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.     

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.     

Hamiltonian description and 6D calculations on the ammonia vibrational levels

In this work, a Hamiltonian formalism and a 6D vibrational calculation procedure is described and implemented, designed for the exploration of vibrational motion in ammonia (and any XH₃ molecule). The 6D potential energy surface of ammonia was modelled in simple analytical form (including the inversion potential) at the planar, totally symmetric (D_3h) reference configuration. Using the described method (which is an adaptation of the formalism, previously developed and applied to benzene), 6D calculations were carried out on the vibrational level system of ammonia ¹⁴NH₃, at the lower levels of vibrational excitation. On the basis of the satisfactory agreement between the calculated and the experimentally measured vibrational frequencies, the values of some important harmonic and anharmonic force constants, characterizing the ammonia PES were determined.     

Pu2+2 分子离子的结构与势能函数

使用密度泛函B3LYP方法对Pu2+2分子离子进行了理论研究,结果表明,Pu2+2分子离子是亚稳定结构,基态电子状态为 13Σg,势能函数可以用Z-W函数来表征,并首次计算获得基态分子离子的力常数和光谱数据.     

Geometrical properties of local dynamics in Hamiltonian systems: The Generalized Alignment Index (GALI) method

We investigate the detailed dynamics of multi-dimensional Hamiltonian systems by studying the evolution of volume elements formed by unit deviation vectors about their orbits. The behavior of these volumes is strongly influenced by the regular or chaotic nature of the motion, the number of deviation vectors, their linear (in)dependence and the spectrum of Lyapunov exponents. The different time evolution of these volumes can be used to identify rapidly and efficiently the nature of the dynamics, leading to the introduction of quantities that clearly distinguish between chaotic behavior and quasiperiodic motion on N-dimensional tori. More specifically we introduce the Generalized Alignment Index of order k () as the volume of a generalized parallelepiped, whose edges are k initially linearly independent unit deviation vectors with respect to the orbit studied whose magnitude is normalized to unity at every time step. We show analytically and verify numerically on particular examples of N-degree-of-freedom Hamiltonian systems that, for chaotic orbits, tends exponentially to zero with exponents that involve the values of several Lyapunov exponents. In the case of regular orbits, fluctuates around non-zero values for 2≤k≤N and goes to zero for N<k≤2N following power laws that depend on the dimension of the torus and the number m of deviation vectors initially tangent to the torus: ∝t^{−2(k−N)+m} if 0≤m<k−N, and ∝t^−(k−N) if m≥k−N. The is a generalization of the Smaller Alignment Index (SALI) (). However, provides significantly more detailed information on the local dynamics, allows for a faster and clearer distinction between order and chaos than SALI and works even in cases where the SALI method is inconclusive.     

He-N_2势能表面对散射截面的影响

从总散射截面、微分散射截面和分波散射截面三方面对He-N2体系的三个势能表面进行了详细比较。计算中采用了精确度较高的密耦(Close-Coupling)近似方法(E=64meV),计算结果与MKeil等的实验结果基本相符。研究结果表明:势能球平均零点能位置、势阱深度、排斥势的强度以及势能在势阱附近的方向性都对散射截面有较大的影响,为根据散射截面准确地确定He-N2体系的相互作用势能参数提供了一种新依据。     

N2HF体系的结构与势能函数

用QCISD/6-311++G方法对N2HF体系进行优化得到其基态的平衡几何结构,属于C∞v构型,(1∑)态.计算表明N2HF分子是一特殊的van der Waals分子.应用多体项展式方法,导出了N2HF分子的解析势能函数,该函数正确的复现了N2HF体系的平衡结构及能量变化.势能面的静态特征表明:N2+HF→N2-HF反应是一个有阈能的反应,即是需活化能的反应,反应过程需克服144.21 kJ/mol的势垒.然后,就N2HF→N2+HF反应机理进行了讨论.     

S2O分子的局域势能面和振动光谱的解析

用MRCISD和MRPT2计算了S2O分子的局域势能面，对计算点完成了力场多项式拟合和振动组态相互作用的计算.然后，对其基态(1A′)和激发态(1A′)的振动模式和振动光谱进行分析.通过调节力常数，势能面得到进一步改进.与已有的实验能谱数据进行比较，基态与激发态的均方差分别为3852cm-1和644cm-1. 关键词： S2O 势能面 能谱 MRCISD MRPT2     

Ag2La分子的结构与势能函数

采用密度泛函理论DFT中的UB3LYP方法,对Ag2La分子的结构进行优化,得到Ag2La分子基态结构为具有C2v对称性的弯曲结构,电子态为2A1,结合能为3.48eV。采用最小二乘法拟合出Ag2和AgLa分子的Murrell-Sorbie势能函数,在此基础上推导出光谱数据和力常数;通过多体展示理论导出基态Ag2La分子的势能函数,其等值势能图准确再现了Ag2La分子的结构特征及其势阱深度与位置。     

Ag2La分子的结构与势能函数

采用密度泛函理论DFT中的UB3LYP方法,对Ag2La分子的结构进行优化,得到Ag2La分子基态结构为具有C2v对称性的弯曲结构,电子态为2A1,结合能为3.48eV。采用最小二乘法拟合出Ag2和AgLa分子的Murrell-Sorbie势能函数,在此基础上推导出光谱数据和力常数;通过多体展示理论导出基态Ag2La分子的势能函数,其等值势能图准确再现了Ag2La分子的结构特征及其势阱深度与位置。     

