Perdew , Burke And Ernzerhof Research Articles

Vacancy formation energies in metals: A comparison of MetaGGA with LDA and GGA exchange–correlation functionals

We report on the results of density-functional-theory based calculations of the vacancy formation energies in metals using the revised Tao–Perdew–Staroverov–Scuseria (revTPSS) functional (Pedrew et al., 2009), which is a self-consistent semilocal meta-generalized gradient approximation functional. The motivation for this work is to determine if the improved accuracy of surface energies for revTPSS compared to local and generalized gradient approximation functionals also leads to improved vacancy formation energies since vacancies can be viewed as internal surfaces. In addition, we report on the lattice constants, cohesive energies and bulk moduli predicted by revTPSS. By comparing the vacancy formation energies and bulk properties, the performance of revTPSS is assessed against four functionals: the local spin density approximation (LSDA), Perdew, Burke and Ernzerhof (PBE), Perdew–Wang-91 (PW91), and PBE for solids (PBEsol). Using an automated computational approach, we calculate the vacancy formation energies and the macroscopic properties of 34 metal systems for the five functionals. For macroscopic properties (lattice constants, cohesive energies and bulk modulus), we find the results for revTPSS typically lie between LDA and PBE with a mean absolute percentage deviation of 1.1% and 12.1% from the experimental data for lattice constants and cohesive energies respectively. Further, it is found that revTPSS predicts higher vacancy formation energies when compared to the four other functionals surveyed. We have observed the following order for the functionals with respect to the computed vacancy formation energies, Efxc:EfrevTPSS>EfPBEsol∼EfLDA>EfPBE>EfPW91. We also consider the effects of a surface-energy error correction that has been proposed for standard LDA and GGA functionals. This correction increases the vacancy formation energies of LDA, PBE and PW91 functionals. The revTPSS computed VFEs are greater than the surface-energy-corrected PBE VFEs by a mean relative difference of 14.8%.

Modeling the Electronic, Structural and Vibrational Properties of Cubic SiC Nanocrystals Built from Diamondoid Structures

Silicon carbide diamondoids are used as building blocks of cubic SiC nanocrystals. Density functional theory (DFT) at the generalized gradient approximation level of Perdew, Burke and Ernzerhof (PBE) with 6-31G(d) basis is used to investigate the electronic structure of these diamondoids up to 12 cages. The results show that the energy gap and bond lengths generally decrease with shape fluctuations as the number of atoms increases. Electronic and structural properties are in good agreement with both previous experimental and theoretical results. Vibrational modes converge to the SiC experimental bulk limit of the radial breathing mode while hydrogen related modes are nearly constant in their frequencies. It is suggested in this work to identify SiC-diamondoids from their hydrogen vibrational modes finger print in the range (1000-3000 cm−1) and identify the size of the diamondoid from low frequency vibrational modes (0-1000 cm−1) such as radial breathing modes.

DFT study on the interaction between atomic aluminum and graphene

In the present work, molecular orbital calculations using cluster models were performed within density functional theory (DFT) in order to study the adsorption of an Al atom on regular and defective graphene. Depending on the theoretical treatment of electronic exchange and correlations effects, different bonding results for the adsorption on the perfect surface are obtained. On the other hand, they are very similar for Al adsorbed on a carbon monovacancy. On regular graphene, the adsorption is exothermic when the Perdew, Burke and Ernzerhof (PBE) functional is used and endothermic with the Becke, 3-parameter, Lee–Yang–Parr (B3LYP) functional. Regarding the defective graphene surface, it was shown that the carbon atoms of concave angles in the vacancy are the most reactive to a radical attack. The adsorption of an Al atom on the vacancy restores the trigonal symmetry lost after the extraction of the C atom from regular graphene. Complementary calculations performed at PBE level on both regular and defective surfaces imposing periodic conditions qualitatively support the results obtained with the cluster model.

Density Functional Theory Calculations of Atomic Hydrogen Adsorption on (3, 3) Single-Wall Carbon Nanotubes with Vacancy Defects

In this paper, we have employed density functional theory (DFT) to investigate the adsorption mechanisms of atomic hydrogens on the sidewalls of (3, 3) single-wall carbon nanotubes (CNTs) which have vacancy defects. All the calculations were performed using the generalized gradient approximation (GGA) with the Perdew, Burke and Ernzerhof (PBE) correlation functional.Our results show that hydrogen atoms can chemically adsorb on the defective nanotube. Bonding energy of per hydrogen atom decreases with the number of adsorbed hydrogen atoms. The hydrogen atoms will enhance the electrical conductivity of the (3, 3) nanotube. Besides one hydrogen atom adsorbing on the nanotube with a vacancy defect (MVD), hydrogen atoms move towards the MVD of the nanotube.

