双原子分子体系的振动结构研究

最近通过微扰理论得到了双原子分子体系的能量表达式、振动光谱常数和转动光谱常数 ,并建议用代数方法和势能变分法由有限的振动能级求得收敛的振动能级的完全谱和高阶的振动力常数 .用该方法对一些双原子分子电子态的计算结果表明 :(1)代数方法得到的最高振动能收敛于正确的分子离解能 ;(2 )代数方法产生的振动能级不但能重复已知的精确能级 ,而且还能得到实验上和其他理论方法难以得到的高振动激发态的能级 ;(3)可用获得的各阶振动力常数fn比较同一分子的不同电子态的化学键的相对强度. Alternative expressions for vibrational and rotational spectrum constants and energies of diatomic molecular electronic states are suggested based on the perturbation theory. An algebraic method (AM) is proposed to generate converged full vibrational spectrum from limited energy data, and a potential variational method (PVM) is suggested to produce the vibrational force constants f n s and rotational spectrum constants using the perturbation formulae and the AM vibrational constants. Applying this method...     

变分代数能量自洽法研究Li_2分子部分电子态的解析势能

在课题组前期建立的计算双核分子体系解析势能函数的代数能量自洽法(algebraic energy consistent method,AECM)的基础上,引入了经改进得到的精确研究双核分子完全振动能谱的变分代数法(variational algebraic method,VAM),获得了计算双核分子体系精确解析势能函数的变分代数能量自洽法(variational algebraic energy consistent method,VAECM)。基于有限的精确实验振动能谱数据,利用VAECM方法研究了Li_2分子1~3Δ_g,3~3Σ_g~+,1~3Σ_g~-和b~3Π_u等4个电子态的完全振动能谱和解析势能函数。获得了各电子态包含高阶的振动光谱常数、完全振动能谱、振动力常数fn和势能展开系数an,并通过可调变分参数λ最终确定了VAECM解析势能函数的具体表达形式。计算结果与其他方法的研究结果进行了比较,VAECM方法获得的振动能谱数据和势能解析表达形式能更好地描述这些电子态在渐近区和离解区的物理行为,消除了利用前期AECM方法研究这些电子态在离解区出现的非物理势垒现象。     

Variational Calculation of Energies of Highly Excited Rovibrational States of CO2

Accurate variational calculations of energies of highly excited rovibrational states of ¹²C¹⁶O₂ using a Lanczos recursion are presented. In a first step, we use experimental rovibrational transition frequencies to determine by a least-square fitting procedure a potential energy surface for the CO₂ molecule. This potential energy surface is expressed as a multidimensional power series expansion in the normal coordinates. It is then used to determine all the rovibrational energies for symmetry e levels up to a rotational number J=200, a vibrational energy of 13 000 cm⁻¹, and a vibrational angular momentum l=13.     

Fermi Resonances and Vibrational Spectrum of a Polyatomic Molecule XY4: an Algebraic Approach

A U(2) algebraic model is introduced for the spectrum of a molecule XY₄, where the interactions between the stretch and bend modes are described by T_d symmetric Fermi resonance terms. The presented algebraic model in a limit corresponds to another model in recent literature. The vibrational spectrum of methane (CH₄) measured recently with modern spectroscopy techniques is employed to test those models. The obtained standard deviation between the observed and the calculated vibrational energy levels in the algebraic model is smaller than that in the corresponding model.     

Scaled DFT Force Constants and Vibrational Spectrum of Cyclopropylamine

Abstract

The molecular structure and harmonic vibrational frequencies of cyclopropylamine have been calculated using the B3LYP density functional method with the 6‐31G(2d,2p) basis set. The scaled DFT force field gives very good reproduction of the experimental vibrational frequencies. Several of the vibrational fundamental modes assigned previously are reassigned on the basis of the B3LYP/6‐31G(2d,2p) method and the scaled force field calculations. The optimized scaling factors were used to scale the B3LYP/6‐31G(2d,2p) force field of cyclopropane and cyclopropylamine (–ND₂) molecules.     

Concurrence of Quantum States： Algebraic Dynamical Method Study XXX Models in a Time-Depending Random External Field

Based on algebraic dynamics and the concept of the concurrence of the entanglement, we investigate the evolutive properties of the two-qubit entanglement that formed by Heisenberg XXX models under a time-depending external field. For this system, the property of the concurrence that is only dependent on the coupling constant J and total values of the external field is proved. Furthermore, we found that the thermal concurrence of the system under a static random external field is a function of the coupling constant J, temperature T, and the magnitude of external field.     