Kr-CS2体系势能面及束缚态能级的理论研究

本文采用单双迭代(包括非迭代三重激发)耦合簇CCSD(T)方法,对C、S原子采用aug-cc-PVTZ基组,对Kr原子采用cc-PVTZ –DK基组,并且加上中心键函数(3s3p2d2f1g),计算得到Kr-CS2体系的势能面。该势能面为T型结构,存在一个全局极小值和两个等价的局域极小值。全局极小值位于R =7.05 a0,θ= 90°处,势能值为-396.194 cm-1。两个局域极小值分别位于R = 10.15 a0,θ= 0°和180°处,势能为-243.647 cm-1。利用该势能面,通过数值求解相应的薛定谔方程,计算得出体系J≤10的束缚态能级及微波谱跃迁频率,并通过跃迁频率拟合得到相应的光谱常数。     

AuY、Au2Y分子的结构和势能函数

用密度泛函DFT中的 B3LYP 方法,选择LANL2DZ基组,对AuY、Au2Y分子的结构进行优化,得到了它们的平衡几何构型和谐振频率.采用最小二乘法拟合出AuY分子的 Murrell-Sorbie势能函数,在此基础上推导出光谱数据和力常数;并通过多体展示理论导出Au2Y分子的势能函数,正确地反应了其平衡构型特征.     

Mg2Ni分子的结构和势能函数

采用密度泛函B3LYP方法在6-311+g(d,p)基组水平上对MgNi、Mg2和Mg2Ni分子的各种可能的结构进行优化,得到了它们的几何构型、平衡核间距、离解能和谐振频率.采用最小二乘法拟合MgNi和Mg2分子的Murrell-Sorbie势能函数,在此基础上导出光谱数据和力常数.通过多体项展式理论导出Mg2Ni分子的解析势能函数,并绘出了Mg2Ni分子的等值势能面,其等值势能面正确地反应了基态Mg2Ni分子的平衡构型特征.     

Ar-CS_2体系势能面和微波谱的从头算研究

本文采用单双迭代(包括非迭代三重激发)耦合簇CCSD(T)方法,使用了扩展的相关一致基组aug-cc-p VTZ,并且加入了(3s3p2d2f1g)中心键函数,计算得到Ar-CS2体系的势能面.结果显示势能面有一个全局极小值和两个等价的局域极小值,为T型结构.全局极小值位于R=6.936 a0,θ=90°处,势能为-273.89 cm~(-1).两个局域极小值分别位于θ=0°和180°,R=9.960 a0的位置上,势能为-165.391 cm~(-1).在该势能面的基础上,通过求解体系的薛定谔方程,计算出体系(J≤10)的束缚态能级及微波跃迁频率,拟合得到体系的光谱常数,与实验结果吻合较好.     

Ar-CS2体系势能面和微波谱的从头算研究

本文采用单双迭代(包括非迭代三重激发)耦合簇CCSD(T)方法,使用了扩展的相关一致基组aug-cc-pVTZ,并且加入了(3s3p2d2f1g)中心键函数,计算得到Ar-CS2体系的势能面。结果显示势能面有一个全局极小值和两个等价的局域极小值,为T型结构。全局极小值位于R = 6.936 a0,θ=90º 处,势能为-273.89 cm-1 。两个局域极小值分别位于θ=0º 和θ=180º ,R = 9.960 a0 的位置上,势能为-165.391 cm-1。在该势能面的基础上,通过求解体系的薛定谔方程,计算出体系( J≤10)的束缚态能级及微波跃迁频率,拟合得到体系的光谱常数,与实验结果吻合较好。     

具有D3h对称性构型的B2H6分子的杨-泰勒效应与能级分裂

文中依据杨-泰勒效应理论与配位场理论,利用群论和对称性分析的方法探讨了B2H6分子在具有D3h对称性构型的情况下,E e′系统的杨-泰勒效应及其相关问题。研究了B2H6分子的电子态与声子态以及活跃声子态,构建了B2H6分子的E e′杨-泰勒系统的电声耦合哈密顿量,利用么正平移变换将系统的哈密顿量分解为无声子激发部分与有声子激发部分之和,由此计算出了E e′杨-泰勒系统的基态与激发态及其能级。结果表明由于电声耦合作用的缘故,在E e′系统的势能面上形成了四个具有C2v对称性势阱。无论系统处在哪一个势阱中,系统初始的二重简并的能级都将发生分裂,因此杨-泰勒畸变导致系统能级的简并性完全被消除。文中利用群论又进一步探讨了系统的杨-泰勒畸变方向与能级分裂方式,发现系统的杨-泰勒畸变方向是D3h→C2v,能级的分裂方式为E′→A1+B2或者E″→A2+B1。     

Microscopically derived potential energy surfaces from mostly structural considerations

A simple procedure to estimate the quadrupole Potential-Energy-Surface (PES) is presented, using mainly structural information, namely the content of the shell model space and the Pauli exclusion principle. Further microscopic properties are implicitly contained through the use of results from the Möller and Nix tables or experimental information. A mapping to the geometric potential is performed yielding the PES. The General Collective Model is used in order to obtain an estimate on the spectrum and quadrupole transitions, adjusting only the mass parameter. First, we test the conjecture on known nuclei, deriving the PES and compare them to known data. We will see that the PES approximates very well the structure expected. Having acquired a certain confidence, we predict the PES of several chain of isotopes of heavy and super-heavy nuclei and at the end we investigate the structure of nuclei in the supposed island of stability. One of the main points to show is that simple assumptions can provide already important information on the structure of nuclei outside known regions and that spectra and electromagnetic transitions can be estimated without using involved calculations and assumptions. The procedure does not allow to calculate binding energies. The method presented can be viewed as a starting point for further improvements.