On the calculation of matrix elements in diatomic molecules

Group theoretical techniques similar to those employed for transition-metal complexes are applied to diatomic molecules. Expressions are given for reduced matrix elements between configurations with one, two and three electrons outside closed shells. The results agree with previous calculations but predict deviations from simple applications of the hypothesis of pure precession.     

Systematics of diatomic molecular transition moments: Encouraging progress

Literature absolute transition moments for A-X (0-0) bands have been used to obtain “best” values of R_e for some 30 molecules. For isoelectronic sequences, R_e vs Z (heavy)/Z (light) is steeper at abscissae near 1.0 than a larger abscissae, contrary to expectation. For isovalent sequences, e.g. CH, SiH, R_e (WY) is in each lower (average, 53%) than R_e (WX). Suggestions will emerge for measurements which would be helpful in furthering diatomic molecular transition moment systematics.     

Systematics of diatomic molecular transition moments: Encouraging progress—II

Literature absolute transition moments for A-X(0-0) bands have been compiled and used to obtain “best” values of R_e for some 90 transitions. Correlations were sought between R_e and various molecular parameters such as multiplicity, average internuclear separation, etc. None was found. The A-X (and related) R_e have been plotted for isoelectronic molecules against the nuclear charge difference and fitted with simple curves which seem to approach the R_e axis with zero slope. Both of these results are in accord with theory. The concept of isovalence has been clarified to allow for the orbital structure of molecules. It appears that the heavier of two isovalent hydrides has the greater R_e. Graphs of R_e for groups of isovalent molecules can be fitted with simple curves.     

Recommended conventions for defining transition moments and intensity factors in diatomic molecular spectra

Two recommendations are made that can eliminate persistent confusion in the study of diatomic spectroscopy by providing uniform and consistent definitions of the electronic transition moments and the rotational line intensity factors. First, it is recommended that the equation for the line strength of a single rotational line be adopted to specify the relationship between the electronic transition moment and the rotational line intensity factor. Second, it is recommended that the electronic transition moment operator for perpendicular transitions be defined by (1/2^1/2)(μ_x ± iμ_y). The adoption of these conventions results in a value of (2S + 1)(2J + 1) for the sum rule of the rotational line intensity factor for Σ^± ↔ Σ^± transitions and a value of 2(2S + 1)(2J + 1) for the sum rule for all other spin-allowed transitions.     

The C (2 Π)→X(2Σ+) transition in thermal emission spectra of the diatomic alkaline earth bromides) transition in thermal emission spectra of the diatomic alkaline earth bromides

The extensive thermal emission spectrum attributed to the diatomic bromides of calcium, strontium and barium has been observed in the visible region at temperatures about 2200–2400° C, using a vacuum graphite furnace. Many new bands,viz., 141 in CaBr, 53 in SrBr and 68 in BaBr, have been recorded and classified. The vibrational constants agree with those determined by earlier workers and involved the ground state in each case. The transition C→X apears in each molecule and consists of two equally intense systems,viz., C₁→X and C₂→X. The general spectroscopic features of the C→X systems of the bromides of the II A sub group of the periodic table have been compared. They exhibit a close structural similarity and furnish a good example of homologous spectra. The system C→X in all these molecules arises from a C² π−X² Σ ⁺ transition where the² π state appears to be intermediate between Hund’s cases (a) and (b).     

A calculation of some parameters in Migdal's theory of nuclei

Some of the parameters in Migdal's theory of nuclei have been calculated. We used principally Landau's phenomenological approach to obtain the quasi-particle interaction. The energy was calculated by Brueckner's theory. We have used effective interactions which in infinite nuclear matter give the same potential energies in (¹S₀+¹D₂ and (³S₁+³D₁) states as the Hamada-Johnston potential. Other contributions to the binding energy were neglected. The nuclear compressibility K was calculated both from the energy-versus-density curve and from the calculated parameters of Migdal's theory. The results were not in conflict with each other. The values of K obtained were 100–150 MeV, which agrees reasonably well with other calculations in infinite nuclear matter, but they are only about of the values bsed by Migdal and collaborators. We obtained 0.7 for the effective mass and 22–25 MeV for the symmetry energy. The latter result agrees reasonably well with empirical values. An attempt to use the Green function approach in the calculations of the parameters was not successful because of poor convergence, if any.     

Vibrational excitation of diatomic molecular ions in strong field ionization of diatomic molecules

A model based on the strong-field and Born-Oppenheimer approximations qualitatively describes the distribution over vibrational states formed in a diatomic molecular ion following ionization of the neutral molecule by intense laser pulses. Good agreement is found with a recent experiment [X. Urbain et al., Phys. Rev. Lett. 92, 163004 (2004)]. In particular, the observed deviation from a Franck-Condon-like distribution is reproduced. Additionally, we demonstrate control of the vibrational distribution by a variation of the peak intensity or a change of frequency of the laser pulse.     

High order vibrational matrix elements for diatomic molecules; dipole moment function and transition moments of CO

The fifth and sixth-order contributions to the vibrational matrix elements are obtained for the transitions v→v'(v'?v+4) using an eight power internuclear Dunham potential and a quartic power series expansion of the dipole moment function. The results for the dipole moment coefficients M₀ to M₄ of CO and the transition moments R_v^v' (with v=5, 10, 20) deduced from a calculation including succesively third, fourth, fifth and sixth-order perturbation theory are compared. The validity of these results is discussed.Using a quintic dipole moment function, general expressions for the vibrational matrix elements corresponding to the transitions v→v'(v'? v+5) are also presented and the influence of these contributions on the calculation of the dipole moment coefficients as well as the hot band transition moments of CO is shown.     

