A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions o...A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.展开更多
In this paper,we mainly focus on the following Choquard equation-{△u-V(x)(I_(a*)|u|^(p))|u|^(p-2)u=λu,x∈R^(N),u∈H^(1)(R^(N))where N≥1,λ∈R will arise as a Lagrange multiplier,0<a<N and N+a/N<p<N+a+2/...In this paper,we mainly focus on the following Choquard equation-{△u-V(x)(I_(a*)|u|^(p))|u|^(p-2)u=λu,x∈R^(N),u∈H^(1)(R^(N))where N≥1,λ∈R will arise as a Lagrange multiplier,0<a<N and N+a/N<p<N+a+2/N Under appropriate hypotheses on V(x),we prove that the above Choquard equation has a normalized ground state solution by utilizing variational methods.展开更多
Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric d...Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of scattering states are attained. The normalized wave functions expressed in terms of hypergeometrie functions of scattering states on the "k/2π scale" and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solutions is discussed.展开更多
The analytic solution of the radial Schrodinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely ana...The analytic solution of the radial Schrodinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely analytic solutions and the conditions that decide the existence of analytic solution have been searched when the potential of the radial Schrodinger equation is V(r) =α1r^8 +α2r^3 + α3r^2 +β3r^-1 +β2r^-3 +β1r6-4. Generally speaking, there is only an approximate solution, but not analytic solution for SchrSdinger equation with several potentials' superposition. However, the conditions that decide the existence of analytic solution have been found and the analytic solution and its energy level structure are obtained for the Schrodinger equation with the potential which is motioned above in this paper. According to the single-value, finite and continuous standard of wave function in a quantum system, the authors firstly solve the asymptotic solution through the radial coordinate r → ∞ and r →0; secondly, they make the asymptotic solutions combining with the series solutions nearby the neighborhood of irregular singularities; and then they compare the power series coefficients, deduce a series of analytic solutions of the stationary state wave function and corresponding energy level structure by tight coupling among the coefficients of potential functions for the radial SchrSdinger equation; and lastly, they discuss the solutions and make conclusions.展开更多
The analytical solutions to the Schrodinger equation with the Eckart potential in arbitrary dimension D is investigated by using the Nikiforov-Uvarov method, and the centrifugal term is treated approximatively with th...The analytical solutions to the Schrodinger equation with the Eckart potential in arbitrary dimension D is investigated by using the Nikiforov-Uvarov method, and the centrifugal term is treated approximatively with the scheme of Greene and Aldrich. The discrete spectrum is obtained and the wavefunetion is expressed in terms of the Jacobi polynomial or the hypergeometric function. Some special cases of the Eckart potential are discussed for D=3, and the resulting energy equation agrees well with that obtained by other methods.展开更多
We search for analytical wave solutions of an electronically and biologically important model named as the Fitzhugh–Nagumo model with truncated M-fractional derivative, in which the expafunction and extended sinh-Gor...We search for analytical wave solutions of an electronically and biologically important model named as the Fitzhugh–Nagumo model with truncated M-fractional derivative, in which the expafunction and extended sinh-Gordon equation expansion(ESh GEE) schemes are utilized. The solutions obtained include dark, bright, dark-bright, periodic and other kinds of solitons. These analytical wave solutions are gained and verified with the use of Mathematica software. These solutions do not exist in literature. Some of the solutions are demonstrated by 2D, 3D and contour graphs. This model is mostly used in circuit theory, transmission of nerve impulses, and population genetics. Finally, both the schemes are more applicable, reliable and significant to deal with the fractional nonlinear partial differential equations.展开更多
The bending problem of a functionally graded anisotropic cantilever beam subjected to thermal and uniformly dis-tributed load is investigated,with material parameters being arbitrary functions of the thickness coordin...The bending problem of a functionally graded anisotropic cantilever beam subjected to thermal and uniformly dis-tributed load is investigated,with material parameters being arbitrary functions of the thickness coordinate. The heat conduction problem is treated as a 1D problem through the thickness. Based on the elementary formulations for plane stress problem,the stress function is assumed to be in the form of polynomial of the longitudinal coordinate variable,from which the stresses can be derived. The stress function is then determined completely with the compatibility equation and boundary conditions. A practical example is presented to show the application of the method.展开更多
