# Electronic Structure and Momentum Density of BaO and BaS

Authors: R. Kumar; B. K. Sharma; G. Sharma
Journal: Advances in Condensed Matter Physics
 (2013)

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## Abstract

The electronic structure and electron momentum density distribution in BaO and BaS are presented using Compton spectroscopy. The first-ever Compton profile measurements on polycrystalline BaO and BaS were performed using 59.54 keV gamma-rays. To interpret the experimental data, we have computed the theoretical Compton profiles of BaO and BaS using the linear combination of atomic orbitals method. In the present computation, the correlation scheme proposed by Perdew-Burke-Ernzerhof and the exchange scheme of Becke were considered. The hybrid B3PW and Hartree-Fock based profiles were also computed for both  compounds. The ionic configurations are performed to estimate the charge transfer on compound formation, and the present study suggests charge transfer from Ba to O and S atoms. On the basis of equal-valence-electron-density profiles, it is found that BaO is more ionic as compared to BaS.


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## Body

## 1. Introduction

The II–VI alkaline earth compounds have interesting bond characteristics and simple crystal structures. BaO and BaS have potential applications in light-emitting diodes (LEDs), laser diodes (LDs), and magnetooptical devices [1–4]. BaO is an indirect bandgap, whereas BaS is a direct bandgap material. At normal conditions, BaO and BaS crystallize in NaCl (B1) structure, but under pressure, they show structural phase transition from B1 to B2 structure [5, 6]. Using the full-potential linearized augmented plane wave (FP-LAPW) method, Drablia et al. [7] reported the electronic and optical properties of BaO and BaS in cubic phase at normal and under hydrostatic pressure. Lin et al. [8] observed that the electronic structure of these compounds containing oxygen atoms always obeys a different relationship from the compounds not containing oxygen atoms using density functional theory (DFT).Most of the earlier studies, both experimental and theoretical, involve the electronic, optical, and structural properties of BaO and BaS [5–15]. To the best of our knowledge, no one attempted the electronic structure and momentum density of BaO and BaS using Compton spectroscopy. It is well established that Compton spectroscopy provides a useful test to examine the bonding in solids [16, 17]. Thus, we found it worth to study the electronic structure in BaO and BaS using Compton profile. The Compton profile, J(pz), is related to the ground state electron momentum density n(p) as [16, 17]
(1)J(pz)=∬-∞+∞n(p)dpxdpy,
where integration is performed over a constant-pz plane, z is scattering vector direction, and n(p) is given as
(2)n(p)α∑i|∫ψi(r)exp(-ip·r)dr|2,
where ψi(r) is the electron wave function and summation extends over all occupied states. In this paper, the results of a Compton scattering study on BaO and BaS are presented. For the theoretical Compton profiles, first-principles calculations based on linear combination of atomic orbitals (LCAO) method are performed using CRYSTAL06 code [18]. The ionic model has been applied to estimate the charge transfer in these compounds. The nature of bonding in isostructural and isovalent BaO and BaS is also compared using equal-valence-electron-density (EVED) profiles. The paper is organized as follows. Section 2 gives the experimental details and data analysis. The theoretical calculations are presented in Section 3 and Section 4 is devoted to the results and discussion. Finally, the conclusions are drawn in Section 5.


## 2. Experimental Details and Data Analysis

The measurements on BaO and BaS were performed using 5 Ci241Am gamma-rays Compton spectrometer. The details of the experimental setup are available in [19]. The incident gamma-rays of 59.54 keV were scattered at an angle of 166°  ± 3.0° by the polycrystalline sample of BaO and BaS (pellet of 18 mm dia, 3.2 mm thickness, and effective density for BaO 2.9329 gm/cm3 and BaS 1.7815 gm/cm3). The scattered radiation was analyzed using an HPGe detector (Canberra model, GL0110S) which was cooled with liquid nitrogen providing overall momentum resolution of 0.6 a.u. The spectra were recorded with a multichannel analyzer (MCA) with 4096 channels. The calibration of the spectrometer was checked regularly using weak 241Am gamma-rays source. The Compton spectra were measured for BaO near about 48.529 h to collect 2 × 104 counts and BaS around 56.25 h to collect 2.5 × 104 counts at the Compton peak. To deduce the true Compton profile, the raw data were processed for several systematic corrections like background, instrumental resolution, sample absorption, scattering cross-section, and multiple scattering using the computer code of the Warwick Group [20, 21]. Finally, the corrected profiles were normalized to 23.200 for BaO and 26.434 for BaS electrons in the range of 0 to +5 a.u., being the area of free atom Compton profile [22] in the given range. The 1 s electrons of Ba were neglected for both compounds since these do not contribute in the present experimental setup.


