We physically discuss sources of the phenomena and indicate how to select an appropriate functional for a given pressure. We show that these discrepancies are due to the inaccuracy of the DFT + U scheme with arbitrary Ueff and that hybrid functionals can provide better agreement with experimental data at zero pressure. The hybrid B3PW91 approach provides much better agreement with experimental data than the GGA + U. The DFT + U scheme proves to be rather unreliable since it yields completely unpredictable oscillations for the bulk modulus with increasing values of Ueff. Our B3PW91 results show that the best lattice parameter (bulk modulus) is obtained using a larger value of α parameter, 0.4 (0.3 or 0.2), than that of usually considered for the AFM phase. We find that for hybrid functionals, the amount of non-local exchange must first be calibrated before conclusions are drawn. Therefore, we first systematically optimize the α parameter and using it investigate the magnetic and electronic properties of the system. We present a theoretical interpretation of the experimental results and reproduce them satisfactorily.Two dramatic discrepancies between previous reliable experimental and  For instance, here we identify two dramatic discrepancies between previous reliable experimental and accurate theoretical DFT + GGA results for CeIn3 at two different pressure regimes. The first discrepancy is concerned with the Néel temperature, TN, of the compound under question. The previous experimental results showed that the TN of the compound was pressure dependent and completely suppressed at critical pressure Pc = 2.5 GPac ≈ 16 GPa, which is very far from the experimental value11μB per Ce atom while the experimental valueμB. In contrast to the critical pressure, WC-GGA not only could not improve the TOT, but also made it worseμB. In this paper, we show that the theoretical results are drastically far from the experimental results due to the high pressure dependency of the Ce 4f-electrons localization. We attribute these discrepancies to high sensitivity of the degree of Ce 4f-electrons localization in the compound under study to an exerted external pressure.Cerium based materials have recently received considerable attention due to their interesting properties123567ε and 3 in terms of pressure. Our calculations show that the LDA functional due to its low degree of localization can remarkably improve the first discrepancy by providing the suppressed pressure of TN in close agreement with experiment. However, LDA functional not only cannot improve the second discrepancy but also more deteriorates it by predicting worse TOT at zero pressure than that of GGA. On the contrary, the more advanced band correlated methods  due to their high degree of localization improve the second discrepancy by describing the TOT satisfactorily at zero pressure in agreement with experiment. However, this time the strongly correlated LDA + U and hybrid functionals not only fail to improve the first discrepancy but also make the suppressed pressure worse compared to the previously reported GGA results. These evidences reveal that similar to previously reported GGA results, the other functionals also fail to cure both of the discrepancies at the same time. In this paper, we physically discuss what happens to the system by imposing pressure and how pressure can change the nature of the Ce 4f localization as well as why none of the functionals alone can successfully treat both of the discrepancies simultaneously. This study shows that the Ce 4f-electrons behave differently in different pressures and hence cause the discrepancies to occur.To make progress in understanding the basic physics behind these discrepancies more calculations with a variety of functionals are required. A. J. Ochoa-Calle and coworkers by performing systematic DFT calculations on the ↑) and the other with spin down (Ce↓). We consider a mesh of 182 special k points in the irreducible wedge of the first Brillouin zone that corresponds to the grids of 12 × 12 × 12 in the Monkhorst-Pack schemeMT’s) to be 2.2 a.u. for In and 2.8 a.u. for Ce. The cutoff parameters Kmax = 7/RMT and lmax = 10 are used for the expansions of the wave functions inside the muffin-tin spheres and the interstitial region in terms of the lattice harmonics and the plane waves, respectively. The periodic charge density and potential are Fourier expanded up to Gmax = 16 eff and B3PW91 hybrid with several α as well as B3LYP functionals. In the hybrid functionals generally some portion of the exchange term in the semilocal functional is replaced by the Hartree-Fock (HF) exchange so that general form of these functionals can be written as:All the calculations presented here are performed in the framework of the density functional theory2022α is a parameter which determines the portion of the Hartree-Fock exchange, where α = 0.2, β = 0.72 and γ = 0.81α parameter in the range of 0 to 0.4 to seek better optimization for our case. One would notice that the LDA + U and hybrid can be considered as semiempirical schemes since by varying the adjustable U parameter in LDA + U and α parameter in hybrid schemes one can try to tune the methods to predict more closely some experimental data while deviating more for other data. Thus, in this case it is important to optimize these parameters by taking different physical quantities into account and making sure that the optimized parameters can optimally reproduce the experimental data corresponding to the different physical quantities. In structural properties section, we will follow this strategy and optimize the α parameter in B3PW91 to obtain both lattice parameter and bulk modulus in closer agreement with the experimental data. In magnetic properties section, we will show that our optimized α parameter can predict also the magnetic moment in better agreement with the experiment compared to the other values of the α parameter.where 3 compound in the FM and AFM phases. To this end, the results, as tabulated in 32eff in LDA + U and α in hybrid schemes. M. Caffarel and coworkers recently showed that the spatial distribution of the DFT spin density distribution was very sensitive to and depended on the fraction of HF exchange used in the functional employed for CuCl2 molecule having a single unpaired electroneff in GGA + U and dependence of α in B3PW91 functional schemes for the AFM phase of the system. In order to provide a better understanding of the results, lattice parameter and bulk modulus are also presented in eff in GGA + U and α in B3PW91 vary. The lattice constant is more increased by increasing the Ueff of the GGA + U in worse agreement with the experimental data than PBE-GGA, see eff parameter are farther away from the experimental result compared to that of PBE-GGA, see α- and γ-Ce compounds. The GGA + U with Ueff = 4.4 eV (PBE-GGA) predictsγ-Ce (α-Ce) in agreement with experiment. The B3LYP with α = 0.2 lattice parameter is larger and bulk modulus is smaller than those of GGA + U. Therefore, the onsite hybrid B3LYP functional only aggravates the unsatisfactory GGA + U results and thereby yields the worst presented results in α parameter increases with the B3PW91 XCF. However, this is not the case for the bulk modulus, see α parameter increases from zero to 0.4 by step 0.05. The B3PW91 XCF with α = 0.4 predicts the lattice parameter in the best agreement with the experimental result compared to other values of α, however, it fails to satisfactorily predict the bulk modulus. α parameter and both of the lattice parameter and bulk modulus would be taken into account for optimizing the α parameter. We also calculate the structural properties using the LDA-EECE method. However, this method, as shown in 3 lattice constant and bulk modulus. The phase transition pressure and coexistence pressure range were predicted14ε and 2 by B3PW91 with 20% of HF exchange to be 75 GPa and 75–145 GPa in an acceptable agreement with the experimental dataε and α = 0.2 on the structural properties of the CeIn3 compound are more impressive and better than the other functionals.Here, we intend to evaluate the accuracy of the B3PW91 hybrid functional18N, of the CeIn3 compound decreases by applying pressure. The previous theoretical calculations3 decrease by imposing pressure. Our PBE-GGA calculations also validate the latter theoretical results, as shown in N of the compound. The experimental results show that the TN of CeIn3 compound decreases with increasing pressure and may be completely suppressed at the critical pressure Pc = 2.5 GPa, viz. s = 16 GPa, viz. s = 16 GPa by PBE-GGA is much larger than the corresponding experimental Pc = 2.5 GPa. It was tried to improve this discrepancy by using the WC-GGA functionals = 9 GPa is closer to the corresponding experimental Pc = 2.5 GPa, the predicted Ps using the WC-GGA functionals is still very far from Pc. The second discrepancy is concerned with the TOT of the system. Reliable neutron-diffraction results show that the TOT of the CeIn3 is 0.65 ± 0.1 μB at T = 5 K and zero pressureμB within PBE-GGA and 0.112 μB within the WC-GGA. Our PBE-GGA calculations lead to the TOT = 0.24  μB at zero pressure which is fairly comparable with the previous PBE-GGA result. In addition to spin magnetic moment per atom in the muffin-tin shpere, we have also considered and included the spin magnetic moment per atom in the interstitial region and this is why our calculations a little bit differ from the previous theoretical work. Regardless of the latter small difference between theoretical results, a comparison elucidates that the theoretically predicted TOT’s by PBE-GGA and WC-GGA are much smaller than the corresponding experimental TOT = 0.65 μB. Therefore, these functionals are not enough successful in predicting the TOT at zero pressure.It is generally believed that magnetic ordering can be changed by pressure103738z. , see . A compas is far from the experimental Pc, and 2) there are a large discrepancy between the theoretical and experimental TOT’s at zero pressure. We show that the discrepancies between experiment and theory originate from high pressure dependency of the Ce 4f-electrons localization. On the other hand, the validity of the selected exchange-correlation functional for simulating CeIn3 are highly sensitive to the pressure regime at which the DFT calculations are performed. Therefore, these discrepancies cannot be well resolved simultaneously only by increasing the accuracy of the calculations within a single specific currently available functional as they occur in two different pressure regimes.As