Most existing algorithms for the underdetermined blind source separation(UBSS) problem are two-stage algorithm, i.e., mixing parameters estimation and sources estimation. In the mixing parameters estimation, the previ...Most existing algorithms for the underdetermined blind source separation(UBSS) problem are two-stage algorithm, i.e., mixing parameters estimation and sources estimation. In the mixing parameters estimation, the previously proposed traditional clustering algorithms are sensitive to the initializations of the mixing parameters. To reduce the sensitiveness to the initialization, we propose a new algorithm for the UBSS problem based on anechoic speech mixtures by employing the visual information, i.e., the interaural time difference(ITD) and the interaural level difference(ILD), as the initializations of the mixing parameters. In our algorithm, the video signals are utilized to estimate the distances between microphones and sources, and then the estimations of the ITD and ILD can be obtained. With the sparsity assumption in the time-frequency domain, the Gaussian potential function algorithm is utilized to estimate the mixing parameters by using the ITDs and ILDs as the initializations of the mixing parameters. And the time-frequency masking is used to recover the sources by evaluating the various ITDs and ILDs. Experimental results demonstrate the competitive performance of the proposed algorithm compared with the baseline algorithms.展开更多
For a physical system, regardless of time reversal symmetry, a potential function serves also as a Lyapunov function, providing convergence and stability information. In this paper, the converse is constructively prov...For a physical system, regardless of time reversal symmetry, a potential function serves also as a Lyapunov function, providing convergence and stability information. In this paper, the converse is constructively proved that any dynamics with a Lyapunov function has a corresponding physical realization： a friction force, a Lorentz force, and a potential function. Such construction establishes a set of equations with physical meaning for Lyapunov function and suggests new approaches on the significant unsolved problem namely to construct Lyapunov functions for general nonlinear systems. In addition, a connection is found that the Lyapunov equation is a reduced form of a generalized Einstein relation for linear systems, revealing further insights of the construction.展开更多
In this paper, the effects of a bistable potential function U（x） = -ax2/2＋b｜x＋｜2y/（2y） on stochastic resonance （SR） is discussed. We investigate the effects of index y on the performance of the SR system wit...In this paper, the effects of a bistable potential function U（x） = -ax2/2＋b｜x＋｜2y/（2y） on stochastic resonance （SR） is discussed. We investigate the effects of index y on the performance of the SR system with fixed parameters a and b, and with fixed potential barriers, respectively. To measure the performance of the SR system in the presence of an aperiodic input, the bit error rate is employed, as is commonly used in binary communications. The numerical simulations strongly support the theoretical results. The goal of this investigation is to explore the effects of the shape of potential functions on SR and give a guidance of nonlinear systems in the application of information processing.展开更多
In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with ...In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.展开更多
Using the density functional B3P86/cc-PV5Z method, the geometric structure of BH molecule under different external electric fields is optimized, and the bond lengths, dipole moments, vibration frequencies, and other p...Using the density functional B3P86/cc-PV5Z method, the geometric structure of BH molecule under different external electric fields is optimized, and the bond lengths, dipole moments, vibration frequencies, and other physical properties parameters are obtained. On the basis of setting appropriate parameters, scanning single point energies are obtained by the same method and the potential energy curves under different external fields are also obtained. These results show that the physical property parameters and potential energy curves may change with external electric field, especially in the case of reverse direction electric field. The potential energy function without external electric field is fitted by Morse potential, and the fitting parameters are obtained which are in good agreement with experimental values. In order to obtain the critical dissociation electric parameter, the dipole approximation is adopted to construct a potential model fitting the corresponding potential energy curve of the external electric field. It is found that the fitted critical dissociation electric parameter is consistent with numerical calculation, so that the constructed model is reliable and accurate. These results will provide important theoretical and experimental reference for further studying the molecular spectrum, dynamics, and molecular cooling with Stark effect.展开更多