## 3. Theoretical Details

### 3.1. DFT-LCAO Method

To compute the theoretical Compton profiles of BaO and BaS, the LCAO method embodied in the CRYSTAL06 code [18, 23] was employed. This code provides a platform to calculate electronic structure of periodic systems considering Gaussian basis sets. In the LCAO technique, each crystalline orbital is built from the linear combination of Bloch functions. The Bloch functions are defined in terms of local functions constructed from the atom-centered certain number of Gaussian functions. For Ba, O, and S, the local functions were constructed from the Gaussian type basis sets [24]. In the present DFT calculation, the crystal Hamiltonian was generated using the correlation functional proposed by Perdew et al. [25] and exchange scheme of Becke [26]. The hybrid B3PW and Hartree-Fock (HF) based profiles were also computed for both compounds [18]. The computations were performed by taking B1 structure and 145 k points in the irreducible wedge of the Brillouin zone for BaO and BaS.


### 3.2. Ionic Model

The theoretical ionic profiles of BaO and BaS for various charge transfer configurations were calculated from the free atom Compton profiles of Ba, O, and S atoms [22]. The valence profiles for various (Ba)+x(O-x) and (Ba)+x(S-x)(0.0≤x≤2.0) configurations were computed by transferring x electrons from the s shell of Ba to the p shell of O and S atoms. The valence profiles for (Ba)+x(O-x) and (Ba)+x(S-x) configurations were then added to the core contribution to get total profiles. All these profiles were then convoluted and normalized to compare with the measured profiles of BaO and BaS.


## 3.1. DFT-LCAO Method

To compute the theoretical Compton profiles of BaO and BaS, the LCAO method embodied in the CRYSTAL06 code [18, 23] was employed. This code provides a platform to calculate electronic structure of periodic systems considering Gaussian basis sets. In the LCAO technique, each crystalline orbital is built from the linear combination of Bloch functions. The Bloch functions are defined in terms of local functions constructed from the atom-centered certain number of Gaussian functions. For Ba, O, and S, the local functions were constructed from the Gaussian type basis sets [24]. In the present DFT calculation, the crystal Hamiltonian was generated using the correlation functional proposed by Perdew et al. [25] and exchange scheme of Becke [26]. The hybrid B3PW and Hartree-Fock (HF) based profiles were also computed for both compounds [18]. The computations were performed by taking B1 structure and 145 k points in the irreducible wedge of the Brillouin zone for BaO and BaS.


## 3.2. Ionic Model

The theoretical ionic profiles of BaO and BaS for various charge transfer configurations were calculated from the free atom Compton profiles of Ba, O, and S atoms [22]. The valence profiles for various (Ba)+x(O-x) and (Ba)+x(S-x)(0.0≤x≤2.0) configurations were computed by transferring x electrons from the s shell of Ba to the p shell of O and S atoms. The valence profiles for (Ba)+x(O-x) and (Ba)+x(S-x) configurations were then added to the core contribution to get total profiles. All these profiles were then convoluted and normalized to compare with the measured profiles of BaO and BaS.


