Segmented all-electron basis set of triple zeta valence quality plus polarization functions(TZP)for the elements of the fifth row to be used together with the zero-order regular approximation(ZORA)is carefully constru...Segmented all-electron basis set of triple zeta valence quality plus polarization functions(TZP)for the elements of the fifth row to be used together with the zero-order regular approximation(ZORA)is carefully constructed.To correctly describe electrons distant from atomic nuclei,the basis set is augmented with diffuse functions giving rise to a set designated as ATZP-ZORA.At the ZORA-B3LYP theoretical level,these sets are used to calculate the ionization energy and mean dipole polarizability of some atoms,bond length,dissociation energy,and harmonic vibrational frequency of diatomic molecules.Then,these results are compared with the theoretical and experimental data found in the literature.Even considering that our sets are relatively compact,they are sufficiently accurate and reliable to perform property calculations involving simultaneously electrons from the inner shell and outer shell.The performances of the ZORA and second-order Douglas-Kroll-Hess Hamiltonians are evaluated and the results are also discussed.展开更多
A scheme based on treating uniform singlet-pair and triplet-pair interactions is suggested to extrapolate electron correlation energy of ammonia, calculated at two basis-set levels of ab initio theory in the infinite ...A scheme based on treating uniform singlet-pair and triplet-pair interactions is suggested to extrapolate electron correlation energy of ammonia, calculated at two basis-set levels of ab initio theory in the infinite one-electron basis-set limit. The dual-level method is tested on the extrapolation of the full correlation in coupled-cluster singles and doubles and in the case also a noniterative perturbative correction for connected triple energies for the C3v and D3h structures of ammonia, with correlation-consistent basis sets of the type cc-pVXZ (X = D, T, Q, 5, 6) and aug-cc-pVXZ (X = D, T, Q, 5). For testing and comparison purposes, the energies reported by Klopper [J. Comput. Chem. 22 1306 (2001)] have been taken. From a corresponding extrapolation of CCSD(T)/AVXZ energies for X = 4, 5, we obtain total inversion barriers of 1833.87 cm-1/1832.33 cm^-1 for the two/three-parameter extrapolation rules, which are in good agreement with other theoretical extrapolation and empirical values in the literature.展开更多
Many physical problems involve unbounded domains where the physical quantities vanish at infinities.Numerically,this has been handled using different techniques such as domain truncation,approximations using infinitel...Many physical problems involve unbounded domains where the physical quantities vanish at infinities.Numerically,this has been handled using different techniques such as domain truncation,approximations using infinitely extended and vanishing basis sets,and mapping bounded basis sets using some coordinate transformations.Each technique has its own advantages and disadvantages.Yet,approximating simultaneously and efficiently a wide range of decaying rates has persisted as major challenge.Also,coordinate transformation,if not carefully implemented,can result in non-orthogonal mapped basis sets.In this work,we revisited this issue with an emphasize on designing appropriate transformations using sine series as basis set.The transformations maintain both the orthogonality and the efficiency.Furthermore,using simple basis set(sine function)help avoid the expensive numerical integrations.In the calculations,four types of physically recurring decaying behaviors are considered,which are:non-oscillating and oscillating exponential decays,and non-oscillating and oscillating algebraic decays.The results and the analyses show that properly designed high-order mapped basis sets can be efficient tools to handle challenging physical problems on unbounded domains.Decay rate ranges as large of 6 orders of magnitudes can be approximated efficiently and concurrently.展开更多
For a perspective set that is derived by finite consequences with probabilities, this paper introduces the conception of basis that is proved and the uniqueness of basis over a perspective set holds. These give the ch...For a perspective set that is derived by finite consequences with probabilities, this paper introduces the conception of basis that is proved and the uniqueness of basis over a perspective set holds. These give the characteristic properties of perspective sets and finite consequences with probabilities. These properties are applied to the utility defined by the consequences.展开更多