The bending problem of a functionally graded anisotropic cantilever beam subjected to a linearly distributed load is investigated. The analysis is based on the exact elasticity equations for the plane stress problem. ...The bending problem of a functionally graded anisotropic cantilever beam subjected to a linearly distributed load is investigated. The analysis is based on the exact elasticity equations for the plane stress problem. The stress function is introduced and assumed in the form of a polynomial of the longitudinal coordinate. The expressions for stress components are then educed from the stress function by simple differentiation. The stress function is determined from the compatibility equation as well as the boundary conditions by a skilful deduction. The analytical solution is compared with FEM calculation, indicating a good agreement.展开更多
An analytical solution of the unit pressure on a thin workpiece under compression has been obtained by using the inverse function of φ to the integral integral from 0 to x φ dx. Its result is basically the same as t...An analytical solution of the unit pressure on a thin workpiece under compression has been obtained by using the inverse function of φ to the integral integral from 0 to x φ dx. Its result is basically the same as the prevailing numerical formula integral from 0 to x φdx=∑√<sub>1</sub>-Δx<sub>1</sub>. However, the new integral is simpler and more convenient to use.展开更多
In this paper, the specific solutions of orthotropic plane problems with body forces are derived. Then, based on the general solution in the case of distinct eigenvalues and the specific solution for density functiona...In this paper, the specific solutions of orthotropic plane problems with body forces are derived. Then, based on the general solution in the case of distinct eigenvalues and the specific solution for density functionally graded orthotropic media, a series of beam problem, including the problems of cantilever beam with body forces depending only on z or on x coordinate and expressed by z or x polynomial is solved by the principle of superposition and the trial-and-error method.展开更多
The geometric structures of an Nit radical in different external electric fields are optimized by using the density functional B3P86/cc-PVSZ method, and the bond lengths, dipole moments, vibration frequencies and IR s...The geometric structures of an Nit radical in different external electric fields are optimized by using the density functional B3P86/cc-PVSZ method, and the bond lengths, dipole moments, vibration frequencies and IR spectrum are obtained. The potential energy curves are gained by the CCSD (T) method with the same basis set. These results indicate that the physical property parameters and potential energy curves may change with the external electric field, especially in the reverse direction electric field. The potential energy function of zero field is fitted by the Morse potential, and the fitting parameters are in good accordance with the experimental data. The potential energy functions of different external electric fields are fitted adopting the constructed potential model. The fitted critical dissociation electric parameters are shown to be consistent with the numerical calculation, and the relative errors are only 0.27% and 6.61%, hence the constructed model is reliable and accurate. The present results provide an important reference for further study of the molecular spectrum, dynamics and molecular cooling with Stark effect.展开更多
The analytical solution for an annular plate rotating at a constant angular velocity is derived by means of direct displacement method from the elasticity equations for axisymmetric problems of functionally graded tra...The analytical solution for an annular plate rotating at a constant angular velocity is derived by means of direct displacement method from the elasticity equations for axisymmetric problems of functionally graded transversely isotropic media. The displacement components are assumed as a linear combination of certain explicit functions of the radial coordinate, with seven undetermined coefficients being functions of the axial coordinate z. Seven equations governing these z-dependent functions are derived and solved by a progressive integrating scheme. The present solution can be degenerated into the solution of a rotating isotropic functionally graded annular plate. The solution also can be degenerated into that for transversely isotropic or isotropic homogeneous materials. Finally, a special case is considered and the effect of the material gradient index on the elastic field is illustrated numerically.展开更多
