AuZn和AuAl分子基态与低激发态的势能函数与热力学性质

用密度泛函理论B3LYP方法计算研究AuZn和AuAl分子基态与低激发态的结构与势能函数,导出分子的光谱数据.结果表明,AuZn和AuAl分子基态分别为X²Σ和X¹Σ,基态与低激发态的势能函数均可用Murrell-Sorbie函数来表达.AuZn分子低激发态a⁴Σ的绝热激发能为43529kJ/mol,AuAl分子低激发态a³Σ的绝热激发能为19991kJ/mol.计算固体AuZn和AuAl的内能和熵时,近似以气体分子的电子能和振动能代替固体分子的内能,用电子熵和振动熵代替固体分子的熵.在此近似下,计算得到AuZn和AuAl基态与低激发态固态分子生成反应热力学性质与温度的关系. 关键词： AuZn和AuAl B3LYP 热力学性质 势能函数     

新型胺类毒品分子的结构、光谱和热力学性质研究

采用密度泛函理论B3LYP/6-31++G**方法对2-胺基苯基丙烷(a)、2-甲胺-1-苯基丙烷(b)、7-甲氧基-a-甲基-1,3-苯骈二氧杂环戊烯-5-乙胺(c)、2,5-二甲氧基-a-甲基苯乙酰胺(d)四个新型胺类毒品分子进行结构优化,并进行频率和热容、熵、焓、自由能等气态热力学性质计算,获得它们的红外光谱、电子光谱和分子轨道图,模拟出标准摩尔热容Cpm、标准摩尔熵Sm、标准摩尔焓Hm等气态热力学性质与温度之间的函数关系式.     

负绝对温度系统的热力学性质

负绝对温度首先由Purcell和Pound等人在LiF晶体核自旋实验中实现。后经Ramsey从理论上进行了系统的研究和整理,形成了完整的理论。这里将其主要热力学性质作一简单介绍。 一、负绝对温度系统的热学性质 热力学系统的绝对温度可表示为其中U和S分别是系统的内能和熵。V为体积。 一般的热力学系统,如一摩尔理想气体或一摩尔晶体,具有无穷多能级。随着内能的增加(温度升高),分布在高能级上的原子或分子也随着增加,由此引起了原子能级范围的增大,无序性增大,从而系统的熵增大。即当dU>0时,一般有dS>0。因此由 (1)式给出的绝对温度是正的。 如…     

新型含马来酰亚胺环氧树脂固化剂分子的结构、光谱和热力学性质研究

使用密度泛函理论,采用B3LYP/6-311++G**方法计算研究了N-(4-马来酰亚胺基苯基)缩水甘油胺(a)、4-马来酰亚胺基苯基缩水甘油醚(b)、N-(4-氨基苯基马来酰亚胺)二缩水甘油胺(c)三个新型含马来酰亚胺固化剂分子的几何结构、电子吸收光谱、热力学性质.获得了它们的稳定结构、红外光谱、电子光谱和分子轨道图,模拟出标准摩尔热容C_(pm)~θ、标准摩尔熵S_m~θ、标准摩尔焓H_m~θ等气态热力学性质与温度之间的函数关系式.     

2,5-二(4-溴甲基苯基)-1,3,4噁二唑分子的光谱

采用密度泛函理论在B3LYP/6-31+G*水平计算研究2,5-二(4-溴甲基苯基)-1,3,4噁二唑分子的结构、光谱、热力学性质.结果显示,优化得到的最稳定结构的三个环构处于同一平面,两个溴原子分别位于平面的上下两侧.气相中最低能量跃迁与最强吸收峰均出现在315 nm,对应HOMO到LUMO的电子跃迁,溶剂作用使其红移4—6 nm.热力学计算表明,标准摩尔焓、标准摩尔热容和标准摩尔熵等热力学性质与温度之间存在很好的二次函数关系.298.15 K,2,5-二(4-溴甲基苯基)-1,3,4噁二唑分子的标准摩尔生成焓和标准摩尔生成自由能分别为2708.95和2972.13 kJ/mol.     

2,5-二(4-溴甲基苯基)-1,3,4噁二唑分子的光谱

采用密度泛函理论在B3LYP/6-31+G*水平计算研究2,5-二(4-溴甲基苯基)-1,3,4噁二唑分子的结构、光谱、热力学性质.结果显示,优化得到的最稳定结构的三个环构处于同一平面,两个溴原子分别位于平面的上下两侧.气相中最低能量跃迁与最强吸收峰均出现在315 nm,对应HOMO到LUMO的电子跃迁,溶剂作用使其红移4—6 nm.热力学计算表明,标准摩尔焓、标准摩尔热容和标准摩尔熵等热力学性质与温度之间存在很好的二次函数关系.298.15 K,2,5-二(4-溴甲基苯基)-1,3,4噁二唑分子的标准摩尔生成焓和标准摩尔生成自由能分别为2708.95和2972.13 kJ/mol.     