The splitting of potential energy levels for ground state X^2∏g of O^x2 （x = ＋1,-1） under spin-orbit coupling （SOC） has been calculated by using the spin-orbit （SO） multi-configuration quasi-degenerate perturb...The splitting of potential energy levels for ground state X^2∏g of O^x2 （x = ＋1,-1） under spin-orbit coupling （SOC） has been calculated by using the spin-orbit （SO） multi-configuration quasi-degenerate perturbation theory （SO-MCQDPT）. Their Murrell-Sorbie （M S） potential functions are gained, and then the spectroscopic constants for electronic states 2^∏1/2 and 2^∏3/2 are derived from the M S function. The vertical excitation energies for O^x2 （x = ＋1,-1） are v[O2＋1^（2∏3/2→X^2∏1/2）] =195.652cm^-1, and v[O2^-1（2^∏1/2 →X^2∏3/2）] =182.568cm^-1, respectively. All the spectroscopic data for electronic states 2^∏1/2 and 2^∏3/2 are given for the first time.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
In this paper, the electronic states of the ground states and dissociation limits of BC and BC- are correctly determined based on group theory and atomic and molecular reaction statics. The equilibrium geometries, har...In this paper, the electronic states of the ground states and dissociation limits of BC and BC- are correctly determined based on group theory and atomic and molecular reaction statics. The equilibrium geometries, harmonic frequencies and dissociation energies of the ground state of BC and BC- are calculated by using density function theory and quadratic CI method including single and double substitutions. The analytical potential energy functions of these states have been fitted with Murrell-Sorbie potential energy function from our ab initio calculation results. The spectroscopic data （αe, ωe and ωeχe） of each state is calculated via the relation between analytical potential energy function and spectroscopic data. All the calculations are in good agreement with the experimental data.展开更多
The reasonable dissociation limit of the second excited singlet state B1∏ of ^7LiH molecule is obtained. The accurate dissociation energy and equilibrium geometry of the B^∏ state are calculated using a symmetry-ada...The reasonable dissociation limit of the second excited singlet state B1∏ of ^7LiH molecule is obtained. The accurate dissociation energy and equilibrium geometry of the B^∏ state are calculated using a symmetry-adaptedcluster configuration interaction method in full active space. The whole potential energy curve for the B1H state is obtained over the internuclear distance ranging from about 0.10 nm to 0,54 nm, and has a least-square fit to the analytic Murrell-Sorbie function form. The vertical excitation energy is calculated from the ground state to the B^1∏ state and compared with previous theoretical results. The equilibrium internuclear distance obtained by geometry optimization is found to be quite different from that obtained by single-point energy scanning under the same calculation condition. Based on the analytic potential energy function, the harmonic frequency value of the B^1∏ state is estimated. A comparison of the theoretical calculations of dissociation energies, equilibrium interatomic distances and the analytic potential energy function with those obtained by previous theoretical results clearly shows that the present work is more comprehensive and in better agreement with experiments than previous theories, thus it is an improvement on previous theories.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 comparison between single-point energy scanning （SPES） and geometry optimization （OPT） in determining the equilibrium geometries of c^3∑g^＋ and B^1-Пu states of dimer 7Li2 is made at numerous basis sets by ...The comparison between single-point energy scanning （SPES） and geometry optimization （OPT） in determining the equilibrium geometries of c^3∑g^＋ and B^1-Пu states of dimer 7Li2 is made at numerous basis sets by using a symmetryadapted-cluster configuration-interaztion （SAC-CI） method in the Gaussian 03 program package. In this paper the difference of the equilibrium geometries obtained by SPES and by OPT is reported. The results obtained by SPES are found to be more reasonable than those obtained by OPT in full active space at the present SAC-CI level of theory. And the conclusion is attained that the cc-PVTZ is a most suitable basis set for these states. The calculated dissociation energies and equilibrium geometries are 0.8818 eV and 0.3090 nm for c^3∑g^＋ state, and 0.3668 eV and 0.2932 nm for B^1-Пu state respectively. The potential energy curves are calculated over a wide internuclear distance range from about 2.5α0 to 37α0 and have a least-squares fit into the Murrell-Sorbie function. According to the calculated analytic potential energy functions, the harmonic frequencies （We） and other spectroscopic data （ωeXe, Be and αe） are calculated. Comparison of the theoretical determinations at present work with the experiments and other theories clearly shows that the present work is the most complete effort and thus represents an improvement over previous theoretical results.展开更多