## 4. Results and Discussion

The numerical values of unconvoluted spherically averaged theoretical Compton profiles (DFT-PBE, B3PW, HF, and Ionic) of BaO and BaS are presented in Table1. The experimental Compton profiles of BaO and BaS are also given in the table including experimental errors at selected points.Table 1
The unconvoluted theoretical (DFT-PBE, DFT-B3PW, HF, and Ionic) and experimental Compton profiles for BaO and BaS. The experimental errors at few points are also presented, and all profiles are normalized to the free atom area.
p
z  (a.u.)
J (pz) in e/a.u.
BaO
BaS
DFT-PBE
DFT-B3PW
HF
Ionic
Experiment
DFT-PBE
DFT-B3PW
HF
Ionic
Experiment
0.0
12.516
12.626
12.605
13.775
12.498
±
0.050
14.410
14.417
14.412
15.455
14.718 ± 0.053
0.1
12.419
12.528
12.508
13.275
12.400
14.290
14.296
14.291
15.119
14.567
0.2
12.271
12.377
12.358
12.333
12.148
14.094
14.101
14.096
14.499
14.259
0.3
12.023
12.125
12.107
11.509
11.786
13.656
13.663
13.659
13.702
13.791
0.4
11.613
11.709
11.693
10.890
11.339
13.242
13.249
13.247
13.073
13.148
0.5
11.079
11.167
11.155
10.362
10.804
12.519
12.526
12.527
12.273
12.347
0.6
10.434
10.511
10.504
9.792
10.181
11.739
11.746
11.750
11.363
11.450
0.7
9.715
9.777
9.776
9.176
9.496
10.847
10.854
10.861
10.436
10.539
0.8
8.957
9.002
9.008
8.525
8.791
9.913
9.920
9.929
9.521
9.668
1.0
7.472
7.476
7.494
7.286
7.426
±
0.037
8.141
8.148
8.163
7.918
8.081
±
0.037
1.2
6.200
6.163
6.186
6.250
6.225
6.708
6.712
6.722
6.638
6.798
1.4
5.307
5.248
5.266
5.483
5.371
5.932
5.932
5.932
5.921
5.933
1.6
4.719
4.662
4.670
4.922
4.786
5.368
5.367
5.362
5.375
5.288
1.8
4.314
4.267
4.268
4.494
4.341
4.966
4.965
4.960
4.983
4.915
2.0
4.005
3.966
3.965
4.149
4.023
±
0.027
4.638
4.637
4.633
4.662
4.627
±
0.028
3.0
2.781
2.769
2.767
2.826
2.811
±
0.022
3.268
3.268
3.267
3.291
3.260
±
0.022
4.0
1.887
1.884
1.883
1.902
1.986
±
0.018
2.207
2.207
2.207
2.223
2.270
±
0.018
5.0
1.394
1.393
1.393
1.404
1.391
±
0.014
1.602
1.602
1.602
1.611
1.653
±
0.015In Figures1 and 2, the experimental Compton profiles of BaO and BaS are compared with various ionic arrangements to estimate the charge transfer. For a quantitative comparison of the ionic and experiment, the difference profiles ΔJ=JTheory(pz)-JExpt(pz) have been deduced after convoluting all ionic profiles with a Gaussian function of 0.6 a.u. FWHM. All ionic profiles are normalized to 23.200 electrons for BaO and 26.434 electrons for BaS in the range of 0 to +5 a.u. Figure 1 depicts that the effect of charge transfer from Ba to O atoms is largely visible within 0.0 to 3.0 a.u. for BaO. The best agreement is found for x=1.0. Figure 2 shows that the charge transfer configuration x=1.5 is closet to the experiment for BaS. Beyond 3.0 a.u., all configurations show identical behavior for both compounds. On the basis of χ2 checks and from Figures 1 and 2, it is found that Ba+1.0O−1.0 and Ba+1.5S−1.5 configurations give the best agreement for BaO and BaS, respectively. Thus, the model suggests the transfer of 1.0 and 1.5 electrons from the valence s state of Ba to the p states of O and S for BaO and BaS, respectively.Figure 1
Difference (ΔJ) between convoluted ionic and experimental Compton profiles of BaO. Experimental errors (±σ) are also shown at points. All ionic profiles are convoluted with the Gaussian of 0.6 a.u. FWHM.Figure 2
Difference(ΔJ) between convoluted ionic and experimental Compton profiles of BaS. Experimental errors (±σ) are also shown at points. All ionic profiles are convoluted with the Gaussian of 0.6 a.u. FWHM.The differences(ΔJ=JTheory(pz)-JExpt(pz)) between experimental and LCAO scheme based Compton profiles are presented in Figures 3 and 4 for BaO and BaS, respectively. Figure 3 shows that for BaO all theories (DFT-PBE, B3PW, and HF) predict lower momentum density as compared to experiment in the momentum range of 0.0<pz<0.5 a.u., while the trend reversed in the momentum range of 0.5<pz<2.0 a.u. The difference between theory and experiment is negligible in the high momentum region, because the contribution in this region is mostly due to core electrons, which remain unaffected in the compound formation. Similar features are also visible in Figure 4, but the effect of exchange and correlation is not seen for BaS.Figure 3