广义不确定性原理下费米气体低温热力学性质

在考虑到广义不确定性原理时, 统计物理中的态密度必须做出修正, 这导致对传统统计物理的所有结果都有不同程度的修正. 在高能、高温条件下, 此修正是颠覆传统观念的, 在低温条件下, 也有一定的修正. 研究了低温条件下考虑到广义不确定性原理时, 理想费米气体和具有弱相互作用费米气体的热力学性质, 分别给出理想费米气体和弱相互作用费米气体的化学势、内能和定容热容的解析表达式, 并以铜电子气体为例进行了具体数值计算, 将计算结果与不考虑广义不确定性原理时的费米气体的热力学性质进行了比较, 探讨了广义不确定性原理对系统热力学性质的影响. 考虑到广义不确定性原理后费米气体的化学势、费米能和基态能增大, 热容减少, 内能随温度的增加先增大, 到某一温度(对于铜电子气体, T/T_F0～0.3)时, 增值为零, 温度再增加内能减少. 这些修正的具体数值主要由粒子数密度决定, 粒子数密度越大, 修正越大.     

新型胺类毒品分子的结构、光谱和热力学性质研究

采用密度泛函理论B3LYP/6-31++G**方法对2-胺基苯基丙烷（a）、2-甲胺-1-苯基丙烷（b）、7-甲氧基- a -甲基-1,3-苯骈二氧杂环戊烯-5-乙胺（c）、2,5-二甲氧基- a -甲基苯乙酰胺（d）四个新型胺类毒品分子进行结构优化,并进行频率和热容、熵、焓、自由能等气态热力学性质计算,获得它们的红外光谱、电子光谱和分子轨道图,模拟出标准摩尔热容Cθpm、标准摩尔熵Sθm、标准摩尔焓Hθm等气态热力学性质与温度之间的函数关系式.     

NO分子的基态(X~2П)和激发态(a~4П and B~2П)光谱常量和振动能级的计算(英文)

本文使用完全活性空间自洽场/多组态相互作用(CASSCF/MRCI)理论,以cc-pVDZ为基组,计算了NO分子基态(X2Π)和激发态(a4ПandB2П)的平衡结构和单点能扫描曲线.采用最小二乘法拟合了Murrell-Sorbie函数,得到了NO分子的解析势能曲线,并利用Rydberg-Klein-Rees方法,计算得到的NO分子相应态的谐振频率和其它的光谱数据(ωe、αe、ωeχe、βe)与实验值十分一致,和其它理论计算方法进行比较,发现该方法有更好的准确性.以得到的解析势能函数为基础,求解NO分子核运动的一维径向Schrdinger方程,获得了更高振动态的振动能级.     

~7Li_2~(0,±1)分子体系基态振-转能级的全电子计算

采用单参考与多参考耦合簇理论结合相关一致高斯基组计算研究了7~7Li_2~((0,±1))分子体系的电子基态的势能曲线,计算考虑了体系所有电子的关联效应与相对论效应,拟合得到了体系的光谱常数,并获得了电子基态的振动-转动能级信息.计算得到的中性与阳离子体系的光谱常数与实验值符合得很好;对于阴离子体系,平衡核间距的计算仍需进一步改进,其他光谱常数符合较好.计算结果表明,中性和阳离子体系基态波函数具有明显的单参考组态特点,而阴离子分子基态应采用多参考组态波函数描述.对于基态的振动-转动能级,与现有实验值符合得很好;尽管各种计算方法对阴离子基态的平衡核间距计算结果仍有差异,但振动能级间隔的结果相互符合得很好.本文的研究可为Li_2分子体系基态,尤其是光谱学信息很少的阴离子体系的电子结构与光谱的精确研究提供了有用的光谱信息.     

Quantum vibrational partition function in the non-extensive Tsallis framework

The quantum vibrational partition function has been obtained in the Tsallis statistics framework for the entropic index, q, between 1 and 2. The effect of non-extensivity on the population of states and thermodynamic properties have been studied and compared with their corresponding values obtained in the Boltzmann-Gibbs (BG) statistics. Our results show that the non-extensive partition function of harmonic oscillator at any temperature is larger than its corresponding values for an extensive system and that their differences increase with temperature and entropic index. Also, the number of accessible states increases with q but, compared to the BG statistics, the occupation number decreases for low energy levels while the population of the higher energy levels increases. The internal energy and heat capacity have also been obtained for the non-extensive harmonic oscillator system. Results indicate that the heat capacity is greater than its corresponding value in the extensive (BG) system at low temperatures but that this trend is reversed at higher temperatures.     

Consideration of the temperature dependence of infrared spectra in the context of classical specific heat theory

The dependence of harmonic frequencies on the temperature and broadening of vibrational energy levels is considered in the context of classical Debye and Einstein specific heat theories. Analytical expressions for the vibrational thermodynamic functions are derived with allowance for these factors. It is shown that consideration of these two factors leads to the fact that the average energy of low-frequency oscillators differs from the statistical temperature, and the high-frequency fluctuations give a nonzero contribution to the specific heat. These expressions are used to calculate the thermodynamic functions of liquid water, and reliable agreement with the experiment is obtained. Voronezh State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 81–88, June, 2000.     