1H NMR spectra of alcohols and diols in chloroform: DFT/GIAO calculation of chemical shifts.

Proton nuclear magnetic resonance (NMR) shifts of aliphatic alcohols in chloroform have been computed on the basis of density functional theory, the solvent being included by the integral-equation-formalism polarisable continuum model of Gaussian 09. Relative energies of all conformers are calculated at the Perdew, Burke and Ernzerhof (PBE)0/6-311+G(d,p) level, and NMR shifts by the gauge-including atomic orbital method with the PBE0/6-311+G(d,p) geometry and the cc-pVTZ basis set. The 208 computed CH proton NMR shifts for 34 alcohols correlate very well with the experimental values, with a gradient of 1.00 ± 0.01 and intercept close to zero; the overall root mean square difference (RMSD) is 0.08 ppm. Shifts for CH protons of diols in chloroform are well correlated with the theoretical values for (isotropic) benzene, with similar gradient and intercept (1.02 ± 0.01, -0.13 ppm), but the overall RMSD is slightly higher, 0.12 ppm. This approach generally gives slightly better results than the CHARGE model of Abraham et al. The shifts of unsaturated alcohols in benzene have been re-examined with Gaussian 09, but the overall fit for CH protons is not improved, and OH proton shifts are worse. Shifts of vinyl protons in alkenols are systematically overestimated, and the correlation of computed shifts against the experimental data for unsaturated alcohols follows a quadratic equation. Splitting the 20 compounds studied into two sets, and applying empirical scaling based on the quadratic for the first set to the second set, gives an RMSD of 0.10 ppm. A multi-standard approach gives a similar result.

Diamondoids and large unit cell method as building blocks of InAs nanocrystals: A density functional theory study

Indium Arsenide diamondoids are suggested in this work as building blocks of InAs nanocrystals. In addition, the large unit cell method is used to investigate size dependence of electronic properties of InAs nanocrystals by investigating larger nanocrystal sizes. Both methods are complementary in the number of atoms and particle sizes. All-electron density functional theory at the generalized gradient approximation level of Perdew, Burke and Ernzerhof (PBE) is used in present work combined with large unit cell and molecular structure optimization methods. Results show that energy gap and bond lengths generally decrease with shape and size fluctuations as the number of atoms increases. Bond lengths and tetrahedral angles of diamondoids show that InAs diamondoid molecules are the closest molecular structures to ideal zincblende structure. Electronic and structural properties are in a very good agreement with both previous experimental and theoretical results.

Structural, electronic, optical and thermodynamic properties of cubic REGa3 (RE = Sc or Lu) compounds: Ab initio study

Structural, elastic, optoelectronic and thermodynamic properties of REGa3 (RE=Sc and Lu) compounds have been studied self consistently by employing state of the art full potential (FP) linearized (L) approach of augmented plane wave (APW) plus local orbitals method. Calculations were executed at the level of Perdew–Burke and Ernzerhof (PBE) parameterized generalized gradient approximation (GGA) for exchange correlation functional in addition to modified Becke–Johnson (mBJ) potential. Our obtained results of lattice parameters show reasonable agreement to the previously reported experimental and other theoretical studies. Analysis of the calculated band structure of ScGa3 and LuGa3 compounds demonstrates their metallic character. Moreover, a positive value of calculated Cauchy pressure, in addition to reflecting their ductile nature, endorses their metallic character as well. To understand optical behavior calculations related to the important optical parameters; real and imaginary parts of the dielectric function, reflectivity R(ω), refractive index n(ω) and electron energy-loss function L(ω) have also been performed. In the present work, thermodynamically properties are also investigated by employing lattice vibrations integrated in quasi harmonic Debye model. Obtained results of volume, heat capacity and Debye temperature as a function of temperature for both compounds, at different values of pressure, are found to be consistent. The calculated value of melting temperature for both compounds (ScGa3 and LuGa3) is found to be similar to the experimental data with an underestimation of 5%.