discussed above there are two dramatic inconsistencies between theory and experiment: 1) theoretical Pc40c. This has motivated us to investigate the effects of the localization degree of Ce 4f-electrons and pressure on the magnetic properties of CeIn3. For this purpose, we calculate magnetic moments per Ce atom of this compound versus pressure within several exchange-correlation functionals (XCFs). These XCFs contain PBE-GGA + U with varying Ueff from 0.5 to 5.5 eV by step 0.5 eV, B3PW91 hybrid functional with varying α from 0 to 0.4 by step 0.05, B3LYP hybrid functional with α = 0.2, LDA, LDA-EECE, and PBE-GGA. The degree of localization is adjusted by Ueff and α parameters of the GGA + U and hybrid methods, respectively. Our results are presented in 11The main idea to overcome these inconsistencies is inspired from the following experimental observations. The dHvA experiments revealed that the character of 4f-electrons was changed from localized to itinerant above the Ps using the GGA + U, B3LYP and B3PW91, we anticipate that the Ps using these functionals must be much larger than experimental Pc. This anticipation can be verified by the results given in c for all of the considered Ueff values using the GGA + U and all of the α parameters with the B3PW91. Consequently, like GGA + U, the hybrid functionals cannot also predict the Ps in acceptable agreement with experiment. These results indicate that increasing the 4f-correlation using GGA + U and hybrid functionals even make worse the predicted Ps than that of the PBE-GGA with respect to the Pc. Therefore, the 4f-correlation must be decreased to improve the Ps compared to the experimental Pc. As another alternative, we then use the LDA functional which has the least correlation. The LDA calculations predict that Ps = 0, because TOT is zero above the zero pressure, see s prediction in much better agreement with the experimental value Pc compared to those of PBE-GGA and even WC-GGA as well as the other considered functionals. Hence, LDA could solve the first inconsistency problem between theoretical Ps and experimental Pc by decreasing the degree of 4f localization.The GGA + U results presented in α = 0.2 is the most successful functional for the TOT prediction at zero pressure among the other considered functionals, because in this case TOT becomes 0.67 μB, which is in more agreement with the experimental resultμB. As can be seen from the results presented in α parameter to values more or less than 0.2. Therefore, α = 0.2 would be considered as an optimized parameter for B3PW91 in this case in agreement with the discussion presented in structural properties section. Thus, B3PW91 with α = 0.2 can cause to overcome the second inconsistency by increasing the degree of localization.We now concentrate on the second problem, i.e., the disagreement between theoretical and experimental TOT at zero pressure. The LDA functional leads to zero TOT at zero pressure. Thus, LDA deteriorates the TOT predictions of PBE-GGA and WC-GGA at zero pressure compared to the experiments in good agreement with Pc, but it is unsuccessful in reproducing the TOT at zero pressure. Conversely, the B3PW91 with α = 0.2 can only predict the TOT at zero pressure, but it fails to predict the Ps compared to the experimental Pc. All these indicate that increasing the degree of localization increases the TOT and makes the theoretical prediction consistent with the experimental result at zero pressure. This is in agreement with the recent theoretical works and thereby decreases the inconsistency between the theory and experiment. Hence, the degree of 4f-localization can influence the effects of pressure on the magnetic properties. Therefore, it is not possible to describe magnetic properties of CeIn3 for every pressure only by one fixed degree of 4f-localization. Thus, the degree of localization depends on the pressure and should be tuned in terms of the pressure. High pressure is equivalent to the low 4f localization, and vice versa. This is in agreement with the mentioned dHvA observations which show the changes in the degree of 4f-localization above the Pc40xIn3−x using the Gd3+ electron resonance experiments at the critical xc ≈ 0.65 where TN → 0ε and 214As discussed above, the LDA functional can only predict the P3. To this end, we investigate the electronic structure of CeIn3 at two different pressures within three different functionals corresponding to three different degrees of 4f-localization. The selected two pressures are P = 0 corresponding to a = 4.68 Å and P = 14 GPa corresponding to a = 4.44 Å. These pressures are calculated by B3PW91 with α = 0.2. The latter 14 GPa pressure is equivalent to the predicted LDA pressure 3.5 GPa, which is close to the experimental Pc = 2.5 GPa. Since we intend to investigate the effects of 4f-localization degree on the electronic properties, three functionals are selected. These functionals are B3PW91 with α = 0.2 having high degree of 4f localization, B3PW91 with α = 0.1 having intermediate degree of 4f localization, and LDA having low degree of 4f localization. The total and 4f partial DOSs ] and valence [see ij)] regions separately and 4f partial DOSs are also shown in ij), where i = 1, 2 and j = 1 to 3. The DOSs calculated by B3PW91 with α = 0.2 at zero pressure, as shown in 11), (b11), and (c11), are in good agreement with those of previously calculatedeff = 5.5 eV. There are two peaks in the semicore region near −15 eV and −14 eV energies for the considered three functionals and two pressures, see ij) . Pressure causes these peaks to be broadened and decreased in magnitude, as can be seen by comparing 11) with (a21), and 12) with (a22), as well as 13) with (a23). However, pressure has no remarkable effect on the locations of these peaks. The results obtained from the considered three functionals show that the semicore states look precisely alike at P = 0, see j1) (j = 1 to 3). This observation at zero pressure remains correct at P = 14 GPa as well, see j2) (j = 1 to 3). These show that the reduction of the 4f localization cannot significantly affect the semicore states. All these show that the effects of pressure on the semicore states are more considerable than those of the 4f-localization degree. The semicore states are mostly composed of the d-In states while the valence states are mostly made up of 4f-Ce states. Thus, it is expected that the effects of the 4f localization are more considerable on the valence states than the semicore states. The reduction of the 4f localization at zero pressure causes the total DOSs in the valence region to be narrower and pile up with taller height around the Fermi level, see j1) (j = 1 to 3). The same result can be clearly seen at P = 14 GPa by comparing the narrow and piled up DOSs around the Fermi level in 23) with the broad total DOSs shown in 21,b22). Although the effects of pressure on the valence states is almost negligible using the B3PW91 with α = 0.2 [compare 11) with (b21)], the valence DOSs can be also changed by pressure. For example, the LDA results show that the total valence LDA DOS is substantially affected by the pressure, compare 13) with (b23). Thus, the effects of pressure on the valence states increase by reduction of the 4f localization. This implies that the effects of pressure on the valence DOS depend on the degree of 4f localization. This dependency is what we have emphasized on it in the magnetic properties of CeIn3, see magnetic properties section. The 4f partial DOSs more clearly reveal the pressure dependence of the valence states on the degree of 4f localization. There are two nonequivalent Ce atoms in the considered unit cell. These Ce atoms are labeled as Ce1 and Ce2. The results show that up and down 4f DOSs of Ce1 are asymmetric with respect to each other at zero pressure using all considered functionals, see j1) (j = 1 to 3). This is the case for Ce2 at zero pressure as well, see j1) (j = 1 to 3). These imply that the up 4f DOS of each Ce atom cannot be canceled out by its own down 4f DOS and thereby yields nonzero total magnetic moment per Ce atom. But, the up 4f DOS of the Ce1 cancels the down 4f DOS of the Ce2 out and vice versa which yields zero for the total magnetic moment per unit cell as expected for the AFM phases. The same results are also observed at P = 14 GPa using the B3PW91 with α = 0.2 and 0.1, see j2) (j = 1 to 3). However, an interesting different behavior is observed at P = 14 GPa using LDA, see 23). In contrast to the LDA 4f DOSs at zero pressure, the LDA 4f DOSs at P = 14 GPa show that up and down 4f DOSs of Ce1 are symmetric with respect to each other. Thus, the up 4f DOS of each Ce atom can be canceled out by its own down 4f DOS and thereby yields zero total magnetic moment per Ce atom. Therefore, LDA predicts that CeIn3 would behave as a paramagnetic (PM) system at the considered pressure (14 GPa). But, one should not here conclude that the phase transition form AFM to PM occurs at 14 GPa, since LDA results in 3 which evidently exhibits the dependence of pressure effects on the 4f localization and vice versa.Total DOSs are shown in semicore [see min and Emax of the bands in α = 0.2 (in this work). Then, we report on the results obtained by the intermediately localized functional, i.e., B3PW91 with α = 0.1, and finally concentrate on the least localized functional, i.e., LDA. Thus, the degree of 4f localization is gradually reduced step by step through the discussion presented in this section.The band structures per spin are calculated using the considered three functionals and two pressures. The results are presented in α = 0.2 at P = 0 and P = 14 GPa, we concentrate only on γ1, γ2 and γ3. The minimum energy of these bands are negative (Emin < 0) while their maximum energies are positive (Emax > 0). Their occupancy numbers are also smaller than unity. Applying the pressure causes the bandwidths, occupancy numbers and the shape of the bands to be changed. For example, pressure increases the bandwidth and occupancy number of γ1. Furthermore, pressure causes the Emax of γ1 and γ2 bands to decrease which means that pressure pushes these bands downward below the Fermi level. The Emin and Emax of γ3 band are also increased by pressure, which means that pressure pushes the γ3 upward above the Fermi level. But, the pressure cannot cause these bands to be located completely below or above the Fermi level. Thus γ1, γ2 and γ3 cross the Fermi level again at P = 14 GPa. In addition, pressure increases the 4f states around the Fermi level. The thickness of the bands around the Fermi level is larger at P = 14 