Accurate studies on the full vibrational energy spectra and molecular dissociation energies for some electronic states of N_2 molecule

1 IntroductionAccurate results of high-lying vibrational energies and molecular dissociation energy De of diatomic electronic states are very important for thermodynamics, molecular spec- troscopy, reactive scatterings, and the collision physics of ultracold atoms. For example, the binding energy of the highest bound vibrational state to the ground vibrational state determines the s-wave scattering length. This in turn determines the low- energy (pre- dominantly s-wave) atomic elastic-scatteri…     

Na2分子部分电子态的完全振动能谱和离解能的精确研究

对于大多数双原子分子的电子态，用现代实验方法或精确的量子理论方法往往可以获得含m个振动能级的能谱子集合［Ev］，而不易得到包含最高振动能级在内的所有高振动量子态能级的完全振动能谱{Ev}.鉴于Na2分子电子态的振动能谱和分子离解能De在实际研究和应用中的重要性，使用基于微扰理论的代数方法（AM），获得了Na2分子一些电子态的振动光谱常数和完全振动能谱；使用基于AM的代数能量方法（AEM）获得了这些电子态的正确离解能.研究结果表明：AM方法能从少数精确的实验能级获得精确的分子振动光谱常数集合和正确的完全振动能谱{Ev}，AEM方法获得的分子离解能比由文献发表的振动光谱常数计算得到的近似离解能值更准确，对于难以获得分子离解能的那些电子激发态，AEM方法能给出合理的离解能数据. 关键词： Na2分子 代数方法 振动能级 离解能 电子激发态     

Accurate studies on the full vibrational energy spectra and molecular dissociation energies for some electronic states of N<Subscript>2</Subscript> molecule

It is usually very difficult to directly obtain molecular dissociation energy D _e and all accurate high-lying vibrational energies for most diatomic electronic states using modern experimental techniques or quantum theories, and it, is also very difficult to give accurate analytical expression for diatomic molecular dissociation energy. This study proposes a new analytical formula for obtaining accurate molecular dissociation energy based on the LeRoy and Bernstein’s energy expression in dissociation limit. A set of full vibrational energy spectra for some electronic states of N₂ molecule are studied using the algebraic method (AM) suggested recently, and the corresponding accurate molecular dissociation energies are evaluated using the proposed new formula and high-lying AM vibrational energies. The results show that the AM spectra and the new theoretical dissociation energies agree excellently with experimental data, and thereby providing a new physical approach to generating accurate dissociation energies for electronic states of diatomic molecules.     

Accurate studies on the full vibrational energy spectra and molecular dissociation energies for some electronic states of the Li2 molecule

It is usually very difficult to directly obtain molecular dissociation energy D_e and all accurate high-lying vibrational energies for most diatomic electronic states using modern experimental techniques or quantum theories, and it is also very difficult to give accurate analytical expression for diatomic molecular dissociation energy. This study proposes a new analytical formula for obtaining accurate molecular dissociation energy based on the LeRoy and Bernstein's energy expression in dissociation limit. A set of full vibrational energy spectra for some electronic states of Li₂ molecule are studied using the algebraic method (AM) suggested recently, and the corresponding accurate molecular dissociation energies are evaluated using the proposed new formula and high-lying AM vibrational energies. The results show that the AM spectra and the new theoretical dissociation energies agree very well with experimental data, and thereby providing a new physical approach to generating accurate dissociation energies for electronic states of diatomic molecules.     

用代数能量方法研究氢化物双原子分子的完全振动能谱和离解能

本文用研究双原子分子振动能谱的新方法-代数方法(AM),研究了KH-X1Σ+,RbH-X1Σ+,DF-X1Σ+和DCl-X1Σ+等四个氢化物双原子分子的电子基态的振动光谱常数和振动能谱;用代数能量方法(AEM)研究了相应电子态的分子离解能.研究结果表明:使用实验获得的少数精确的振动能级[Eυ],由AM方法得到的振动能谱不仅能够重复这些电子态的已知实验能级,还能够得到用现代实验方法或精确的量子理论方法很难得到的所有高振动激发态的能级.由AEM方法能够得到比用文献发表的振动光谱常数计算获得的离解能值更准确的分子离解能.     

Accurate studies on the full vibrational energy spectra and molecular dissociation energies for some electronic states of halogen molecule

This paper obtains accurate vibrational spectroscopic constants and full vibrational energy spectrum by the algebraic method (AM) for some electronic states of halogen diatomic molecules.Motivated by the recent success of obtaining the dissociation energies of Li 2 molecule by using a new analytical formula,it further extends the formula to study the dissociation energies of halogen diatomic molecules.The results show that the AM spectrum and the theoretical dissociation energies agree well with RKR data and experimental data respectively.     

