We report a theoretical study on the rotational spectra of Ar-D232S. The intermolecular po- tential energy surface was transformed from our latest ab initio three-dimensional potential of Ar-H232S. The rotational ener...We report a theoretical study on the rotational spectra of Ar-D232S. The intermolecular po- tential energy surface was transformed from our latest ab initio three-dimensional potential of Ar-H232S. The rotational energy levels and wavefunctions of the complex were calcu- lated by using the radial discrete variable representation/angular finite basis representation method and the Lanczos algorithm. The calculated rotational transition frequencies and structural parameters were found to be in good agreement with the available experimental values.展开更多
The potential energy surface for the electronic ground state of the HXeI molecule is constructed by using the internally contracted multi-reference configuration interaction with the Davidson correction（icMRCI＋Q）me...The potential energy surface for the electronic ground state of the HXeI molecule is constructed by using the internally contracted multi-reference configuration interaction with the Davidson correction（icMRCI＋Q）method and large basis sets. The stabilities and dissociation barriers are identified from the potential energy surfaces.The three-body dissociation channel is found to be the dominate dissociation channel for HXeI.Based on the obtained potentials,vibrational energy levels of HXeI are calculated using the Lanczos algorithm.Our theoretical results are in excellent agreement with the available observed values.展开更多
The potential energy surface for the electronic ground state of the HXeBr molecule is constructed from more than 4200 ab initio points calculated using the internally contracted multi-reference configuration interacti...The potential energy surface for the electronic ground state of the HXeBr molecule is constructed from more than 4200 ab initio points calculated using the internally contracted multi-reference configuration interaction method with the Davidson correction （icMRCI ＋ Q）. The stabilities and dissociation barriers are identified from the potential energy surface. The three-body dissociation channel is found to be the dominant dissociation channel for HXeBr. Low-lying vibrational energy levels of HXeBr calculated using the Lanczos algorithm are found to be in good agreement with the available experimental band origins.展开更多
The formation of oligomeric hydrogen peroxide triggered by Criegee intermediate maybe contributes significantly to the formation and growth of secondary organic aerosol(SOA).However,to date,the reactivity of C2 Criege...The formation of oligomeric hydrogen peroxide triggered by Criegee intermediate maybe contributes significantly to the formation and growth of secondary organic aerosol(SOA).However,to date,the reactivity of C2 Criegee intermediates(CH_(3)CHOO)in areas contaminated with acidic gas remains poorly understood.Herein,high-level quantum chemical calculations and Born-Oppenheimer molecular dynamics(BOMD)simulations are used to explore the reaction of CH_(3)CHOO and H_(2)SO_(4)both in the gas phase and at the airwater interface.In the gas phase,the addition reaction of CH_(3)CHOO with H_(2)SO_(4)to generate CH_(3)HC(OOH)OSO_(3)H(HPES)is near-barrierless,regardless of the presence of water molecules.BOMD simulations showthat the reaction at the air-water interface is even faster than that in the gas phase.Further calculations reveal that the HPES has a tendency to aggregate with sulfuric acids,ammonias,and water molecules to form stable clusters,meanwhile the oligomerization reaction of CH_(3)CHOO with HPES in the gas phase is both thermochemically and kinetically favored.Also,it is noted that the interfacial HPES−ion can attract H_(2)SO_(4),NH_(3),(COOH)_(2)and HNO_(3)for particle formation from the gas phase to the water surface.Thus,the results of this work not only elucidate the high atmospheric reactivity of C2 Criegee intermediates in polluted regions,but also deepen our understanding of the formation process of atmospheric SOA induced by Criegee intermediates.展开更多
A function projective synchronization of two identical hyperchaotic systems is defined and the theorem of sufficient condition is given. Based on the active control method and symbolic computation Maple, the scheme of...A function projective synchronization of two identical hyperchaotic systems is defined and the theorem of sufficient condition is given. Based on the active control method and symbolic computation Maple, the scheme of function projective synchronization is developed to synchronize the two identical new hyperchaotic systems constructed by Yan up to a scaling function matrix with different initial values. Numerical simulations are used to verify the effectiveness of the scheme.展开更多
Coexistence of attractors with striking characteristics is observed in this work, where a stable period-5 attractor coexists successively with chaotic band-ll, period-6, chaotic band-12 and band-6 attractors. They are...Coexistence of attractors with striking characteristics is observed in this work, where a stable period-5 attractor coexists successively with chaotic band-ll, period-6, chaotic band-12 and band-6 attractors. They are induced by dif- ferent mechanisms due to the interaction between the discontinuity and the non-invertibility. A characteristic boundary collision bifurcation, is observed. The critical conditions are obtained both analytically and numerically.展开更多