GPa than P = 0. However, the 4f states at the Fermi level are negligible at the two considered pressures and they are mostly dispersed away from the Fermi level.As the first step for describing the band structures using the B3PW91 with α = 0.1 at P = 0 and P = 14 GPa. Therefore, we concentrate only on max of γ1, γ2 and γ3 are positive while their Emin are negative. Their occupancy numbers are also smaller than unity. These results imply that these three bands cross the Fermi level at zero pressure. This is the same as the situation of the first step. The results reveal an interesting event at P = 14 GPa in this step. The Emax of the γ1 band is negative and its occupancy number is unity at P = 14 GPa. This means that pressure causes the γ1 to be located below the Fermi level, which is quite different from that of the first step. Pressure also changes the Emin and Emax of γ2 and γ3, but it cannot prevent these bands to cross the Fermi level. Therefore, two bands γ2 and γ3 cross the Fermi level at P = 14 GPa compared to the P = 0 situation where three bands  do this. A manifold of the 4f bands is displayed in We now go to the second step and describe the results with the B3PW91 functional with max of γ1 is negative and its occupancy number is unity at zero pressure. This implies that the γ1 is located below the Fermi level and does not cross it. However, the Emaxs of γ2 and γ3 are positive and their Emins are negative. The occupancy numbers of γ2 and γ3 are also smaller than unity. This implies that γ2 and γ3 cross the Fermi level. The same results are also obtained at P = 14 GPa. This means that pressure cannot change the number of the bands which cross the Fermi level using the LDA functional. However, pressure changes the position, bandwidths, occupancy numbers and the shape of the bands. For example, pressure increases the bandwidths of the γ1, γ2 and γ3 bands. The results also show a manifold of the 4f bands which straddles the Fermi level at zero pressure. This manifold is dispersed up to 1 eV above the Fermi level. The same result is also seen at P = 14 GPa. This implies that pressure cannot change significantly the position and dispersion of this manifold using the LDA.Let us now consider the last step to describe the LDA results. Therefore, we concentrate on γ1, γ2 and γ3 at zero pressure. We conclude the section by the fact that it is crucial to first specify the pressure, and then for each specified pressure use a suitable functional with an appropriate degree of 4f-localization.In essence, we have shown that the effects of pressure on the band structure can strongly depend on the used functional. This implies that the effects of pressure can be influenced by the degree of 4f localization. Every functional has its own specified degree of 4f localization which will be assumed for and applied on the case under the theoretical study. For example, comparison of 3 compound is changed as pressure increases from P < Pc to P ≥ Pc, which can be explained by changing the character of 4f electrons from localized for P < Pc to itinerant for P ≥ Pc. A variety of approaches have been proposed to describe the FS topology of cerium based compounds. The FS measurements can be well described by the DFT + LDA/GGA band structure calculations in some compounds for which their f-electron shells are completely either filled or empty so that contributions of their f-electrons to the corresponding FSs are negligible. Even if the f-electron shells are neither completely filled nor completely empty, they can be still well described by the DFT + LDA/GGA, provided that the f-electrons of the compounds under question are itinerant and behave as band-like electrons. It was observed that the Ce based compounds with f-itinerant electrons had larger FS than those with f-localized electrons473. Then, we have calculated the FS using the B3PW91 with α = 0.2, B3PW91 with α = 0.1 and LDA functionals at zero pressure and P = 14 GPa. The FS of a compound includes some branches which are produced by the partially filled bands. The branches of CeIn3 Fermi surface are calculated using the three considered functionals for the two pressures and displayed as S1, S2 and S3 in j branch is produced by the γj band provided that the γj band crosses the Fermi level, as expected from the definition of FS. We have also tabulated contributions of the partial DOSs and interstitial (Int) DOS to the DOS(EF) in Electronic properties of compounds can be more clearly analyzed by shedding light into their Fermi surface (FS) topologies which contain important experimental information. Several dHvA experiments40414445α = 0.2 at P = 0, as depicted in j1) for j = 1 to 3. These three branches also exist at P = 14 GPa using this functional, see j2) for j = 1 to 3. The shapes of these branches at P = 14 GPa are approximately the same as those at P = 0, but the sizes of these branches are changed by pressure. For example, a comparison of 11) and (a21) shows that pressure only reduces the sizes of the small packets of S1 branch (located in the corners of the first Brillouin zone) and does not drastically change their shapes. Note that the packets shapes remain unchanged, as pressure does not also remarkably change the shapes of the γ1, γ2 and γ3 bands at the Fermi level and the points where these bands cross the Fermi level using this functional, see γ1 and γ3 bands but decreases the occupation number of γ2 band using the B3PW91 functional with α = 0.2. Moreover, the results in f(EF) while it decreases the DOSp(EF), DOSd(EF) and DOSInt(EF) using this functional. The DOSs(EF) is also increased by pressure which is negligible with respect to the DOSf(EF).There are three FS branches with the B3PW91 with 1,S2 and S3 branches at zero pressure using the B3PW91 with α = 0.1, as shown in j1) for j = 1 to 3. A comparison of γ1 and γ3 bands at the Fermi level are not significantly changed by decreasing the α parameter at P = 0. This causes the shapes of the S1 and S3 branches to remain approximately unchanged at P = 0 by reducing α parameter from 0.2 to 0.1, compare 11) with (b11) and 13) with (b13). But, the shape of the γ2 band is changed at the Fermi level by decreasing the α parameter at P = 0. For example, the γ2 band is touching the Fermi level between W and L points in 2 branch using the B3PW91 with α = 0.2 to be different from that of B3PW91 with α = 0.1, compare 12) with (b12). This change is due to the degree change of the 4f localization. The results in f(EF) is significantly increased by decreasing the α parameter using the B3PW91 functional while change in the magnitude of the other partial DOSs is negligible at the Fermi level. This causes the character of the bands at the Fermi level and thereby size of the branches to be changed by changing the α parameter. These results are in agreement with previous experimental and theoretical measurements3 FS at AFM phase. In contrast to the case of P = 0, there are only two S2 and S3 branches for the case of P = 14 GPa using the B3PW91 with α = 0.1, i.e., S1 branch is not reproduced at P = 14 GPa after reducing α, see j2) j = 1 to 3. Pressure causes the γ1 band to be located below the Fermi level at P = 14 GPa using the B3PW91 with α = 0.1, as discussed in band structures section. This is why the S1 branch is disappeared at P = 14 GPa when reducing α, see 21). A comparison of 12,b22) elucidates that pressure changes the S2 branch. This change originates from the effects of pressure on the shape of the γ2 band at the Fermi level. The γ2 band is tangent to the Fermi level between W and L points in 3 branch at P = 0; the existed empty spaces in 13) are filled in 23) by increasing pressure. The results in f(EF) is remarkably increased at P = 14 GPa while the DOSs(EF), DOSd(EF) and DOSInt(EF) are decreased with respect to those obtained at P = 0 using the B3PW91 with α = 0.1.There are also three Sij) for i = 1, 2 and j = 1 to 3, there are only two S2 and S3 branches at P = 0 or similarly at P = 14 GPa, i.e., the S1 branch is absent. The γ1 band is located below the Fermi level within this functional and as a result the S1 branch is absent in the FS. The results as presented in f(EF) is much larger than those of the other states. In addition, γ1 and γ2 bands are high and approximately equal. The shapes of these bands using the LDA are very different from those of the other functionals. Thus, the cross-sectional areas of the FS are filled by LDA much more than the other functionals.Using the LDA functional, as illustrated in 3 FS with LDA at both P = 0 and P = 14 GPa  to predict the experimental Pc (see magnetic properties section). This means that P = 14 GPa is greater than Ps using the LDA but less than Ps using the B3PW91. This implies that for P = 14 GPa the system lies in the PM phase using the LDA, but it still lies in the AFM phase using the B3PW91. These results reveal that the FSs using those functionals that treat f-electrons as itinerant electrons such as LDA are in better agreement with experiment for P > Pc than those functionals that treat f-electrons as localized electrons such as B3PW91. Conversely, FSs using those functionals that treat f-electrons as localized electrons such as B3PW91 are in better agreement with experiment for P~0 than those functionals that treat f-electrons as itinerant electrons such as LDA.We conclude this section by the following points. There are only two branches for the CeInc. The electric field gradient (EFG) is a tensor of rank 2 which has only two independent components in the principal axes system. These components are the main component of EFG, Vzz, and the asymmetry parameter, η is zero. Thus, we only focus on Vzz. The EFG contribution of the electrons inside (at the surface and outside) of the muffin-tin sphere is called the valence (lattice) EFG which is denoted by In this section we take the main point of this work into account and show that the electric field gradient (EFG) as an extremely sensitive quantity can be calculated as a function of pressure and show how the EFG can be affected before and after P3 compound using the B3PW91 with α = 0.2, B3PW91 with α = 0.1 and LDA functionals. These calculations are performed by taking the equilibrium lattice constant a = 4.68 Å into account which is predicted by B3PW91 with α = 0.2. The calculated Vzz, and their components 3 4f electrons at zero pressure. Among the high localized functionals, B3PW91 with α = 0.2 is in better agreement with experiment than previous theoretical calculations even GGA + U + SO calculations. The success of this functional can be explained by the relation