双原子分子振动能谱与离解能的精确研究

代数方法(AM)的建立解决了实验方法和精确量子力学理论方法难以获得双原子分子的包含最高振动能级在内的所有高阶振动能级的精确数值这一问题.基于LeRoy与Bernstein的工作,孙卫国等又建立了精确计算双原子分子离解能的新解析表达式.应用新公式和代数方法(AM),研究了一些双原子分子部分电子态的振动能谱和分子离解能,获得了与实验值符合非常好的理论结果.该方法在理论上提供了获得双原子分子完全振动能谱和精确分子离解能的物理新方法.     

Accurate vibrational energy spectra and dissociation energies of some diatomic electronic states

An algebraic method (AM) used to study the full vibrational spectra of diatomic systems, and an analytical formula used to calculate accurate molecular dissociation energies are applied to study the full vibrational spectra and molecular dissociation energies of some electronic states of homonuclear and heteronuclear diatomic molecules and diatomic ions. Studies show that the AM method and the analytical expression are reliable and economical physical methods for studying full vibrational spectra and molecular dissociation energies of diatomic electronic systems theoretically. They are particularly useful for those diatomic systems whose highlying vibrational energies may not be available.     

Accurate vibrational energy spectra and dissociation energies of some diatomic electronic states

An algebraic method (AM) used to study the full vibrational spectra of diatomic systems, and an analytical formula used to calculate accurate molecular dissociation energies are applied to study the full vibrational spectra and molecular dissociation energies of some electronic states of homonuclear and heteronuclear diatomic molecules and diatomic ions. Studies show that the AM method and the analytical expression are reliable and economical physical methods for studying full vibrational spectra and molecular dissociation energies of diatomic electronic systems theoretically. They are particularly useful for those diatomic systems whose high-lying vibrational energies may not be available.      

理论离实验有多远?——用代数方法精确研究双原子分子的完全振动能谱和离解能

本文较系统地简介了双原子分子振动能谱和离解能的研究历史、现状及若干研究方法,重点介绍了孙卫国等最近建立的研究双原子分子完全振动能谱的代数方法(AM)和计算双原子分子离解能的新物理公式。然后应用AM方法和离解能新公式对一批同核和异核双原子分子,以及双原子分子离子电子态的完全振动能谱和离解能进行了研究。结果表明,AM方法和新建立的离解能解析式相结合的理论方法对研究双原子分子及离子的完全振动能谱和离解能是行之有效的、简单经济的物理方法,为实验技术难以精确测量其高激发振动能级或离解能的双原子分子或离子体系提供了获得精确的完全振动能谱和体系离解能的一种理论新方法。     

Li_2部分电子态的完全振动能谱与离解能的精确研究

本文将孙卫国等建立的精确计算双原子分子离解能的解析表达式作为分子振动能级正确收敛的重要物理判据,应用代数方法,进一步研究了重要的碱金属Li2的5个电子态的完全振动能谱和离解能,获得了这些电子态的精确振动光谱常数,同时也得到了包括接近分子离解极限在内的完全振动能谱和与实验值符合得很好的理论离解能.这些计算结果为许多需要这些电子态振动数据的研究领域提供了重要的研究数据.     

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...     

双原子离子振动光谱与离解能的研究

结合代数方法(AM)和最近建立的计算精确的分子离解能的新解析表达式,进一步研究了部分双原子离子电子态的完全振动能谱和离解能,获得了与实验值符合得非常好的理论结果.研究结果表明,AM方法和新解析式相结合的理论方法同样也适用于双原子离子体系,该方法在理论上提供了获得双原子离子精确的振动光谱和离解能的物理新方法.     

用差分收敛法研究NaLi分子部分电子态的完全振动能谱

基于双核分子振动能级的普遍表达式和差分收敛法(difference converging method, DCM), 利用微分思想将DCM应用于双核分子体系完全振动能谱的研究中. 应用DCM方法, 分别选用实验上获得的一组(10条)精确的振动能级, 对NaLi分子3¹Π, 4¹Π 和A¹Σ⁺电子态进行了研究, DCM的研究结果正确重复了已知数据并预测出了在实验上未能获得的包含高激发态在内的完全振动能谱数据, 同时计算得到了这3个电子态的振动光谱常数.     

Universal reduced potential function for diatomic systems

The potential energy functions of 200 diatomic systems, with dissociation energies De ranging from few eV to hundreds of mueV, are well described by a new three-parameter potential energy function. Identification of the evaluated values of a dimensionless quantity, xin=L2/Ln [Ln=(n!De/fn)1/n, a scaled length parameter, and fn, the nth force constant evaluated at the equilibrium internuclear distance Re], is proposed as a reliable criterion to search for the universal scaling features of potentials and spectroscopic constants for bound diatomic systems. Our study suggests a useful approach to predicting future molecular spectroscopic constants.     

