A first principles study of the phonon anharmonicity, electronic structure and optical characteristics of LaAlO 3

: The way elementary excitations work together with their couplings and interact as condensed matter systems is very important when designing optimum energy-conversion devices. We investigated the electronic structure of LaAlO 3 , and we show that the bandgap insulator of LaAlO 3 obtained theoretically by the hybrid functional HSE06 is an indirect 5.649eV that show a very good agreement with experimental data. The lattice constant is obtained exactly as experiment. In thermos-electric materials, the concept of conversion-efficiency (heat to electricity) is improved instantly by suppressing the phonon quasi-particles propagations that are responsible for draft macroscopic thermal transport. The material presented here for thermo-electric conversion-efficiency of cubic perovskite LaAlO 3 , show that it has an ultralow thermal-conductivity, while the formalism to its strong phonon scattering interactions resides mostly unclear. From the bases of Ab-initio simulations, the 4-dimensional phonon-dispersion surfaces of the cubic perovskite LaAlO 3 , have been mapped and we found that the origins of the ionic potential an-harmonicity being responsible for the unique behaviour and properties of LaAlO 3 . It is investigated that these phonon scattering arise solely from the LaAlO 3 unstable electronic-structure, with its orbital interactions resulting to lattice instability similar to the ferroelectric instabilities. Our results show a microscopic insight bonding electronic-structure and phonon anharmonicity in LaAlO 3 , and provides some new picture the way interactions happen between phonon – electron and phonon – phonon this lead to understand the concept of ultralow thermal-conductivity. Ab-initio calculations was performed on cubic perovskite LaAlO 3 to obtain the phonon density of states (DOS) from 50 K to 5000 K, we find that the anharmonic behaviour starts around temperature limits of 500 K. The computed optical spectra were obtained using both the Beth Slapter Equation BSE and compared with the perturbed method using HSE06, optical spectra show that the inter-band transition occur precisely from the O-valence bands to the La-conduction bands throughout the low energy area. The energy-loss spectrum, optical conductivity and reflectivity and the refractive index are computed from first principles by using HSE06 hybrid functional. The optical band gap of material shows about 6.21 eV, which agrees with some cited experimental measurements phase transition of 𝑡𝑜 𝑅3̅𝑐 the studies limits of pressure and temperature. This work provides a precise calculations of the cubic perovskite Lanthanum Aluminate LaAlO 3 crystal structure, using Ab-initio examination of the structural, electronic, optical, phonon and thermodynamic properties under both high Temperature and pressure ranges.


Introduction
Many of the special characteristics of Lanthanum Aluminate (LaAlO3) in its cubic perovskite form is owed to its uniquely large band gap [1]. LaAlO3 exhibits a wide variety of structural, electronic, optical, phonon, thermal and other unique properties under certain applied conditions. The La-based oxides' geometry holds an important part to their thermodynamic 163 phonon mean-free-path thermal transport. Lattice dynamics of LaAlO3 has attracted attention owing to its unique dielectric properties, LaAlO3 is also widely used in the superconducting microwave devices [3,4]. At the present time, LaAlO3 offer an excellent candidate to alongside silicon-dioxide SiO2 or silicon itself [1 0 0] where a single crystalline of LaAlO3 has a large dielectric constant with a huge optical band-gap of about 6.3 eV [5] and stable thermodynamics. Improving our knowledge of the phonon dynamics is very important to obtain precise thermoelectric efficiency. The cubic perovskite LaAlO3 is particularly interesting with its = / reaching values above the unity, where , , , are the temperature, Seebeck coefficient, electrical, and thermal conductivities, respectively. Thanks to the low lattice thermal conductivities in the single crystal. Many factors are held accountable for this low , ranging from heavy atomic masses, soft bonds, and to the strong anharmonicity at high pressures and temperatures, which is reflected in the proximity to the lattice instability. The half-filled resonant p band and the nonlinear Al polarizability induce a relatively strong anharmonicity at a long-range interatomic potential [29][30][31][32][33][34][35][36][37][38]. Such interactions along the crystallographic directions [100] may cause the transverse-optic (TO) phonon branch that dip to low energy at the zone centre. The strong anharmonicity causes this zone-centre TO phonon to stiffen as T increases in the cubic paraelectric phase in a clear quasi-harmonic lattice [38] but in general agreement with the soft-mode picture of the ferroelectric transition [39]. Although the studies mentioned above assessed and accurately described the lattice dynamics of LaAlO3, but to our knowledge there no study of phonons in LaAlO3 at the studied temperatures and pressures limit, which are important for assessing phonon anharmonicity at higher pressures and temperatures, which is also owed to the character of thermal conductivity at all temperatures. In this work, we explain the origin of the complex spectral function, by performing systematic first-principles simulations of the temperature-dependent phonon selfenergy. Our results establish that, the TO mode in LaAlO3 is more paraelectric oriented. We try to explain how these results arise from a resonance in the phonon self-energy, which is more pronounced in LaAlO3, owing to a better nest in dispersion. We found that the thermal changes in phonon frequencies were a factor of 7 larger than expected from the quasiharmonic model, indicating a large effect from phonon anharmonicity. The thermal broadening of features in the phonon spectrum also indicates anharmonicity.