Benchmark calculations on the molar atomization enthalpy, geometry, and vibrational frequencies of uranium hexafluoride （UF6） have been performed by using relativistic density functional theory （DFT） with various ...Benchmark calculations on the molar atomization enthalpy, geometry, and vibrational frequencies of uranium hexafluoride （UF6） have been performed by using relativistic density functional theory （DFT） with various levels of relativistic effects, different types of basis sets, and exchange-correlation functionals. Scalar relativistic effects are shown to be critical for the structural properties. The spin-orbit coupling effects are important for the calculated energies, but are much less important for other calculated ground-state properties of closed-shell UF6. We conclude through systematic investigations that ZORA- and RECP-based relativistic DPT methods are both appropriate for incorporating relativistic effects. Comparisons of different types of basis sets （Slater, Gaussian, and plane-wave types） and various levels of theoretical approximation of the exchange-correlation functionals were also made.展开更多
By backstepping control law and the active control method, adaptive function projective synchronization of 2D and 3D discrete-time chaotic systems with Uncertain parameters are investigated. To illustrate the effectiv...By backstepping control law and the active control method, adaptive function projective synchronization of 2D and 3D discrete-time chaotic systems with Uncertain parameters are investigated. To illustrate the effectiveness of the new scheme, some numerical examples are given.展开更多
In this paper, the Adomian decomposition method is developed for the numerical solutions of a class of nonlinear evolution equations with nonlinear term of any order, utt＋auxx ＋ bu ＋ cu^p＋ du^2p-1=0, which contain...In this paper, the Adomian decomposition method is developed for the numerical solutions of a class of nonlinear evolution equations with nonlinear term of any order, utt＋auxx ＋ bu ＋ cu^p＋ du^2p-1=0, which contains some important famous equations. When setting the initial conditions in different forms, some new generalized numerical solutions： numerical hyperbolic solutions, numerical doubly periodic solutions are obtained. The numerical solutions are compared with exact solutions. The scheme is tested by choosing different values of p, positive and negative, integer and fraction, to illustrate the efficiency of the ADM method and the generalization of the solutions.展开更多
The density functional theory was employed to investigate the adsorption of Nin(n=1–4)on the perfect and O-defect CuAl2O4 surfaces.The computational results show that for single Ni atom on the perfect spinel(100)surf...The density functional theory was employed to investigate the adsorption of Nin(n=1–4)on the perfect and O-defect CuAl2O4 surfaces.The computational results show that for single Ni atom on the perfect spinel(100)surface,the adsorption energy is-5.30 eV,much larger than Ni on other CuAl2O4 surfaces.The adsorption of Nin(n=1–4)absorbed on the O-defect CuAl2O4(100)surface is less stable than on the perfect CuAl2O4(100)surface.However,the adsorption energy for Nin(n=1–4)on the O-defect CuAl2O4(110)surface is close to on the perfect CuAl2O4(110)surface.Bader charge and partial density of states(PDOS)analysis revel that the adsorption of Ni on the CuAl2O4 spinel surface is accompanied by charge transfer from the metal to the support.The growth and aggregations analysis show that the general growth and aggregation ability for Nin clusters follow the order:gas phase>γ-Al2O3(110)>CuAl2O4(110)>CuAl2O4(100).This result can give reasonable explanations for the experimental phenomenon that Ni supported on the CuAl2O4 spinel performs much better stability than on theγ-Al_(2)O_(3).展开更多
This paper investigates an important high-dimensional model in the atmospheric and oceanic dynamics-（3＋1）- dimensional nonlinear baroclinic potential vorticity equation by the classical Lie group method. Its symmet...This paper investigates an important high-dimensional model in the atmospheric and oceanic dynamics-（3＋1）- dimensional nonlinear baroclinic potential vorticity equation by the classical Lie group method. Its symmetry algebra, symmetry group and group-invariant solutions are analysed. Otherwise, some exact explicit solutions are obtained from the corresponding （2＋1）-dimensional equation, the inviscid barotropic nondivergent vorticy equation. To show the properties and characters of these solutions, some plots as well as their possible physical meanings of the atmospheric circulation are given out.展开更多
Based on the general direct method developed by Lou et al. [J. Phys. A： Math. Gen. 38 （2005） L129], the symmetry group theorem is obtained, from that both the Lie point groups and the non-Lie symmetry groups of the...Based on the general direct method developed by Lou et al. [J. Phys. A： Math. Gen. 38 （2005） L129], the symmetry group theorem is obtained, from that both the Lie point groups and the non-Lie symmetry groups of the Konopelchenk-Dubrovsky （KD） equation are obtained. From the theorem, some exact solutions of KD equation are derived from a simple travelling wave solution and a multi-soliton solution.展开更多
