The structural, electronic, and optical properties of Cu2Zn1−xBaxSn1−ySiyS4 compounds have been calculated using GGA-PBE function within the framework of Density Functional Theory (DFT). In the present work, lattice p...The structural, electronic, and optical properties of Cu2Zn1−xBaxSn1−ySiyS4 compounds have been calculated using GGA-PBE function within the framework of Density Functional Theory (DFT). In the present work, lattice parameters remained the same, that is tetragonal crystal structure for 0% and 100% doping concentration. The electronic band gap of Cu2Zn1−xBaxSn1−ySiyS4 compounds has been gradually increased for continuous increment of doping concentration where the highest electronic band gap is 1.117 eV for Cu2BaSiS4 structure. Moreover, the band gap changes from direct to indirect band gap with the increase of doping concentration in the parent compound. The absorption coefficient has been found to be high (> 104 cm−1) in UV-region for all the doping concentration which makes the studied compound as a potential candidate of absorber layer in the UV detector. The theoretical study of the effect of double doping in the CZTS compound is very interesting for improving the quality of it and it would be a reference for the theoretical and experimental researchers.展开更多
In Quantum Information Theory(QIT) the classical measures of information content in probability distributions are replaced by the corresponding resultant entropic descriptors containing the nonclassical terms generate...In Quantum Information Theory(QIT) the classical measures of information content in probability distributions are replaced by the corresponding resultant entropic descriptors containing the nonclassical terms generated by the state phase or its gradient(electronic current). The classical Shannon(S[p]) and Fisher(I[p]) information terms probe the entropic content of incoherent local events of the particle localization, embodied in the probability distribution p, while their nonclassical phase-companions, S[ Φ ] and I[ Φ ], provide relevant coherence information supplements.Thermodynamic-like couplings between the entropic and energetic descriptors of molecular states are shown to be precluded by the principles of quantum mechanics. The maximum of resultant entropy determines the phase-equilibrium state, defined by "thermodynamic" phase related to electronic density,which can be used to describe reactants in hypothetical stages of a bimolecular chemical reaction.Information channels of molecular systems and their entropic bond indices are summarized, the complete-bridge propagations are examined, and sequential cascades involving the complete sets of the atomic-orbital intermediates are interpreted as Markov chains. The QIT description is applied to reactive systems R = A―B, composed of the Acidic(A) and Basic(B) reactants. The electronegativity equalization processes are investigated and implications of the concerted patterns of electronic flows in equilibrium states of the complementarily arranged substrates are investigated. Quantum communications between reactants are explored and the QIT descriptors of the A―B bond multiplicity/composition are extracted.展开更多
Under high pressure, the long believed single-phase material CaB6 was latterly discovered to have a new phase tI56. Based on the density-functional theory, the pressure effects on the structural and elastic properties...Under high pressure, the long believed single-phase material CaB6 was latterly discovered to have a new phase tI56. Based on the density-functional theory, the pressure effects on the structural and elastic properties of CaB6 are obtained. The calculated bulk, shear, and Young’s moduli of the recently synthesized high pressure phase tI56-CaB6 are larger than those of the low pressure phase. Moreover, the high pressure phase of CaB6 has ductile behaviors, and its ductility increases with the increase of pressure. On the contrary, the calculated results indicate that the low pressure phase of CaB6 is brittle. The calculated Debye temperature indicates that the thermal conductivity of CaB6 is not very good. Furthermore, based on the Christoffel equation, the slowness surface of the acoustic waves is obtained.展开更多