Methods and Modeling
First-principles calculations were performed in the framework of density functional theory (DFT). Using the Projector Augmented PAW method, which was developed by Blöchl (1994) [40]. The basis wave functions were calculated within the ATOMPAW code [41]. The details of the PAW method have already been given several times in the literature [42,43,44]. The accuracy of our obtained phonon calculations was carefully evaluated through the use of a powerful Exchange and correlation functionals, throughout this work the hybrid Heyd-Scuseria-Ernzerhof (HSE06) functional [45] with the scalar-relativistic BY3LP Pseudopotentials is carried out, in order to get as realistic as possible to predict correct values of the band gap since HSE06 gave a very satisfactory band gap estimation. Hybrid density functional, which includes a certain amount of Hartree-Fock (HF) exchange, has further improved upon the BY3LP results. This improvement originates from the inclusion of non-dynamic correlations that effectively delocalize the BY3LP exchange hole. Nowadays, the new hybrid density functional of HSE06 is particularly successful in describing the band gap and the ground-state properties of a whole range of materials, which recovers the correct behaviour HSE06 is a screened Coulomb hybrid functional by separating the short-range and long-range HF exchange, which offers highly efficient computations on extended periodic systems. In HSE06, the XC energy is described as follows [45]: 164 where E X HF,SR , E X PBE,SR , E X PBE,LR , and E C PBE represent the short-range HF exchange, short-range Perdew-Burke-Ernzerhof (PBE) exchange, long-range PBE exchange, and PBE correlation terms, respectively. The data obtained through the HSE06 functional is presented as our main results as implemented in the open-source ABINIT code package [46]. The plane-wave cut-off energy achieved convergence at about 435.4 eV. On the other hand, the k-point sampling was dense and the 8 8 8 = 512 (2048 atoms) Monkhorst and Pack [47] mesh grid was used sampling of the first Brillouin zone when implementing the Hybrid functional HSE06, this sampling was chosen carefully due to the timing and the processing power. However, tests showed that the 24 24 24 = 13824 was optimum when using the hybrid functional HSE06, tests of high grid number reaching 48 48 48 = 110592 does not lead to any more sufficient difference in converging the electron energy. The states : 5 1 6 2 , : 2 2 2 4 , : 3 2 3 1 were treated as valence states. Setting the parameters in this form, lead to well converged calculations. In order to get well-relaxed crystal structure, the first step in any theoretical AB-initio study is to optimize geometry at equilibrium. The structural optimization was conducted using the Broyden-Fletcher-Goldfarb-Shanno minimization (BFGS) [48], which is more efficient for structural optimization than viscous damping, when the number of degrees of freedom needed to optimize is lesser than ten. Recovering the optimized crystal structure requires optimization of each of the internal atomic coordinates, the lattice parameters, and the minimization of forces on each atom. These forces are obtained by Hellmann Feynman theorem [49].

Structure and Stability
The Studied LaAlO3 is a cubic 3 ̅ structure with the unit cell is shown in (Figure 1). To determine the lattice parameters at equilibrium, about 200 values of volumes around the expected equilibrium result are used to estimate the relaxed volume with respect to the ions and shapes, the obtained lattice parameter values are in a great precision with the experimental values, all the presented calculations are performed under zero temperature, also the drown experimental data were obtained at room temperature [50,51,52]. The lattice parameter is = = 3.715 Å, the use of the hybrid HSE06 estimates the equilibrium volume of LaAlO3 exactly Figure 2 shows a comparison of the estimated volume and its compared experimental analogue.