The effects of Gaussian white noise and Gaussian colored noise on the periodic orbits of period-5（P-5） and period-6（P-6） in their coexisting domain of a piecewise linear map are investigated numerically.The probab...The effects of Gaussian white noise and Gaussian colored noise on the periodic orbits of period-5（P-5） and period-6（P-6） in their coexisting domain of a piecewise linear map are investigated numerically.The probability densities of some orbits are calculated.When the noise intensity is D = 0.0001,only the orbits of P-5 exist,and the coexisting phenomenon is destroyed.On the other hand,the self-correlation time τ of the colored noise also affects the coexisting phenomenon.When τc〈τ〈τc,only the orbits of P-5 appear,and the stability of the orbits of P-5 is enhanced.However,when τ〉τc（τc and τc are critical values）,only the orbits of P-6 exist,and the stability of the P-6 orbits is enhanced greatly.When τ〈τc,the orbits of P-5 and P-6 coexist,but the stability of the P-5 orbits is enhanced and that of P-6 is weakened with τ increasing.展开更多
Accurate and efficient integration of the equations of motion is indispensable for molecular dynamics(MD)simulations.Despite the massive use of the conventional leapfrog(LF)integrator in modern computational tools wit...Accurate and efficient integration of the equations of motion is indispensable for molecular dynamics(MD)simulations.Despite the massive use of the conventional leapfrog(LF)integrator in modern computational tools within the framework of MD propagation,further development for better performance is still possible.The alternative version of LF in the middle thermostat scheme(LFmiddle)achieves a higher order of accuracy and efficiency and maintains stable dynamics even with the integration time stepsize extended by several folds.In this work,we perform a benchmark test of the two integrators(LF and LF-middle)in extensive conventional and enhanced sampling simulations,aiming at quantifying the time-stepsizeinduced variations of global properties(e.g.,detailed potential energy terms)as well as of local observables(e.g.,free energy changes or bondlengths)in practical simulations of complex systems.The test set is composed of six chemically and biologically relevant systems,including the conformational change of dihedral flipping in the N-methylacetamide and an AT(AdenineThymine)tract,the intra-molecular proton transfer inside malonaldehyde,the binding free energy calculations of benzene and phenol targeting T4 lysozyme L99A,the hydroxyl bond variations in ethaline deep eutectic solvent,and the potential energy of the blue-light using flavin photoreceptor.It is observed that the time-step-induced error is smaller for the LFmiddle scheme.The outperformance of LF-middle over the conventional LF integrator is much more significant for global properties than local observables.Overall,the current work demonstrates that the LF-middle scheme should be preferably applied to obtain accurate thermodynamics in the simulation of practical chemical and biological systems.展开更多
One objective of developing machine learning(ML)-based material models is to integrate them with well-established numerical methods to solve boundary value problems(BVPs).In the family of ML models,recurrent neural ne...One objective of developing machine learning(ML)-based material models is to integrate them with well-established numerical methods to solve boundary value problems(BVPs).In the family of ML models,recurrent neural networks(RNNs)have been extensively applied to capture history-dependent constitutive responses of granular materials,but these multiple-step-based neural networks are neither sufficiently efficient nor aligned with the standard finite element method(FEM).Single-step-based neural networks like the multi-layer perceptron(MLP)are an alternative to bypass the above issues but have to introduce some internal variables to encode complex loading histories.In this work,one novel Frobenius norm-based internal variable,together with the Fourier layer and residual architectureenhanced MLP model,is crafted to replicate the history-dependent constitutive features of representative volume element(RVE)for granular materials.The obtained ML models are then seamlessly embedded into the FEM to solve the BVP of a biaxial compression case and a rigid strip footing case.The obtained solutions are comparable to results from the FEM-DEM multiscale modelling but achieve significantly improved efficiency.The results demonstrate the applicability of the proposed internal variable in enabling MLP to capture highly nonlinear constitutive responses of granular materials.展开更多