The symmetry-adapted-duster configuration-interaction method is used to investigate the spectroscopicproperties of ~7Li_2(A^1∑_u^+) over the internuclear distance ranging from 2.4ao to 37ao.The complete potential ene...The symmetry-adapted-duster configuration-interaction method is used to investigate the spectroscopicproperties of ~7Li_2(A^1∑_u^+) over the internuclear distance ranging from 2.4ao to 37ao.The complete potential energycurves are calculated at numbers of basis sets.All the ab initio calculated points are fitted to the analytic MurrellSorbie function and then employed to compute the spectroscopic constants.By comparison,the spectroscopic constantsreproduced by the potential attained at D95(3df,3pd) are found to be very close to the experiments,a^d the values (T_e,D_e,R_e,ω_e,ω_eχ_e,α_e and B_e) are of 1.732 93 eV,1.161 36 eV,0.313 27 nm,251.95 cm^(-1),1.623 cm^(-1),0.005 35 cm^(-1),and0.490 cm^(-1),respectively.With the potential obtained at D95(3df,3pd),the totally 75 vibrational states are found whenJ=0.The vibrational levels,the classical turning points and the inertial rotation constants of the first 68 vibrationalstates are calculated for the first time and compared with the available measurements.Good agreement is obtained.The centrifugal distortion constants of the first 32 vibrational states are also reported for the first time.The reasonabledissociation limit for ~7Li_2(A^1∑_u^+) is deduced using the calculated results at present.展开更多
The multi-reference configuration interaction method and aug-cc-pvqz (AVQZ) have been used to calculate potential energy curves (PECs) of the singlet and triplet states of the riu and rig symmetry of B2++. All o...The multi-reference configuration interaction method and aug-cc-pvqz (AVQZ) have been used to calculate potential energy curves (PECs) of the singlet and triplet states of the riu and rig symmetry of B2++. All of the four states (^l∏u, ^1∏g, ^3∏u and ^3∏g) are found to be metastable states, though the potential well of ^3∏u symmetry is very shallow. Based on the PECs, the analytical potential energy functions (APEFs) of these states have been fitted using the least square fitting method and two models of function. The spectroscopic parameters of each state are also calculated, and are compared with other investigations in the literature. The credibility and veracity of the two functions are evaluated. Some ideas to improve the fitting accuracy are presented. Also the vibrational levels for each state are predicted by solving the SchrSdinger equation of nuclear motion.展开更多
The potential energy curves(PECs) of the first electronic excited state of S2(a^1△g) are calculated employing a multi-reference configuration interaction method with the Davidson correction in combination with a ...The potential energy curves(PECs) of the first electronic excited state of S2(a^1△g) are calculated employing a multi-reference configuration interaction method with the Davidson correction in combination with a series of correlationconsistent basis sets from Dunning: aug-cc-p VX Z(X = T, Q, 5, 6). In order to obtain PECs with high accuracy, PECs calculated with aug-cc-p V(Q, 5)Z basis sets are extrapolated to the complete basis set limit. The resulting PECs are then fitted to the analytical potential energy function(APEF) using the extended Hartree–Fock approximate correlation energy method. By utilizing the fitted APEF, accurate and reliable spectroscopic parameters are obtained, which are consistent with both experimental and theoretical results. By solving the Schr o¨dinger equation numerically with the APEFs obtained at the AV6 Z and the extrapolated AV(Q, 5)Z level of theory, we calculate the complete set of vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants.展开更多
In this paper the equilibrium structure of HCO has been optimized by using density functional theory (DFT)/ B3P86 method and CC-PVTZ basis. It has a bent (Cs, X^2A') ground state structure with an angle of 124.40...In this paper the equilibrium structure of HCO has been optimized by using density functional theory (DFT)/ B3P86 method and CC-PVTZ basis. It has a bent (Cs, X^2A') ground state structure with an angle of 124.4095 °. The vibronic frequencies and force constants have also been calculated. Based on the principles of atomic and molecular reaction statics, the possible electronic states and reasonable dissociation limits for the ground state of HCO molecule have been determined. The analytic potential energy function of HCO (X^2A') molecule has been derived by using the many-body expansion theory. The contour lines are constructed, which show the static properties of HCO (X^2A'), such as the equilibrium structure, the lowest energies, etc. The potential energy surface of HCO (X^2A') is reasonable and very satisfactory.展开更多
