Focusing on revealing the origin of high ammonia yield rate on Cu via nitrate reduction(NO3RR),we herein applied constant potential method via grand-canonical density functional theory(GC-DFT)with implicit continuum s...Focusing on revealing the origin of high ammonia yield rate on Cu via nitrate reduction(NO3RR),we herein applied constant potential method via grand-canonical density functional theory(GC-DFT)with implicit continuum solvation model to predict the reaction energetics of NO3RR on pure copper surface in alkaline media.The potential-dependent mechanism on the most prevailing Cu(111)and the minor(100)and(110)facets were established,in consideration of NO_(2)_(−),NO,NH_(3),NH_(2)OH,N_(2),and N_(2)O as the main products.The computational results show that the major Cu(111)is the ideal surface to produce ammonia with the highest onset potential at 0.06 V(until−0.37 V)and the highest optimal potential at−0.31 V for ammonia production without kinetic obstacles in activation energies at critical steps.For other minor facets,the secondary Cu(100)shows activity to ammonia from−0.03 to−0.54 V with the ideal potential at−0.50 V,which requires larger overpotential to overcome kinetic activation energy barriers.The least Cu(110)possesses the longest potential range for ammonia yield from−0.27 to−1.12 V due to the higher adsorption coverage of nitrate,but also with higher tendency to generate di-nitrogen species.Experimental evaluations on commercial Cu/C electrocatalyst validated the accuracy of our proposed mechanism.The most influential(111)surface with highest percentage in electrocatalyst determined the trend of ammonia production.In specific,the onset potential of ammonia production at 0.1 V and emergence of yield rate peak at−0.3 V in experiments precisely located in the predicted potentials on Cu(111).Four critical factors for the high ammonia yield and selectivity on Cu surface via NO3RR are summarized,including high NO3RR activity towards ammonia on the dominant Cu(111)facet,more possibilities to produce ammonia along different pathways on each facet,excellent ability for HER inhibition and suitable surface size to suppress di-nitrogen species formation at high nitrate coverage.Overall,our work provides comprehensive potential-dependent insights into the reaction details of NO3RR to ammonia,which can serve as references for the future development of NO3RR electrocatalysts,achieving higher activity and selectivity by maximizing these characteristics of copper-based materials.展开更多
A photon structure is advanced based on the experimental evidence and the vector potential quantization at a single photon level. It is shown that the photon is neither a point particle nor an infinite wave but behave...A photon structure is advanced based on the experimental evidence and the vector potential quantization at a single photon level. It is shown that the photon is neither a point particle nor an infinite wave but behaves rather like a local “wave-corpuscle” extended over a wavelength, occupying a minimum quantization volume and guided by a non-local vector potential real wave function. The quantized vector potential oscillates over a wavelength with circular left or right polarization giving birth to orthogonal magnetic and electric fields whose amplitudes are proportional to the square of the frequency. The energy and momentum are carried by the local wave-corpuscle guided by the non-local vector potential wave function suitably normalized.展开更多
Using a field equation with a phase factor, a universal analytic potential-energy function applied to the interactions between diatoms or molecules is derived, and five kinds of potential curves of common shapes are o...Using a field equation with a phase factor, a universal analytic potential-energy function applied to the interactions between diatoms or molecules is derived, and five kinds of potential curves of common shapes are obtained adjusting the phase factors. The linear thermal expansion coefficients and Young's moduli of eleven kinds of face-centered cubic (fcc) metals - Al, Cu, Ag, etc. are calculated using the potential-energy function; the computational results are quite consistent with experimental values. Moreover, an analytic relation between the linear thermal expansion coefficients and Young's moduli of fcc metals is given using the potential-energy function. Finally, the force constants of fifty-five kinds of diatomic moleculars with low excitation state are computed using this theory, and they are quite consistent with RKR (Rydberg-Klein-Rees) experimental values.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
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
Lithium has been paid great attention in recent years thanks to its significant appli-cations for battery and lightweight alloy.Developing a potential model with high ac-curacy and efficiency is impor-tant for theoret...Lithium has been paid great attention in recent years thanks to its significant appli-cations for battery and lightweight alloy.Developing a potential model with high ac-curacy and efficiency is impor-tant for theoretical simulation of lithium materials.Here,we build a deep learning potential(DP)for elemental lithium based on a concurrent-learning scheme and DP representation of the density-functional theory(DFT)potential energy surface(PES),the DP model enables material simulations with close-to DFT accuracy but at much lower computational cost.The simulations show that basic parameters,equation of states,elasticity,defects and surface are consistent with the first principles results.More notably,the liquid radial distribution func-tion based on our DP model is found to match well with experiment data.Our results demon-strate that the developed DP model can be used for the simulation of lithium materials.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