At the second order Douglas–Kroll–Hess(DKH2) level, the B3 PW91 functional in conjunction with the relativistic all-electron basis set of valence triple zeta quality plus polarization functions are employed to com...At the second order Douglas–Kroll–Hess(DKH2) level, the B3 PW91 functional in conjunction with the relativistic all-electron basis set of valence triple zeta quality plus polarization functions are employed to compute bond lengths, dissociation energies, vertical ionization potentials, and the highest occupied molecular orbital-lowest unoccupied molecular orbital energy gaps of the small iridium clusters(Irn, n≤8). These results are compared with the experimental and theoretical data available in the literature. Our results confirm the theoretical predictions made by Feng et al. about the catalytic activities of the Ir4 and Ir6 clusters. From the optimized geometries, DKH2 calculations of static electric mean dipole polarizabilities and polarizability anisotropies are also carried out. It is the first time that the polarizabilities of small iridium clusters have been studied. For n≤4, the mean dipole polarizabilities per atom present an odd–even oscillatory behavior,whereas from Ir5 to Ir8, they decrease with the cluster size increasing. The dependence of the polarizability anisotropy on the structure symmetry of the iridium cluster is verified.展开更多
In this study, the energy for the ground state of helium and a few helium-like ions (Z=1-6) is computed variationally by using a Hylleraas-like wavefunction. A four-parameters wavefunction, satisfying boundary condi...In this study, the energy for the ground state of helium and a few helium-like ions (Z=1-6) is computed variationally by using a Hylleraas-like wavefunction. A four-parameters wavefunction, satisfying boundary conditions for coalescence points, is combined with a Hylleraas-like basis set which explicitly incorporates r12 interelectronic distance. The main contribution of this work is the introduction of modified correlation terms leading to the definition of integral transforms which provide the calculation of expectation value of energy to be done analytically over single-particle coordinates instead of Hylleraas coordinates.展开更多
The electronic structure and electronic absorption spectra of binuclear Au(Ⅰ) complexes with bidentate phophines and a bidentate ylid ligand have been studied using quasirelativistic pseudopotential ab initio calcula...The electronic structure and electronic absorption spectra of binuclear Au(Ⅰ) complexes with bidentate phophines and a bidentate ylid ligand have been studied using quasirelativistic pseudopotential ab initio calculations at the HF and MP2 levels by the LANL2DZ basis sets. The electronic properties of the spectral transition and Au(Ⅰ)-Au(Ⅰ) interaction were also discussed.展开更多
At the Douglas-Kroll-Hess (DKI4) level, the B3PW91 functional along with the all-eleclron relativistic basis sets of valence triple and quadruple zeta qualities are used to determine the structure, stability, and el...At the Douglas-Kroll-Hess (DKI4) level, the B3PW91 functional along with the all-eleclron relativistic basis sets of valence triple and quadruple zeta qualities are used to determine the structure, stability, and electronic properties of the small silver clusters (Agn, n ≤ 7). The results presented in this study are in good agreement with the experimental data and theoretical values obtained at a higher level of theory from the literature. Static polarizability and hyperpolarizability are also reported. It is verified that the mean dipole polarizability per atom exhibits an odd-even oscillation and that the polarizability anisotropy is directly related to the cluster shape. In this article, the first study of hyperpolarizabilities of small silver clusters is presented. Except for the monomer, the second hyperpolarizabilities of the silver clusters are significantly larger than those of the copper clusters.展开更多
The density function B3LYP method has been used to optimize the geometries of the luteolin, thymine and lute- olin-thymine complexes at 6-31+G* basis. The vibrational frequencies have been studied at the same level ...The density function B3LYP method has been used to optimize the geometries of the luteolin, thymine and lute- olin-thymine complexes at 6-31+G* basis. The vibrational frequencies have been studied at the same level to ana- lyze these seventeen complexes, respectively. Theories of atoms in molecules (AIM) and natural bond orbital (NBO) have been utilized to investigate the hydrogen bonds involved in all the systems. The interaction energies of the complexes corrected by basis set superposition error are between -93.00-76.69 kJ/mol. The calculating results indicate that strong hydrogen bonding interactions have been found in the luteolin-thymine complexes.展开更多