between EFG and total DOS(EF). The previous calculations have revealed that EFG ∝ DOS(EF)F) calculated by B3PW91 (α = 0.2) is F) we also anticipate that EFG must increase as the 4f localization decreases, as the DOS(EF) is increased by decreasing the 4f localization  and Δd(EF) are also calculated using the three mentioned functionals at P = 0 and P = 14 GPa. The results are tabulated in p(EF) is one order of magnitude greater than that of Δd(EF) at In site. This result is consistent with the previous calculationsHere, we calculate the EFGs of CeIntion see . Our calα = 0.2 as a function of pressure, as shown in α = 0.2 at zero pressure, and using the B3PW91 with α = 0.1 at P = 2 GPa, as well as using the LDA at P = 5 and 10 GPa. As it can be clearly seen from Finally, we have calculated the EFG at In site using the B3PW91 with 3 compound as an appropriate sample to show how the degree of localization can be strongly affected by pressure in a highly correlated system within the density functional theory. To this end, we have systematically calculated the effects of pressure and 4f localization degree on the structural, magnetic, and electronic properties of this compound. The calculations were performed employing a variety of localized and itinerant functionals versus pressure. Our PBE-GGA results in agreement with the previous results reported by the others predict that the total magnetic moment per cerium atom (TOT) is suppressed for this compound at a pressure of about 16 GPa. However, this prediction of PBE-GGA is very far from the experimental value of 2.5 GPa. This inconsistency between theory and experiment can be improved using LDA functional. The LDA functional yields better results for the suppressed pressure in closer agreement with experiment than those of the other considered functionals. The Fermi surface calculations using the LDA functional are also found to be consistent with the experimental measurements. In addition to the aforementioned inconsistency, the PBE-GGA functional also fails to satisfactorily predict the TOT at zero pressure. The PBE-GGA predicts that the TOT of the compound is 0.24 μB at zero pressure, which is inconsistent with the experimental value of 0.65 μB. In this case, the LDA functional not only dose not improve the predicted TOT at zero pressure, but decreases the accuracy compared to that of PBE-GGA. Our results show that high localized B3PW91 functional with α = 0.2 can well predict the TOT of the system at zero pressure (0.67 μB) in better agreement with the experimental value (0.65 μB). Lattice parameter and bulk modulus of the system are systematically studied using the GGA + U and B3PW91 functionals by varying their corresponding Ueff and α parameters, respectively. Our GGA + U calculations show that the bulk modulus of the system unreliably fluctuates as Ueff parameter increases. This behavior which does not allow to select an appropriate value for the Ueff indicates that the DFT + U scheme is rather unreliable. The hybrid B3PW91 approach provides much better agreement with the experimental data than the GGA + U scheme. The lattice parameters (bulk moduli) for the AFM phase are calculated to be 4.69 Å (52.41 GPa), 4.68 Å (61.77 GPa), and 4.68 Å (62.30 GPa) by B3PW91 with α = 0.4, 0.3, and 0.2, respectively. The comparison of these results and the corresponding experimental data, 4.69 Å (67.00 GPa), shows that the best lattice parameter is obtained using a larger value of α (0.4) than that of usually considered for the AFM phase, see eff parameter since not only its predicted bulk modulus unpredictably fluctuates by increasing Ueff but also the fluctuations are performed around a value which are far from the experimental bulk modulus. However, it is worth mentioning that the hybrid B3PW91 gives reliable results for the AFM phase of the system using the larger value of α = 0.3. The latter result together with the excellent prediction of the lattice parameter by even a larger value of α (0.4) in agreement with the previous study of CuCl2 compoundα = 0.2 and 0.3. By considering both of the lattice parameter and bulk modulus results and calibrating them to the corresponding experimental data we found that the B3PW91 with α = 0.2 can predict the structural properties more consistent with the experimental data. The agreement with the experimental results is acceptable with the standard B3PW91 approach for the FM phase. It is worth mentioning that these consistencies can only partially validate the correctness of the reported results. Furthermore, the Fermi surface calculations using this functional are in agreement with experimental measurements for the AFM phase. In addition, the calculated electric field gradients at In sites by this hybrid functional are found to be very closer to the experimental data at zero pressure compared to the other considered functionals. However, this hybrid functional makes the predicted suppressed pressure worse than that of PBE-GGA compared to the experimental result. Thus, the high localized B3PW91 functional with α = 0.2 is suitable functional in predicting the CeIn3 properties at zero pressure while the LDA is a suitable functional for high pressures. This means that the character of 4f electrons is changed by applying the pressure in this compound in agreement with the dHvA experiments. Therefore, the degree of 4f localization must be tuned in terms of the pressure. High localization is suitable for low pressures and vice versa; viz., low localization is suitable for high pressures. Based on these results we conclude that the GGA failure originates from the degree of 4f localization which is considered in GGA functional. The GGA is not low localized enough to become suitable for studying the CeIn3 at high pressures. The 4f-electrons are more localized using the GGA than those of LDA and thereby GGA predicts the critical pressure much larger than those of experiment and LDA. On the other hand, GGA is not highly localized enough to become suitable for studying the CeIn3 at very low pressures around the P = 0. Thus, the TOT is predicted by the PBE-GGA functional at zero pressure to be smaller than those of the experiment and B3PW91 functional with α = 0.2. Our electronic structure, including DOS, band structure, and Fermi surface analyses reveal that if a fixed exchange-correlation functional is used for every pressure, then the effects of pressure on the electronic structure will not be well considered for the highly correlated systems. This is in contrast to what happens in nature, because if the degree of 4f-electron localization decreases, the electronic structure can be changed. Our results show that the GGA functional can be considered as an appropriate functional for studying the CeIn3 compound at intermediate pressures but not for every pressure regime. In essence, this state-of-the-art DFT study demonstrates that the variation of a physical quantity with respect to pressure can sensitively depend on the used exchange-correlation functional in such a system. This in turn implies that the behavior of a physical quantity as a function of pressure can be valid within DFT only over a specific pressure range. Therefore, a physical quantity-versus-pressure curve cannot always be obtained reliably by only one currently available exchange-correlation functional over an arbitrary range of pressure. Instead, it would be more reliable to first divide the arbitrary pressure interval into some specific pressure intervals. Then, the degree of localization is determined for each pressure interval. Eventually, based on the latter determination the best exchange-correlation functional is selected and/or tuned for every pressure interval. Otherwise, consistency between experimental and theoretical DFT results using a specifically fixed exchange-correlation functional cannot be guaranteed for any pressure interval so that even one may expect to encounter an extraordinary large discrepancy between theory and experiment. By this strategy, we have explained why there are two dramatic discrepancies between previous reliable experimental and accurate ab initio DFT results in CeIn3 and discussed how these discrepancies can be resolved.We have used the CeInet al. Pressure dependency of localization degree in heavy fermion CeIn3: A density functional theory analysis. Sci. Rep. 6, 31734; doi: 10.1038/srep31734 (2016).How to cite this article: Yazdani-Kachoei, M.


Calculations of geometries and frequencies at different density functional theory (DFT) and Hartree–Fock/Møller–Plesset (HF/MP2) levels have been performed. Results have been assessed and evaluated against those obtained at the coupled cluster single-double (Triplet) (CCSD(T)) level of theory. The characteristics of the C–Br and O–Br bonds have been identified via analysis of the electrostatic potential, natural bond orbital (NBO), and quantum theory of atoms in molecules (QTAIM). Analysis of the electrostatic potential (ESP) maps enabled the quantitative characterization of the Br σ-holes. Its magnitude seems very sensitive to the environment and the charge accumulated in the adjacent centers. Some quantum topological parameters, namely ∇2ρ, ellipticity at bond critical points and the Laplacian bond order, were computed and discussed. The potential energy function for internal rotation has been computed and Fourier transformed to characterize the conformational preferences and origin of the barriers. NBO energetic components for rotation about the C–Br and O–Br bonds as a function of torsion angle have been computed and displayed.The present study aims at a fundamental understanding of bonding characteristics of the C–Br and O–Br bonds. The target molecular systems are the isomeric CH The important role of bromine species in ozone depletion ,2,3,4 in3OBr has been reported in the 230 < λ < 400 nm range [3OBr. In order to evaluate the role of bromine species, in general and that of CH3OBr in particular, in ozone depletion, knowledge of the heat of formation and the electronic characteristics of the bromine bonds are required. The isomeric system CH3OBr/CH3BrO/BrCH2OH is suggested to play the major role in these photochemical processes, yet no systematic study of the energies, structures and dynamics of the excited states has been published.The electronic absorption spectrum, in the gas phase, of CHnm range ,11. Howe3OBr [3OF and CH3OCl [2OH have been studied using ab initio multi-reference configuration interaction calculations for ground and excited states [Quantum mechanical calculations have been carried out to study chemical bonding ,13,14 