The activities of dimethyl carbonate and dimethyl sulfate as a methylation reagent were studied by density- functional theory （DFT）. B3LYP/6-31G（d, p） methods were used to optimize the structures of dirnethyl carb...The activities of dimethyl carbonate and dimethyl sulfate as a methylation reagent were studied by density- functional theory （DFT）. B3LYP/6-31G（d, p） methods were used to optimize the structures of dirnethyl carbonate and dimethyl sulfate and calculate theirs charge densities. Dimethyl sulfate is easier than dimethyl carbonate to react with a nucleophUic reagent. In dimethyl sulfate, the alkoxy carbons are the only reactive atomic nucleus because of steric hindrance. A nucleophilic reagent is more likely to react with carbonyl carbons than alkoxy carbons of dimethyl carbonate; in the presence of a Lewis acid, the phenyl nucleophilic reagent reacts with the Lewis acid first. Lewis acid increases the negative charge density of a nucleophUic reagent in polar solvent, and also incurs an accretion of steric hindrance. Polar solvent avails to ionize dimethyl carbonate and thus enables the reaction of methylation. The frequencies of transition state calculated by Gaussion 03 confirm the inferred reaction mechanism. The harvest rates of 4-methoxyphenol in the experiments of methylation reactions of hydroquinone with respectively dimethyl carbonate and dimethyl sulfate support the foregoing theortical conclusions.展开更多
In this paper, we reported a first-principles investigation on the structural and electronic properties of O adsorption on the γ-TiAI（111） surface, to illustrate the oxidation process. It has been found that： （1...In this paper, we reported a first-principles investigation on the structural and electronic properties of O adsorption on the γ-TiAI（111） surface, to illustrate the oxidation process. It has been found that： （1） rather than stopping with one full monolayer of coverage, oxygen adsorption continues till two monolayer coverage, rendering an oxide-like structure; （2） full structural relaxation makes the surface oxide layer denser and more stable, which hinders the subsequent O adsorption （oxidation） process. In addition, the transformation from metal to oxide surface was identified by analyzing the local density of states through the oxidation steps, which was in good agreement with experimental results.展开更多
The electronic structures, optical dielectric functions, elastic properties, and lattice dynamics of Ba2ZnWO6 have been investigated by using the generalized gradient approximation. The density of states and distribut...The electronic structures, optical dielectric functions, elastic properties, and lattice dynamics of Ba2ZnWO6 have been investigated by using the generalized gradient approximation. The density of states and distributions of charge density show that O and Ba tend toward ionic bond, but O and W or Zn display the covalent bond character. The calculated energy band structure shows that Ba2ZnWO6 is a wide indirect band gap semiconductor. The static value 2.28 of the refractive index is attained. The analysis of the elastic properties of Ba2ZnWO6 indicates a rather weak elastic anisotropy. The phonon dispersion is calculated, suggesting no structural instability, which is agreement with the recent low temperature neutron diffraction experiments. The mensurability Cv （phonon heat capacity） as the function of the temperature is also calculated to judge our results for future experiment.展开更多
This paper investigates the lowest-energy structures, stabilities and electronic properties of （BAs）n clusters （n=1- 14） by means of the density-functional theory. The results show that the lowest-energy structure...This paper investigates the lowest-energy structures, stabilities and electronic properties of （BAs）n clusters （n=1- 14） by means of the density-functional theory. The results show that the lowest-energy structures undergo a structural change from two-dimensional to three-dimensional when n ： 4. With the increase of the cluster size （n=6）, the （BAs）n clusters tend to adopt cage-like structures, which can be considered as being built from B2As2 and six-membered rings with B-As bond alternative arrangement. The binding energy per atom, second-order energy differences, vertical electron affinity and vertical ionization potential are calculated and discussed. The caculated HOMO-LUMO gaps reveal that the clusters have typical semiconductor characteristics. The analysis of partial density of states suggests that there are strong covalence and molecular characteristics in the clusters.展开更多