Full-dimensional adiabatic potential energy surfaces of the electronic ground state X and nine excited states A,I,B,C,D,D',D'',E' and F of H_(2)O molecule are developed at the level of internally contr...Full-dimensional adiabatic potential energy surfaces of the electronic ground state X and nine excited states A,I,B,C,D,D',D'',E' and F of H_(2)O molecule are developed at the level of internally contracted multireference configuration interaction with the Davidson correction.The potential energy surfaces are fitted by using Gaussian process regression combining permutation invariant polynomials.With a large selected active space and extra diffuse basis set to describe these Rydberg states,the calculated vertical excited energies and equilibrium geometries are in good agreement with the previous theoretical and experimental values.Compared with the well-investigated photodissociation of the first three low-lying states,both theoretical and experimental studies on higher states are still limited.In this work,we focus on all the three channels of the highly excited state,which are directly involved in the vacuum ultraviolet photodissociation of water.In particular,some conical intersections of D-E',E'-F,A-I and I-C states are clearly illustrated for the first time based on the newly developed potential energy surfaces(PESs).The nonadiabatic dissociation pathways for these excited states are discussed in detail,which may shed light on the photodissociation mechanisms for these highly excited states.展开更多
Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart.We use the constraint phase space devel...Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart.We use the constraint phase space developed in J.Chem.Phys.145,204105(2016);151,024105(2019);J.Phys.Chem.Lett.12,2496(2021),non-covariant phase space functions,time-dependent weight functions,and time-dependent normalization factors to construct a novel class of phase space representations of the exact population dynamics of the two-state quantum system.The equations of motion of the trajectory on constraint phase space are isomorphic to the time-dependent Schrödinger equation.The contribution of each trajectory to the integral expression for the population dynamics is always positive semi-definite.We also prove that the triangle window function approach,albeit proposed as a heuristic empirical model in J.Chem.Phys.145,144108(2016),is related to a special case of the novel class and leads to an isomorphic representation of the exact population dynamics of the two-state quantum system.展开更多
By Lie symmetry method, the Lie point symmetries and its Kac-Moody-Virasoro (KMV) symmetry algebra of (2+1)-dimensional dispersive long-wave equation (DLWE) are obtained, and the finite transformation of DLWE is given...By Lie symmetry method, the Lie point symmetries and its Kac-Moody-Virasoro (KMV) symmetry algebra of (2+1)-dimensional dispersive long-wave equation (DLWE) are obtained, and the finite transformation of DLWE is given by symmetry group direct method, which can recover Lie point symmetries. Then KMV symmetry algebra of DLWE with arbitrary order invariant is also obtained. On basis of this algebra the group invariant solutions and similarity reductions are also derived.展开更多
Methane hydrates(MHs)play important roles in the fields of chemistry,energy,environmental sciences,etc.In this work,we employ the generalized energy-based fragmentation(GEBF)approach to compute the binding energies an...Methane hydrates(MHs)play important roles in the fields of chemistry,energy,environmental sciences,etc.In this work,we employ the generalized energy-based fragmentation(GEBF)approach to compute the binding energies and Raman spectra of various MH clusters.For the GEBF binding energies of various MH clusters,we first evaluated the various functionals of density functional theory(DFT),and compared them with the results of explicitly correlated combined coupled-cluster singles and doubles with noniterative triples corrections[CCSD(T)(F12^(*))]method.Our results show that the two best functionals are B3PW91-D3 and B97D,with mean absolute errors of only 0.27 and 0.47 kcal/mol,respectively.Then we employed GEBF-B3PW91-D3 to obtain the structures and Raman spectra of MH clusters with mono-and double-cages.Our results show that the B3PW91-D3 functional can well reproduce the experimental C-H stretching Raman spectra of methane in MH crystals,with errors less than 3 cm^(-1).As the size of the water cages increased,the C-H stretching Raman spectra exhibited a redshift,which is also in agreement with the experimental“loose cage-tight cage”model.In addition,the Raman spectra are only slightly affected by the neighboring environment(cages)of methane.The blueshifts of C-H stretching frequencies are no larger than 3 cm^(-1) for CH_(4) from monocages to doublecages.The Raman spectra of the MH clusters could be combined with the experimental Raman spectra to investigate the structures of methane hydrates in the ocean bottom or in the interior of interstellar icy bodies.Based on the B3PW91-D3 or B97D functional and machine learning models,molecular dynamics simulations could be applied to the nucleation and growth mechanisms,and the phase transitions of methane hydrates.展开更多
文摘We report a theoretical study on the rotational spectra of Ar-D232S. The intermolecular po- tential energy surface was transformed from our latest ab initio three-dimensional potential of Ar-H232S. The rotational energy levels and wavefunctions of the complex were calcu- lated by using the radial discrete variable representation/angular finite basis representation method and the Lanczos algorithm. The calculated rotational transition frequencies and structural parameters were found to be in good agreement with the available experimental values.