Electronic Properties
The band structures along high symmetry lines are very useful for examining the main character of electronic properties. Single crystal cubic Perovskite LaAlO3 has a Dirac-cone structure with the high order symmetry directions R, G, Γ, K, and R, in the first Brillouin zone (BZ) and at the K-points, which can be seen Figure 3, the linear-energy bands are forming the parabolic mesh in the increase of the state energy. Furthermore, ℎ bands, which arise partially from the sp 2 bonding, are due forming the Γ point at the deeper energy.
The Fermi level is positioned at the Dirac valence cone such that the free holes exist in between the Dirac valence point and the Fermi level ( = 0) LaAlO3 has a completely empty − ℎ , so that the valence states consist of the oxygen levels at the top of the valence band is greatly flattened, especially between the R and M points with a difference in the energy limited only to 0.04 eV in SrTiO3. In most compounds, the The band-structure of LaAlO3 in the BZ is examined within HSE06. Our calculations show that an indirect bandgap Γ-R holding a value of 5.649 separates the valence bands from the conduction bands of the cubic perovskite LaAlO3. the valence bands start with a lower limit at -7.78. and end with the Fermi level ( = 0). We estimate the optical bandgap to be 6.21eV, which agrees with the experimental value at 6.3 eV [5]. Table 1 Calculated band gaps ( ) of LaAlO3 at equilibrium.  The conduction-band is relatively more dissipative than the valence-band. La-atoms are located at the centre of the cubic site affecting the valence bands and forcing them to widen. The conduction-band holds its lowest bottom state at La − , followed by the − at the − . In Table 2, we list the calculated direct and indirect band gaps. A comparison of the obtained equilibrium values of the band gap is examined under GGA, LDA, By3LP and HSE06 are given in Table 2, with available experimental band gap measurements of about 5.6 . The results computed within LDA tend to underestimate this value by 40%, running the calculations under GW-approximation and changing to a k-point mesh of 8 8 8 = 512 within the BZ, gives an approximation of 5.3 eV. While BY3LP underestimated the gap's value by about 14%. The results obtained with HSE06 gave the value of 5.649 eV. The significant splitting of the spin up and down energy bands is revealed near ( = 0); furthermore, the largest energy spacing reaches 0.5 eV. eigenvalue close to R point constitutes the absolute maximum of the valence band. Generally, a big improvement of the estimated band transition energies. In the HSE06 functional, the Mean Absolute Error (MAE) gave about 0.42 eV, the Mean Error (ME) has the exact value as the MAE and the negative sign, which represents an improvement by roughly a factor of three compared to the BY3LP that has MEA of 1.48 eV. For that we could that the error of predicted and experimental value depends on the type of the material.

Lattice Dynamics
When phonon frequencies are determined, most of the thermodynamic properties can be obtained using statistical physics without further approximations. To decompose the Helmholtz free energy at temperature into two additive contributions [52,53] ( , ) = ( ) + ( , ) (2) where is the total static free-energy per unit cell at 0 K, and is the vibrational Helmholtz free energy contribution given by where is Boltzmann constant and ( , ) is the phonon mode density. The term quasiharmonic-approximation is given from the approach that for a particular volume, ( , ) can be calculated under the regular harmonic approximation, and that anharmonic effects are to be included solely through the volume-dependence on the phonon frequencies.