BCS Ground State and XXZ Antiferromagnetic Model as SU(2), SU(1,1) Coherent States: An Algebraic Diagonalization Method

An algebraic diagonalization method is proposed. As two examples, the Hamiltonians of BCS ground stateunder mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized byusing SU(2), SU(1,1) Lie algebraic method, respectively. Meanwhile, the eigenstates of the above two models are revealedto be SU(2), SU(1,1) coherent states, respectively. The relation between the usual Bogoliubov Valatin transformationand the algebraic method in a special case is also discussed.     

用能量自洽法研究双原子分子离子XY+的五阶解析势能函数

将用于研究双原子分子离子XY⁺解析势能函数的能量自洽法(energy consistent method for ion XY⁺,ECMI)从三阶推广到五阶,并将双原子分子离子XY⁺的三阶解析势能函数ECMI(3)推广为五阶的解析势能函数ECMI(5),研究CO⁺的B²Σ⁺态和SO⁺的b⁴Σ^-态的解析势能函数.结果表明,CO⁺的B²Σ⁺态和SO⁺的b⁴Σ^-态的新解析势能函数ECMI(5)势与基于实验的RKR数据符合得很好,优于常用的中性双原子分子势能函数Morse势、HMS势和双原子分子离子XY⁺的ECMI(3)势在这两个离子状态下的表现.不仅如此,ECMI势给出了对原子分子碰撞等诸多研究非常重要的正确理解极限和全程势能数据.     

Statistical Properties and Algebraic Characteristics of Quantum Superpositions of Negative Binomial States

We introduce new kinds of states of quantized radiation fields,which are the superpositions of megative binomial states.They exhibit remarkable nonclassical properties and reduce to Schrodinger cat states in a certain limit.The algebras involved in the even and odd negative binomial states turn out to be generally deformed oscillator algebras.It is found that the even and odd negative binomial states satisfy the same eigenvalue equation with the same eigenvalue and they can be viewed as two-photon nonlinear coherent states.Two methods of generating such the states are proposed.     

分子高激发振动的经典代数方法研究——以C_2H_2的C-H弯曲振动为例

本文以目前探讨得较多的C2H2的CH弯曲振动为例,说明如何应用代数方法来研究分子的高激发振动。由于分子的高激发振动态具有很强的模间非线性偶合以及能量的传递,传统的动力学方法似乎很难有效地用来研究其性质。问题的核心是高激发振动态由于其量子数很大,因此具有经典(或半经典)的性质。同时模间能量的传递可以用二次量子化算子来表示,而这些算子所具有的代数性质,使得人们可以用几何的概念来描述其性质。因此,整个问题就变为用几何的观点来分析分子的高激发振动态。最后,我们用所得的经典的代数哈密顿量和哈密顿方程对CHtrans弯曲和cis弯曲振动模间能量的传递速度与体系所含能量之高低的关系做了探讨     

Algebraic structure and Poisson＇s theory of mechanico-electrical systems

The algebraic structure and Poisson's integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic forms for mechanico-electrical systems are obtained. The Lie algebraic structure and the Poisson's integral theory of Lagrange mechanico-electrical systems are derived. The Lie algebraic structure admitted and Poisson's integral theory of the Lagrange--Maxwell mechanico-electrical systems are presented. Two examples are presented to illustrate these results.     

H函数在分子内振动能量再分配中的代数方法:水和氰化氘的共振研究

运用经典哈密顿代数方法 ,结合陪集表象构造了类比于热力学中熵的H函数。研究表明 ,H函数随时间增加而增大的特性可以用来表示分子内振动能量传递的方向和限度。同时 ,H函数的速率能够很好地表明水和氰化氘体系的共振特性     

基于代数动力学方法实现一类相干态的构建

最近提出的一个构建相干态的方案中,需要精确求解一个时间相关的常微分方程.基于代数动力学理论,利用该方程具有的SU(1,1)动力学对称性,提出了对此方程在含时系数取任意函数形式时的统一的精确求解方法,并且得到了严格的解析解.运用这个精确解,就可以构造相应物理系统的精确相干态的具体表达式.给出了一个解例,即频率取"快变"函数的情形.利用得到的精确结果,讨论了这个系统的量子涨落(量子噪声)随时间演化的情况.针对动量算符不确定度随时间演化的曲线的性态,指出在制备这个系统压缩态时可以利用的一些性质.最后,讨论了这个量子系统的不确定关系随时间演化的情况.     