The difference of DFT-PBE, B3PW, and HF with experimental Compton profile of BaO. All profiles are convoluted with the Gaussian of 0.6 a.u. FWHM.Figure 4
The difference of DFT-PBE, B3PW, and HF with experimental Compton profile of BaS. All profiles are convoluted with the Gaussian of 0.6 a.u. FWHM.The directional Compton profiles of BaO and BaS along[100], [110], and [111] directions have been computed to examine the anisotropies [100]–[110], [110]-[111], and [100]–[111] in the electron momentum density. All these anisotropies are derived from convoluted B3PW hybrid scheme and presented in Figures 5 and 6 for BaO and BaS, respectively. Figure 5 depicts that all anisotropies are positive in nature at pz=0.0 a.u. for BaO. It indicates larger occupied states along [100] direction with low momentum. A close inspection of this figure reveals that maximum anisotropy is seen between [100] and [111] directions at 0.6 a.u. and 1.2 a.u. All anisotropies are visible up to 3.0 a.u. In Figure 6, the anisotropies are plotted for BaS. This figure shows similarity with BaO, but all anisotropies are diminished beyond 2.0 a.u. Measurements on single crystalline samples of BaO and BaS along principal directions would be valuable to examine these findings.Figure 5
Directional anisotropies,ΔJ(pz), for BaO for the pair of directions [100]–[110], [110]-[111], and [100]–[111].Figure 6
Directional anisotropies,ΔJ(pz), for BaS for the pair of directions [100]–[110], [110]-[111], and [100]–[111].The nature of bonding in isostructural and isovalent BaO and BaS has been compared and plotted in Figure7. In this figure, the experimental EVED profiles of these compounds are considered. We also plot the theoretical EVED profiles in the inset. The EVED profiles were derived by normalizing valence electron profiles to 4.0 electrons and scaling the resulting profiles by the Fermi momentum (pF). For BaO and BaS, pF turned out to be 0.938 and 0.813 a.u., respectively, using the expression (3π2n)1/3, where n is the valence electron density. A number of researchers have proved that this scheme offers a way to understand the nature of bonding in isovalent and isostructural compounds [27–31]. It is seen from Figure 7 that, near pz=0 a.u., the sharpness of Compton profiles is higher for BaS, which suggests more localization of charges in BaS in the bonding direction as compared to BaO. It is worth mentioning here that the covalent bonding is a result of sharing of electrons, and hence, it increases localization of charge in bonding direction which results in a sharper Compton line shape [32, 33]. Therefore, we conclude that the ionic character is higher for BaO as compared to BaS. The larger ionic character of BaO as compared to BaS is well supported by the bulk modulus and cohesive energy data [34].Figure 7
The equal-valence-electron-density (EVED) profiles of BaO and BaS (pF=0.938 and 0.813 a.u., resp.). These profiles are deduced from the experimental valence profiles. The inset shows the EVED profiles derived from the theoretical valence profiles of these compounds. All these profiles are normalized to 4.0 electrons.


## 5. Conclusions

Electronic structure and momentum density in BaO and BaS using Compton scattering technique are reported. The experimental values of Compton profiles are compared with the LCAO based values for both compounds. The anisotropies in momentum densities depict larger occupied states along[100] direction with low momentum. In addition, the ionic model based calculations have also been used to estimate the charge transfer in the compounds, and the model suggests a transfer of 1.0 and 1.5 electrons from s state of Ba atom to p state of O and S atoms. The EVED profiles for the compounds conclude higher ionic character in BaO as compared to BaS.



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