an3OBr  in compad CH3OCl . It was d CH3OCl . The phod states . Severald states ,19,20.3OBr/CH3BrO/BrCH2OH. Several different decomposition and/or isomerization channels have been proposed including the HCOBr (cis)/trans system. The first step to achieve this goal, which is addressed in the present communication, aims at a fundamental understanding of bonding characteristics of the C–Br and O–Br bonds. The target molecular systems are the isomeric CH3OBr/BrCH2OH system and their decomposition products which are suggested to play a major role in ozone depletion processes. We are interested in evaluating the significance and relative importance of stereoelectronic effects in these systems. The characteristics of the C–Br and O–Br bonds will be theoretically explored and analyzed via natural bond orbital (NBO), quantum theory of atom in molecules (QTAIM) and electrostatic potential analyses. The ultimate goal of the present research project is to investigate the decomposition/isomerisation dynamics of the isomeric system CHThe appropriate theoretical model should result in as accurate and flexible wave functions as possible and should also be cost-effective, bearing in mind that these wave functions will ultimately be used in very demanding computations of the on-the-fly dynamics for the decomposition/isomerization of the bromine-containing species in their excited states. To achieve this goal, we have carried out sophisticated calculations of the geometries and frequencies at the couple-cluster single-double (triple) CCSD(T)/6-311++G** level of theory. These very expensive calculations have been used as reference for the more economic models. Calculations at the different density functional theory (DFT) levels and at the HF-MP2 level of theory are compared to the CCSD(T) results in 3OBr/CH3BrO/BrCH2OH, the alcohol form is more stable than CH3OBr and its hypervalent bromine isomer by 35.12 and 75.25 kcal/mol, respectively. For the isomeric system HCOBr(cis)/HCOBr(trans)/BrCHO, the aldehyde form is much more stable than the HCOBr(cis) and its trans form by 67.11 and 75.89 kcal/mol, respectively. Increasing the quality of the basis set (mainly polarization functions) from double zeta (DZ) to quadruple-zeta (QZ) increases the relative energies by 0.28 to 0.48 atomic unit (au). Most of this energy stabilization (79%) is due to the increase in quality in going from DZ to triple-zeta (TZ), the other 21% may be gained at a much higher cost on going to QZ. In order to evaluate the effect of the diffuse functions on the computed energies we have carried out similar CCSD(T) calculations using the cc-pVTZ basis set. Results are also included in 3BrO where diffuse functions seems to be much more effective where its effect exceeds 0.09 au.Furthermore, in addition to assessing the appropriate theoretical model detailed in the aforementioned paragraph, we carried out further exhaustive calculations to determine accurate energy values to be used in thermochemical analysis of the studied systems. In such calculations, we attempt to reach complete basis set limit. In the present section, we will attempt to localize and identify the structural characteristics and energetic of the C–Br and O–Br bonding interactions. 3OBr/CH3BrO/BrCH2OH. The alcohol form BrCH2OH is much more stable by 33.9 and 106.2 kcal/mol than CH3OBr and its hypervalent bromine isomer CH3BrO isomer, respectively. The three isomers possess staggered structures with Cs symmetry.Let us start by studying the geometric features of the isomeric system CH3OBr/CH3BrO/BrCH2OH. The optimized geometries deviate strikingly from idealized PG form particularly with respect to Br…H separation and the dihedral angle specifically in case of BrCH2OH. For CH3OBr the optimized C–O–Br angle open significantly 112.5° thereby partially relieve the apparent steric congestion. This is a result of the mutual repulsion of the lone pair electrons localized on both the Br and O atoms. The isomeric form, CH3BrO is also enjoying a staggered conformation with the C–Br–O angle much smaller ca. 103°. This smaller value of the C–Br–O angle suggests that there is a π-overlap between the lone-pair electrons of the bromine atom and that of the oxygen atom. This π-overlap imparts partial double bond character to the Br–O bond leading to decrease in its length to ~1.7 Å with the consequent decrease in electron repulsion in the carbon–bromine bond region. This point may be further clarified by NBO analysis of the total self-consistent field (SCF), deletion and delocalization energies of the tautomeric system. In these calculations, all the Rydberg and antibond orbitals, which are the non-Lewis NBO orbitals, that usually appear in the NBO analysis are deleted. The result of this deletion is the energy of the idealized NBO natural Lewis structure, with all Lewis NBOs doubly occupied. Unlike other deletions, in which there is a slight loss of variational self-consistency due to the redistributed occupancy of the deleted orbitals, the result of this deletion corresponds rigorously to the variational expectation value of the determinant of doubly occupied Lewis NBOs. This analysis is presented in The geometry differences are associated and focus on methyl torsions; the associated potential energy functions often exhibit significant skeletal flexing perturbations (couplings to stretching and bonding degrees of freedom) that modify an idealized rigid-rotor picture. The basic issue is whether the stabilizing interactions in this tautomeric system should be primarily regarded as decrease of “steric repulsion” or increase of “bonding attraction”. Direct calculation of the potential energy function for rotation around the C–Br and the O–Br bonds and its Fourier transform analysis can be brought to bear on this issue.2OH and that of the CH3OBr and CH3BrO indicate clearly that rotation about C–Br and O–Br bonds is of a completely different nature than that about the C–O bond. Delocalization interaction underlies the large rotation barrier for rotation about the C–O bond in BrCH2OH. The origin of this rotational barrier can be identified by Fourier analysis of internal rotation function as detailed by Pople et al. [1(φ) (1 − cos φ) + V2(φ) (1 − cos2φ) + V3(φ) (1 − cos3φ), where φ is the rotation angle, the V1 represents the interaction of bond dipoles, V2 represents the conjugative interaction, and V3 is an electrostatic bond–bond repulsion term. Fourier decomposition of the potential function for CH3BrO has been performed; results are displayed in The computed rotation barriers are depicted in e et al. ,23. In t2 term, is maximum at φ = 0°and 180°. The three fold electrostatic interaction component shows maximum stabilization at φ = 0° and 120° and is repulsive otherwise. The potential energy function of rotation for CH3OBr shows almost the same trend.All three components of the Fourier transform contribute significantly to the potential barrier. Thus, the one-fold term shows maximum repulsion between local dipoles at φ = 180°, and maximum attraction at φ = 0°. Conjugative stabilization, as reflected by the V3OBr/CH3BrO, which is believed to play a central role in O3 depletion in the Arctic troposphere. This species can exit in a cis(I) or a trans(II) conformations. It should be mentioned that the optimization of this species always falls into the cis-conformation, which seems to be the global minimum structure on the potential energy hypersurface. The trans-conformation can only be obtained by freezing the dihedral angle during full optimization. The cis form (I) is more stable by 10.825 kcal/mol. The geometric features of this species shows the longest C–Br bond length of an average value of 2.5 Å, reflecting a minimal attractive interaction of the d-orbitals of Br– with the p-orbitals of carbon. The C–O bond length shows its minimum value in this species which reflects a tight binding and pronounced double bond character. This is further confirmed by a C–O–Br bond angle approaching 120°, a typical sp2 hybridization scheme for the oxygen atom. The isoelectronic compound BrCHO  (III) shows the same bonding characteristics as the HCOBr species. Comparison of the NBO results for the total SCF, deletion and delocalization energies of the tautomeric system I, II and III is presented in HCOBr is one of the decomposition products of the isomeric system CH−1 range) with much higher intensities than that of the C–O stretching vibrations which appear at lower frequencies (in the 1050–1100 cm−1 range). The correspondence with the literature values are satisfactory bearing in mind that our frequency calculations are carried out within the harmonic approximation. In order to evaluate and assess the importance of anharmonic corrections of vibration modes, calculations have been performed taking in account the anharmonicity of the vibrations. The calculations were carried out in the gas phase using the VPT2 method as implemented by Barone [−1 as compared to 620–730 cm−1 range for this mode in case of CH3OBr, its tautomer CH3BrO and isomer BrCH2OH. Calculation of the vibration spectrum of the OBr radical predicted the stretching vibration mode of the O–Br bond at 742 cm−1. In case of the CH3BrO where a methyl group is attached to the bromine, νBr–O shifts but slightly down field where as such a shift became more pronounced in case of the tautomeric compound CH3OBr, where νBr–O appears at 625 cm−1.y Barone ,25 in thy Barone . In all 2O4→σ*C1–Br3, σ*C1–Br3→σ*C1–O4, σ*C1–Br3→n2O4 and n1O4→n2O4 interactions that yielded 187.75, 11.16, 13.13 and 15.38 kcal/mol for the former and 195.27, 4.81, 6.93 and 1.23 kcal/mol for the later. It is clear that although the n2O4→σ*C1–Br3 interaction favours II by 7.52 kcal/mol; the later three interactions favour I by 26.70 kcal/mol.The competitiveness of I compared to II is due to the strong nAs shown in 3 bulky groups in both IV and VI. It is worth mentioning that V is more stable than VI by 42.553 kcal/mol. Not just that, also the ideal Lewis Structure of V is more stable than that of VI by 75.054 kcal/mol.3 and Br groups and the ineffective electrostatic repulsion between the negatively charged carbon and oxygen atoms and the attraction between the negatively charged carbon atom and positively charged bromine atom. However, the total energies of the two tautomers are comparable. The competitiveness of VI is due to hyperconjugation that yielded 32.501 kcal/mol compared to that of V.This stems from the strong steric hindrance between the two bulky CHcf. 2O4)n2Br5→σ*C1–Br6, (n2O4)n2Br5→σ*C1–H3(σ*C1–H5), (n2Br6)n3O6→σ*C1–Br5(σ*C1–O4) and n3Br6→σ*C1–O4, have contributed 21.09, 3.57, ˂0.5 and 5.25 kcal/mol respectively for IV; 5.61, 5.61, 1.48 and 1.61 kcal/mol respectively for V and 2.30, 2.19, ˂0.5 and 15.83 kcal/mol, respectively for VI. Therefore the origin of preference of IV is mainly due to the n2O4→σ*C1–Br6 and n3Br6→σ*C1–O4 donor–acceptor interactions; while the vicinal antiperiplanar σC1–H2→σ*O4–Br6 and lone pairs-antibonding n2O4→σ*C1–H3 and n2O4→σ*C1–H5 interactions contribute mostly in V. However, the most influential hyperconjugation of VI was a lone pair donor and antibonding bond acceptor (n3O6→σ*C1–Br5).The most influential hyperconjugative interactions cf.  (n2O4)n2The C–F bond has been shown  to impac3OBr an additional donor–acceptor interaction term results from the Br(n) interaction with the σ* acceptor orbitals of the C–O NBO. These interaction curves bear similarity to the potential function for rotation displayed in 3BrO, the two Br(n)-σ*(C–H) interactions work in a reciprocal way but their effects are cooperative, in general. For the CH3OBr case, the Br(n)-σ*CH and the Br(n)-σ*CO work cooperatively in a periodic manner, whereas, the second Br(n)-σ*CH interaction behave differently. It has a destabilizing effect in the 60°–120° region.S,max) and most negative , surface points are given in cf. The 3D electrostatic potential maps for the studied bromine species, are computed and visualized using GaussView 5.0  and are 2OH (IV) shows its smallest value. This is most probably due to the large positive electrostatic potential of 78.902 kcal/mol surrounding the carbon atom. The Br σ-hole in BrCHO(III) is almost double that in the case of I although the bonding situations seem similar. In II, the positive potential is concentrated on H rather than the carbon atom. The isomeric system CH3OBr/CH3BrO shows also different trends for both the σ-holes and the surface minima around the oxygen atoms. Thus, the hypervalent bromine shows a smaller σ-hole and almost double negative potential at the oxygen atom. These represent global minimum on the surface, its large negative value is owing to the lone pair of oxygen. In case of BrOCH (cis)(I) the σ-hole is huge  in contrast to its trans isomer (II) which shows a much smaller value.The bromine σ-hole in BrCH3OBr/CH3BrO/BrCH2OH are all negative indicating accumulation of charge density in the X–Br bond region. However, their magnitudes vary considerably. Thus, while ∇2ρ(r) at the O–Br BCP is remarkably large in case of CH3OBr, its value is very small in case of the alcohol form. This behavior is consistent with the values of VS,max reported in 2ρ(r) values, indicating depletion of charge density away from the bonding region. The ellipticity values are small indicating structure stability to varying extent; its relatively largest values are associated with the hypervalent bromine compound VI.2ρ(r) in fuzzy overlap space and may be given [A,B = −10 × ʃ WA(r)WB(r)∇2ρ(r) dr, where the integration goes for negative values of ∇2ρ(r) only (∇2ρ(r) < 0) where w is a weighting function proposed by Becke representing the fuzzy space. A detailed discussion of LBO is given elsewhere [2ρ(r). Linearly fitting the computed LBO values to νC–Br and νO–Br results in good correlations, with the former performing even better, with a correlation coefficient of 0.99. The computed LBO values reflects nicely the relative strength of the X–Br bonds studied in the present work. There exists a linear correlation of ∇2ρBCP with the vibrational frequencies, although of much lower quality. Thus, for C–Br, the correlation coefficient is 0.74 and the fit invert sign of ∇2ρBCP is at its high end and thus exhibits a wrong nature of the C–Br bond. In the case of O–Br, the fit is of a higher quality (r2 = 0.81) and is the correct sign of the ∇2ρBCP. The delocalization index DI measures the average number of electrons delocalized (shared) between atoms A and B. If A and B are directly connected by a bond path then DI is termed bond index. Values of DI given in cis-over the trans form. On the other hand, DI index for the BrCH2OH/CH3OBr/CH3BrO system, show much fewer variations, and show almost constant accumulation of charge in the C–Br and O–Br bond regions. Ellipticity values given in The final topological parameter to be discussed in the present context is the Laplacian bond order (LBO) also included in be given  by LBOA,lsewhere . In caseet al. [All quantum chemical calculations carried out in the present work were performed using the Gaussian 09 suite of programs . Full geet al. .Chemical bonds were studied and characterized at the QTAIM level of theory ,48,49. T3OBr/CH3BrO/BrCH2OH and the system of decomposition products BrOCH(cis)/BrOCH(trans)/BrCHO. The basic issue here is what type of stereoelectronic effects govern the geometric features in these tautomeric systems. The three isomers possess staggered structures with Cs symmetry. The geometry differences are associated and focus on methyl torsions; the associated potential energy functions often exhibit significant skeletal flexing perturbations (couplings to stretching and bonding degrees of freedom) that modify an idealized rigid-rotor picture. The optimized geometries deviate strikingly from an idealized PG form, particularly with respect to Br…H separation and the dihedral angle. Direct calculation of the potential energy function for rotation around the C–Br and the O–Br bonds and its Fourier transform analysis brought to bear on this issue. The characteristics of the C–Br and O–Br bonds and their cooperative effect have been explored within the QTAIM framework and analysis of the electrostatic potential maps. Various topological parameters have been computed analyzed and discussed. Analysis of the ESP maps indicate that the magnitude of the σ-hole around the Br atom along the X–Br bond is very sensitive to the environment and the charge accumulated in the adjacent centers. The computed LBOs show better ability to discriminate bonding strength than the ∇2ρBCP and Ellipticity, and have good direct correlation with bond vibrational frequency. This is probably due to the fact that LBO is computed in fuzzy atomic space and hence is a measure of the electron density in the whole bonding region.The present work presents detailed analyses of the geometric features of two isomeric bromine systems, namely CH


This is exemplified in osmates that host metal–insulator transitions where magnetic order appears intimately entwined. Here we consider such a material, the 5d perovskite NaOsO3, and observe a coupling between spin and phonon manifested in a frequency shift of 40 cm−1, the largest measured in any material. The anomalous modes are shown to involve solely Os–O interactions and magnetism is revealed as the driving microscopic mechanism for the phonon renormalization. The magnitude of the coupling in NaOsO3 is primarily due to a property common to all 5d materials: the large spatial extent of the ion. This allows magnetism to couple to phonons on an unprecedented scale and in general offers multiple new routes to enhanced coupled phenomena in 5d materials.Enhanced coupling of material properties offers new fundamental insights and routes to multifunctional devices. In this context 5 Transition metal oxides with 5d ions present novel emergent behaviour based on the enhanced coupling of material properties compared to those with 3d ions. Here, the authors demonstrate a large spin-phonon coupling in NaOsO3 which results from a large Os–O electronic orbital overlap. Materials with 5d ions reside in an alternative regime of intermediate electron correlations, extended orbitals, enhanced spin-orbit coupling (SOC) and large crystalline electric field splitting. The competition and cooperation of these new sets of interactions can drive the emergence of novel behaviour beyond that possible in 3d-based materials22IrO4,  measurements. −1 that covers the essential physics of interest. The full spectrum is shown in −1 and fitting these each to a Gaussian, as shown in −1. The results are significant in several regards. First, the onset of the phonon mode shift is concurrent with the magnetic MIT in NaOsO3 at 410 K, indicating a coupling of the phonons to the magnetic and electronic transitions. Second, the phonons show a shift of Δω=40 cm−1, the largest measured in any material for a spin-phonon coupled transition.To follow the behaviour of collective excitations in NaOsO3 we consider the role of the MIT with complimentary neutron measurements on Cd2Os2O7. Cd2Os2O7 was chosen since it has the same 5d3 electronic configuration of the Os5+ ion and hosts a magnetic MIT that is very similar to NaOsO3, with current debate as to whether the mechanism is Slater or Lifshitz172Os2O7 are shown in ω=4 cm−1 is much reduced from NaOsO3. The disparate results for NaOsO3 and Cd2Os2O7 indicate that the underlying mechanism for the anomalously large behaviour in NaOsO3 cannot be attributed to the occurrence of the MIT, since both host similar MITs with similar energy scales. Instead, as we support with further results and calculations, the microscopic mechanism is related to the magnetic ordering and lattice topology of NaOsO3.To begin to understand the microscopic origin of the behaviour in NaOsOd–5d material Ba2FeReO6 that showed a phonon shift of Δω=30 cm−1, we note this occurred concurrent with a structural symmetry change3  calculations. The DFT results show the same three phonon modes observed with INS between 600 to 900 cm−1, see 3 these are themselves composed of three branches, unresolvable in the current powder INS measurement. The theoretical shift is in very close agreement with the measured value of Δω=40 cm−1. This indicates the calculations that probe only the Brillouin zone center accurately reproduce the essential physics of the system as measured by neutrons that probe the entire Brillouin zone. The thermal behaviour was captured in the calculations by increasing the magnetic moment <Si.Sj> to reproduce the onset of G-type antiferromagnetic order in NaOsO3 with the predicted magnetic ordering at 415 K very close to the 411 K observed experimentally. The DFT results, with the need to include magnetism, immediately indicate that the mechanism of the phonon shift is entwined with the onset of magnetic order.To gain a microscopic insight into the origin of the anomalous phonon mode behaviour in NaOsO1g (in phase) and B2g (out of phase) and two asymmetric Jahn–Teller stretching modes Ag (in phase) and B3g (out of phase). To reveal the role of these modes in NaOsO3 we begin by first considering the static behaviour of the octahedra and propensity