双原子分子离子XY+部分电子态完全振动能谱的精确研究

关于双原子分子离子XY 的完全振动能谱,目前还没有实验和理论的数据报道。本文首次应用代数方法AM(Algebraic Method),获得了BeH -X1Σ 态,CO -X2Σ 态,F2 -X2Πg态,O2 -A2Πu态和Li2 -X2Σg 态的精确振动光谱常数和完全振动能谱,解决了实验方法和精确量子力学理论方法难以获得双原子分子离子XY 的包含最高振动能级在内的所有高阶振动能级的精确数值这一问题。所有研究结果表明:由部分较低的实验精确振动能级,可用AM产生双原子分子离子XY 的精确振动光谱常数和包含全部激发态的完全振动能谱;所得的AM振动能谱比其他理论方法得到的结果更好。     

用可变阶数的代数方法研究双原子体系的完全振动能谱和离解能

不同双原子分子电子态的势能(或振动能谱)的展开性质可能不同,文章将固定阶数的代数方法(AM)改进为可变阶数的代数方法,使得该方法可以研究各种不同性质(不同能量展开阶数)的双原子分子电子态,也可以解决光谱计算中可能出现的"蝴蝶效应"问题。利用阶数可变的AM方法研究了原来固定阶数的AM方法难以给出正确结果的N2-a′1Σu-,Li2+-2 2Σg+,4 He D+-X1Σ+和39 K85 Rb-(2)3Σ+等不同双核体系的完全振动能谱与离解能,不但得到了与实验数据精确相符的理论结果,还正确地预言了许多由于实验条件与技术原因而未能测得的物理数据。研究表明阶数可变的AM方法能够更广泛地用于研究各类双核电子态体系的完全振动能谱和体系离解能。     

Accurate studies of dissociation energies and vibrational energies on alkali metals

This paper studies full vibrational spectra {Ev} and molecular dissociation energies De by using conventional least-squares （LS） fitting and an algebraic method （AM） proposed recently for 10 diatomic electronic states of ^7Li2, Na2, NaK and NaLi molecules based on some known experimental vibrational energies in a subset [Ev^expt] respectively. Studies show that： （1） although both the full AM spectrum {Ev^AM} and the LS spectrum {Ev^LS} can reproduce the known experimental energies in [Ev^expt], the {EAM} is superior to the {Ev^LS} in that the high-lying AM vibrational energies which may not be available experimentally have better or much better accuracy than those LS counterparts in {Ev^LS}, and so is the AM dissociation energy De^AM; （2） the main source of the errors in the data obtained by using the LS fitting is that the fitting which is just a pure mathematical process does not use any physical criteria that must be satisfied by the full vibrational spectrum, while the AM method does. This study suggests that when fitting or solving a physical equation using a set of source data, it is important not only to apply a proper mathematical tool, but also to use correct physical criteria which measure the physical properties of the data, kick out those data having bigger errors, and impose conditional convergence on the numerical process.     

碱金属双原子分子部分电子态的完全振动能谱和离解能

对大多数双原子分子电子态的高阶振动能谱,现代实验方法和量子力学理论计算都难以得到较精确的振动能级.文中应用基于二阶微扰理论的代数方法(AM)以及计算双原子分子离解能的新表达式研究了碱金属双原子分子Li₂的3³Σ⁺_g,1³Δ_g和2³Π_g,Na₂的B¹Π_u以及K₂的4¹Σ⁺_g电子态的完全振动能谱{E_υ^AM}和离解能,理论计算结果不仅与已有的实验值相符,而且还给出了实验尚未得到的高阶振动能级.这些结果为碱金属双原子分子精确振动能谱和离解能的科学研究提供了重要数据. 关键词： 碱金属分子 高阶振动能级 离解能 代数方法     

Studies on the Vibrational and Rovibrational Energies and Vibrational Force Constants of Diatomic Molecular States Using Algebraic and Variational Methods

Alternative expressions for vibrational and rotational spectrum constants and energies of diatomic molecular electronic states based on perturbation theory are suggested. An algebraic method (AM) is proposed to generate a converged full vibrational spectrum from limited energy data, and a potential variational method (PVM) is suggested to produce the vibrational force constants f_n and rotational spectrum constants using the perturbation formulae and the AM vibrational constants. The AM and PVM have been applied to study 10 diatomic electronic states: the X¹Σ_g⁺ and C¹Π_u⁻ states of H₂; the X¹Σ_g⁺, A³Σ_u⁺, B′³Σ_u⁻, and B³Π_g states of N₂; the X³Σ_g⁻, A³Σ_u⁺, and c¹Σ_u⁻ states of O₂; and the X¹Σ_g⁺ state of Br₂. Calculations show that (1) the AM E_υmax converges to the correct molecular dissociation energy; (2) the AM not only reproduce the input energies, but also generate the E_υ's of high vibrational excited states which may be difficult to obtain experimentally or theoretically; (3) the PVM vibrational force constants f_n may be used to measure the relative chemical bondstrengths of different diatomic electronic states for a molecule quantitatively.