By using the B3P86/aug-cc-pvtz method, the accurate equilibrium geometry of the AlSO （Cs, X2AH） molecule has been calculated and compared with available theoreticM values. The obtained results show that the AlSO mol...By using the B3P86/aug-cc-pvtz method, the accurate equilibrium geometry of the AlSO （Cs, X2AH） molecule has been calculated and compared with available theoreticM values. The obtained results show that the AlSO molecule has a most stable structure with bond lengths of ROA1= 0.1864 nm, ROS=0.1623 nm, RAIS=0.2450 nm, together with a dissociation energy of 13.88 eV. The possible electronic states and their reasonable dissociation limits for the ground state of the AlSO molecule were determined based on the principle of atomic and molecular reaction statics. The analytic potential energy function of the AlSO molecule was derived by the many-body expansion theory and the contour lines were constructed for the first time, which show the internal information of the AlSO molecule, including the equilibrium structure and stable point. The analysis demonstrates that the obtained potential energy function of AlSO is reaSonable and successful and the present investigations provide important insights for further study on molecular reaction dynamics.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
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
In this paper, the equilibrium geometry, harmonic frequency and dissociation energy of S2^- and S3^- have been calculated at QCISD/6-311＋＋G（3d2f） and B3P86/6-311＋＋G（3d2f） level. The S2^- ground state is of 2II...In this paper, the equilibrium geometry, harmonic frequency and dissociation energy of S2^- and S3^- have been calculated at QCISD/6-311＋＋G（3d2f） and B3P86/6-311＋＋G（3d2f） level. The S2^- ground state is of 2IIg, the S3^- ground state is of 2B1 and S3^- has a bent （C2v） structure with an angle of 115.65° The results are in good agreement with these reported in other literature. For S3^- ion, the vibration frequencies and the force constants have also been calculated. Base on the general principles of microscopic reversibility, the dissociation limits has been deduced. The Murrell-Sorbie potential energy function for S2^- has been derived according to the ab initio data through the least- squares fitting. The force constants and spectroscopic data for S2^- have been calculated, then compared with other theoretical data. The analytical potential energy function of S3^- have been obtained based on the many-body expansion theory. The structure and energy can correctly reappear on the potential surface.展开更多
This paper calculates the equilibrium structure and the potential energy functions of the ground state （X^2∑^＋） and the low lying excited electronic state （A^2Л） of CN radical are calculated by using CASSCF met...This paper calculates the equilibrium structure and the potential energy functions of the ground state （X^2∑^＋） and the low lying excited electronic state （A^2Л） of CN radical are calculated by using CASSCF method. The potential energy curves are obtained by a least square fitting to the modified Murrell-Sorbie function. On the basis of physical theory of potential energy function, harmonic frequency （ωe） and other spectroscopic constants （ωeχe, βe and αe） are calculated by employing the Rydberg-Klei-Rees method. The theoretical calculation results are in excellent agreement with the experimental and other complicated theoretical calculation data. In addition, the eigenvalues of vibrational levels have been calculated by solving the radial one-dimensional SchrSdinger equation of nuclear motion using the algebraic method based on the analytical potential energy function.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
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
The purpose of this paper is to study the theory of conservative estimating functions in nonlinear regression model with aggregated data. In this model, a quasi-score function with aggregated data is defined. When thi...The purpose of this paper is to study the theory of conservative estimating functions in nonlinear regression model with aggregated data. In this model, a quasi-score function with aggregated data is defined. When this function happens to be conservative, it is projection of the true score function onto a class of estimation functions. By constructing, the potential function for the projected score with aggregated data is obtained, which have some properties of log-likelihood function.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.61162014,61210306074)the Natural Science Foundation of Jiangxi Province of China(Grant No.20122BAB201025)the Foundation for Young Scientists of Jiangxi Province(Jinggang Star)(Grant No.20122BCB23002)
文摘Most existing algorithms for the underdetermined blind source separation(UBSS) problem are two-stage algorithm, i.e., mixing parameters estimation and sources estimation. In the mixing parameters estimation, the previously proposed traditional clustering algorithms are sensitive to the initializations of the mixing parameters. To reduce the sensitiveness to the initialization, we propose a new algorithm for the UBSS problem based on anechoic speech mixtures by employing the visual information, i.e., the interaural time difference(ITD) and the interaural level difference(ILD), as the initializations of the mixing parameters. In our algorithm, the video signals are utilized to estimate the distances between microphones and sources, and then the estimations of the ITD and ILD can be obtained. With the sparsity assumption in the time-frequency domain, the Gaussian potential function algorithm is utilized to estimate the mixing parameters by using the ITDs and ILDs as the initializations of the mixing parameters. And the time-frequency masking is used to recover the sources by evaluating the various ITDs and ILDs. Experimental results demonstrate the competitive performance of the proposed algorithm compared with the baseline algorithms.