Rotational statistics and thermodynamic functions of hydrogen peroxide

Partition functions for both the rotational modes (hindered internal rotation and overall rotation) of the hydrogen peroxide (H₂O₂) molecule in the ground electronic state are studied using quantum and classical Gibbsian statistical mechanics. The partition functions are used to calculate rotational thermodynamic functions (internal energy, enthalpy, Helmholtz free energy, Gibbs free energy and entropy) of a hydrogen peroxide gas of weakly interacting molecules at temperatures above 300 K.     

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。     

Characterisation of electric discharge in hollow electrode Z-pinch device by means of Rogowski coils

In this paper, the energy spectra of the general molecular potential are obtained using the asymptotic iteration method within the framework of non-relativistic quantum mechanics.With the energy spectrum obtained, the vibrational partition function is calculated in a closed form and is used to obtain an expression for other thermodynamic functions such as vibrational mean energy U, vibrational mean free energy F, vibrational entropy S and vibrational specific heat capacity C. These thermodynamic functions are studied for the electronic state \(\mathrm{X}^{1}\Sigma _g^+ \) of \(K_2\) diatomic molecules.     

非对易相空间中谐振子体系热力学性质的探讨

2000年以来, 有关非对易空间的各种物理问题一直是研究的热点, 并在量子力学、场论、凝聚态物理、天体物理等各领域中已被广泛地探讨. 采用统计物理方法讨论非对易效应对谐振子体系热力学性质的影响. 先以对易相空间中确定二维和三维谐振子的配分函数求出谐振子体系的热力学函数; 非对易相空间中的坐标和动量通过坐标-坐标和动量-动量之间的线性变换而以对易相空间中的坐标和动量来表示; 最终以非对易相空间中求出配分函数来讨论非对易效应对谐振子体系热力学性质的影响. 结果显示, 在非对易相空间中谐振子体系的配分函数和熵表达式均包含因非对易引起的修正项. 从分析结果得出如下结论: 非对易效应对谐振子的配分函数和熵函数等微观状态函数有一定的影响, 但对谐振子体系的内能、热容量等宏观热力学函数没有影响. 研究结果只是对应于满足玻尔兹曼统计的经典体系, 对于满足费米-狄拉克和玻色-爱因斯坦统计的量子体系需进一步推广研究.     

Thermodynamics of impure anharmonic crystals

The vibrational thermodynamic properties of doped anharmonic solids are investigated using thermodynamic Green's functions. The study uses cubic and quartic anharmonic interactions, and different masses and force constants for the impurity and host lattice atoms. The explicit expressions so derived for the partition function, free energy, entropy, and lattice heat capacity for these solids in the low-impurity-concentration limit are discussed for various situations. Our results are modified due to the presence of interaction terms between the anharmonic and localized fields and reduce to those obtained by earlier workers as limiting cases.     

采用二维坐标和变分方法计算磷烷阳离子的伞型振动

提出一个新的二维变分方法计算PH₃⁺(X²A₂")的对称伸缩振动(v1)和伞形振动(v2). 因为采用了对称化的笛卡尔坐标,所以动能项变得简单,同时伞形振动模式也能得到很好的反映. 相比采用经常使用的一维模型计算伞形振动,这个二维模型不需要约化质量的假设,同时也考虑了v1和v2振动模式之间的相互作用. 用二维模型对PH₃⁺首次进行了计算, 前七个能级的理论值和实验值的平均相对误差小于3 cm^{-1. 用相同的方法也计算了NH₃,结果没有PH₃+理想,说明这个方法有一定的局限性.}     

Klein–Gordon and Dirac Equations with Thermodynamic Quantities

We study the thermodynamic quantities such as the Helmholtz free energy, the mean energy and the specific heat for both the Klein–Gordon, and Dirac equations. Our analyze includes two main subsections: (1) statistical functions for the Klein–Gordon equation with a linear potential having Lorentz vector, and Lorentz scalar parts (2) thermodynamic functions for the Dirac equation with a Lorentz scalar, inverse-linear potential by assuming that the scalar potential field is strong (A ? 1). We restrict ourselves to the case where only the positive part of the spectrum gives a contribution to the sum in partition function. We give the analytical results for high temperatures.     

Algebraic approach to thermodynamic properties of diatomic molecules

A simple model extending Lie algebraic techniques is applied to the analysis of thermodynamic vibrational properties of diatomic molecules. Local anharmonic effects are described by means of a Morse-like potential and the corresponding anharmonic bosons are associated with the SU(2) algebra. The total number of anharmonic bosons, fixed by the potential shape, is determined for a large number of diatomic molecules. A vibrational high-temperature partition function and the related thermodynamic functions are derived and studied in terms of the parameters of the model. The idea of a critical temperature is introduced in relation to the specific heat. A physical interpretation in terms of a quantum deformation associated with the model is given.