This paper reports that the equilibrium structure of NH2 has been optimized at the QCISD/6-311++G (3df, 3pd) level. The ground-state NH2 has a bent (C2v, X^2B1) structure with an angle of 103.0582°. The geo...This paper reports that the equilibrium structure of NH2 has been optimized at the QCISD/6-311++G (3df, 3pd) level. The ground-state NH2 has a bent (C2v, X^2B1) structure with an angle of 103.0582°. The geometrical structure is in good agreement with the other calculational and experimental results. The harmonic frequencies and the force constants have also been calculated. Based on the group theory and the principle of microscopic reversibility, the dissociation limits of NH2(C2v, X^2B1) have been derived. The potential energy surface of NH2(X^2B1) is reasonable. The contour lines are constructed, the structure and energy of NH2 reappear on the potential energy surface.展开更多
In this paper, an exact analytical solution is presented for a transversely isotropic functionally graded magnetomelectro-elastic (FGMEE) cantilever beam, which is subjected to a uniform load on its upper surface, a...In this paper, an exact analytical solution is presented for a transversely isotropic functionally graded magnetomelectro-elastic (FGMEE) cantilever beam, which is subjected to a uniform load on its upper surface, as well as the concentrated force and moment at the free end. This solution can be applied for any form of gradient distribution. For the basic equations of plane problem, all the partial differential equations governing the stress field, electric, and magnetic potentials are derived. Then, the expressions of Airy stress, electric, and magnetic potential functions are assumed as quadratic polynomials of the longitudinal coordinate. Based on all the boundary conditions, the exact expressions of the three functions can be determined. As numerical examples, the material parameters are set as exponential and linear distributions in the thickness direction. The effects of the material parameters on the mechanical, electric, and magnetic fields of the cantilever beam are analyzed in detail.展开更多
The equilibrium structure of flue gas SO2 is optimized using the density functional theory (DFT)/B3P86 method and CC-PV5Z basis. The result shows that it has a bent (C2v, X1A1) ground state structure with an angle...The equilibrium structure of flue gas SO2 is optimized using the density functional theory (DFT)/B3P86 method and CC-PV5Z basis. The result shows that it has a bent (C2v, X1A1) ground state structure with an angle of 119.1184°. The vibronic frequencies and the force constants are also calculated. Based on the principles of atomic and molecular reaction statics (AMIIS), the possible electronic states and reasonable dissociation limits for the ground state of SO2 molecule are determined. The potential functions of SO and 02 are fitted by the modified Murrell-Sorbie+c6 (M-S+c6) potential function and the fitted parameters, the force constants and the spectroscopic constants are obtained, which are all close to the experimental values. The analytic potential energy function of the SO2 (X1A1) molecule is derived using the many-body expansion theory. The contour liues are constructed, which show the static properties of SO2 (XIA1), such as the equilibrium structure, the lowest energies, the most possible reaction channel, etc.展开更多
A kinematically admissible velocity field which is different from Avitzur's is established in Cartesian Coordinates. An upper-bound analytical solution to strip drawing andextrusion is obtained by using the integr...A kinematically admissible velocity field which is different from Avitzur's is established in Cartesian Coordinates. An upper-bound analytical solution to strip drawing andextrusion is obtained by using the integral as a function of the upper limit in this paper.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12261064 and 11861048)the Natural Science Foundation of Inner Mongolia,China (Grant Nos.2021MS01004 and 2022QN01008)the High-level Talents Scientific Research Start-up Foundation of Inner Mongolia University (Grant No.10000-21311201/165)。
文摘A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.
基金Supported by National Natural Science Foundation of China(Grant Nos.11671403 and 11671236)Henan Provincial General Natural Science Foundation Project(Grant No.232300420113)National Natural Science Foundation of China Youth Foud of China Youth Foud(Grant No.12101192).
文摘In this paper,we mainly focus on the following Choquard equation-{△u-V(x)(I_(a*)|u|^(p))|u|^(p-2)u=λu,x∈R^(N),u∈H^(1)(R^(N))where N≥1,λ∈R will arise as a Lagrange multiplier,0<a<N and N+a/N<p<N+a+2/N Under appropriate hypotheses on V(x),we prove that the above Choquard equation has a normalized ground state solution by utilizing variational methods.
基金*Supported by the Natural Science Foundation of Jiangsu Province of China under Grant No. BK2010291, the Professor and Doctor Foundation of Yancheng Teachers University under Grant No. 07YSYJB0203
文摘Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of scattering states are attained. The normalized wave functions expressed in terms of hypergeometrie functions of scattering states on the "k/2π scale" and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solutions is discussed.