We present a variational density-functional perturbation theory （DFPT） to investigate the lattice dynamics and vibra- tional properties of single crystal bismuth telluride material. The phonon dispersion curves and ...We present a variational density-functional perturbation theory （DFPT） to investigate the lattice dynamics and vibra- tional properties of single crystal bismuth telluride material. The phonon dispersion curves and phonon density of states （DOS） of the material were obtained. The phonon dispersions are divided into two fields by a phonon gap. In the lower field, atomic vibrations of both Bi and Te contribute to the DOS. In the higher field, most contributions come from Te atoms. The calculated Born effective charges and dielectric constants reveal a great anisotropy in the crystal. The largest Born effective charge generates a significant dynamic charge transferring along the c axis. By DFPT calculation, the greatest LO-TO splitting takes place in the infrared phonon modes and reaches 1.7 THz in the Brillouin zone center. The Raman spectra and peaks corresponding to respective atomic vibration modes were found to be in good agreement with the experimental data.展开更多
The structural, electronic and optical properties of rocksalt CdO have been studied using the plane-wave-based pseudo-potential density functional theory within generalized gradient approximation. The calculated latti...The structural, electronic and optical properties of rocksalt CdO have been studied using the plane-wave-based pseudo-potential density functional theory within generalized gradient approximation. The calculated lattice parameters are in agreement with previous experimental work. The band structure, density of states, and Mulliken charge population are obtained, which indicates that rocksalt CdO having the properties of a halfmetal due to an indirect band gap of -0.51eV. The mechanical properties show that rocksalt CdO is mechanically stable, isotropic and malleable. Significantly, we propose a correct value for ε1(0) of about 4.75, which offers theoretical data for the design and application for rocksalt CdO in optoelectronic materials.展开更多
Polymer density-functional theories(PDFTs)have distinct advantages in the study of polyelectrolyte(PE)systems over experiments and molecular simulations.Here we give an introductory review of some PDFTs recently devel...Polymer density-functional theories(PDFTs)have distinct advantages in the study of polyelectrolyte(PE)systems over experiments and molecular simulations.Here we give an introductory review of some PDFTs recently developed for PE systems.We start with a general formalism of PDFTs and its relation to the widely used polymer self-consistent field theory(SCFT),then explain the various correlations that are neglected in SCFT but can be accounted for in PDFTs,including those due to the excluded-volume interaction and chain connectivity of uncharged polymers,the electrostatic correlations of small ions,and the chain correlations in PEs.We also list some applications of PDFTs for PE systems,and finally give some perspectives on future work.We hope that our review can attract more researchers to apply and further develop PDFTs as a promising class of theoretical and computational tools.展开更多
In 2014, 50 years following the introduction of density functional theory (DFT), a rigorous understanding of it was published [AIP Advances, 4, 127,104 (2014)]. This understanding includes two features that complete t...In 2014, 50 years following the introduction of density functional theory (DFT), a rigorous understanding of it was published [AIP Advances, 4, 127,104 (2014)]. This understanding includes two features that complete the theory in practice, inasmuch as they are necessary for its correct application in electronic structure calculations;this understanding elucidates what appears to have been the crucial misunderstanding for 50 years, namely, the confusion between a stationary solution, attainable with most basis sets, following self-consistent iterations, with the ground state solution. The latter is obtained by a calculation that employs the well-defined optimal basis set for the system. The aim of this work is to review the above understanding and to extend it to the relativistic generalization of density functional theory by Rajagopal and Callaway [Phys. Rev. B7, 1912 (1973)]. This extension straightforwardly follows similar steps taken in the non-relativistic case, with the four-component current density, in the former, replacing the electronic charge density, in the latter. This new understanding, which completes relativistic DFT in practice, is expected to be needed for the study of heavy atoms and of materials (from molecules to solids) containing them—as is the case for some high temperature superconductors.展开更多
NH_(3)-SCR脱硝技术由于其良好的脱硝效率及稳定性受到广泛应用,其核心是催化剂。γ-Fe_(2)O_(3)是一种具有良好低温脱硝活性的催化剂,采用Cu对其掺杂改性可有效提高其性能。为探究其反应机理,采用密度泛函理论(Density Function Theory...NH_(3)-SCR脱硝技术由于其良好的脱硝效率及稳定性受到广泛应用,其核心是催化剂。γ-Fe_(2)O_(3)是一种具有良好低温脱硝活性的催化剂,采用Cu对其掺杂改性可有效提高其性能。为探究其反应机理,采用密度泛函理论(Density Function Theory,DFT)方法对SCR反应过程中NH_(3)、NO、O_(2)等反应物分子在Cu掺杂γ-Fe_(2)O_(3)催化剂表面的吸附行为进行研究。结果表明,NH_(3)、NO、O_(2)均会吸附在Cu、Fe两个活性位点上,并形成稳定的吸附构型。在NH 3吸附过程中,NH_(3)会失去电子,N原子与Fe、Cu形成稳定的化学键。NO以N原子端靠近催化剂表面时,主要发生化学吸附,而以O原子靠近时发生物理吸附。NO主要表现为失去电子,当以N原子吸附时形成了稳定的化学键。O_(2)吸附时会得到电子并与金属离子之间形成稳定的化学吸附构型。在吸附过程中,小分子吸附于Fe活性位上时较为稳定。展开更多