用代数多重网格法求解一维分裂格式的Euler方程

提出了代数多重网格法(AMG)的一种新算法。新算法改进了插值公式和粗网格方程,并把它应用到求解一维的分裂格式Euler方程。数值结果表明,对于具有高CFL条件数的Euler方程,代数多重网格法可以求解;对于Gaus-Seidel方法求解不能收敛的代数方程组,代数多重网格法求解可以收敛。新算法改进了代数多重网格法的收敛性和扩展了它的应用范围,数值结果表明了它的有效性和强壮性。     

Sinc Collocation Solutions for the Integral Algebraic Equation of Index-1

In this article, Sinc collocation method is considered to obtain the numerical solution of integral algebraic equation of index-1 by reducing it to an explicit system of algebraic equation. It is shown that Sinc collocation solution can produce an error of order $\mathcal{O}(√Ne^{−k√N})$. Moreover, Sinc method is applied to several examples to illustrate the accuracy and implementation of the method.     

用代数-能量自洽法研究双原子分子解析势能函数

基于计算双原子分子完全振动能谱及离解能的代数方法 (algebraic method,AM)和研究双原子分子解析势能函数的能量自洽法(energy consistent method,ECM),建立了计算双核分子体系精确解析势能函数的代数-能量自洽法(AM-ECM).应用AM-ECM方法研究了7Li+2-23Σg,KH-X1Σ+,NaLi-X1Σ+和NaLi-A1Σ+电子态的解析势能表达形式,并与其他方法的研究结果进行了比较,获得了能正确描述这些电子态在渐近区和离解区的精确解析表达结果.     

Effect of Environmental Cations on Force Constants,Vibrational Mean Amplitudes and Bond Order of Metaloxygen Bonds in Some Octahedral Oxyanions

The general valenoe force field (GVFF), modified orbital valence force field (MOVFF), and modified Urey-Bradley force field (MUBFF) have been employed to calculate the force constants of octahedral Te⁶⁺o₆, and Ti⁴⁺o₆ anions in the presence of different environmental cations. The mean amplitudes and generalized mean square amplitudes of vibrations for these anions at temperatures; O°K,298. 16°K, and 500°K have also been calculated. Further, the metaloxygen bond order was estimated with the help of general valence stretching force constants. The effects of environmental cations on the force constants, mean amplitudes and π-bonding of metal-oxygen bonds have been critically discussed. The effect of atomic masses of anions on the ooriolis coupling constants of ‘f_iu species has also been outlined.     

双原子正方晶格光子晶体边界模式的光传输特性

利用平面波展开法,发现双原子正方晶格光子晶体中ΓM方向边界面存在着快慢两类边界模式,并且通过计算色散关系和电场分布研究了边界参量对这两类边界模式传输特性的影响.依据两种模式的色散关系,计算了群指数和群速度色散参量,结果表明边界参量的变化对第一类边界模式传输特性的影响较小,该模式的平均群指数始终维持在5.0左右;第二类边界模式与第一类模式明显不同,边界参量的变化能够有效地影响到这种模式的传输特性,该模式的最大平均群指数可达178左右.利用时域有限差分法记录了不同时刻电场强度在边界附近的分布及监测点处的电场幅度变化情况,结果表明,两类模式都能够被限制在边界附近并向前传播,时域有限差分法得到的群速度与平面波展开法的结果完全吻合.     

Scaled Quantum Chemical Studies of the Molecular Structure and Vibrational Spectra of Minoxidil

The Fourier transform Raman and Fourier transform infrared spectra for minoxidil have been recorded in the region 4000—100 cm^?1 and 4000—450 cm^?1, respectively. The structural and spectroscopy data of the molecule in the ground state were calculated by using density functional theory methods with 6-311G (d, p) basis set. A detailed vibrational analysis of the title compound has been done using normal coordinate analysis following the scaled quantum mechanical force field methodology. The calculated molecular geometry parameters and scaled vibrational wavenumbers are well compared with the experimental data. The electronic properties, such as excitation energies, absorption wavelength, highest occupied molecular orbital (HOMO), and lowest unoccupied molecular orbital (LUMO) energies were performed by time-dependent density functional theory approach, and the results are in good agreement with experimental absorption spectrum. The charge delocalizations of these molecules have been analyzed using natural bond orbital analysis. The molecule orbital contributions are studied by density of energy states. Fukui functions, local softness, and electrophilicity indices for selected atomic sites of the title compound are determined. Finally, the thermal behaviors of the compound have been calculated by different temperature.