1H NMR spectra of butane‐1,4‐diol and other 1,4‐diols: DFT calculation of shifts and coupling constants

The proton nuclear magnetic resonance (NMR) spectra of butane-1,4-diol, pentane-1,4-diol, (S,S)-hexane-2,5-diol, 2,5-dimethylhexane-2,5-diol and cyclohexane-1,4-diols (cis and trans) in benzene and some other solvents have been analysed. The conformer distribution and the NMR shifts of these diols in benzene have been computed on the basis of the density functional theory, the solvent being included by means of the integral-equation-formalism polarizable continuum model implemented in Gaussian 09. Relative Gibbs energies of all conformers are calculated at the Perdew, Burke and Ernzerhof (PBE)0/6-311+G(d,p) level and NMR shifts by the gauge-including atomic orbital method with the PBE0/6-311+G(d,p) geometry and the cc-pVTZ basis set. Vicinal three-bond coupling constants for the acyclic diols are calculated from the relative conformer populations, the geometries and generalized Karplus equations developed by Altona's group; these correlate well with the experimental values. The solvent dependence of coupling constants for butane-1,4-diol is attributed to conformational change. Coupling constants for the rigid cyclohexane-1,4-diols do not change with solvent and are readily explained in terms of their geometries. The NMR shifts of hydrogen-bonded protons in individual conformers of alkane-1,n-diols show a very rough correlation with the OH · · · OH distances. The computed overall NMR shifts for CH protons in 1,2-diols, 1,3-diols and 1,4-diols are systematically high but correlate very well with the experimental values, with a gradient of 1.07 ± 0.01; those for OH protons correlate less well.

Optoelectronic and thermoelectric properties of KAuX5 (X = S, Se): a first principles study

The electronic structure as well as optical and thermoelectric properties of the orthorhombic polychalcogenides of gold KAuX5 (X = S, Se) compounds have been investigated using full-potential linearized augmented plane wave within the framework of the density functional theory (DFT). The local density approximation (LDA), generalized gradient approximation (GGA) by Perdew, Burke and Ernzerhof (PBE), Engel–Vosko generalized gradient approximation (EV-GGA), and the recently modified Becke–Johnson approximation (mBJ) formalism are used for the exchange correlation energy to calculate the total energy. The results show that KAuX5 (X = S, Se) is a direct band gap semiconductor at Γ–Γ point. The total and partial density of states indicate that the states Au-d, S-p, and Se-p of both compounds have strong contributions to valence band in the energy range from −10 up to 0.0 eV. One can notice from electronic charge density that both compounds show greater iconicity and smaller covalency. Optical properties with photon incident energy up to 14.0 eV have been calculated and analyzed. Important transport properties such as Seebeck coefficients as well as thermal and electrical conductivities and effective mass are obtained and discussed in details.

1H NMR spectra of alkane-1,3-diols in benzene: GIAO/DFT shift calculations

The proton nuclear magnetic resonance (NMR) spectra of propane-1,3-diol, 2-methylpropane-1,3-diol, 2,2-dimethylpropane-1,3-diol, butane-1,3-diol, 3-methylbutane-1,3-diol, pentane-2,4-diols (dl and meso), 2-methylpentane-2,4-diol and cyclohexane-1,3-diols (cis and trans) in benzene have been analysed. The conformer distribution and the NMR shifts of these diols have been computed on the basis of density functional theory, the solvent being included by means of the integral equation formalism phase continuum model (IEFPCM) implemented in Gaussian 09. Relative Gibbs energies of all conformers are calculated at the Perdew, Burke and Ernzerhof (PBE)0/6-311 + G(d,p) level, and NMR shifts by the gauge-including atomic orbital method with the PBE0/6-311 + G(d,p) geometry and the cc-pVTZ basis set. Vicinal coupling constants for 1,2- and 1,3-diols are rationalised in terms of relative conformer populations and geometries. The NMR shifts of hydrogen-bonded protons in individual conformers of alkane-1,n-diols show a very rough correlation with the OH⋯OH distances. The computed overall NMR shifts for CH protons in 1,2- and 1,3-diols are systematically high but correlate very well with the experimental values, with a gradient of 1.07 ± 0.01. Some values for nonequivalent methylene protons in 1,3-diols are reversed, calculation giving enhanced values for the proton anti to the COH bonds. Errors in the NMR shifts computed for the OH protons of nonsymmetrical diols appear to be related to relative populations of conformers where one or other of the OH groups is the donor. Some results based on the second-order Møller-Plesset approach, the Becke three-parameter Lee-Yang-Parr method and on the IEFPCM solvation model implemented in Gaussian 03 are included.