The phonon eigen-energies were computed through density functional perturbation theory DFPT [54,55]. The free energy was calculated as The quasi-harmonic approximation ( ) calculations were obtained by minimizing the free energy ( , ) of Eq. (4) with respect to the volume of the supercell. Ground-state energies 0 ( ) were calculated separately and self-consistently for each volume, and the DOS ( ) were calculated with the specific lattice parameter, 0 , that produced the minimized volume. The Helmholtz free energy is the key in the calculation, and once its determined as a function of the volume and temperature, many thermodynamic quantities can be obtained from it, such as entropy = −( / ) , enthalpy = + and so on. The algorithm implemented to compute phonon dispersions was by introducing a generalized force constant Ψ , , (P, Q) as where φ , 168 The evaluation of the dynamical matrix is The crystal LaAlO3 is put under a relative pressure limits of (0, 8, 10-13 GPa] and temperature [0K to 6000K]. Now, temperature and pressure limits are set to meet the phase shift of LaAlO3, and that pressure after 11 GPa breaks the lattice structure and changes it from Cubic 3 ̅ to rhombohedral 3 ̅ . Specific heat capacity CV. At around temperatures ( > 2000 ), tends to approach the Petit-Dulong-limit [38] with a value of (124.62 · −1 · −1 ), a behavior that is common with solids materials. At intimate low temperatures, the vibrational excitations rose purely from acoustic vibrations; CV is proportional to the third power of temperature T 3 . At 0Gpa pressure and ambient room temperature, CV is slightly lower than the Petit-Dulong-limit. Generally, for a given temperature, CV decreases as pressure increases. Figures 4 shows also the variation of enthalpy, free energy and entropy with temperature over a range of 0-6000K under pressure and it shows a great comparison with experiment [56][57][58][59]. The entropy and enthalpy show a direct temperature dependence. Entropy's dependence on temperature reveal signs of bending since ions are forced to polarize while approaching one another. The results of the heat capacity and its temperature dependence results out of the acoustic contributions at the crystal level. The dynamical structure factor was computed from the first principles phonon dispersions and polarization vectors ( ) as follows [59,60]: where , , represent the reciprocal lattice vector, branch index, and atom index in the unit cell, respectively, and − , , are the coherent neutron scattering length, position, and atomic mass for atom d. The Debye-Waller factor was calculated assuming the atomic mean-square displacements are isotropic and using their values from the simulation as described in the work of [59,60,61].  The result was convoluted with a four-dimensional Gaussian instrument resolution function for ( , ). A constant resolution of comparable width as the bin sizes of ( , ) integration and a known energy-dependent energy resolution were used.
Using Ab initio calculations, one can obtain the ground state energy, electronic wave function, energy-gradient, and properties of periodic systems. Hartree-Fock or Kohn-Sham Hamiltonians can be used. Using HSE06 to calculate the Interatomic Force Constants IFCs can take long period of time and is often expensive, the calculations were obtained using parallel computing with cluster of (4 PC's with a CPU of 3.5GHz) the calculations took about 200Hr to complete each simulation run. The phonon DOS and dispersions were calculated using renormalized harmonic force constants starting at 50K to 5000K, from the temperature-dependent effective potential (TDEP) methodology. The total and atom-projected (partial) phonon DOS computed for LaAlO3 using tetrahedron integration are shown in Figures 7. The phonon dispersions of LaAlO3 are shown in Figures 5 and 6. First-principles steady phonon calculations show that, at their respective relaxed lattice parameters, LaAlO3 has a single potential-well with a minimum at the center of the crystal configurational positions. This is in good agreement with the experimental observation that stoichiometric LaAlO3 is indeed paraelectric down to 500 K which in comparison with LABO or Al2O3 is slight more instable ferroelectric. The calculated phonon The total and partial phonon DOS obtained from first-principles calculations of LaAlO3 at 50K, 500K, 1000K, 3000K and 5000K.
173 dispersion curves and corresponding one-phonon DOS for LaAlO3 along the high-symmetry directions are illustrated in Figures 5, 6, 7 which suggests that the dispersion curves and corresponding density of states resemble each other for LaAlO3. The calculated phonon dispersion curves do not contain soft modes at any direction at 50K, which confirms the stability of the compound. The DOS curves show various number of peaks, which is owned to the portions at the top of these dispersions. Where the lowest peak is located between 0.15 and 0.25 meV and is dominated by the top of the − ( ) branches, the other two are mixtures of ( ), , and longitudinal optical branches. A cutoff of the phonon-spectrum occurs at 0.04 eV. Figure 7 shows that the phonon DOS go through a systematic decrease in phonon energy thermal softening, and thermal linewidth broadening with increasing temperature. The