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。     

Studies on the full vibrational energy spectra for some electronic states of diatomic molecular ions XY+

The first accurate studies on the vibrational spectroscopic constants and the corresponding full vibrational energy spectra of some electronic states of diatomic molecular ions XY⁺ were performed using algebraic method(AM). The AM is applied on the X¹Σ⁺ state of BeH⁺, the X²Σ⁺ state of CO⁺, the X²Π_g state of F ₂ ⁺ , the A²Π_u state of O ₂ ⁺ and the X²Σ _g ⁺ state of Li ₂ ⁺ . The results show that AM can generate accurate vibrational spectroscopic constants as well as accurate full vibrational energy spectra by using some accurate experimental vibrational energies, and that the AM vibrational energies are better than other theoretical data. __________ Translated from Chinese Journal of Atomic and Molecular Physics, 2005, 22 (4) (in Chinese)     

On the electronic spectrum of the diatomic molecular ion

Discrete eigenvalues of the electronic Hamiltonian with dilatation analytic potentials for ionized diatomic molecules are shown to depend smoothly on the distancer of the nuclei forr finite and non vanishing. Furthermore the spectrum is analyzed atr=0 andr=∞ and the eigenvalues turn out to be continuous.     

Experimental transition probabilities of some Xe(I) lines

Using the light absorption technique in a ¹³²Xe afterglow plasma, we have measured the relative transition probabilities for several xenon lines which have the metastable 6s[$\text{3}\text{2}$]₂ or the resonant 6s[$\text{3}\text{2}$]₁ states as their lowest transition level. Because the transition probabilities of the 8819 Å (6p[$\text{5}\text{2}$]₃ ? 6s[$\text{3}\text{2}$]²) and 8280 Å (6p[$\text{1}\text{2}$]₀ ? 6s[$\text{3}\text{2}$]₁) lines are relatively well known, we have chosen these as reference lines and have thus been able to determine the absolute values of the transition probabilities for 19 xenon lines corresponding to transitions from 6p, 6p′, 7p, 8p, 9p, 4f and 5f to 6s[$\text{3}\text{2}$]₂, and for four lines corresponding to the transitions 6p?6s[$\text{3}\text{2}$]₁.     

Model potential for calculation of multiphoton processes in diatomic molecules

The model potential, analogous to the Fues atomic potential is suggested for analytical calculation of the perturbation theory matrix elements, defining interaction of molecule with electromagnetic field. The explicit expressions for the Green and wave functions of the molecular optical electron are received.     

The theoretical calculation of transition probabilities for some excited p-d transitions in atomic nitrogen

The atomic transition probabilities are calculated for individual lines between some quartet terms of 3p↦4d and 3p↦5d transition arrays using weakest bound electron potential model theory (WBEPMT). In the determination of relevant parameters which are needed for calculation of transition probabilities, we employed numerical non-relativistic Hartree-Fock wave functions for expectation values of radius in both ground and excited states unlike to NCA method used on traditional WBEPMT procedure. We have obtained very good agreement between our results and the accepted values taken from NIST.     

High resolution lmm auger electron spectra of some first row transition elements

Auger spectra have been recorded from elements of the first transition series using a hemispherical analyser. Highly resolved LMM spectra were obtained showing for the first time the composite nature of these peaks for many of the elements studied. The recorded spectra show a general similarity for the elements Sc → Zn but interesting differences emerge. At the beginning of the transition period the L₃ based transitions have the relative intensities L₃ M_2,3, M_2,3 > L₃ M_2,3, M_4,5<> L₃ M_4,5, M_4,5 whereas towards the end of the series the order L₃ M_4,5, M_4,5 > L₃ M_2,3, M_4,5<> L₃ M_2,3, M_2,3 is observed. Pronounced chemical shifts have been observed upon oxidation. The spectra are interpreted in terms of an L -S coupling scheme and the fine structure discussed in terms of effects produced by multiplet splitting.     

The mapping of charges in carbonyl complexes of some transition elements from XPS data

A method for internal calibration of ESCA (XPS ) spectra is described that permits the use of a simple relation between binding energy (E_b) and atomic charge (q) : E_b = kq + E_b0. This relation has been shown to hold for a large number of elements. In order to test these relations, a procedure is suggested that allows the calculation of the atomic charges in carbonyl complexes of chromium, iron and nickel from gas-phase and solid-state ESCA data. The agreement with theoretically calculated charge values is good.

The charge distribution in carbon monoxide has been estimated in a similar manner and the result is discussed in relation to other investigations.     

过渡金属(Ni)掺杂ZnV2O4的第一性原理计算

采用基于密度泛函理论下的MS软件模拟了过渡金属Ni掺杂ZnV₂O₄前后的能带结构、态密度以及光学性质.结果表明：ZnV₂O₄具有间接的光学跃迁且能带间隙为0.355 eV,Ni掺杂后能带间隙增加为0.785 eV,且带隙类型不变,引入的Ni-3d轨道电子对ZnV₂O₄的价带和导带组成提供了较大贡献.光学性质结果表明ZnV₂O₄为一种低介电材料,在可见光区的吸收系数和折射率较低,主要表现为紫外吸收.掺杂Ni后,在可见光区的吸收特性和光电导率均增大,有效改善了ZnV₂O₄在可见光区的光电性能.     

On the rotation-vibration interaction of diatomic molecular impurities in cubic crystals

Devonshire's model of the dumb-bell, subjected to a stationary potential of octahedral symmetry type is generalized to be applied to a vibrating rotor. In the framework of this model the influence of the interaction of vibration and hindered rotation is investigated for Ar:HCl.