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
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
In this paper are reported the local minimum problem by means of current greedy algorithm for training the empirical potential function of protein folding on 8623 non-native structures of 31 globular proteins and a so...In this paper are reported the local minimum problem by means of current greedy algorithm for training the empirical potential function of protein folding on 8623 non-native structures of 31 globular proteins and a solution of the problem based upon the simulated annealing algorithm. This simulated annealing algorithm is indispensable for developing and testing highly refined empirical potential functions.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
In this paper, the energy, equilibrium geometry, and harmonic frequency of the ground electronic state of PO2 are computed using the B3LYP, B3P86, CCSD(T), and QCISD(T) methods in conjunction with the 6-311++G(...In this paper, the energy, equilibrium geometry, and harmonic frequency of the ground electronic state of PO2 are computed using the B3LYP, B3P86, CCSD(T), and QCISD(T) methods in conjunction with the 6-311++G(3df, 3pd) and cc-pVTZ basis sets. A comparison between the computational results and the experimental values indicates that the B3P86/6-311++G(3df, 3pd) method can give better energy calculation results for the PO2 molecule. It is shown that the ground state of the PO2 molecule has C2v symmetry and its ground electronic state is X2A1. The equilibrium parameters of the structure are Rp-o = 0.1465 am, ZOPO = 134.96°, and the dissociation energy is Ed = 19.218 eV. The bent vibrational frequency Ul = 386 cm-1, symmetric stretching frequency v2 = 1095 cm-1, and asymmetric stretching frequency ua = 1333 em-1 are obtained. On the basis of atomic and molecular reaction statics, a reasonable dissociation limit for the ground state of the PO2 molecule is determined. Then the analytic potential energy function of the PO2 molecule is derived using many-body expansion theory. The potential curves correctly reproduce the configurations and the dissociation energy for the PO2 molecule.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
A new method on constructing analytical potential energy functions is presented, and then a relatively universal analytical potential energy function for precisely calculating the spectra of 'iatomic molecules and io...A new method on constructing analytical potential energy functions is presented, and then a relatively universal analytical potential energy function for precisely calculating the spectra of 'iatomic molecules and ions is derived. Furthermore, six kinds of common potential energy curves containing three main potential curves i,e. steady state, metastable state and repulsive state are obtained from this potential energy function. Finally, spectroscopic parameters of thirteen diatomic molecules and ions including BeD-X^2∑+, BeT-X^2∑^+ and Na2-X^1∑g^+ etc are calculated by using the potential function, as a consequence, all calculation results are in good agreement with experimental data.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 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
We identify a class of transcendental entire maps of finite order, of disjoint-type, satisfying the rapid derivative growth condition. Within this class, we show that there exist hyperbolic transcendental entire maps ...We identify a class of transcendental entire maps of finite order, of disjoint-type, satisfying the rapid derivative growth condition. Within this class, we show that there exist hyperbolic transcendental entire maps that generate a large class of potentials which intersect the so-called tame potentials and form a distinct class of potentials. The methods and techniques derived from the thermodynamic formalism are applied to these potentials for transcendental entire maps acting on some subset of the Julia set which is conjugated to the shift map over a code space with a countable alphabet endowed with the euclidean induced metric on the complex plane.展开更多
In this paper, a new method on constructing analytical potential energy functions is pre-sented, and from this a analytical potential en-ergy function applied to both neutral diatomic molecules and charged diatomic mo...In this paper, a new method on constructing analytical potential energy functions is pre-sented, and from this a analytical potential en-ergy function applied to both neutral diatomic molecules and charged diatomic molecular ions is obtained. This potential energy function in-cludes three dimensionless undetermined pa-rameters which can be determined uniquely by solving linear equations with the experimental spectroscopic parameters of molecules. The solutions of the dimensionless undetermined parameters are real numbers rather than com-plex numbers, this ensures that the analytical potential energy function has extensive uni-versality. Finally, the potential energy function is examined with four kinds of diatomic molecules or ions—homonuclear neutral diatomic mole-cule , and , homonuclear charged diatomic molecular ion , and , heter-nuclear neutral diatomic Molecule , and , heternuclear ch- arged diatomic Molecular ion , and ,as a conseque- nce, good results are obtained.展开更多
We show an example of a bounded potential on the half-line obtained as the image of an Inverse Transformation Operator of the Bessel singular potential of the Reduced Radial Schrödinger Equation, and show us ...We show an example of a bounded potential on the half-line obtained as the image of an Inverse Transformation Operator of the Bessel singular potential of the Reduced Radial Schrödinger Equation, and show us the Estimates of the A(α) amplitude.展开更多
基金supported by is supported by the Shanghai Municipal Science and Technology Major Project.