DOS curves contain several distinct features resulting from Van Hove-singularities. At 500 K, two transverse acoustic modes between 0.0 and 0.05 eV give several peaks near 0.12meV and the shoulder 0.15 meV, the modes in between 0.05eV and 0.09eV holds 2 TO and and 1 LA modes. The higher-energy feature around 0.15 meV is from transverse and longitudinal optical modes. The high-energy optical modes centered around 0.2 meV show the largest thermal shift of approximately between the range 50 to 5000 K starting at 500K. Observing Figures 5, 6, 7, at high temperatures there are more down-conversion processes, but an even greater change in up-conversion processes. Figure 7 shows how the strong downconversion peaks at low temperatures grow approximately linearly with temperature, following the thermal population of phonon modes involved in the interactions. Near the peak at 0.02 eV, one up-conversion band centered at 0.02 eV is also strong. This band comprises scattering channels in which one O-dominated mode is combined with an Al-dominated mode to form a higher frequency La-dominated mode, i.e., O → Al − La. At the low energy side, there is another band below 0.01 meV from two types of up-conversion processes. One is from Agdominated modes alone, i.e., Al → La − O. The other involves two O-dominated modes, i.e., Ag → O − O, owing to the increased number of higher energy O-dominated modes that can participate in these processes at higher temperatures. To understand the temperature dependence of thermal conductivity, one needs to taking into account both the changes in propagation the velocities of the quasiparticles, and the changes in the scattering rates given by (9). In the relaxation time approximation, the phonon gas thermal conductivity is given by where is heat capacity, group velocity, and is scattering rate of the phonon modes representing the wave-vector and the branch index . The temperature effects on group velocities is strong in LaAlO3. This dependence reflects in its turn a strong temperature dependence of interatomic force constants, associated with the bonding. The scattering rates is obtained from the given perturbation theory [62] and the first order terms of the cubic Interatomic Force Constants (IFCs): the Bose occupation (similarly 2 ), where is the phonon frequency. The behavior of LaAlO3 Supplementary Figure 8 including the corresponding IFCs, yields a suppression in the thermal-conductivity and show an increase in Grüneisen parameter of the lowest-energy TO branch at the Γ points, as shown in Figure 8. The large 3 rd order force constant Ψ 0, , ′ , , , combined with the large population, augmented | ( , 1 , 2 , , 1 , 2 )|

174
Eq. (11), therefore is increases the scattering rates as Eq. (10), which leads in most cases to a striking suppression in the thermal-conductivity. It's worth noting that also this kind of distortion corresponds or matches structural evolution of the unit cell from 3 ̅ 3 upon cooling, and thus indicates the role of anharmonicity in bonding the structural phase transition. The distortion overlaps strongly with the zone-centre optical phonon mode, TO at Γ. On the other hand, the LO at Γ mode is rather insensitive. The strong TO anharmonic behavior is revealed in the distortion-potential for the centre of the zone TO vibrational mode, ( , 1 , 2 , , 1 , 2 ) = 1 6 ( ℏ 3 8 1 2 ) , ′ , , ′ , ′′ , , where ( | ) is the eigenvector, is the atomic equilibrium position, and is the atomic mass. From the first-principles cubic IFCs, , was computed. Our analysis of the 3 rd order of the force constants (FC) and the contributions it plays in thermal transport shows how anharmonicity arises from nonlinear restoring forces, owing to the asymmetric changes of the electronic structure of the movements of La atoms inside the lattice.
The cubic IFCs Ψ 0, , ′ , , correspond to the 3 rd derivatives of the potential with respect to the displacements ( , , ) of the triplets of atoms ( , , ). Through a systematic study of Ψ 0, , ′ , , , we could identify the non-degenerate triplets with largest 3 rd order FC.

Optical Properties
Beth-Slapter Equation BSE and GW-approximation were carried out with the added scissors shift of the conduction states to calculate the single-particle states at a fixed geometry, the substitution of only one component of the dielectric tensor for a symmetric LaAlO3 gives rise to the characteristics of the linear optical properties of the compound under study. The real part is presented by ( ) 1 ( ) and the imaginary part by ( ) 2 ( ) The imaginary part of the dielectric function ε2(ω) is calculated using the derived expression given in [63,64]: where ′ ( ) is the dipole matrix element in-between states ′ , Sk is the surface energy with constant value, ′ ( ) is the energy difference in-between the two states. The real part of the dielectric function is then obtained from the imaginary part by deriving it from the Kramer-Kronig relation. From the imaginary and the real parts of the dielectric function, one can compute many important optical functions such as the refractive index, electron energy loss spectra and reflectivity using the expressions below [50]: where, , , , and are the refractive index, extinction coefficient energy loss function, and reflectivity.