文摘The potential energy surface for the electronic ground state of the HXeI molecule is constructed by using the internally contracted multi-reference configuration interaction with the Davidson correction（icMRCI＋Q）method and large basis sets. The stabilities and dissociation barriers are identified from the potential energy surfaces.The three-body dissociation channel is found to be the dominate dissociation channel for HXeI.Based on the obtained potentials,vibrational energy levels of HXeI are calculated using the Lanczos algorithm.Our theoretical results are in excellent agreement with the available observed values.
文摘The potential energy surface for the electronic ground state of the HXeBr molecule is constructed from more than 4200 ab initio points calculated using the internally contracted multi-reference configuration interaction method with the Davidson correction （icMRCI ＋ Q）. The stabilities and dissociation barriers are identified from the potential energy surface. The three-body dissociation channel is found to be the dominant dissociation channel for HXeBr. Low-lying vibrational energy levels of HXeBr calculated using the Lanczos algorithm are found to be in good agreement with the available experimental band origins.
基金supported by the National Natural Science Foundation of China(Nos.22073059 and 22203052)the Natural Science Foundation of Shaanxi Province(No.2022JM-060)+1 种基金the Education Department of Shaanxi Provincial Government(No.23JC023)the Key Cultivation Project of Shaanxi University of Technology(No.SLG2101)。
文摘The formation of oligomeric hydrogen peroxide triggered by Criegee intermediate maybe contributes significantly to the formation and growth of secondary organic aerosol(SOA).However,to date,the reactivity of C2 Criegee intermediates(CH_(3)CHOO)in areas contaminated with acidic gas remains poorly understood.Herein,high-level quantum chemical calculations and Born-Oppenheimer molecular dynamics(BOMD)simulations are used to explore the reaction of CH_(3)CHOO and H_(2)SO_(4)both in the gas phase and at the airwater interface.In the gas phase,the addition reaction of CH_(3)CHOO with H_(2)SO_(4)to generate CH_(3)HC(OOH)OSO_(3)H(HPES)is near-barrierless,regardless of the presence of water molecules.BOMD simulations showthat the reaction at the air-water interface is even faster than that in the gas phase.Further calculations reveal that the HPES has a tendency to aggregate with sulfuric acids,ammonias,and water molecules to form stable clusters,meanwhile the oligomerization reaction of CH_(3)CHOO with HPES in the gas phase is both thermochemically and kinetically favored.Also,it is noted that the interfacial HPES−ion can attract H_(2)SO_(4),NH_(3),(COOH)_(2)and HNO_(3)for particle formation from the gas phase to the water surface.Thus,the results of this work not only elucidate the high atmospheric reactivity of C2 Criegee intermediates in polluted regions,but also deepen our understanding of the formation process of atmospheric SOA induced by Criegee intermediates.
基金＊The project supported by the Natural Science Foundations of Zhejiang Province under Grant No. Y604056 and the Doctoral Foundation of Ningbo City under Grant No. 2005A61030
文摘A function projective synchronization of two identical hyperchaotic systems is defined and the theorem of sufficient condition is given. Based on the active control method and symbolic computation Maple, the scheme of function projective synchronization is developed to synchronize the two identical new hyperchaotic systems constructed by Yan up to a scaling function matrix with different initial values. Numerical simulations are used to verify the effectiveness of the scheme.
基金Project supported by the National Natural Science Foundation of China (Grant No 10275053)
文摘Coexistence of attractors with striking characteristics is observed in this work, where a stable period-5 attractor coexists successively with chaotic band-ll, period-6, chaotic band-12 and band-6 attractors. They are induced by dif- ferent mechanisms due to the interaction between the discontinuity and the non-invertibility. A characteristic boundary collision bifurcation, is observed. The critical conditions are obtained both analytically and numerically.