In this paper,we present solutions for the one-dimensional coupled nonlinear Schrödinger(CNLS)equations by the Constrained Interpolation Profile-Basis Set(CIP-BS)method.This method uses a simple polynomial basis ...In this paper,we present solutions for the one-dimensional coupled nonlinear Schrödinger(CNLS)equations by the Constrained Interpolation Profile-Basis Set(CIP-BS)method.This method uses a simple polynomial basis set,by which physical quantities are approximated with their values and derivatives associated with grid points.Nonlinear operations on functions are carried out in the framework of differential algebra.Then,by introducing scalar products and requiring the residue to be orthogonal to the basis,the linear and nonlinear partial differential equations are reduced to ordinary differential equations for values and spatial derivatives.The method gives stable,less diffusive,and accurate results for the CNLS equations.展开更多
基金the Conselho Nacional de Desenvolvimento Científico Tecnológico(Brazilian Agency)。
文摘Segmented all-electron basis set of triple zeta valence quality plus polarization functions(TZP)for the elements of the fifth row to be used together with the zero-order regular approximation(ZORA)is carefully constructed.To correctly describe electrons distant from atomic nuclei,the basis set is augmented with diffuse functions giving rise to a set designated as ATZP-ZORA.At the ZORA-B3LYP theoretical level,these sets are used to calculate the ionization energy and mean dipole polarizability of some atoms,bond length,dissociation energy,and harmonic vibrational frequency of diatomic molecules.Then,these results are compared with the theoretical and experimental data found in the literature.Even considering that our sets are relatively compact,they are sufficiently accurate and reliable to perform property calculations involving simultaneously electrons from the inner shell and outer shell.The performances of the ZORA and second-order Douglas-Kroll-Hess Hamiltonians are evaluated and the results are also discussed.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.11274149 and 11374353)the Natural Science Foundation of Liaoning Province,China (Grant No.20121032)+2 种基金the Scientific Research Foundation for Doctors of Liaoning Universitythe Natural Science Foundation of Liaoning Universitythe Program of Shenyang Key Laboratory of Optoelectronic Materials and Technology,China (Grant No.F12-254-1-00)
文摘A scheme based on treating uniform singlet-pair and triplet-pair interactions is suggested to extrapolate electron correlation energy of ammonia, calculated at two basis-set levels of ab initio theory in the infinite one-electron basis-set limit. The dual-level method is tested on the extrapolation of the full correlation in coupled-cluster singles and doubles and in the case also a noniterative perturbative correction for connected triple energies for the C3v and D3h structures of ammonia, with correlation-consistent basis sets of the type cc-pVXZ (X = D, T, Q, 5, 6) and aug-cc-pVXZ (X = D, T, Q, 5). For testing and comparison purposes, the energies reported by Klopper [J. Comput. Chem. 22 1306 (2001)] have been taken. From a corresponding extrapolation of CCSD(T)/AVXZ energies for X = 4, 5, we obtain total inversion barriers of 1833.87 cm-1/1832.33 cm^-1 for the two/three-parameter extrapolation rules, which are in good agreement with other theoretical extrapolation and empirical values in the literature.
基金The author would like to thank Qatar National Research Fund as the work is partially supported by NPRP 7-317-1-055.
文摘Many physical problems involve unbounded domains where the physical quantities vanish at infinities.Numerically,this has been handled using different techniques such as domain truncation,approximations using infinitely extended and vanishing basis sets,and mapping bounded basis sets using some coordinate transformations.Each technique has its own advantages and disadvantages.Yet,approximating simultaneously and efficiently a wide range of decaying rates has persisted as major challenge.Also,coordinate transformation,if not carefully implemented,can result in non-orthogonal mapped basis sets.In this work,we revisited this issue with an emphasize on designing appropriate transformations using sine series as basis set.The transformations maintain both the orthogonality and the efficiency.Furthermore,using simple basis set(sine function)help avoid the expensive numerical integrations.In the calculations,four types of physically recurring decaying behaviors are considered,which are:non-oscillating and oscillating exponential decays,and non-oscillating and oscillating algebraic decays.The results and the analyses show that properly designed high-order mapped basis sets can be efficient tools to handle challenging physical problems on unbounded domains.Decay rate ranges as large of 6 orders of magnitudes can be approximated efficiently and concurrently.
文摘For a perspective set that is derived by finite consequences with probabilities, this paper introduces the conception of basis that is proved and the uniqueness of basis over a perspective set holds. These give the characteristic properties of perspective sets and finite consequences with probabilities. These properties are applied to the utility defined by the consequences.
