Kr-CS体系势能面及束缚态能级的理论研究

本文利用从头算方法首次计算得到Kr原子与CS分子在“冻结核”近似下的相互作用离散势能点, 并拟合得到二维势能面. 该体系在R=7.76 a0, =111.4o处存在一个近T型的全域极小值, 势能值为-178.54 cm-1, 整个势能面表现较强的各向异性. 在该势能面基础上数值求解体系的薛定谔方程, 计算得到体系J ≤ 15的束缚态能级及微波谱跃迁频率.     

Kr原子与CS分子相互作用势及束缚态的理论研究

本文利用从头算方法首次计算得到Kr原子与CS分子在"冻结核"近似下的相互作用离散势能点,并拟合得到二维势能面.该体系在R=7.76 a_0,θ=111.4°处存在一个近T型的全域极小值,势能值为-178.54 cm~(-1),整个势能面表现较强的各向异性.在该势能面基础上数值求解体系的薛定谔方程,计算得到体系J≤15的束缚态能级及微波谱跃迁频率.     

Kr原子与CS分子相互作用势及束缚态的理论研究

本文利用从头算方法首次计算得到Kr原子与CS分子在“冻结核”近似下的相互作用离散势能点,并拟合得到二维势能面.该体系在R=7.76 a_0,θ=111.4°处存在一个近T型的全域极小值,势能值为-178.54 cm~(-1),整个势能面表现较强的各向异性.在该势能面基础上数值求解体系的薛定谔方程,计算得到体系J≤15的束缚态能级及微波谱跃迁频率.     

S2O激发态(C1A'')振动光谱及势能面的一种代数研究

利用代数方法研究了非对称弯曲三原子分子S2O分子处于C1A'电子态的能谱及其稳定构型下的势能面,通过对30条光谱数据的拟和得到的rms误差为2.40 cm-1.结果表明,利用此代数Hamiltonian很好的实现了能级再现,它预测了振动总量子数达到20的全部振动能级,同时我们计算了分子的解离能与力常数.通过与实验值比较证明了这种方法在计算这类分子的有效性.     

非线型三原子分子势能面的Lie代数方法

利用Lie代数方法得到三原子分子的代数Hamiltonian ,通过对光谱数据的拟合确定其展开系数 ,再用相干态得到代数Hamiltonian的经典极限 ,从而得到三原子分子的势能面 .以H2 O分子为例进行了计算 ,其理论值与实验结果一致. The algebraic Hamiltonian for a triatomic molecule can be obtained by using dynamical Lie algebra method (the expansion coefficients are obtained by fitting spectroscopic data). Triatomic molecular potential energy surface (PES) is obtained by using coherent state to take the classical limits of algebraic Hamiltonian. This PES is applied to H 2O molecule, and the deduced force constant is in good agreement with the experimental data.     

S2O分子高激发振动光谱及势能面的代数研究

本文利用代数方法研究了非对称弯曲三原子分子S2O分子处于C～1A′电子态的能谱及其稳定构型下的势能面,通过对30条光谱数据的拟和得到的RMS误差为2.40 cm-1.结果表明,利用此代数Hamiltonian很好的实现了能级再现,它预测了振动总量子数达到20的全部振动能级(在本文中我们只列举到v= 9),同时我们计算了分子的解离能与力常数.通过与实验值比较证明了这种方法在计算这类分子的有效性.     

S_2O激发态(~1A′)振动光谱及势能面的一种代数研究(英文)

利用代数方法研究了非对称弯曲三原子分子S_2O分子处于(?)~1A′电子态的能谱及其稳定构型下的势能面,通过对30条光谱数据的拟和得到的rms误差为2.40 cm~(-1)。结果表明,利用此代数Hamiltonian很好的实现了能级再现,它预测了振动总量子数达到20的全部振动能级,同时我们计算了分子的解离能与力常数。通过与实验值比较证明了这种方法在计算这类分子的有效性。     

He-HI复合物势能面及微分散射截面的理论研究

采用超分子单双迭代(包括非迭代三重激发)耦合簇理论CCSD(T)方法和由键函数3s3p2d1f组成的大基组, 计算得到了基态He-HI复合物相互作用的全程势能面. 该势能面上存在2个势阱, 分别对应于线性He-I-H和He-H-I构型, 势阱深度分别为4.473和2.996meV, He原子到HI分子质心的距离R分别为0.363和0.442nm. 使用Barker, Fisher和Watts提出的BFW势函数拟合计算得到的相互作用能数据, 获得了He原子与HI分子相互作用势的解析表达式. 在 关键词： He-HI复合物 势能面 微分散射截面     

碱金属Li原子与CO分子体系相互作用势从头计算研究

采用三重激发项校正CCSD的CCSD(T)方法和AUG-CC-PVnZ(n=2,3,4)基组,优化了CO基态分子结构,并计算了碱金属Li原子与CO分子的相互作用势,共1010个构型势能点得到体系的势能面.结果表明:同一方法下,不同基组得到的CO基态分子的键长、能量等均与实验符合很好.Li-CO势能面体现较小的各向异性势,存在两个势阱,且都为非严格T型结构;基组重叠误差(BSSE)对相互作用势的影响比较明显,采用CP方法(Counterposie method)消除基组重叠误差,不同基组计算的相互作用势显示较好一致.体系各项异性势势阱值远高于CO基态分子转动常数,使得碰撞产生强烈的非弹性碰撞,这将阻止协同冷却制备超冷分子.     