Size variation of infrared vibrational spectra from molecules to hydrogenated diamond nanocrystals: a density functional theory study.

Infrared spectra of hydrogenated diamond nanocrystals of one nanometer length are calculated by ab initio methods. Positions of atoms are optimized via density functional theory at the level of the generalized gradient approximation of Perdew, Burke and Ernzerhof (PBE) using 3-21G basis states. The frequencies in the vibrational spectrum are analyzed against reduced masses, force constants and intensities of vibration. The spectrum can be divided into two regions depending on the properties of the vibrations or the gap separating them. In the first region, results show good matching to several experimentally obtained lines. The 500 cm−1 broad-peak acoustical branch region is characterized by pure C–C vibrations. The optical branch is centered at 1185 cm−1. Calculations show that several C–C vibrations are mixed with some C–H vibrations in the first region. In the second region the matching also extends to C–H vibration frequencies that include different modes such as symmetric, asymmetric, wagging, scissor, rocking and twisting modes. In order to complete the picture of the size dependence of the vibrational spectra, we analyzed the spectra of ethane and adamantane. The present analysis shows that acoustical and optical branches in diamond nanocrystals approach each other and collapse at 963 cm−1 in ethane. Variation of the highest reduced-mass-mode C–C vibrations from 1332 cm−1 of bulk diamond to 963 cm−1 for ethane (red shift) is shown. The analysis also shows the variation of the radial breathing mode from 0 cm−1 of bulk diamond to 963 cm−1 for ethane (blue shift). These variations compare well with experiment. Experimentally, the above-mentioned modes appear shifted from their exact positions due to overlap with neighboring modes.

Ceramic Expansion by Water Layers on Magnesium Oxide: AB InitioStudy

MgO hydration is an expansive process. It is used in cement to compensate for shrinkage, but it can be harmful at higher concentrations. First-principles calculations have been used to investigate the electronic properties of the steps of the hydration of MgO using the general gradient approximation GGA functional method within density functional method (DFT). The energy bands along high symmetry directions, energy of hydration and energy of dissociation cut through various planes are presented. The first principles band structure calculations reported here were carried out using Perdew, Burke and Ernzerhof (PBE) method. The calculations have been applied to investigate water adsorption on the (001, 110, 111 and 210) surfaces of MgO crystal. The hydrated MgO surfaces show a similar band structure that of brucite material. Both molecular adsorption and dissociative adsorption have been found to occur. The MgO surfaces have different tendency to interact with water molecules, and they differ in susceptibility disintegration of expansion. The results show that the safest surface is (001) group, while the harmful surfaces are (210) and (111) groups.

Ab initio study of the properties of CuAlSe2: A chalcopyrite compound

Abstract The ground-state structural, electronic, optical and thermal properties of CuAlSe2 compound in the body centered tetragonal phase have been studied by employing the full potential linearized augmented plane wave plus local orbitals method based on the density functional theory. For the exchange-correlation effects we have adopted the local density approximation (LDA), generalized gradient approximation (GGA) due to Perdew, Burke and Ernzerhof (PBE) and Engel and Vosko (EV). At the equilibrium unit cell volume, ration of the lattice constants, c/a, has been obtained as 1.99 and the unit cell constant a 0 = 5.51Å which are well comparable with the experimental results. The energy band gap obtained using EVGGA (1.92 eV) is in good agreement in comparison to that using LDA (1.09 eV), GGA (PBE) (1.26 eV) and other earlier available data. Upper portion of the valance band is mainly composed of Cu-d and Se-p states and they are highly hybridized. The optical properties such as dielectric function, refraction, reflection, conductivity, absorption and loss of energy of CuAlSe2 are presented. The quasi Harmonic Debye model is applied to study the thermal and vibrational effects for the stable BCT CuAlSe2. Thermal parameters such as Gruneisen parameter, Debye temperature, specific heat etc have been determined as a function of pressure and temperature.