基金NKBRSF (2006CB932305, 2007CB815200) and NNSFC (20525104).The calculations were partially performed using an HP Itanium2 cluster at Tsinghua National Laboratory for Information Science and Technology
文摘Benchmark calculations on the molar atomization enthalpy, geometry, and vibrational frequencies of uranium hexafluoride （UF6） have been performed by using relativistic density functional theory （DFT） with various levels of relativistic effects, different types of basis sets, and exchange-correlation functionals. Scalar relativistic effects are shown to be critical for the structural properties. The spin-orbit coupling effects are important for the calculated energies, but are much less important for other calculated ground-state properties of closed-shell UF6. We conclude through systematic investigations that ZORA- and RECP-based relativistic DPT methods are both appropriate for incorporating relativistic effects. Comparisons of different types of basis sets （Slater, Gaussian, and plane-wave types） and various levels of theoretical approximation of the exchange-correlation functionals were also made.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10747141 and 10735030, Ningbo NSF under Grant No 2007A610049, the Shanghai Leading Academic Discipline Project （No B412）, the Programme for Changjiang Scholars and Innovative Research Team in University （PCSIRT） under Grant No 0734, and the K. C. Wong Magna Fund of Ningbo University.
文摘By backstepping control law and the active control method, adaptive function projective synchronization of 2D and 3D discrete-time chaotic systems with Uncertain parameters are investigated. To illustrate the effectiveness of the new scheme, some numerical examples are given.
基金supported by National Natural Science Foundation of China under Grant No.10735030Natural Science Foundation of Zhejiang Province of China under Grant No.Y604056Doctoral Science Foundation of Ningbo City under Grant No.2005A61030
文摘In this paper, the Adomian decomposition method is developed for the numerical solutions of a class of nonlinear evolution equations with nonlinear term of any order, utt＋auxx ＋ bu ＋ cu^p＋ du^2p-1=0, which contains some important famous equations. When setting the initial conditions in different forms, some new generalized numerical solutions： numerical hyperbolic solutions, numerical doubly periodic solutions are obtained. The numerical solutions are compared with exact solutions. The scheme is tested by choosing different values of p, positive and negative, integer and fraction, to illustrate the efficiency of the ADM method and the generalization of the solutions.
基金the National Natural Science Foundation of China(Nos.21763018,21673270,21503254 and 21875096)the Natural Science Foundation of jiangxi Province,China(Nos.20181BAB203016,20181BCD40004)
文摘The density functional theory was employed to investigate the adsorption of Nin(n=1–4)on the perfect and O-defect CuAl2O4 surfaces.The computational results show that for single Ni atom on the perfect spinel(100)surface,the adsorption energy is-5.30 eV,much larger than Ni on other CuAl2O4 surfaces.The adsorption of Nin(n=1–4)absorbed on the O-defect CuAl2O4(100)surface is less stable than on the perfect CuAl2O4(100)surface.However,the adsorption energy for Nin(n=1–4)on the O-defect CuAl2O4(110)surface is close to on the perfect CuAl2O4(110)surface.Bader charge and partial density of states(PDOS)analysis revel that the adsorption of Ni on the CuAl2O4 spinel surface is accompanied by charge transfer from the metal to the support.The growth and aggregations analysis show that the general growth and aggregation ability for Nin clusters follow the order:gas phase>γ-Al2O3(110)>CuAl2O4(110)>CuAl2O4(100).This result can give reasonable explanations for the experimental phenomenon that Ni supported on the CuAl2O4 spinel performs much better stability than on theγ-Al_(2)O_(3).