基金Project supported by the National Basic Research Program of China(Grant No.2010CB529200)the National Natural Science Foundation of China(Grant Nos.61073087 and 91029738)
文摘For a physical system, regardless of time reversal symmetry, a potential function serves also as a Lyapunov function, providing convergence and stability information. In this paper, the converse is constructively proved that any dynamics with a Lyapunov function has a corresponding physical realization： a friction force, a Lorentz force, and a potential function. Such construction establishes a set of equations with physical meaning for Lyapunov function and suggests new approaches on the significant unsolved problem namely to construct Lyapunov functions for general nonlinear systems. In addition, a connection is found that the Lyapunov equation is a reduced form of a generalized Einstein relation for linear systems, revealing further insights of the construction.
基金Project supported by the National Natural Science Foundation of China(Grant No.60702022)
文摘In this paper, the effects of a bistable potential function U（x） = -ax2/2＋b｜x＋｜2y/（2y） on stochastic resonance （SR） is discussed. We investigate the effects of index y on the performance of the SR system with fixed parameters a and b, and with fixed potential barriers, respectively. To measure the performance of the SR system in the presence of an aperiodic input, the bit error rate is employed, as is commonly used in binary communications. The numerical simulations strongly support the theoretical results. The goal of this investigation is to explore the effects of the shape of potential functions on SR and give a guidance of nonlinear systems in the application of information processing.
基金Supported by the National Natural Science Foundation of China(11671403,11671236,12101192)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.
基金Project supported by the National Natural Science Foundation of China(Grand Nos.11147158 and 11264020)the Natural Science Foundation of Jiangxi Province,China(Grand No.2010GQW0031)the Scientific Research Program of the Education Bureau of Jiangxi Province,China(Grand No.GJJ12483)
文摘Using the density functional B3P86/cc-PV5Z method, the geometric structure of BH molecule under different external electric fields is optimized, and the bond lengths, dipole moments, vibration frequencies, and other physical properties parameters are obtained. On the basis of setting appropriate parameters, scanning single point energies are obtained by the same method and the potential energy curves under different external fields are also obtained. These results show that the physical property parameters and potential energy curves may change with external electric field, especially in the case of reverse direction electric field. The potential energy function without external electric field is fitted by Morse potential, and the fitting parameters are obtained which are in good agreement with experimental values. In order to obtain the critical dissociation electric parameter, the dipole approximation is adopted to construct a potential model fitting the corresponding potential energy curve of the external electric field. It is found that the fitted critical dissociation electric parameter is consistent with numerical calculation, so that the constructed model is reliable and accurate. These results will provide important theoretical and experimental reference for further studying the molecular spectrum, dynamics, and molecular cooling with Stark effect.