Ab initio studies of structural, electronic, optical and thermal properties of CuAlS 2 chalcopyrite

The ground-state structural, electronic, optical and thermal properties of the CuAlS 2 compound in the body centered tetragonal phase have been studied employing the full potential linearized augmented plane wave plus local orbitals method based on the density functional theory. For the exchange–correlation effects we have adopted the generalized gradient approximation (GGA) approaches due to Perdew, Burke and Ernzerhof (PBE) and Engel and Vosko (EV). The optical properties such as dielectric function, loss of energy, reflection, refraction and conductivity of CuAlS 2 are presented. Thermal properties such as Gruneisen parameter, volume expansion coefficient α, bulk modulus, specific heat and entropy have been studied. The direct band gap first increases then starts decreasing with the decrease in unit cell volume. The EV–GGA provides higher value of energy band gap (2.20 eV) than PBE–GGA (1.62 eV). Our obtained value of the refractive index (2.4 eV) is in excellent agreement with the experimental value (2.0–2.5 eV). The peak of maximum conductivity is located at 7.4 eV of energy. The plasma frequency ω p corresponds to the energy 12.45 eV.

Valence-band electronic structure of iron phthalocyanine: An experimental and theoretical photoelectron spectroscopy study

The electronic structure of iron phthalocyanine (FePc) in the valence region was examined within a joint theoretical-experimental collaboration. Particular emphasis was placed on the determination of the energy position of the Fe 3d levels in proximity of the highest occupied molecular orbital (HOMO). Photoelectron spectroscopy (PES) measurements were performed on FePc in gas phase at several photon energies in the interval between 21 and 150 eV. Significant variations of the relative intensities were observed, indicating a different elemental and atomic orbital composition of the highest lying spectral features. The electronic structure of a single FePc molecule was first computed by quantum chemical calculations by means of density functional theory (DFT). The hybrid Becke 3-parameter, Lee, Yang and Parr (B3LYP) functional and the semilocal 1996 functional of Perdew, Burke and Ernzerhof (PBE) of the generalized gradient approximation (GGA-)type, exchange-correlation functionals were used. The DFT/B3LYP calculations find that the HOMO is a doubly occupied π-type orbital formed by the carbon 2p electrons, and the HOMO-1 is a mixing of carbon 2p and iron 3d electrons. In contrast, the DFT/PBE calculations find an iron 3d contribution in the HOMO. The experimental photoelectron spectra of the valence band taken at different energies were simulated by means of the Gelius model, taking into account the atomic subshell photoionization cross sections. Moreover, calculations of the electronic structure of FePc using the GGA+U method were performed, where the strong correlations of the Fe 3d electronic states were incorporated through the Hubbard model. Through a comparison with our quantum chemical calculations we find that the best agreement with the experimental results is obtained for a U(eff) value of 5 eV.

Understanding the p-type defect chemistry of CuCrO2

CuCrO2 is the most promising Cu-based delafossite for p-type optoelectronic devices. Despite this, little is known about the p-type conduction mechanism of this material, with both CuI/CuII and CrIII/CrIV hole mechanisms being proposed. In this article we examine the electronic structure, thermodynamic stability and the p-type defect chemistry of this ternary compound using density functional theory with three different approaches to the exchange and correlation; the generalized-gradient-approximation of Perdew, Burke and Ernzerhof (PBE), PBE with an additional correction for on-site Coulombic interactions (PBE + U) and the nonlocal, screened-exchange hybrid functional HSE06. The fundamental band gap of CuCrO2 is demonstrated to be indirect in nature. Under all growth conditions, the dominant intrinsic p-type defect will be the Cu vacancy, with hole formation centered solely on the Cu sublattice. Mg doping is found to be significantly lower in energy than intrinsic defect formation, explaining the large increases in conductivity seen experimentally. Cu-rich/Cr-poor growth conditions are found to be optimal for both intrinsic and extrinsic (Mg doping) defect formation, and should be adopted to maximize performance.

First-principles study of phase transition and thermodynamic properties of InP

Using first-principles calculations, the structural phase transition between the zinc-blende (ZB) and the rocksalt (RS) phases and the thermodynamic properties of indium phosphide (InP) are investigated by means of the pseudo-potential plane-waves method. The calculations are performed within the generalized gradient approximation (GGA) to density functional theory with the Perdew-Burke and Ernzerhof (PBE) exchange-correlation functional. On the basis of the third-order Birch–Murnaghan equation of states, the transition pressure P t =10 GPa between the ZB and RS phases of InP is determined. The calculated values are in excellent agreement with experiments and similar theoretical calculations. From the theoretical calculations, the relationship of the relative volume V/ V 0, the Debye temperature Θ and the heat capacity C V with the pressure P and temperature T is also successfully obtained.