Geometrical configurations of 16 substituted biphenyls were computed at the B3LYP/6-311G^＊＊ level with Gaussian 98 program. Based on linear solvation energy theory, lgKow as well as the structural and thermodynamic ...Geometrical configurations of 16 substituted biphenyls were computed at the B3LYP/6-311G^＊＊ level with Gaussian 98 program. Based on linear solvation energy theory, lgKow as well as the structural and thermodynamic parameters obtained at this level was taken as theoretical descriptors, and corresponding equation predicting the toxicity of Daphnia magna （-lgEC5o） was thus obtained, in which three parameters were contained, i.e., n-octanol/water partition coefficients （lgKow）, dipole moment of the molecules（ μ） and entropy （S°）. For this equation, R^2 = 0.9582, q^2 = 0.8921 and SD = 0.102. The absolute t-scores of three variables are larger than the standard one in the confidence range of 95%, which confirms the creditability and stability of this model.展开更多
文摘The structural, electronic, and optical properties of Cu2Zn1−xBaxSn1−ySiyS4 compounds have been calculated using GGA-PBE function within the framework of Density Functional Theory (DFT). In the present work, lattice parameters remained the same, that is tetragonal crystal structure for 0% and 100% doping concentration. The electronic band gap of Cu2Zn1−xBaxSn1−ySiyS4 compounds has been gradually increased for continuous increment of doping concentration where the highest electronic band gap is 1.117 eV for Cu2BaSiS4 structure. Moreover, the band gap changes from direct to indirect band gap with the increase of doping concentration in the parent compound. The absorption coefficient has been found to be high (> 104 cm−1) in UV-region for all the doping concentration which makes the studied compound as a potential candidate of absorber layer in the UV detector. The theoretical study of the effect of double doping in the CZTS compound is very interesting for improving the quality of it and it would be a reference for the theoretical and experimental researchers.
文摘In Quantum Information Theory(QIT) the classical measures of information content in probability distributions are replaced by the corresponding resultant entropic descriptors containing the nonclassical terms generated by the state phase or its gradient(electronic current). The classical Shannon(S[p]) and Fisher(I[p]) information terms probe the entropic content of incoherent local events of the particle localization, embodied in the probability distribution p, while their nonclassical phase-companions, S[ Φ ] and I[ Φ ], provide relevant coherence information supplements.Thermodynamic-like couplings between the entropic and energetic descriptors of molecular states are shown to be precluded by the principles of quantum mechanics. The maximum of resultant entropy determines the phase-equilibrium state, defined by "thermodynamic" phase related to electronic density,which can be used to describe reactants in hypothetical stages of a bimolecular chemical reaction.Information channels of molecular systems and their entropic bond indices are summarized, the complete-bridge propagations are examined, and sequential cascades involving the complete sets of the atomic-orbital intermediates are interpreted as Markov chains. The QIT description is applied to reactive systems R = A―B, composed of the Acidic(A) and Basic(B) reactants. The electronegativity equalization processes are investigated and implications of the concerted patterns of electronic flows in equilibrium states of the complementarily arranged substrates are investigated. Quantum communications between reactants are explored and the QIT descriptors of the A―B bond multiplicity/composition are extracted.
文摘Under high pressure, the long believed single-phase material CaB6 was latterly discovered to have a new phase tI56. Based on the density-functional theory, the pressure effects on the structural and elastic properties of CaB6 are obtained. The calculated bulk, shear, and Young’s moduli of the recently synthesized high pressure phase tI56-CaB6 are larger than those of the low pressure phase. Moreover, the high pressure phase of CaB6 has ductile behaviors, and its ductility increases with the increase of pressure. On the contrary, the calculated results indicate that the low pressure phase of CaB6 is brittle. The calculated Debye temperature indicates that the thermal conductivity of CaB6 is not very good. Furthermore, based on the Christoffel equation, the slowness surface of the acoustic waves is obtained.