基金supported by the National Natural Science Foundation of China under Grant No.10575140the Basic Research of Chongqing Education Committee under Grant No.KJ060813
文摘The analytic solution of the radial Schrodinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely analytic solutions and the conditions that decide the existence of analytic solution have been searched when the potential of the radial Schrodinger equation is V(r) =α1r^8 +α2r^3 + α3r^2 +β3r^-1 +β2r^-3 +β1r6-4. Generally speaking, there is only an approximate solution, but not analytic solution for SchrSdinger equation with several potentials' superposition. However, the conditions that decide the existence of analytic solution have been found and the analytic solution and its energy level structure are obtained for the Schrodinger equation with the potential which is motioned above in this paper. According to the single-value, finite and continuous standard of wave function in a quantum system, the authors firstly solve the asymptotic solution through the radial coordinate r → ∞ and r →0; secondly, they make the asymptotic solutions combining with the series solutions nearby the neighborhood of irregular singularities; and then they compare the power series coefficients, deduce a series of analytic solutions of the stationary state wave function and corresponding energy level structure by tight coupling among the coefficients of potential functions for the radial SchrSdinger equation; and lastly, they discuss the solutions and make conclusions.
基金Supported by the National Natural Science Foundation of China under Grant No 14101020155the Fundamental Research Funds for the Central Universities under Grant No GK201402012
文摘The analytical solutions to the Schrodinger equation with the Eckart potential in arbitrary dimension D is investigated by using the Nikiforov-Uvarov method, and the centrifugal term is treated approximatively with the scheme of Greene and Aldrich. The discrete spectrum is obtained and the wavefunetion is expressed in terms of the Jacobi polynomial or the hypergeometric function. Some special cases of the Eckart potential are discussed for D=3, and the resulting energy equation agrees well with that obtained by other methods.
文摘We search for analytical wave solutions of an electronically and biologically important model named as the Fitzhugh–Nagumo model with truncated M-fractional derivative, in which the expafunction and extended sinh-Gordon equation expansion(ESh GEE) schemes are utilized. The solutions obtained include dark, bright, dark-bright, periodic and other kinds of solitons. These analytical wave solutions are gained and verified with the use of Mathematica software. These solutions do not exist in literature. Some of the solutions are demonstrated by 2D, 3D and contour graphs. This model is mostly used in circuit theory, transmission of nerve impulses, and population genetics. Finally, both the schemes are more applicable, reliable and significant to deal with the fractional nonlinear partial differential equations.
基金Project supported by the National Natural Science Foundation of China (Nos. 10472102 and 1043203)the Foundation of Ningbo University (No. 2005014), China
文摘The bending problem of a functionally graded anisotropic cantilever beam subjected to thermal and uniformly dis-tributed load is investigated,with material parameters being arbitrary functions of the thickness coordinate. The heat conduction problem is treated as a 1D problem through the thickness. Based on the elementary formulations for plane stress problem,the stress function is assumed to be in the form of polynomial of the longitudinal coordinate variable,from which the stresses can be derived. The stress function is then determined completely with the compatibility equation and boundary conditions. A practical example is presented to show the application of the method.
基金Project supported by the National Natural Science Foundation of China(Nos.10472102 and 10432030)
文摘The bending problem of a functionally graded anisotropic cantilever beam subjected to a linearly distributed load is investigated. The analysis is based on the exact elasticity equations for the plane stress problem. The stress function is introduced and assumed in the form of a polynomial of the longitudinal coordinate. The expressions for stress components are then educed from the stress function by simple differentiation. The stress function is determined from the compatibility equation as well as the boundary conditions by a skilful deduction. The analytical solution is compared with FEM calculation, indicating a good agreement.
文摘An analytical solution of the unit pressure on a thin workpiece under compression has been obtained by using the inverse function of φ to the integral integral from 0 to x φ dx. Its result is basically the same as the prevailing numerical formula integral from 0 to x φdx=∑√<sub>1</sub>-Δx<sub>1</sub>. However, the new integral is simpler and more convenient to use.
基金Project (Nos. 10432030 and 10472102) supported by the NationalNatural Science Foundation of China
文摘In this paper, the specific solutions of orthotropic plane problems with body forces are derived. Then, based on the general solution in the case of distinct eigenvalues and the specific solution for density functionally graded orthotropic media, a series of beam problem, including the problems of cantilever beam with body forces depending only on z or on x coordinate and expressed by z or x polynomial is solved by the principle of superposition and the trial-and-error method.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11147158 and 11264020the Jiangxi Province Natural Science Foundation under Grant No 2010GQW0031the Jiangxi Province Scientific Research Program of the Education Bureau under Grant No GJJ12483
文摘The geometric structures of an Nit radical in different external electric fields are optimized by using the density functional B3P86/cc-PVSZ method, and the bond lengths, dipole moments, vibration frequencies and IR spectrum are obtained. The potential energy curves are gained by the CCSD (T) method with the same basis set. These results indicate that the physical property parameters and potential energy curves may change with the external electric field, especially in the reverse direction electric field. The potential energy function of zero field is fitted by the Morse potential, and the fitting parameters are in good accordance with the experimental data. The potential energy functions of different external electric fields are fitted adopting the constructed potential model. The fitted critical dissociation electric parameters are shown to be consistent with the numerical calculation, and the relative errors are only 0.27% and 6.61%, hence the constructed model is reliable and accurate. The present results provide an important reference for further study of the molecular spectrum, dynamics and molecular cooling with Stark effect.