基金supported by the CNPq,CAPES,and FAPES(Brazilian Agencies)
文摘At the second order Douglas–Kroll–Hess(DKH2) level, the B3 PW91 functional in conjunction with the relativistic all-electron basis set of valence triple zeta quality plus polarization functions are employed to compute bond lengths, dissociation energies, vertical ionization potentials, and the highest occupied molecular orbital-lowest unoccupied molecular orbital energy gaps of the small iridium clusters(Irn, n≤8). These results are compared with the experimental and theoretical data available in the literature. Our results confirm the theoretical predictions made by Feng et al. about the catalytic activities of the Ir4 and Ir6 clusters. From the optimized geometries, DKH2 calculations of static electric mean dipole polarizabilities and polarizability anisotropies are also carried out. It is the first time that the polarizabilities of small iridium clusters have been studied. For n≤4, the mean dipole polarizabilities per atom present an odd–even oscillatory behavior,whereas from Ir5 to Ir8, they decrease with the cluster size increasing. The dependence of the polarizability anisotropy on the structure symmetry of the iridium cluster is verified.
基金Project supported by the Cumhuriyet University National MOVPE Crystal Growth and Characterization Laboratory,DPT-K120,TUBITAK (Grant Nos TBAG 105T492,TBAG 107T012,and TBAG-108T015)
文摘In this study, the energy for the ground state of helium and a few helium-like ions (Z=1-6) is computed variationally by using a Hylleraas-like wavefunction. A four-parameters wavefunction, satisfying boundary conditions for coalescence points, is combined with a Hylleraas-like basis set which explicitly incorporates r12 interelectronic distance. The main contribution of this work is the introduction of modified correlation terms leading to the definition of integral transforms which provide the calculation of expectation value of energy to be done analytically over single-particle coordinates instead of Hylleraas coordinates.
文摘The electronic structure and electronic absorption spectra of binuclear Au(Ⅰ) complexes with bidentate phophines and a bidentate ylid ligand have been studied using quasirelativistic pseudopotential ab initio calculations at the HF and MP2 levels by the LANL2DZ basis sets. The electronic properties of the spectral transition and Au(Ⅰ)-Au(Ⅰ) interaction were also discussed.
基金Project supported by CNPq,CAPES,and FAPES(Brazilian Agencies)
文摘At the Douglas-Kroll-Hess (DKI4) level, the B3PW91 functional along with the all-eleclron relativistic basis sets of valence triple and quadruple zeta qualities are used to determine the structure, stability, and electronic properties of the small silver clusters (Agn, n ≤ 7). The results presented in this study are in good agreement with the experimental data and theoretical values obtained at a higher level of theory from the literature. Static polarizability and hyperpolarizability are also reported. It is verified that the mean dipole polarizability per atom exhibits an odd-even oscillation and that the polarizability anisotropy is directly related to the cluster shape. In this article, the first study of hyperpolarizabilities of small silver clusters is presented. Except for the monomer, the second hyperpolarizabilities of the silver clusters are significantly larger than those of the copper clusters.
文摘The density function B3LYP method has been used to optimize the geometries of the luteolin, thymine and lute- olin-thymine complexes at 6-31+G* basis. The vibrational frequencies have been studied at the same level to ana- lyze these seventeen complexes, respectively. Theories of atoms in molecules (AIM) and natural bond orbital (NBO) have been utilized to investigate the hydrogen bonds involved in all the systems. The interaction energies of the complexes corrected by basis set superposition error are between -93.00-76.69 kJ/mol. The calculating results indicate that strong hydrogen bonding interactions have been found in the luteolin-thymine complexes.
文摘In this paper,we present solutions for the one-dimensional coupled nonlinear Schrödinger(CNLS)equations by the Constrained Interpolation Profile-Basis Set(CIP-BS)method.This method uses a simple polynomial basis set,by which physical quantities are approximated with their values and derivatives associated with grid points.Nonlinear operations on functions are carried out in the framework of differential algebra.Then,by introducing scalar products and requiring the residue to be orthogonal to the basis,the linear and nonlinear partial differential equations are reduced to ordinary differential equations for values and spatial derivatives.The method gives stable,less diffusive,and accurate results for the CNLS equations.