towards Jahn–Teller distortion. This can be quantified by introducing parameters Q2 and Q3, which are shown schematically in Q2=(x1−x4−y2+y5)/√2 and Q3=(2z3−2z6−x1+x4−y2+y5)/√6, where x, y and z are the oxygen positionsQ2 and Q3 reveals the degree of static octahedral anisotropy, with the larger the value the more distorted the octahedra. Calculations from experimentally determined atomic parameters for NaOsO3  a.u. and at 300 K Q2=0.0035(11) a.u. While at 500 K Q3=0.0171(18) a.u and at 300 K Q3=0.0114(14) a.u. Therefore this reveals that in NaOsO3 the octahedra actually become more isotropic in three dimensions within the low temperature insulating regime. This behaviour is at odds to the normal Jahn–Teller distortions of increased anisotropy and does not favour the asymmetric stretching modes Ag and B3g. Instead the increased static octahedral isotropy is more conducive to the symmetric breathing distortions B1g and B2g. Indeed the abnormal behaviour of the intensity increase of the pDOS, in inset of 2g and consequently appears central to the behaviour of NaOsO3.The calculations reveal all of the phonon modes and are shown in sO3 ref.  reveal Q2g mode further we find that sufficiently large breathing distortions of the octahedra, much larger than accessed in our measurements, offers a potential route to opening the insulating gap in the paramagnetic regime, see 3 the gap opening can occur since the octahedral breathing causes neighbouring octahedra to expand/contract that in turn creates a periodic charge disproportionation on the Os ion. In addition there is apparent isosymmetric ordering and coupling between the G-type antiferromagnet and octahedral B2g mode ordering , with every nearest neighbouring octahedra oppositely expanded/contracted  are characterized by simultaneous bond-stretching/shrinking between the oxygen and osmium ions of the OsO6 octahedra. Therefore as these modes vibrate they change the O–Os–O wavefunction overlap. Since the magnetism in NaOsO3 is mediate by the superexchange interaction this provides a direct route to couple to the Os–O modes. In the non-magnetic regime the frequency of the Os–O modes do not change, as expected. However, as the magnetic order develops via the Os–O superexchange interactions this couples to the Os–O modes. The degree of the coupling is governed by the 5d(Os)-2p(O) orbital overlap, which is much larger in 5d oxides compared to analogous 3d systems. The consequence is that in NaOsO3 the large wavefunction overlap results in a magnification of the spin-phonon coupling, with the expectation that similar behaviour will be found in further 5d-based systems since the extended orbitals are an intrinsic property. With this expectation for designing 5d materials with strong coupling in mind the reduced spin-phonon coupling in Cd2Os2O7 provides useful insights. The reduced spin-phonon magnitude in Cd2Os2O7 naturally occurs by considering the differences in the lattice topology, specifically the Os–O–Os bond that mediates the emergent behaviour. While the Os–O–Os bond distance is nearly identical in NaOsO3 and Cd2Os2O7 the bond angles diverge. In NaOsO3 it is 155°, whereas in Cd2Os2O7 it is 137°, appreciably further from 180°. Consequently the propagation of …–Os–O–Os–… vibrations throughout the lattice can be sufficiently suppressed within the pyrochlore structure resulting in a reduced coupling of phonons to the magnetic interactions and a smaller, although still finite, spin-phonon coupling. Collectively our results indicate that new cases of similarly enhanced spin-phonon coupling, along with further coupled phenomena, should be found in cubic 5d perovskites with near ideal 180° Os–O–Os bonds.All of the modes uncovered that show an anomalous shift JH=1 eV, so Ueff=0.7 eV to treat the localized d electron states in Os. Within GGA+U, this small U gives excellent agreement between the experimental Neel temperature (TN=411 K) and calculated one  in mean-field approximation. The projector augmented wave potentialss2 2p6 3s1 ), 14 for Os (5p6 5d5 6s2) and 6 for oxygen (2s2 2p4). To capture spin-phonon coupling with respect to temperature we employed the method successfully used for various magnetic perovskites19First-principles calculations were performed using density functional theory within the generalized gradient approximation GGA+U method with the Perdew–Becke–Erzenhof parameterization as implemented in the Vienna Our calculations use the harmonic approximation throughout. This route is supported by the experimental observation that the peak widths are resolution limit and do not show any broadening that would be associated with anhormonicity.3 from 370 to 460 K. The data were analyzed and modelled with pdfguiNeutron pair density functional measurements were performed on the Nanoscale-Ordered Materials Diffractometer (NOMAD) beamline at the spallation neutron source on a powder sample of NaOsO2 and L3 edges. Analysis was performed with the Athena softwareX-ray absorption measurements were performed at the advanced photon source on sector 4-ID-D. Spectra were collected at room temperature on a powder sample (∼100 mg) in transmission mode through the Os LHow to cite this article: Calder, S. et al. Enhanced spin-phonon-electronic coupling in a 5d oxide. Nat. Commun. 6:8916 doi: 10.1038/ncomms9916 (2015).Supplementary Figures 1-4, Supplementary Note 1 and Supplementary References


Large amount of Ti3+ defects are introduced into the bulk of brookite nanoparticles, which increases the solar energy absorption and enhances the photocatalytic activity.Black brookite TiO CO2 photoreduction in engineered systems, however, still faces severe challenges like low conversion yields and quantum efficiencies due to fast electron-hole recombination, narrow sunlight absorption range, and backward reactions3457892) is by far the most popular catalyst because of its low cost, suitable bandgap and nature abundance11122 is still a promising photocatalyst for CO2 photoreduction due to its favorable band edges because TiO2 has a higher CB edge, which will promote the reaction of CO2 reduction with H2O that has a high reduction potentialThe emission of greenhouse gases, particularly carbon dioxide CO, could r2 naturally exists in three polymorphs: anatase, brookite and rutile. Among them, only TiO2 anatase, rutile, and anatase-rutile mixed phase  have been studied for CO2 photoreduction1718202 photoreduction.TiO2 has been limited to the ultraviolet (UV) range, which makes it an inefficient photocatalyst for fully exploiting solar light. Narrowing down the TiO2 bandgap to turn it into an efficient material for solar energy conversion has been an ongoing challenge. Recently, the chemistry of structurally defective TiO2 with Ti3+ self-doping has been developed to solve the challenges in broad spectral range of photon absorption. Reduction of Ti4+ into Ti3+ is often achieved by harsh and costly physical methods, such as high temperature and pressurized hydrogenation272829312 with Ti3+ self-doping.Many efforts have been made in decades to improve the photocatalytic activity of brookite, including preparation of nanosized brookite with various morphologies and studies of the involved shape-dependent photocatalytic performance222324253+ self-doped brookite TiO2 single-crystalline nanosheets (denoted as TiO2−x if no further heat treatment). By post-annealing at different temperatures, Ti3+ self-doped brookite TiO2 with controllable amounts of Ti3+ defects is achieved. The black brookite TiO2−x (T500) shows drastically enhanced visible-light absorption and exhibits excellent photocatalytic activity toward CO2 reduction.In this work, we developed an innovative facial oxidation-based hydrothermal method to synthesize bulk Ti3+-self doped TiO2 is displayed in 2 becomes stronger and sharper due to the increase in the crystallinity. When the temperature reaches 700 °C, no rutile or anatase characteristic diffraction peaks were detected, indicating that the brookite phase can be stabilized at higher temperatures.The X-ray diffraction (XRD) patterns of the high quality brookite Ti3+-self doped brookite shows platelike features with uniform sizes of length up to 400 nm and thickness up to 10 nm. The obtained TiO2 particles are uniformly dispersed without obvious aggregation. There is no further particle growth with an increase of the post-annealing temperature. Distinct crystal planes and smooth fringes can be observed clearly from the magnified image of a single particle as shown in The morphology of the synthesized brookite powders is investigated by scanning electron microscopy (SEM) and transmission electron microscopy (TEM) as shown in 2−x sample treated at 500 °C were examined by high resolution transmission electron microscopy (HRTEM) as shown in 3+ self-doped brookite TiO2 nanoparticles are highly crystallized. In addition, the spacing of the fringes paralleling to the top and bottom of the vertical nanoplate is 0.351 nm (2) indicating that the as-prepared sample is pure brookite phase. This result is consistent with XRD analysis. Additionally, as shown in In order to unveil the microstructure transformation of the brookite after post-annealing treatment, the TiO0.351 nm , inset, 3+ self-doped brookite TiO2 samples prepared with postannealing treatment at different temperatures for 3 h in a N2 gas flow and their optical band gap estimated by Kubelka-Munk function. The results show that the color of brookite TiO2 samples is remarkably different from white perfect TiO2 nanocrystal particles. From previous research, this phenomenon indicates the existence of Ti3+ defectsThe top insert of 2−x, T300, T500 and T700 nanoparticles, and Deguass P25 as reference was also examined. The absorption peak at 390 nm is attributed to the intrinsic bandgap absorption of crystalline brookite TiO2−x. The as-prepared TiO2−x sample (blue in color) exhibits an obvious stronger absorption between 400 and 800 nm compared to P25. This strong absorption is attributed to the existence of Ti3+ defects which induce a continuous vacancy band of electronic states just below the conduction band edge of TiO2−x. The existence of Ti3+ defects is supported by ESR measurements that will be discussed in later section. Compared with TiO2−x, the absorption in the visible light region is greatly enhanced after post-annealing treatment. As the annealing temperature increases from 300 °C to 500 °C, the light absorption increases gradually, in good agreement with the color transformation of brookite. However, the light absorption of T700 presents a dramatically decrease in comparison