The calculated optical properties are shown in Figure 9. The real part of the dielectric functions 1 ( ) starts at the point (0, 0) and continues to achieve maxima at about 8eV, the real part 1 ( ) always remains positive throughout the range of the studied energies. The imaginary part of the dielectric function, 2 ( ), is directly related to the optical and electronic band structure of the material. Figure 9 shows that the optical spectra of the imaginary part 2 ( ) for LaAlO3, which starts with a non-zero value and continues to hit a maximum intensity at about 8eV, then goes to negative values around 10eV and 20eV. An inverse relation exists between the band gap and 1 (0), the smaller the value of the energy gap the larger 1 (0) value. The Penn model [63] explains the case based on the expression 1 (0) ≈ 1 + (ħ / ). The 1 ( ) for the studied compound starts increasing from the limited zero frequency and reaches its maximum value, then it starts to decreases after hitting an incline, and at a certain energy range it goes to zero. The refractive index of optical materials is known for its importance, especially its use in optical devices. Figure 9 inspects the refractive indices variations for LaAlO3 as a function of the incident photon energy. The refractive index tends to have the same pattern of variation as that of 1 ( ), However, the extinction coefficient ( ) on the other hand experiences the same pattern as 2 ( ). The reflectivity ( ) for the studied compounds is frequency dependent.

R(ω)
Energy(eV) Figure 9 The Real, Re(ε) and Imaginary Im(ε) parts of dielectric function, refractive index n(ω) and extinction coefficient k(ω), energy loss function L(ω), reflectivity R(ω), the inter and intra bands and Total Chi for LaAlO3 withing BSE and HSE06 What brings up consideration is the fact that maximum reflectivity points occur at negative points of 1 ( ). At the later mentioned values of 1 ( ), the material experiences a metallic behavior in their nature [1]. Generally, reflectivity increases as the metallicity behavior of the compound increases, reaching its maximum range at the lowest negative value of 2 ( ) of 20eV. The reflectivity starts at 50% of its maximum value, then it oscillates to maximum of 1.4. The electron loss energy function ( ), plays an important role in describing the loss of energy due to fast moving electrons through the crystal lattice of our material. The plot presents a sharp peak located at about 20eV. This peak clearly shows how screening affects the plasma frequency . There are also peaks of optical conductivity spectrum, which is assigned to the charge transfer between interbands. A detailed information of the large spectral conductivity weighted change at low frequency is important for analysis of the interaction of localized d-orbital electrons and the delocalized splitup between bands in lanthanum compounds. Figure 9 displays our calculated interband and intraband valence to conduction absorption spectrum and the corresponding transitions between single-particle energy levels, the broadening allows most the transitions to be resolved, however, as such a resolution is not yet accessible. A number of types of the complex dielectric functions ( ) = 1 ( ) + 2 ( ), provide sufficient information to obtain the optical properties. The imaginary part 2 ( ) was calculated from the momentum matrix elements. Moreover, the real part is obtained from the Kramer-Kronig relationship. Contributions to ε (ω) are namely, transitions of intra-band and inter-band. The interband part can furthermore split into a direct and an indirect part , both of the intraband (2 ) and (1 ) starts from zero and continues to achieve maximum at 2.0eV and a negative maxima at 3.0eV, on the other hand the intrabands (2 ) and (1 ) starts from zero and continues to achieve maximum at around 4.0eV and a negative maxima at 5.0eV.

Conclusion
In conclusion, we have studied the Structural, electronic, phonon, thermal and the optical properties of perovskite LaAlO3 using Ab-initio calculations. The structural changes under nonhydrostatic conditions depend on the degrees of freedom within the LaAlO3 structure. we found that the 3 ̅ phase is energetically stable under the studied temperature and pressure limits. The material goes through the 3 ̅ 3 phase shift upon cooling. An indirect bandgap Γ-R of 5.649eV separates the valence from the conduction bands, it seems that using HSE06 and greatly enhanced the estimation of the band gap. The value of 6.21 eV is in agreement with recent ultraviolet spectroscopic measurements. The thermal properties were computed by using the IFC's and using the hybrid functional HSE06, the phonon structure indicates anharmonicity upon the studied pressure and temperature. The anharmonicity lattice dynamics of the Perovskite thermoelectric LaAlO3 were investigated with first-principles calculations, our calculations of the phonon DOS of LaAlO3 from 50 to 5000K showed significant thermalsoftening and an amount of thermal-broadening. The effect of pressure on the phonons and volume on phonon frequencies, the quasi-harmonic contribution to the non-harmonicity was obtained. We present studies of the optical properties of LaAlO3 using the BSE and HSE06 calculations. Our calculated dielectric-function was shown to agree well with the available experimental measurements. It is clear to note that the difference between the direct band gap and the optical band gap is due to the limitation of the selection-rules in the interband and intraband transitions.