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10735030,90718041 and 40975038)Shanghai Leading Academic Discipline Project(Grant No.B412)Program for Changjiang Scholars and Innovative Research Team in University(Grant No.IRT0734)
文摘This paper investigates an important high-dimensional model in the atmospheric and oceanic dynamics-（3＋1）- dimensional nonlinear baroclinic potential vorticity equation by the classical Lie group method. Its symmetry algebra, symmetry group and group-invariant solutions are analysed. Otherwise, some exact explicit solutions are obtained from the corresponding （2＋1）-dimensional equation, the inviscid barotropic nondivergent vorticy equation. To show the properties and characters of these solutions, some plots as well as their possible physical meanings of the atmospheric circulation are given out.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10747141 and 10735030Zhejiang Provincial Natural Science Foundations of China under Grant No.605408+3 种基金Ningbo Natural Science Foundation under Grant Nos.2007A610049 and 2008A610017National Basic Research Program of China (973 Program 2007CB814800)Shanghai Leading Academic Discipline Project under Grant No.B412K.C.Wong Magna Fund in Ningbo University
文摘Based on the general direct method developed by Lou et al. [J. Phys. A： Math. Gen. 38 （2005） L129], the symmetry group theorem is obtained, from that both the Lie point groups and the non-Lie symmetry groups of the Konopelchenk-Dubrovsky （KD） equation are obtained. From the theorem, some exact solutions of KD equation are derived from a simple travelling wave solution and a multi-soliton solution.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10875076)the Science Foundation of the Education Bureau of Shaanxi Province,China (Grant No. 12JK0962)the Science Foundation of Baoji University of Science and Arts of China (Grant No. ZK11053)
文摘The effects of Gaussian white noise and Gaussian colored noise on the periodic orbits of period-5（P-5） and period-6（P-6） in their coexisting domain of a piecewise linear map are investigated numerically.The probability densities of some orbits are calculated.When the noise intensity is D = 0.0001,only the orbits of P-5 exist,and the coexisting phenomenon is destroyed.On the other hand,the self-correlation time τ of the colored noise also affects the coexisting phenomenon.When τc〈τ〈τc,only the orbits of P-5 appear,and the stability of the orbits of P-5 is enhanced.However,when τ〉τc（τc and τc are critical values）,only the orbits of P-6 exist,and the stability of the P-6 orbits is enhanced greatly.When τ〈τc,the orbits of P-5 and P-6 coexist,but the stability of the P-5 orbits is enhanced and that of P-6 is weakened with τ increasing.
基金supported by the National Natural Science Foundation of China(No.21961142017)the Ministry of Science and Technology of China(No.2017YFA0204901)。
文摘Accurate and efficient integration of the equations of motion is indispensable for molecular dynamics(MD)simulations.Despite the massive use of the conventional leapfrog(LF)integrator in modern computational tools within the framework of MD propagation,further development for better performance is still possible.The alternative version of LF in the middle thermostat scheme(LFmiddle)achieves a higher order of accuracy and efficiency and maintains stable dynamics even with the integration time stepsize extended by several folds.In this work,we perform a benchmark test of the two integrators(LF and LF-middle)in extensive conventional and enhanced sampling simulations,aiming at quantifying the time-stepsizeinduced variations of global properties(e.g.,detailed potential energy terms)as well as of local observables(e.g.,free energy changes or bondlengths)in practical simulations of complex systems.The test set is composed of six chemically and biologically relevant systems,including the conformational change of dihedral flipping in the N-methylacetamide and an AT(AdenineThymine)tract,the intra-molecular proton transfer inside malonaldehyde,the binding free energy calculations of benzene and phenol targeting T4 lysozyme L99A,the hydroxyl bond variations in ethaline deep eutectic solvent,and the potential energy of the blue-light using flavin photoreceptor.It is observed that the time-step-induced error is smaller for the LFmiddle scheme.The outperformance of LF-middle over the conventional LF integrator is much more significant for global properties than local observables.Overall,the current work demonstrates that the LF-middle scheme should be preferably applied to obtain accurate thermodynamics in the simulation of practical chemical and biological systems.
基金supported by the National Natural Science Foundation of China(NSFC)(Grant No.12072217).
文摘One objective of developing machine learning(ML)-based material models is to integrate them with well-established numerical methods to solve boundary value problems(BVPs).In the family of ML models,recurrent neural networks(RNNs)have been extensively applied to capture history-dependent constitutive responses of granular materials,but these multiple-step-based neural networks are neither sufficiently efficient nor aligned with the standard finite element method(FEM).Single-step-based neural networks like the multi-layer perceptron(MLP)are an alternative to bypass the above issues but have to introduce some internal variables to encode complex loading histories.In this work,one novel Frobenius norm-based internal variable,together with the Fourier layer and residual architectureenhanced MLP model,is crafted to replicate the history-dependent constitutive features of representative volume element(RVE)for granular materials.The obtained ML models are then seamlessly embedded into the FEM to solve the BVP of a biaxial compression case and a rigid strip footing case.The obtained solutions are comparable to results from the FEM-DEM multiscale modelling but achieve significantly improved efficiency.The results demonstrate the applicability of the proposed internal variable in enabling MLP to capture highly nonlinear constitutive responses of granular materials.