文摘Focusing on revealing the origin of high ammonia yield rate on Cu via nitrate reduction(NO3RR),we herein applied constant potential method via grand-canonical density functional theory(GC-DFT)with implicit continuum solvation model to predict the reaction energetics of NO3RR on pure copper surface in alkaline media.The potential-dependent mechanism on the most prevailing Cu(111)and the minor(100)and(110)facets were established,in consideration of NO_(2)_(−),NO,NH_(3),NH_(2)OH,N_(2),and N_(2)O as the main products.The computational results show that the major Cu(111)is the ideal surface to produce ammonia with the highest onset potential at 0.06 V(until−0.37 V)and the highest optimal potential at−0.31 V for ammonia production without kinetic obstacles in activation energies at critical steps.For other minor facets,the secondary Cu(100)shows activity to ammonia from−0.03 to−0.54 V with the ideal potential at−0.50 V,which requires larger overpotential to overcome kinetic activation energy barriers.The least Cu(110)possesses the longest potential range for ammonia yield from−0.27 to−1.12 V due to the higher adsorption coverage of nitrate,but also with higher tendency to generate di-nitrogen species.Experimental evaluations on commercial Cu/C electrocatalyst validated the accuracy of our proposed mechanism.The most influential(111)surface with highest percentage in electrocatalyst determined the trend of ammonia production.In specific,the onset potential of ammonia production at 0.1 V and emergence of yield rate peak at−0.3 V in experiments precisely located in the predicted potentials on Cu(111).Four critical factors for the high ammonia yield and selectivity on Cu surface via NO3RR are summarized,including high NO3RR activity towards ammonia on the dominant Cu(111)facet,more possibilities to produce ammonia along different pathways on each facet,excellent ability for HER inhibition and suitable surface size to suppress di-nitrogen species formation at high nitrate coverage.Overall,our work provides comprehensive potential-dependent insights into the reaction details of NO3RR to ammonia,which can serve as references for the future development of NO3RR electrocatalysts,achieving higher activity and selectivity by maximizing these characteristics of copper-based materials.
文摘A photon structure is advanced based on the experimental evidence and the vector potential quantization at a single photon level. It is shown that the photon is neither a point particle nor an infinite wave but behaves rather like a local “wave-corpuscle” extended over a wavelength, occupying a minimum quantization volume and guided by a non-local vector potential real wave function. The quantized vector potential oscillates over a wavelength with circular left or right polarization giving birth to orthogonal magnetic and electric fields whose amplitudes are proportional to the square of the frequency. The energy and momentum are carried by the local wave-corpuscle guided by the non-local vector potential wave function suitably normalized.
基金This work was supported by the National Natural Science Foundation of China (No. 40274044).
文摘Using a field equation with a phase factor, a universal analytic potential-energy function applied to the interactions between diatoms or molecules is derived, and five kinds of potential curves of common shapes are obtained adjusting the phase factors. The linear thermal expansion coefficients and Young's moduli of eleven kinds of face-centered cubic (fcc) metals - Al, Cu, Ag, etc. are calculated using the potential-energy function; the computational results are quite consistent with experimental values. Moreover, an analytic relation between the linear thermal expansion coefficients and Young's moduli of fcc metals is given using the potential-energy function. Finally, the force constants of fifty-five kinds of diatomic moleculars with low excitation state are computed using this theory, and they are quite consistent with RKR (Rydberg-Klein-Rees) experimental values.
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 Founda-tion of China(No.22203026,No.22203025,and No.12174080)the National Key R&D Program of China(No.2022YFA1602601)+1 种基金the Fundamental Research Funds for the Central Universities(JZ2022HGTA0313 and JZ2022HGQA0198)the Anhui Provincial Nat-ural Science Foundation(2208085QB44).