基金supported by the National Natural Science Foundation of China (Grant Nos 10574096 and 10676025)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No 20050610010)the Scientific Research Foundation of Young Teacher of Guizhou Normal University, China
文摘The splitting of potential energy levels for ground state X^2∏g of O^x2 （x = ＋1,-1） under spin-orbit coupling （SOC） has been calculated by using the spin-orbit （SO） multi-configuration quasi-degenerate perturbation theory （SO-MCQDPT）. Their Murrell-Sorbie （M S） potential functions are gained, and then the spectroscopic constants for electronic states 2^∏1/2 and 2^∏3/2 are derived from the M S function. The vertical excitation energies for O^x2 （x = ＋1,-1） are v[O2＋1^（2∏3/2→X^2∏1/2）] =195.652cm^-1, and v[O2^-1（2^∏1/2 →X^2∏3/2）] =182.568cm^-1, respectively. All the spectroscopic data for electronic states 2^∏1/2 and 2^∏3/2 are given for the first time.
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.
文摘In this paper, the electronic states of the ground states and dissociation limits of BC and BC- are correctly determined based on group theory and atomic and molecular reaction statics. The equilibrium geometries, harmonic frequencies and dissociation energies of the ground state of BC and BC- are calculated by using density function theory and quadratic CI method including single and double substitutions. The analytical potential energy functions of these states have been fitted with Murrell-Sorbie potential energy function from our ab initio calculation results. The spectroscopic data （αe, ωe and ωeχe） of each state is calculated via the relation between analytical potential energy function and spectroscopic data. All the calculations are in good agreement with the experimental data.
基金Project supported by the National Natural Science Foundation of China （Grant No 10174019）, Henan Innovation for University Prominent Research Talents （2006KYCX002） and the Natural Science Foundation of Henan Province, China （Grant No 2006140008）.Acknowledgment The authors would like to heartily thank Professor Zhu Z H, of Sichuan University, for his helpful discussion about the reasonable dissociation limits at the planning stages of these calculations.
文摘The reasonable dissociation limit of the second excited singlet state B1∏ of ^7LiH molecule is obtained. The accurate dissociation energy and equilibrium geometry of the B^∏ state are calculated using a symmetry-adaptedcluster configuration interaction method in full active space. The whole potential energy curve for the B1H state is obtained over the internuclear distance ranging from about 0.10 nm to 0,54 nm, and has a least-square fit to the analytic Murrell-Sorbie function form. The vertical excitation energy is calculated from the ground state to the B^1∏ state and compared with previous theoretical results. The equilibrium internuclear distance obtained by geometry optimization is found to be quite different from that obtained by single-point energy scanning under the same calculation condition. Based on the analytic potential energy function, the harmonic frequency value of the B^1∏ state is estimated. A comparison of the theoretical calculations of dissociation energies, equilibrium interatomic distances and the analytic potential energy function with those obtained by previous theoretical results clearly shows that the present work is more comprehensive and in better agreement with experiments than previous theories, thus it is an improvement on previous theories.
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 （Grant No 10574039）, the Henan Innovation for University Prominent Research Talents （Grant No 2006KYCX002） and the National Natural Science Foundation of Education Bureau of Henan Province, China （Grant No 2007140015）. We heartily thank Professor Zhu Zheng-Hem of Sichuan University for his helpful discussion about the reasonable dissociation stages of these calculations limits during the planning
文摘The comparison between single-point energy scanning （SPES） and geometry optimization （OPT） in determining the equilibrium geometries of c^3∑g^＋ and B^1-Пu states of dimer 7Li2 is made at numerous basis sets by using a symmetryadapted-cluster configuration-interaztion （SAC-CI） method in the Gaussian 03 program package. In this paper the difference of the equilibrium geometries obtained by SPES and by OPT is reported. The results obtained by SPES are found to be more reasonable than those obtained by OPT in full active space at the present SAC-CI level of theory. And the conclusion is attained that the cc-PVTZ is a most suitable basis set for these states. The calculated dissociation energies and equilibrium geometries are 0.8818 eV and 0.3090 nm for c^3∑g^＋ state, and 0.3668 eV and 0.2932 nm for B^1-Пu state respectively. The potential energy curves are calculated over a wide internuclear distance range from about 2.5α0 to 37α0 and have a least-squares fit into the Murrell-Sorbie function. According to the calculated analytic potential energy functions, the harmonic frequencies （We） and other spectroscopic data （ωeXe, Be and αe） are calculated. Comparison of the theoretical determinations at present work with the experiments and other theories clearly shows that the present work is the most complete effort and thus represents an improvement over previous theoretical results.