基金Project supported by the National Natural Science Foundation of China (Nos. 10472102 and 10432030)the Natural Science Foun-dation of Zhejiang Province (No. Y605040)Ningbo City (No.2005A610024), China
文摘The analytical solution for an annular plate rotating at a constant angular velocity is derived by means of direct displacement method from the elasticity equations for axisymmetric problems of functionally graded transversely isotropic media. The displacement components are assumed as a linear combination of certain explicit functions of the radial coordinate, with seven undetermined coefficients being functions of the axial coordinate z. Seven equations governing these z-dependent functions are derived and solved by a progressive integrating scheme. The present solution can be degenerated into the solution of a rotating isotropic functionally graded annular plate. The solution also can be degenerated into that for transversely isotropic or isotropic homogeneous materials. Finally, a special case is considered and the effect of the material gradient index on the elastic field is illustrated numerically.
基金The project supported by National Natural Science Foundation of China under Grant Nos.10574039 and 10174019
文摘The symmetry-adapted-duster configuration-interaction method is used to investigate the spectroscopicproperties of ~7Li_2(A^1∑_u^+) over the internuclear distance ranging from 2.4ao to 37ao.The complete potential energycurves are calculated at numbers of basis sets.All the ab initio calculated points are fitted to the analytic MurrellSorbie function and then employed to compute the spectroscopic constants.By comparison,the spectroscopic constantsreproduced by the potential attained at D95(3df,3pd) are found to be very close to the experiments,a^d the values (T_e,D_e,R_e,ω_e,ω_eχ_e,α_e and B_e) are of 1.732 93 eV,1.161 36 eV,0.313 27 nm,251.95 cm^(-1),1.623 cm^(-1),0.005 35 cm^(-1),and0.490 cm^(-1),respectively.With the potential obtained at D95(3df,3pd),the totally 75 vibrational states are found whenJ=0.The vibrational levels,the classical turning points and the inertial rotation constants of the first 68 vibrationalstates are calculated for the first time and compared with the available measurements.Good agreement is obtained.The centrifugal distortion constants of the first 32 vibrational states are also reported for the first time.The reasonabledissociation limit for ~7Li_2(A^1∑_u^+) is deduced using the calculated results at present.
文摘The multi-reference configuration interaction method and aug-cc-pvqz (AVQZ) have been used to calculate potential energy curves (PECs) of the singlet and triplet states of the riu and rig symmetry of B2++. All of the four states (^l∏u, ^1∏g, ^3∏u and ^3∏g) are found to be metastable states, though the potential well of ^3∏u symmetry is very shallow. Based on the PECs, the analytical potential energy functions (APEFs) of these states have been fitted using the least square fitting method and two models of function. The spectroscopic parameters of each state are also calculated, and are compared with other investigations in the literature. The credibility and veracity of the two functions are evaluated. Some ideas to improve the fitting accuracy are presented. Also the vibrational levels for each state are predicted by solving the SchrSdinger equation of nuclear motion.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11304185 and 11074151)
文摘The potential energy curves(PECs) of the first electronic excited state of S2(a^1△g) are calculated employing a multi-reference configuration interaction method with the Davidson correction in combination with a series of correlationconsistent basis sets from Dunning: aug-cc-p VX Z(X = T, Q, 5, 6). In order to obtain PECs with high accuracy, PECs calculated with aug-cc-p V(Q, 5)Z basis sets are extrapolated to the complete basis set limit. The resulting PECs are then fitted to the analytical potential energy function(APEF) using the extended Hartree–Fock approximate correlation energy method. By utilizing the fitted APEF, accurate and reliable spectroscopic parameters are obtained, which are consistent with both experimental and theoretical results. By solving the Schr o¨dinger equation numerically with the APEFs obtained at the AV6 Z and the extrapolated AV(Q, 5)Z level of theory, we calculate the complete set of vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants.