文摘Lithium has been paid great attention in recent years thanks to its significant appli-cations for battery and lightweight alloy.Developing a potential model with high ac-curacy and efficiency is impor-tant for theoretical simulation of lithium materials.Here,we build a deep learning potential(DP)for elemental lithium based on a concurrent-learning scheme and DP representation of the density-functional theory(DFT)potential energy surface(PES),the DP model enables material simulations with close-to DFT accuracy but at much lower computational cost.The simulations show that basic parameters,equation of states,elasticity,defects and surface are consistent with the first principles results.More notably,the liquid radial distribution func-tion based on our DP model is found to match well with experiment data.Our results demon-strate that the developed DP model can be used for the simulation of lithium materials.
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.
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.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Supported by the National Nataral Science Foundation of China(No.39980 0 0 5 )
文摘In this paper are reported the local minimum problem by means of current greedy algorithm for training the empirical potential function of protein folding on 8623 non-native structures of 31 globular proteins and a solution of the problem based upon the simulated annealing algorithm. This simulated annealing algorithm is indispensable for developing and testing highly refined empirical potential functions.
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.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11047176)the Research Foundation of Education Bureau of Hubei Province, China (Grant Nos. Q20111305 and B20101303)
文摘In this paper, the energy, equilibrium geometry, and harmonic frequency of the ground electronic state of PO2 are computed using the B3LYP, B3P86, CCSD(T), and QCISD(T) methods in conjunction with the 6-311++G(3df, 3pd) and cc-pVTZ basis sets. A comparison between the computational results and the experimental values indicates that the B3P86/6-311++G(3df, 3pd) method can give better energy calculation results for the PO2 molecule. It is shown that the ground state of the PO2 molecule has C2v symmetry and its ground electronic state is X2A1. The equilibrium parameters of the structure are Rp-o = 0.1465 am, ZOPO = 134.96°, and the dissociation energy is Ed = 19.218 eV. The bent vibrational frequency Ul = 386 cm-1, symmetric stretching frequency v2 = 1095 cm-1, and asymmetric stretching frequency ua = 1333 em-1 are obtained. On the basis of atomic and molecular reaction statics, a reasonable dissociation limit for the ground state of the PO2 molecule is determined. Then the analytic potential energy function of the PO2 molecule is derived using many-body expansion theory. The potential curves correctly reproduce the configurations and the dissociation energy for the PO2 molecule.
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the National Natural Science Foundation of China (40274044)
文摘A new method on constructing analytical potential energy functions is presented, and then a relatively universal analytical potential energy function for precisely calculating the spectra of 'iatomic molecules and ions is derived. Furthermore, six kinds of common potential energy curves containing three main potential curves i,e. steady state, metastable state and repulsive state are obtained from this potential energy function. Finally, spectroscopic parameters of thirteen diatomic molecules and ions including BeD-X^2∑+, BeT-X^2∑^+ and Na2-X^1∑g^+ etc are calculated by using the potential function, as a consequence, all calculation results are in good agreement with experimental data.
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.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.
文摘We identify a class of transcendental entire maps of finite order, of disjoint-type, satisfying the rapid derivative growth condition. Within this class, we show that there exist hyperbolic transcendental entire maps that generate a large class of potentials which intersect the so-called tame potentials and form a distinct class of potentials. The methods and techniques derived from the thermodynamic formalism are applied to these potentials for transcendental entire maps acting on some subset of the Julia set which is conjugated to the shift map over a code space with a countable alphabet endowed with the euclidean induced metric on the complex plane.
文摘In this paper, a new method on constructing analytical potential energy functions is pre-sented, and from this a analytical potential en-ergy function applied to both neutral diatomic molecules and charged diatomic molecular ions is obtained. This potential energy function in-cludes three dimensionless undetermined pa-rameters which can be determined uniquely by solving linear equations with the experimental spectroscopic parameters of molecules. The solutions of the dimensionless undetermined parameters are real numbers rather than com-plex numbers, this ensures that the analytical potential energy function has extensive uni-versality. Finally, the potential energy function is examined with four kinds of diatomic molecules or ions—homonuclear neutral diatomic mole-cule , and , homonuclear charged diatomic molecular ion , and , heter-nuclear neutral diatomic Molecule , and , heternuclear ch- arged diatomic Molecular ion , and ,as a conseque- nce, good results are obtained.
文摘We show an example of a bounded potential on the half-line obtained as the image of an Inverse Transformation Operator of the Bessel singular potential of the Reduced Radial Schrödinger Equation, and show us the Estimates of the A(α) amplitude.