文摘The activities of dimethyl carbonate and dimethyl sulfate as a methylation reagent were studied by density- functional theory （DFT）. B3LYP/6-31G（d, p） methods were used to optimize the structures of dirnethyl carbonate and dimethyl sulfate and calculate theirs charge densities. Dimethyl sulfate is easier than dimethyl carbonate to react with a nucleophUic reagent. In dimethyl sulfate, the alkoxy carbons are the only reactive atomic nucleus because of steric hindrance. A nucleophilic reagent is more likely to react with carbonyl carbons than alkoxy carbons of dimethyl carbonate; in the presence of a Lewis acid, the phenyl nucleophilic reagent reacts with the Lewis acid first. Lewis acid increases the negative charge density of a nucleophUic reagent in polar solvent, and also incurs an accretion of steric hindrance. Polar solvent avails to ionize dimethyl carbonate and thus enables the reaction of methylation. The frequencies of transition state calculated by Gaussion 03 confirm the inferred reaction mechanism. The harvest rates of 4-methoxyphenol in the experiments of methylation reactions of hydroquinone with respectively dimethyl carbonate and dimethyl sulfate support the foregoing theortical conclusions.
基金supported by the National Basic Research Program of China under grant No.2006CB605103
文摘In this paper, we reported a first-principles investigation on the structural and electronic properties of O adsorption on the γ-TiAI（111） surface, to illustrate the oxidation process. It has been found that： （1） rather than stopping with one full monolayer of coverage, oxygen adsorption continues till two monolayer coverage, rendering an oxide-like structure; （2） full structural relaxation makes the surface oxide layer denser and more stable, which hinders the subsequent O adsorption （oxidation） process. In addition, the transformation from metal to oxide surface was identified by analyzing the local density of states through the oxidation steps, which was in good agreement with experimental results.
基金supported by the Fundamental Research Funds for the Central Universities (Grant No. 2013QNA32)
文摘The electronic structures, optical dielectric functions, elastic properties, and lattice dynamics of Ba2ZnWO6 have been investigated by using the generalized gradient approximation. The density of states and distributions of charge density show that O and Ba tend toward ionic bond, but O and W or Zn display the covalent bond character. The calculated energy band structure shows that Ba2ZnWO6 is a wide indirect band gap semiconductor. The static value 2.28 of the refractive index is attained. The analysis of the elastic properties of Ba2ZnWO6 indicates a rather weak elastic anisotropy. The phonon dispersion is calculated, suggesting no structural instability, which is agreement with the recent low temperature neutron diffraction experiments. The mensurability Cv （phonon heat capacity） as the function of the temperature is also calculated to judge our results for future experiment.
基金supported by the National Natural Science Foundation of China (Grant No. 10964012)the Priority Subject Program for Theoretical Physics of Xinjiang Normal University and the Fund of the Education Department of Xinjiang Uygur Autonomous Region of China (Grant No. xjedu2009i27)the Science and Technology Innovation Foundation for Graduate Students of Xinjiang Normal University (Grant No. 20101205)
文摘This paper investigates the lowest-energy structures, stabilities and electronic properties of （BAs）n clusters （n=1- 14） by means of the density-functional theory. The results show that the lowest-energy structures undergo a structural change from two-dimensional to three-dimensional when n ： 4. With the increase of the cluster size （n=6）, the （BAs）n clusters tend to adopt cage-like structures, which can be considered as being built from B2As2 and six-membered rings with B-As bond alternative arrangement. The binding energy per atom, second-order energy differences, vertical electron affinity and vertical ionization potential are calculated and discussed. The caculated HOMO-LUMO gaps reveal that the clusters have typical semiconductor characteristics. The analysis of partial density of states suggests that there are strong covalence and molecular characteristics in the clusters.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.50971101 and 51074127)the Research Fund of the State Key Laboratory of Solidification Processing(NPU)of China(Grant No.SKLSP201010)
文摘We present a variational density-functional perturbation theory （DFPT） to investigate the lattice dynamics and vibra- tional properties of single crystal bismuth telluride material. The phonon dispersion curves and phonon density of states （DOS） of the material were obtained. The phonon dispersions are divided into two fields by a phonon gap. In the lower field, atomic vibrations of both Bi and Te contribute to the DOS. In the higher field, most contributions come from Te atoms. The calculated Born effective charges and dielectric constants reveal a great anisotropy in the crystal. The largest Born effective charge generates a significant dynamic charge transferring along the c axis. By DFPT calculation, the greatest LO-TO splitting takes place in the infrared phonon modes and reaches 1.7 THz in the Brillouin zone center. The Raman spectra and peaks corresponding to respective atomic vibration modes were found to be in good agreement with the experimental data.