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10974139 and 10964002)the Natural Science Foundation of Hainan Province,China(Grant No.110001)+3 种基金Guizhou Province,China(Grant No.[2009]2066)the Scientific Research Foundation by Zhejiang University of Technology,China(Grant No.109003729)the Science-Technology Foundation of Sichuan Province,China(Grant No.09ZQ026-049)the Fund of Aiding Elites' Research Condition of Guizhou Province, China(Grant No.TZJF-2008-42)
文摘By using the B3P86/aug-cc-pvtz method, the accurate equilibrium geometry of the AlSO （Cs, X2AH） molecule has been calculated and compared with available theoreticM values. The obtained results show that the AlSO molecule has a most stable structure with bond lengths of ROA1= 0.1864 nm, ROS=0.1623 nm, RAIS=0.2450 nm, together with a dissociation energy of 13.88 eV. The possible electronic states and their reasonable dissociation limits for the ground state of the AlSO molecule were determined based on the principle of atomic and molecular reaction statics. The analytic potential energy function of the AlSO molecule was derived by the many-body expansion theory and the contour lines were constructed for the first time, which show the internal information of the AlSO molecule, including the equilibrium structure and stable point. The analysis demonstrates that the obtained potential energy function of AlSO is reaSonable and successful and the present investigations provide important insights for further study on molecular reaction dynamics.
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.
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 No 10574039）,the Key Program of Science and Technology Research of Education Ministry, China （Grant No 206084）, Innovation Talents of Institution of Higher Education of Henan Province, China （Grant No 2006KYCX002）, the Natural Science Foundation of Education Bureau of Henan Province, China （Grant No 200510476004）.
文摘In this paper, the equilibrium geometry, harmonic frequency and dissociation energy of S2^- and S3^- have been calculated at QCISD/6-311＋＋G（3d2f） and B3P86/6-311＋＋G（3d2f） level. The S2^- ground state is of 2IIg, the S3^- ground state is of 2B1 and S3^- has a bent （C2v） structure with an angle of 115.65° The results are in good agreement with these reported in other literature. For S3^- ion, the vibration frequencies and the force constants have also been calculated. Base on the general principles of microscopic reversibility, the dissociation limits has been deduced. The Murrell-Sorbie potential energy function for S2^- has been derived according to the ab initio data through the least- squares fitting. The force constants and spectroscopic data for S2^- have been calculated, then compared with other theoretical data. The analytical potential energy function of S3^- have been obtained based on the many-body expansion theory. The structure and energy can correctly reappear on the potential surface.
基金Project supported by the National Natural Science Foundation of China （Grant No 60771038）.
文摘This paper calculates the equilibrium structure and the potential energy functions of the ground state （X^2∑^＋） and the low lying excited electronic state （A^2Л） of CN radical are calculated by using CASSCF method. The potential energy curves are obtained by a least square fitting to the modified Murrell-Sorbie function. On the basis of physical theory of potential energy function, harmonic frequency （ωe） and other spectroscopic constants （ωeχe, βe and αe） are calculated by employing the Rydberg-Klei-Rees method. The theoretical calculation results are in excellent agreement with the experimental and other complicated theoretical calculation data. In addition, the eigenvalues of vibrational levels have been calculated by solving the radial one-dimensional SchrSdinger equation of nuclear motion using the algebraic method based on the analytical potential energy function.
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 (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The purpose of this paper is to study the theory of conservative estimating functions in nonlinear regression model with aggregated data. In this model, a quasi-score function with aggregated data is defined. When this function happens to be conservative, it is projection of the true score function onto a class of estimation functions. By constructing, the potential function for the projected score with aggregated data is obtained, which have some properties of log-likelihood function.