基金Project supported by the National Natural Science Foundation of China and CAEP (Grant No 10676025), by the scientific project of Jiangxi education departments of China (Grant Nos 2006261 and 2006236), and by the Research Funds of College of Jinggangshan, China (Grant No JZ0616).
文摘In this paper the equilibrium structure of HCO has been optimized by using density functional theory (DFT)/ B3P86 method and CC-PVTZ basis. It has a bent (Cs, X^2A') ground state structure with an angle of 124.4095 °. The vibronic frequencies and force constants have also been calculated. Based on the principles of atomic and molecular reaction statics, the possible electronic states and reasonable dissociation limits for the ground state of HCO molecule have been determined. The analytic potential energy function of HCO (X^2A') molecule has been derived by using the many-body expansion theory. The contour lines are constructed, which show the static properties of HCO (X^2A'), such as the equilibrium structure, the lowest energies, etc. The potential energy surface of HCO (X^2A') is reasonable and very satisfactory.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10574039 and 10174019)Henan Innovation Project For University Prominent Research Talents (Grant No HAIPUTT2006KYCX002)the Natural Science Foundation of Education Commission of Henan Province (Grant Nos 2003140028 and 200510476004)
文摘This paper reports that the equilibrium structure of NH2 has been optimized at the QCISD/6-311++G (3df, 3pd) level. The ground-state NH2 has a bent (C2v, X^2B1) structure with an angle of 103.0582°. The geometrical structure is in good agreement with the other calculational and experimental results. The harmonic frequencies and the force constants have also been calculated. Based on the group theory and the principle of microscopic reversibility, the dissociation limits of NH2(C2v, X^2B1) have been derived. The potential energy surface of NH2(X^2B1) is reasonable. The contour lines are constructed, the structure and energy of NH2 reappear on the potential energy surface.
基金supported by the National Natural Science Foundation of China(Nos.10772106 and11072138)the Shanghai Leading Academic Discipline Project(No.S30106)+1 种基金the Research Fund for the Doctoral Program of Higher Education of China(No.20113108110005)the Natural Science Foundation Project of Shanghai(No.15ZR1416100)
文摘In this paper, an exact analytical solution is presented for a transversely isotropic functionally graded magnetomelectro-elastic (FGMEE) cantilever beam, which is subjected to a uniform load on its upper surface, as well as the concentrated force and moment at the free end. This solution can be applied for any form of gradient distribution. For the basic equations of plane problem, all the partial differential equations governing the stress field, electric, and magnetic potentials are derived. Then, the expressions of Airy stress, electric, and magnetic potential functions are assumed as quadratic polynomials of the longitudinal coordinate. Based on all the boundary conditions, the exact expressions of the three functions can be determined. As numerical examples, the material parameters are set as exponential and linear distributions in the thickness direction. The effects of the material parameters on the mechanical, electric, and magnetic fields of the cantilever beam are analyzed in detail.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11147158 and 10965002)the Natural Science Foundation of Jiangxi Province, China (Grant No. 2010GQW0031)the Scientific Project of Jiangxi Education Department, China (Grant No. GJJ11540)
文摘The equilibrium structure of flue gas SO2 is optimized using the density functional theory (DFT)/B3P86 method and CC-PV5Z basis. The result shows that it has a bent (C2v, X1A1) ground state structure with an angle of 119.1184°. The vibronic frequencies and the force constants are also calculated. Based on the principles of atomic and molecular reaction statics (AMIIS), the possible electronic states and reasonable dissociation limits for the ground state of SO2 molecule are determined. The potential functions of SO and 02 are fitted by the modified Murrell-Sorbie+c6 (M-S+c6) potential function and the fitted parameters, the force constants and the spectroscopic constants are obtained, which are all close to the experimental values. The analytic potential energy function of the SO2 (X1A1) molecule is derived using the many-body expansion theory. The contour liues are constructed, which show the static properties of SO2 (XIA1), such as the equilibrium structure, the lowest energies, the most possible reaction channel, etc.
文摘A kinematically admissible velocity field which is different from Avitzur's is established in Cartesian Coordinates. An upper-bound analytical solution to strip drawing andextrusion is obtained by using the integral as a function of the upper limit in this paper.