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     

Accurate studies on dissociation energies of diatomic molecules

The molecular dissociation energies of some electronic states of hydride and N2 molecules were studied using a parameter-free analytical formula suggested in this study and the algebraic method (AM) proposed recently. The results show that the accurate AM dissociation energies DeAM agree excellently with experimental dissociation energies Deexpt, and that the dissociation energy of an electronic state such as the 23△g state of 7Li2 whose experimental value is not available can be predicted using the new formula.     

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.      

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.     

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.     

部分气体双原子分子的完全振动能谱和离解能的精确研究

鉴于气体双原子分子H2、O2、N2和CO的高振动激发态能级和离解行为在实际研究中的重要性,本文应用代数方法(AM)和代数能量方法(AEM),以部分气体双原子分子有限的实验能级[Ev]为基础,获得了H2-X1∑ g、O2-A3∑ u、O2-c1∑-u、N2-X1∑ g和CO-X1∑ 共5个电子态的完全振动能谱{Ev}及其分子的离解能,为研究部分离解气体的物理和化学性质提供了重要的高振动激发态能级和可靠的离解能数据.     

Normalized temperature and dissociation energy of diatomic molecules

The normalized temperatures known for spectral lines of atoms and ions can also be determined for band systems of diatomic molecules. Because of their dependence on at least five parameters, formulas of general applicability cannot be evaluated.Some similarities with the behaviour of atomic and ionic lines, however, can be found. The temperature range of maximum emissivity of a band system of diatomics is determined in first order by the dissociation energy of the corresponding molecule.Effects of dilution, the influence of pressure and interference problems in poly-component systems, as well as restrictions for the applicability of the normalized temperature concept, are discussed.     

Studies on dissociation energies of diatomic molecules using vibrational spectroscopic constants

New analytical expression and numerical approach are suggested to calculate dissociation energies De of diatomic molecular states using an extreme value method (EVM). Studies on some electronic states of OH, BH, N2, Br2, ClF and CO molecules show that the accuracy of the EVM dissociation energies depends on the number of correct vibrational constants used in the calculations. The convergence qualities of De are suggested to be an alternative physical criterion to measure the qualities of the various sets of vibrational constants from different literature for the same diatomic state.     

Studies on heteronuclear diatomic molecular dissociation energies using algebraic energy method

The algebraic energy method (AEM) is applied to the study of molecular dissociation energy $D_e$ for 11 heteronuclear diatomic electronic states: $a^3\Sigma^+$ state of NaK, $X^2\Sigma^+$ state of XeBr, $X^2\Sigma^+$ state of HgI, $X^1\Sigma^+$ state of LiH, $A^3\Pi(1)$ state of ICl, $X^1\Sigma^+$ state of CsH, $A(^3\Pi_1)$ and $B0^+(^3\Pi)$ states of ClF, $2^1\Pi$ state of KRb, $X^1\Sigma^+$ state of CO, and $c^3\Sigma^+$ state of NaK molecule. The results show that the values of $D_e$ computed by using the AEM are satisfactorily accurate compared with experimental ones. The AEM can serve as an economic and useful tool to generate a reliable $D_e$ within an allowed experimental error for the electronic states whose molecular dissociation energies are unavailable from the existing literature.     

双原子离子部分电子态的离解能的精确研究

本文使用基于微扰理论的代数方法(AM),研究了双原子离子F2+的X2Ⅱg,CO+的X2∑+,O2+的A2Ⅱu,BeH+的X1∑+四个电子态的离解能,然后使用最近提出的新公式计算了这些电子态的离解能,并分别与离解能的实验值进行了比较.研究结果表明:使用新公式得到的分子离解能与实验值更加接近;同时AM和新公式相结合的理论方法也适用于双原子离子体系.     

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.     

双原子离子部分电子态的离解能的精确研究

本文使用孙卫国提出的基于微扰理论的代数方法(AM),研究了双原子离子F2+的X2Πg,CO + 的X2Σ+, O2+的A2Πu ,BeH +的X1Σ+ 四个电子态的离解能,然后使用最近提出的新公式计算了这些电子态的离解能,并分别与离解能的实验值进行了比较．研究结果表明：使用新公式得到的分子离解能与实验值更加接近;同时AM和新公式相结合的理论方法也适用于双原子离子体系。     

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.     

Spectroscopic dissociation energies of diatomic alkaline earth oxides

Numerical procedures are employed to determine uncoupled hartree-Fock polarizabilities α₀ for members of the Ne, Mg and Ar isoelectronic sequences. For each system the first-order correction (α₁) to the polarizability is evaluated and it is found that both α₀ + α₁ and the ‘geometric approximation’ α₀/(1 - α₁/α₀) are generally in accord with polarizabilities determined from the fully coupled Hartree-Fock scheme. It is concluded that, as for smaller systems, this approach provides an economical means of obtaining a satisfactory approximation to the coupled Hartree-Fock polarizability of an atom.     

Dissociation energy of diatomic molecules

The dissociation energy of twelve diatomic molecules has been determined by fitting four-parameter potential functionU(r)=D _e[[1−exp{−b(r−r _e)}]/ [1−Cexp{−b(r−r _e)}]]² to the true Rydberg-Klein-Rees (RKR) curves for their fifteen electronic states using the mean square deviation as the criterion for the selection of the best fit. Average deviation ofD _e has been found to be 2.7% as compared to 20.5% obtained with Lippincott’s potential function for these molecules. In addition the anharmonocity constantω _ex_e has also been calculated for the same electronic states yielding average mean deviation 8.9%.     

Dissociation energy of diatomic molecules

We propose a modified potential energy function that is as easily used as the Hulburt-Hirschfelder (H-H) function. Dissociation energies have been estimated for MgO, CaO, and SrO and other molecules.     

Scaling properties of adsorption energies for hydrogen-containing molecules on transition-metal surfaces

Density functional theory calculations are presented for CHx, x=0,1,2,3, NHx, x=0,1,2, OHx, x=0,1, and SHx, x=0,1 adsorption on a range of close-packed and stepped transition-metal surfaces. We find that the adsorption energy of any of the molecules considered scales approximately with the adsorption energy of the central, C, N, O, or S atom, the scaling constant depending only on x. A model is proposed to understand this behavior. The scaling model is developed into a general framework for estimating the reaction energies for hydrogenation and dehydrogenation reactions.     

Self-entanglement and the dissociation of homonuclear diatomic molecules

The concept of self-entanglement is introduced to describe a mixed state or ensemble density as a pure state in an augmented Hilbert space formed by the products of the individual states forming a mixed state (or ensemble). We use this representation of mixed states to show that upon dissociation a neutral homonuclear diatomic molecule will separate into two neutral atoms.     

Multiphoton dissociation of diatomic molecules at high intensities

A non-perturbative method is used to obtain an analytic expression for the rate of multiphoton dissociation of diatomic molecules as a function of the incident radiation. The two-photon dissociation process is considered as an example.