基金supported by the National Natural Science Foundation of China(No.12047532,No.21733006,No.22073042,and No.22122302)。
文摘Full-dimensional adiabatic potential energy surfaces of the electronic ground state X and nine excited states A,I,B,C,D,D',D'',E' and F of H_(2)O molecule are developed at the level of internally contracted multireference configuration interaction with the Davidson correction.The potential energy surfaces are fitted by using Gaussian process regression combining permutation invariant polynomials.With a large selected active space and extra diffuse basis set to describe these Rydberg states,the calculated vertical excited energies and equilibrium geometries are in good agreement with the previous theoretical and experimental values.Compared with the well-investigated photodissociation of the first three low-lying states,both theoretical and experimental studies on higher states are still limited.In this work,we focus on all the three channels of the highly excited state,which are directly involved in the vacuum ultraviolet photodissociation of water.In particular,some conical intersections of D-E',E'-F,A-I and I-C states are clearly illustrated for the first time based on the newly developed potential energy surfaces(PESs).The nonadiabatic dissociation pathways for these excited states are discussed in detail,which may shed light on the photodissociation mechanisms for these highly excited states.
文摘Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart.We use the constraint phase space developed in J.Chem.Phys.145,204105(2016);151,024105(2019);J.Phys.Chem.Lett.12,2496(2021),non-covariant phase space functions,time-dependent weight functions,and time-dependent normalization factors to construct a novel class of phase space representations of the exact population dynamics of the two-state quantum system.The equations of motion of the trajectory on constraint phase space are isomorphic to the time-dependent Schrödinger equation.The contribution of each trajectory to the integral expression for the population dynamics is always positive semi-definite.We also prove that the triangle window function approach,albeit proposed as a heuristic empirical model in J.Chem.Phys.145,144108(2016),is related to a special case of the novel class and leads to an isomorphic representation of the exact population dynamics of the two-state quantum system.
基金Supported by the Natural Science Foundation of China under Grant No. 10735030Ningbo Natural Science Foundation under Grant No. 2008A610017+3 种基金National Basic Research Program of China (973 Program 2007CB814800)Shanghai Leading Academic Discipline Project under Grant No. B412Program for Changjiang Scholars and Innovative Research Team in University (IRT0734)K.C. Wong Magna Fund in Ningbo University
文摘By Lie symmetry method, the Lie point symmetries and its Kac-Moody-Virasoro (KMV) symmetry algebra of (2+1)-dimensional dispersive long-wave equation (DLWE) are obtained, and the finite transformation of DLWE is given by symmetry group direct method, which can recover Lie point symmetries. Then KMV symmetry algebra of DLWE with arbitrary order invariant is also obtained. On basis of this algebra the group invariant solutions and similarity reductions are also derived.
基金supported by the National Natural Science Foundation of China(No.22033004,No.21833002,No.21873046,and No.22073043)the Natural Science Foundation of Jiangsu Province(No.BK20210175)。
文摘Methane hydrates(MHs)play important roles in the fields of chemistry,energy,environmental sciences,etc.In this work,we employ the generalized energy-based fragmentation(GEBF)approach to compute the binding energies and Raman spectra of various MH clusters.For the GEBF binding energies of various MH clusters,we first evaluated the various functionals of density functional theory(DFT),and compared them with the results of explicitly correlated combined coupled-cluster singles and doubles with noniterative triples corrections[CCSD(T)(F12^(*))]method.Our results show that the two best functionals are B3PW91-D3 and B97D,with mean absolute errors of only 0.27 and 0.47 kcal/mol,respectively.Then we employed GEBF-B3PW91-D3 to obtain the structures and Raman spectra of MH clusters with mono-and double-cages.Our results show that the B3PW91-D3 functional can well reproduce the experimental C-H stretching Raman spectra of methane in MH crystals,with errors less than 3 cm^(-1).As the size of the water cages increased,the C-H stretching Raman spectra exhibited a redshift,which is also in agreement with the experimental“loose cage-tight cage”model.In addition,the Raman spectra are only slightly affected by the neighboring environment(cages)of methane.The blueshifts of C-H stretching frequencies are no larger than 3 cm^(-1) for CH_(4) from monocages to doublecages.The Raman spectra of the MH clusters could be combined with the experimental Raman spectra to investigate the structures of methane hydrates in the ocean bottom or in the interior of interstellar icy bodies.Based on the B3PW91-D3 or B97D functional and machine learning models,molecular dynamics simulations could be applied to the nucleation and growth mechanisms,and the phase transitions of methane hydrates.
