom shifts (in % of the bulk lattice constant a0).
Computed (001) Surf.ReO3WO3BaTiO3SrTiO3BaZrO3
LayerAtomReO2-Ter.WO2-Ter.TiO2-Ter.TiO2-Ter.ZrO2-Ter.
1B−3.19−2.07−3.08−2.25−1.79
O−1.17+0.42−0.35−0.13−1.70
2ANo atomNo atom+2.51+3.55+1.94
O−0.32+0.11+0.38+0.57+0.85
3B−0.17−0.01--−0.03
O−0.110.00--0.00
Table
Table 6. O-terminated ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 (001) surface upper three-layer atom shifts (in % of the bulk lattice constant a0).
Table 6. O-terminated ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 (001) surface upper three-layer atom shifts (in % of the bulk lattice constant a0).
Computed (001) Surf.ReO3WO3BaTiO3SrTiO3BaZrO3
LayerAtomO-Termin.O-Termin.BaO-Ter.SrO-Ter.BaO-Ter.
1ANo atomNo atom−1.99−4.84−4.30
O−3.73−4.24−0.63+0.84−1.23
2B+2.71+2.65+1.74+1.75+0.47
O−0.53−0.11+1.40+0.77+0.18
3ANo atomNo atom--−0.01
O−0.44−0.48--−0.14
Table
Table 7. Surface rumpling s and relative displacements Δdij for the 3 near-surface planes of SrO-terminated SrTiO3 (001) surface [94,95,96,97,98].
Table 7. Surface rumpling s and relative displacements Δdij for the 3 near-surface planes of SrO-terminated SrTiO3 (001) surface [94,95,96,97,98].
SrO-Terminated SrTiO3 (001) Surface
sΔd12Δd23
Our B3PW results+5.66−6.58+1.75
Ab initio [94]+5.8−6.9+2.4
Ab initio [95] +7.7−8.6+3.3
Shell model [48]+8.2−8.6+3.0
LEED exp. [96] 4.1 ± 2−5 ± 12 ± 1
RHEED exp. [97]4.12.61.3
SXRD exp. [98]1.3 ± 12.1−0.3 ± 3.6−6.7 ± 2.8
Table
Table 8. Our ab initio computed Re-O, W-O and B-O chemical bond populations (in e) for the ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 crystal bulk as well as their ReO2-, WO2- and BO2-terminated ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 (001) surfaces.
Table 8. Our ab initio computed Re-O, W-O and B-O chemical bond populations (in e) for the ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 crystal bulk as well as their ReO2-, WO2- and BO2-terminated ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 (001) surfaces.
MaterialFunctionalRe-O, W-O and B-O Chemical Bond Populations (in e)
BulkReO2, WO2, BO2-Term. (001) Surfaces
ReO3B3LYP0.2120.170
WO3B3LYP0.1420.108
BaTiO3B3PW0.0980.126
SrTiO3B3PW0.0880.118
BaZrO3B3PW0.1080.132
Table
Table 9. Our ab initio computed bulk Γ-Γ bandgaps as well as Γ-Γ bandgaps near the BO2 or AO-terminated ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 (001) surfaces (in eV). Experimental bulk Γ-Γ bandgaps are listed for comparison purposes.
Table 9. Our ab initio computed bulk Γ-Γ bandgaps as well as Γ-Γ bandgaps near the BO2 or AO-terminated ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 (001) surfaces (in eV). Experimental bulk Γ-Γ bandgaps are listed for comparison purposes.
MaterialFunctionalBulk (Γ-Γ)Exp. (Γ-Γ)BO2-T. (001)AO-T. (001)
ReO3B3LYP5.76No data0.221.86
WO3B3LYP4.953.741.161.98
BaTiO3B3PW3.553.22.963.49
SrTiO3B3PW3.963.753.953.72
BaZrO3B3PW4.935.34.484.82
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Eglitis, R.I.; Purans, J.; Popov, A.I.; Bocharov, D.; Chekhovska, A.; Jia, R. Ab Initio Computations of O and AO as well as ReO2, WO2 and BO2-Terminated ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 (001) Surfaces. Symmetry 2022, 14, 1050. https://0-doi-org.brum.beds.ac.uk/10.3390/sym14051050

AMA Style

Eglitis RI, Purans J, Popov AI, Bocharov D, Chekhovska A, Jia R. Ab Initio Computations of O and AO as well as ReO2, WO2 and BO2-Terminated ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 (001) Surfaces. Symmetry. 2022; 14(5):1050. https://0-doi-org.brum.beds.ac.uk/10.3390/sym14051050

Chicago/Turabian Style

Eglitis, Roberts I., Juris Purans, Anatoli I. Popov, Dmitry Bocharov, Anastasiia Chekhovska, and Ran Jia. 2022. "Ab Initio Computations of O and AO as well as ReO2, WO2 and BO2-Terminated ReO3, WO3, BaTiO3, SrTiO3 and BaZrO3 (001) Surfaces" Symmetry 14, no. 5: 1050. https://0-doi-org.brum.beds.ac.uk/10.3390/sym14051050

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