文摘The structural, electronic and optical properties of rocksalt CdO have been studied using the plane-wave-based pseudo-potential density functional theory within generalized gradient approximation. The calculated lattice parameters are in agreement with previous experimental work. The band structure, density of states, and Mulliken charge population are obtained, which indicates that rocksalt CdO having the properties of a halfmetal due to an indirect band gap of -0.51eV. The mechanical properties show that rocksalt CdO is mechanically stable, isotropic and malleable. Significantly, we propose a correct value for ε1(0) of about 4.75, which offers theoretical data for the design and application for rocksalt CdO in optoelectronic materials.
基金support for this work provided by the National Natural Science Foundation of China(Nos.22173051 and 21829301).
文摘Polymer density-functional theories(PDFTs)have distinct advantages in the study of polyelectrolyte(PE)systems over experiments and molecular simulations.Here we give an introductory review of some PDFTs recently developed for PE systems.We start with a general formalism of PDFTs and its relation to the widely used polymer self-consistent field theory(SCFT),then explain the various correlations that are neglected in SCFT but can be accounted for in PDFTs,including those due to the excluded-volume interaction and chain connectivity of uncharged polymers,the electrostatic correlations of small ions,and the chain correlations in PEs.We also list some applications of PDFTs for PE systems,and finally give some perspectives on future work.We hope that our review can attract more researchers to apply and further develop PDFTs as a promising class of theoretical and computational tools.
文摘In 2014, 50 years following the introduction of density functional theory (DFT), a rigorous understanding of it was published [AIP Advances, 4, 127,104 (2014)]. This understanding includes two features that complete the theory in practice, inasmuch as they are necessary for its correct application in electronic structure calculations;this understanding elucidates what appears to have been the crucial misunderstanding for 50 years, namely, the confusion between a stationary solution, attainable with most basis sets, following self-consistent iterations, with the ground state solution. The latter is obtained by a calculation that employs the well-defined optimal basis set for the system. The aim of this work is to review the above understanding and to extend it to the relativistic generalization of density functional theory by Rajagopal and Callaway [Phys. Rev. B7, 1912 (1973)]. This extension straightforwardly follows similar steps taken in the non-relativistic case, with the four-component current density, in the former, replacing the electronic charge density, in the latter. This new understanding, which completes relativistic DFT in practice, is expected to be needed for the study of heavy atoms and of materials (from molecules to solids) containing them—as is the case for some high temperature superconductors.
文摘NH_(3)-SCR脱硝技术由于其良好的脱硝效率及稳定性受到广泛应用,其核心是催化剂。γ-Fe_(2)O_(3)是一种具有良好低温脱硝活性的催化剂,采用Cu对其掺杂改性可有效提高其性能。为探究其反应机理,采用密度泛函理论(Density Function Theory,DFT)方法对SCR反应过程中NH_(3)、NO、O_(2)等反应物分子在Cu掺杂γ-Fe_(2)O_(3)催化剂表面的吸附行为进行研究。结果表明,NH_(3)、NO、O_(2)均会吸附在Cu、Fe两个活性位点上,并形成稳定的吸附构型。在NH 3吸附过程中,NH_(3)会失去电子,N原子与Fe、Cu形成稳定的化学键。NO以N原子端靠近催化剂表面时,主要发生化学吸附,而以O原子靠近时发生物理吸附。NO主要表现为失去电子,当以N原子吸附时形成了稳定的化学键。O_(2)吸附时会得到电子并与金属离子之间形成稳定的化学吸附构型。在吸附过程中,小分子吸附于Fe活性位上时较为稳定。
基金This work was supported by the Natural Science Research Fund of Universities in Jiangsu Province (04KJB150149)
文摘Geometrical configurations of 16 substituted biphenyls were computed at the B3LYP/6-311G^＊＊ level with Gaussian 98 program. Based on linear solvation energy theory, lgKow as well as the structural and thermodynamic parameters obtained at this level was taken as theoretical descriptors, and corresponding equation predicting the toxicity of Daphnia magna （-lgEC5o） was thus obtained, in which three parameters were contained, i.e., n-octanol/water partition coefficients （lgKow）, dipole moment of the molecules（ μ） and entropy （S°）. For this equation, R^2 = 0.9582, q^2 = 0.8921 and SD = 0.102. The absolute t-scores of three variables are larger than the standard one in the confidence range of 95%, which confirms the creditability and stability of this model.