四原子分子的转动-振动能级的李代数处理-Ⅰ线性X_2Y_2型分子

本大利用李代数方法与二次量子化理论计算了四原子分子的转动—振动能级.结果表明,如果将分子的转动与振动均看作是谐振子,则可以导出线性X_2V_2型分子的转动—振动能级公式。     

The potential energy surface and chaos in 2D Hamiltonian systems

We provide a new insight into the relationship between the geometric property of the potential energy surface and chaotic behavior of 2D Hamiltonian dynamical systems, and give an indicator of chaos based on the geometric property of the potential energy surface by defining Mean Convex Index (MCI). We also discuss a model of unstable Hamiltonian in detail, and show our results in good agreement with HBLSL's (Horwitz, Ben Zion, Lewkowicz, Schiffer and Levitan) new Riemannian geometric criterion.     

Non-trivial effect of the in-plane shear elasticity on the phase transitions of fixed-connectivity meshwork models

We numerically study the phase structure of two types of triangulated spherical surface models, which includes an in-plane shear energy in the Hamiltonian, and we found that the phase structure of the models is considerably influenced by the presence of the in-plane shear elasticity. The models undergo a first-order collapsing transition and a first-order (or second-order) transition of surface fluctuations; the latter transition was reported to be of second-order in the first model without the in-plane shear energy. This leads us to conclude that the in-plane elasticity strengthens the transition of surface fluctuations. We also found that the in-plane elasticity decreases the variety of phases in the second model without the in-plane energy. The Hamiltonian of the first model is given by a linear combination of the Gaussian bond potential, a one-dimensional bending energy, and the in-plane shear energy. The second model is obtained from the first model by replacing the Gaussian bond potential with the Nambu-Goto potential, which is defined by the summation over the area of triangles.     

极性晶体外表面电子的量子像势及其极化子的基态能量

本从与真空接触的存在二支声子的半无限极性晶体表面附近极化子的哈密顿算符入手，应用二支模型理论，分别对GaAs和ZnO两种材料计算了外表面电子的量子像势及其极化子的基态能量，计算结果表明，利用二支模型理论求出的外表面极化子的基态能量与利用一支模型理论求出的外表在面极化子的基态能量相差较大，对GaAs，误差约为31.1%, 对ZnO，误差约为14.8%。     

Under-coordinated atoms induced local strain, quantum trap depression and valence charge polarization at W stepped surfaces

We have explored the effects of atoms under-coordination on surface structure relaxation, binding energy shift of W stepped surfaces and valence charge polarization by the method of incorporating bond order-length-strength (BOLS) correlation mechanism into high-resolution X-ray photoluminescence spectra (XPS) measurements as well as density functional theory (DFT) calculations. Results show that the 4f_7/2 energy levels of bulk, surface skin and step edge W atoms shift deeper from 2.17 to 2.69 eV with respect to that of the isolated W (28.91±0.01 eV) atoms, while the valence charge energy shift upper from inner to outer layer and from bulk to stepped edge. The surface bond contraction occurs around under-coordinated atoms after geometry relaxation calculation. Consistency among BOLS calculations, DFT calculation and experimental measurements clarifies that the surface bond contraction and consolidation due to the effects of under-coordination atoms induce potential trap depression, which provides perturbation to the Hamiltonian and hence contributes to the surface core level shift deeper, and that the surface valence charge are polarized by the densely trapped core-level electrons to upper energy.     

The kinetic energy partition method applied to a confined quantum harmonic oscillator in a one-dimensional box

A new, physically motivated, basis set expansion method for solving quantum eigenvalue problems with competing interaction potentials is presented. In contrast to the usual dissection of the potential energy into unperturbed and perturbing terms, we divide the kinetic energy into partial terms by modifying the mass factor. The partition scheme results in partial kinetic energies with their effective mass factors. By distributing each partial kinetic energy to a respective potential energy to form a subsystem, the total Hamiltonian is written as the sum of subsystem Hamiltonians. Using a linear combination of the subsystem wave-functions to represent the system wave-function we obtain a set of coupled equations for the expansion coefficients, by solving these energies and wave-functions can be obtained. We demonstrate the solution scheme with a standard model system: a confined harmonic oscillator in a one-dimensional box. With only a few (less than ten) basis functions from each subsystem, we can reproduce the exact solutions very accurately, thus showing the applicability of this method.     

Weak turbulent Kolmogorov spectrum for surface gravity waves

We study the long-time evolution of surface gravity waves on deep water excited by a stochastic external force concentrated in moderately small wave numbers. We numerically implemented the primitive Euler equations for the potential flow of an ideal fluid with free surface written in Hamiltonian canonical variables, using the expansion of the Hamiltonian in powers of nonlinearity of terms up to fourth order. We show that because of nonlinear interaction processes a stationary Fourier spectrum of a surface elevation close to <|eta(k)|(2)> approximately k(-7/2) is formed. The observed spectrum can be interpreted as a weak-turbulent Kolmogorov spectrum for a direct cascade of energy.     

Potential energy surfaces in algebraic molecular models using coherent states

The potential energy surfaces provided by the coherent states formalism for the case of interacting one-dimensional oscillators is investigated. The case of two interacting oscillators modelled with Morse potentials are considered in detail. First the traditional treatment is presented in order to identify the need to establish a new transformation between the parameters and the classical variables that allow the full Hamiltonian to be recovered. To this end the connection between the su(2) algebraic model and the usual treatment in configuration space was taken into account. It is shown that the coherent state approach when applied to recover the potential energy surface (PES) from a polyad preserving Hamiltonian is viable only in systems with a local mode behaviour. For molecules with a normal mode behaviour the approach is still valid, but the polyad must be broken in order to recover the PES. Our approach is evaluated through the calculation of the force constants for H₂O and CO₂, representative examples of local and normal behaviours.