with the T500 sample, which is coincident with the observed color change trend of the samples  in the TiO2−x bulk2.2−x was explored by the heterogeneous photoreduction of CO2 under visible light illumination  attained after 6 h of visible-light irradiation are shown in In this work, photoactivity of as prepared defective brookite TiOmination . CH4 and2 containing materials2−x and the annealed defective TiO2 at different temperatures display the typical Raman spectra of brookite, and 16 bands are identified in total, including seven A1g , four B1g , four B2g , and one B3g (287 cm−1). The characteristic Raman signals at 399 cm−1 and 519 cm−1 for anatase or at 447 cm−1 and 612 cm−1 for rutile are not observed. This further proves the high phase purity of brookite for the TiO2−x and the annealed defective TiO2 samples, in good agreement with the XRD results.The low symmetry and large unit cell of brookite result in a diagnostically complex Raman spectrum compared to the other two polymorphs (anatase and rutile), thus Raman spectroscopy has been widely used to detect the presence of the brookite phase in TiO3+. The fact that the Ti3+-doped TiO2 has quite different high-resolution Eg modes in Raman spectra with different defects distribution and concentration suggests that Ti3+ should mainly localize within the bulk of the samples.In addition, the intensity of high-resolution Eg Raman vibration modes increases as the post-annealing treatment temperature increases up to 500 °C. This is attributed to the effect of enhanced crystallinity upon the increase in annealing temperature, because higher crystallinity contains more Raman active facets, which is proportional to the Eg intensity fluctuations. When the temperature increases to 700 °C, the intensity of Raman vibration modes is decreased and the peak width is broadened, which may be due to the change in the distribution and concentration of Ti3+ defects. As indicated in 2 contains almost completely Ti4+ (3d0) and shows a negligible paramagnetic signal peak under the present EPR measurement condition at 110 K. In general, the surface Ti3+ tends to adsorb O2, which could be reduced to superoxide radical anions (O2−) with an EPR signal feature at g = 2.023+.Electron paramagnetic resonance (EPR), which is highly sensitive to paramagnetic species containing unpaired electrons, has been widely used to characterize the existence of Ti2 nanoparticles show intense axially symmetry signals centered at the g value of 1.9984, which have been reported for Ti3+ ions in brookite crystallite3+ defects in bulk. Accordingly, the chemical equation in our work can be expressed as below:On the other hand, the EPR spectra of brookite defective TiO2+ as reference, the amount of Ti3+ centers for TiO2−x sample is calculated to be 0.7 × 1019 spins/mol, equivalent to one Ti3+ out of every 2.9 × 104 Ti4+. Whereas, the amount of Ti3+ centers for T500 sample is almost 10 times larger than that for TiO2−x, namely, one Ti3+ in every 2.9 × 103 Ti4+. This suggests that the concentration of bulk Ti3+ defect is greatly enhanced by the high temperature post-annealing treatment. From our previous study, the decreased Ti3+ defects upon treatment at 700 °C is mainly due to the difficulty of further diffusion of Ti3+ in enhanced crystallinity, leading to the dilution of the “colour center”Furthermore, the EPR intensity increases along with the post-annealing temperature. The strongest value is obtained for T500, but the signal intensity declines sharply when further increasing the treatment temperature to 700 °C. By numerical double integration of the EPR spectra with an aqueous solution of Cu3+, additional characterizations are performed. X-ray photoelectron spectroscopy (XPS) is performed to further investigate the transformation of surface chemical bonding and to detect the electronic valence band position of the brookite samples. As shown in 2−x, T300, T500 and T700 samples show the typical pattern of Ti4+ –O bonds in TiO2 with Ti 2p3/2 and 2p1/2 peaks centered at binding energies of 458.5 eV and 464.2 eV3+ species are separately located at bulk of the samples, and no different chemical states and disorders on the surface of samples. This agrees with the HRTEM observation, i.e., no obvious disordered layer in the edge of the samples.In order to confirm the existence of Ti2 reduction rate is presented in 2 reduction rate of annealed brookite TiO2 also improves dramatically; it shows drastically enhanced CO2 reduction rate when brookite TiO2−x is annealled at 500 °C (11.9 μmol·gcat−1h−1 for CH4 and 23.5 μmol·gcat−1h−1 for CO). However, defective brookite prepared at 700 °C shows lower CO2 reduction rate (4.4 μmol·gcat−1h−1 for CH4 and 7.3 μmol·gcat−1h−1 for CO), but is still higher than untreated TiO2−x sample. It can be deduced that the photocatalytic reduction performance agrees well with the light absorption and Ti3+ defects (numbers and distribution); the more the light absorption and the Ti3+ defects, the higher the photocatalytic reduction activity is.The CO3+-self doped brookite catalysts developed in this work demonstrate a superior activity. It is the first time to present a facile approach to controllablly synthesize Ti3+-self doped brookite TiO2 as an outstanding candidate for CO2 photoreduction to produce CO and CH4. Further study on the selectivity of CO2 reduction is going on.Clearly, the engineered Ti3+ self-doped brookite TiO2 is an effective strategy to prepare uniform Ti3+ self-doped brookite TiO2 nanosheets. The introduction of Ti3+ defects in the bulk of brookite enhances the visible light absorption and narrows the bandgap. Our study demonstrates that brookite can be successfully tuned to be highly active toward photocatalytic performance for CO2 reduction through post-annealing at different temperatures, which illuminates the future research of brookite; the oxidation-based hydrothermal synthesis combined with post-annealing treatment may provide a novel path for tuning the photocatalysts from relatively inert to highly active and shine light on the greenhouse gases conversion into sustainable energy.In summary, this work illustrates that the oxidation-based hydrothermal synthesis of Ti2, 98.0%) powder was purchased from Sigma–Aldrich Co., LLC. Hydrogen peroxide , sodium borohydride , hydrochloric acid  and sodium hydroxide  were obtained from Sinopharm Chemical Reagent Co., Ltd. and used as received without any further purification. Double distilled water was used throughout the experiments.Titanium hydride (TiH2 (0.256 g) and H2O (2 mL) were mixed in a 50 mL round-bottomed flask magnetically stirred for 5 min. Then H2O2 (30 mL 30.0 wt%) as the oxidation was added dropwise to this dark gray suspensions, and this mixture was vigorously stirred for 12 h till it changed to yellowish gel-like state. After that, double distilled water (40 mL) was added under continuous magnetic stirring. A certain amount of NaOH (1.0 M) solution as the pH regulator was added gradually until the pH of the mixture solution was tuned to 9.0. NaBH4 (0.4 g) as reducing agent was added to this light yellow transparency mixture and then transferred to the Teflon-lined stainless-steel autoclave immediately and hydrothermally treated at 180 °C for 24 h. The sample was then collected and added into HCl  solution to eliminate the sodium boron compounds. After stirring for 10 h, the powders were washed by distilled water and ethanol repetitively to remove the impurities . The obtained precipitate was dried under vacuum for 12 h to yield a grey blue TiO2 nanocrystals powder, denoted as TiO2−x. Postannealing treatment of the TiO2−x sample was conducted under a N2 gas flow (150 sccm) in a tube furnace at an elevated temperature of 300 °C, 500 °C and 700 °C for 3 h. Therefore, the samples obtained at the specific temperatures are designated as T300, T500 and T700, respectively.In a typical synthetic process, TiH4 as reference to obtain absorption spectra for determining the band gap. Raman spectra were obtained on a laser Raman spectrometer  with a back scattering configuration using an Ar+ laser  as excitation source. The surface electronic state analysis was studied by X-ray photoelectron spectra (XPS), and the measurements were carried out on an X-ray photoelectron spectrometer (ESCALAB MK II) using Mg Ka (1253.6 eV) X-rays as the excitation source, with C 1s (284.6 eV) for calibration. Electron paramagnetic resonance (EPR) spectra were recorded on a Bruker Elexsys E500 spectrometer by applying an X-band  microwave with sweeping magnetic field at 110 K in cells that can be connected to a conventional high-vacuum apparatus . The concentration of Ti3+ was determined by a numerical double integration of the EPR spectra in comparison with an aqueous solution of Cu2+.The crystal structures of the samples were identified on a Bruker D8 X-ray diffractometer with Cu Kα radiation (λ = 0.15418 nm). The morphology photographs of the samples were recorded by field emission scanning electron microscopy  and transmission electron microscopy . Ultraviolet–visible (UV–vis) diffusion reflectance spectra of the samples were obtained on a SolidSpec-3700DUV spectrophotometer (Shimadzu) using BaSO3+-self doped brookite TiO2 single-crystalline nanosheets were studied using a CO2 photoreduction system at ambient condition in a continuous gas flow reactor. The CO2 photoreduction process was performed under visible light irradiation with a 300 W Xe lamp  equipped with an ultraviolet cut-off filter to provide visible light (≥420 nm). The illumination intensity at the surface was 0.216 W/cm2 as measured by a calibrated precision optical power meter . The amount of photocatalyst used was held constant in all runs. Highly pure CO2 (99.99%) was bubbled through water to produce a mixture of CO2 and water vapor into the photoreactor at atmospheric pressure. Before switching on the light source, wet CO2 was permitted to flow through the photoreactor at 30 mL/min for 30 min to eliminate any excess air and to ensure the complete adsorption of gas molecules. The photoreactor was operated in a continuous flow mode (2.0 mL/min flow rate), and the gaseous products in the reactor effluent were continuously analyzed for 6 h by a gas chromatograph  equipped with both a thermal conductivity detector (TCD) and a flame ionization detector (FID).The photocatalytic activities of the TiHow to cite this article: Xin, X. et al. Ti3+-self doped brookite TiO2 single-crystalline nanosheets with high solar absorption and excellent photocatalytic CO2 reduction. Sci. Rep. 6, 23684; doi: 10.1038/srep23684 (2016).