Theoretical study of the structure and analytic potential energy function for the ground state of the PO₂ molecule

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 PO 2 molecule. It is shown that the ground state of the PO2 molecule has C2v symmetry and its ground electronic state is X2 A1 . The equilibrium parameters of the structure are R P O = 0.1465 nm, ∠OPO = 134.96°, and the dissociation energy is Ed = 19.218 eV. The bent vibrational frequency ν 1 = 386 cm-1 , symmetric stretching frequency ν 2 = 1095 cm-1 , and asymmetric stretching frequency ν 3 = 1333 cm-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.     

SeN_2自由基解析势能函数的耦合簇理论研究

利用单双迭代耦合簇理论CCSD结合相关一致四重基组cc-pVQZ对SeN2基态的平衡结构和谐振频率进行了优化计算.计算结果表明:基态SeN2自由基分子稳定态为C2v构型,基态电子组态为X1A1,平衡核间距RSe-N=0.1691 nm,RN-N=0.1970 nm,αN-Se-N=71.289?,离解能De=4.78 eV.基态简正振动频率分别为:ν1=326.9288 cm-1,ν2=808.0161 cm-1以及ν3=948.3430 cm-1.对SeN基态和N2基态采用上述相同方法进行几何构型与谐振频率的计算并进行单点能扫描,使用Murrell-Sorbie函数进行最小二乘拟合得到其势能函数和光谱常数,通过和其他理论值以及实验值做比较,显示本文的计算工作达到了很高的精度.应用多体项展式理论导出了基态SeN2的全空间解析势能函数,其势能函数等值势能图准确再现了SeN2分子的结构特征和能量变化.     

INFLUENCE ANALYSIS ON EXPONENTIAL NONLINEAR MODELS WITH RANDOM EFFECTS

This paper presents a unified diagnostic method for exponential nonlinearmodels with random effects based upon the joint likelihood given by Robinson in 1991.The authors show that the case deletion model is equivalent to mean shift outlier model.From this point of view, several diagnostic measures, such as Cook distance, score statistics     

钨丝电热蒸发-氩/氢火焰原子吸收光谱分析方法

基于钨丝电热蒸发设备,建立了一种全新的钨丝电热蒸发-氩/氢火焰串联原子吸收光谱系统.研究了系统抗酸、抗盐能力,结果表明:Na<'+>和Ca<'2+>质量浓度小于400 mg/L、Mg<'2+>质量浓度小于1500 mg/L时不干扰测定.在优化的仪器条件下:Pb、Cd、Au和Ag的检出限分别为:0.016、0.0005、...     

Nonuniform self-imaging of achromatic Talbot lithography

Achromatic Talbot lithography(ATL) with high resolution has been demonstrated to be an excellent technique for large area periodic nano-fabrication. In this work, the uniformity of pattern distribution in ATL was studied in detail. Two ATL transmission masks with ~50% duty cycle in a square lattice were illuminated by a spatial coherent broadband extreme ultraviolet beam with a relative bandwidth of 2.38%. Nonuniform dot size distribution was observed by experiments and finite-difference time-domain simulations. The sum of the two kinds of diffraction patterns, with different lattice directions(45° rotated) and different intensity distributions,results in the final nonuniform pattern distribution.     

A CRITERION FOR THE STABILITY OF MOTION OF NONLINEAR SYSTEM

As to an autonomous nonlinear system, the stability of the equilibrium state in a sufficiently small neighborhood of the equilibrium state can be determined by eigenvalues of the linear part of the nonlinear system provided that the eigenvalues are not in a critical case. Many methods may be used to detect the stability for a linear system. A lot of researches for determining the stability of a nonlinear system are completed by mathematicians and mechanicians but most of them are methods for the special forms of nonlinear systems. Till now, none of these methods can be conveniently applied to all nonlinear systems. The method introduced by this paper gives the necessary and sufficient conditions of the stability of a nonlinear system. The familiar Krasovski's method is a special case of this method     

A criterion for the stability of motion of nonlinear system

As to an autonomous nonlinear system, the stability of the equilibrium state in a sufficiently small neighborhood of the equilibrium state can be determined by eigenvalues of the linear part of the nonlinear system provided that the eigenvalues are not in a critical case. Many methods may be used to detect the stability for a linear system. A lot of researches for determining the stability of a nonlinear system are completed by mathematicians and mechanicians but most of them are methods for the special forms of nonlinear systems. Till now, none of these methods can be conveniently applied to all nonlinear systems. The method introduced by this paper gives the necessary and sufficient conditions of the stability of a nonlinear system. The familiar Krasovski's method is a special case of this method.     

卡尔费休滴定法测水简易装置的改进

用带橡皮塞的导管将滴定管的上口与锥形瓶连接构成一个密闭的滴定装置,将此装置应用于卡尔费休容量法测定水含量,在滴定过程中所有试剂与外界完全隔开,防止了滴定过程中空气中水蒸气的干扰．滴定终点明显,且能稳定8h以上。用该装置对甲醇样品中的水进行测定,回收率为100．4％～100．9％,测定结果的相对标准偏差小于0．25％。     

Theoretical study of the structure and analytic potential energy function for the ground state of the PO2 molecule

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.     

KH(KD)分子基态(X~1Σ~+)的结构与势能函数研究

利用群论及原子分子反应静力学的有关原理,推导了KH(KD)分子基态X1Σ+的电子态和合理的离解极限.采用Gaussian03程序包中的多种方法和基组,对KH(KD)分子基态X1Σ+的平衡结构和谐振频率进行了优化计算.通过比较计算结果,发现B3LYP为最优方法,6-311g(3df,3pd)为最佳基组.运用优选出的方法和基组对KH(KD)分子基态进行了单点势能扫描,然后分别采用Murrell-Sorbie函数及修正的Murrell-Sorbie+c6函数进行了非线性最小二乘拟合,得到了KH(KD)分子基态的势能函数和相应的光谱常数.计算结果表明,利用修正的Murrell-Sorbie+c6函数计算所得的光谱常数与实验数据吻合得更好.