Density functional theory study of the relative stability of the iron disulfide polymorphs pyrite and marcasite

The performance of density functional theory has been widely examined with regard to its ability to predict the properties of minerals, though less attention has been given to the correct determination of the relative stability of structurally similar polymorphs. Here a detailed examination is performed of the numerical and theoretical factors that may influence the structure and relative energetics of two such polymorphs of iron disulfide, namely, pyrite and marcasite, within density functional theory. Both the local-density approximation and commonly used generalized gradient approximation exchange-correlation functionals, such as Perdew, Burke and Ernzerhof (PBE), are found to predict that marcasite is more stable than pyrite, at variance with experiment. Allowing for the zero-point energy of vibration fails to remedy this discrepancy. While inclusion of a sufficiently large Hubbard $U$ parameter for iron is found to reverse the stability, this comes at the expense of a very poor description of other properties. Examination of three generalized gradient approximations developed specifically for the solid state, namely, AM05, Wu-Cohen and PBEsol, demonstrates that all of these functionals offer a superior description of the structures and relative energies of pyrite and marcasite through correctly predicting that the former is the ground-state phase at ambient conditions.

Specific features of electronic structure and linear optical properties of some pseudocubic compounds

Abstract We have performed ab initio theoretical calculations of the electronic structure and the linear optical susceptibilities for the pseudocubic compounds X 3 As 4 (X = C, Si, Ge, and Sn) using two approximations for the exchange correlation (XC) potentials: the generalized gradient approximation (GGA) by Perdew, Burke and Ernzerhof (PBE) and Engel–Vosko generalized gradient approximation (EVGGA) scheme. Our calculations show that the C 3 As 4 compound is metallic with density of states at the Fermi energy E F , N ( E F ) of 3.808 and 1.904 states/Ry-cell or a bare electronic specific heat coefficient of 0.660 and 0.330 mJ/mole-K 2 for GGA and EVGGA, respectively. The overlapping between the valence and conduction bands is strong resulting in metallic behavior. The EVGGA try to reduce the overlapping around E F by around the half value. Also we notice that the effect of EVGGA cause increase/reduce the peaks high and to make noticeable anisotropy between e 2 II ( ω ) and e 2 ⊥ ( ω ) for Ge 3 As 4 compound. We found that X-s/p and As-s/p/d states are controlled the overlapping around E F . The effect of using EVGGA over GGA on the density of states and linear optical properties is very pronounced. Detail comparison of our calculated partial density of states and the frequency dependent dielectric function with the available calculations were made. We hope that future experiments will help in deciding which calculation is better.

Density functional calculations of the electronic structure of 3-phenylamino-4-phenyl-1,2,4-triazole-5-thione

Starting with the X-ray diffraction data on the 3-phenylamino-4-phenyl-1,2,4-triazole-5-thione compound obtained by Wang et al. [Molecules, 2009, 14, 608], we have optimised the atomic positions by minimization of the forces acting on the atoms using a full potential linear augmented plane wave method within density-functional theory along with the generalized gradient approximation (GGA) by Perdew, Burke and Ernzerhof (PBE) exchange-correlation potential. In addition, for the electronic band-structure and the calculation of the gap the Engel-Vosko (EV-GGA) scheme has applied. The full potential calculations show that the valence band maximum (VBM) is located at the Gamma point and the conduction band minimum (CBM) is located at the Z point of the Brillouin zone resulting in an indirect energy gap of 3.1 eV. The upper VBM is mainly formed by S-p states while the lower CB has mainly C-p states character. Thus the S-p states in the upper valence band and the C-p states in the lower conduction band have a significant effect on the energy band gap. We present an analysis of the partial densities of states which gives useful information on hybridization and the orbital character of the states. We have calculated the bond lengths and bond angles and find better agreement with the experimental data than the density functional theory calculations at B3LYP/6-311G** and PBE1PBE/6-311G** levels of theory by the Berny method within the Gaussian 03 software package. This is attributed to the fact that the values obtained by these methods belong to the isolated molecule in the gas-phase whereas the experimental and the full potential linear augmented plane wave method values are attributed to the molecule in the solid state.