On the dipole moments of some excited electronic states of HfS and HfO

Stark measurements of the dipole moments in excited states of hafnium mono-sulfide, ¹⁸⁰Hf³²S, and hafnium mono-oxide, ¹⁸⁰Hf¹⁶O, have been performed. The molecules were produced using a laser ablation source combined with a time-of-flight mass spectrometer, where a static electric field was applied. From the first order Stark effect splitting the permanent electric dipole moments, μ, were determined to be 3.416(23) D and 3.478(25) D for the HfS and v=1 states, respectively, and 2.665(29) D for the HfO state. The e- and f-parity mixing due to the Stark effect was examined. Field-free low temperature spectra for the (0,0), (1,0), and (2,0) bands of the - transition of HfS and the (0,0) band of the - transition of HfO were recorded and analyzed. Term-value calculations were performed, including most previously reported spectra, and potential energy curves and sets of molecular parameters were extracted.     

Magnetic dipole moments of collective quadrupole excited states

Magnetic dipole moments for low-lying collective quadrupole excitations are studied in heavy and medium-heavy nuclei within the framework of the Interacting Boson Model (IBM-2). In the present study, we concentrate mainly on the fully symmetric representations of the U(6) group and their magnetic dipole moments. We shortly discuss the lowest non-symmetric 1⁺ level. Comparison with other collective model calculations of g_R and microscopic studies as well as with experimental data is performed.The authors are most grateful to A.E.L.Dieperink and coworkers for the generous help and permission to quote largely from their recent results on magnetic dipole moments in nuclei.They are also indebted to A.Richter,O.Scholten and Iachello for many stimulating discussions. They thank the NFWO,IIKW and the IWONL for financial support.     

Method of describing highly excited vibrational-rotational states of diatomic molecules

Institute of Applied Physics, Academy of Sciences of the USSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 33, No. 3, pp. 281–289, March, 1990.     

A new generalized spectral luminescent method for determining dipole moments of molecules in the ground and excited states

An original spectral luminescent method for determining dipole moments of molecules in the ground and excited states was proposed, and its preliminarily tests were made. It is based on a combined quantitative analysis of experimental data on the linear (solvation) and nonlinear (complex formation) components of the orientation shift of electronic and vibrational spectra of molecules in two-and three-component solutions. To realize the method in practice, one should make a series of standard measurements of the position of absorption bands or the stationary luminescence of diluted solutions of a substance under study in several rationally chosen liquid individual and binary solvents at the room temperature. The distinctive feature of the method is that it is based on the use of spectroscopic data only and does not require that the equilibrium value of the effective radius of the intermolecular interaction (Onsager radius of a molecule of a diluted substance) be specified and the angles between the moments of ground and excited states be known.     

On the Zeeman effect in electronic transitions of diatomic molecules

The Zeeman effect for diatomic molecules is calculated in a representation with Hund's case (a) wave functions as a basis set. The resulting expressions are simpler and easier to handle than those obtained from previous calculations on the basis of cace (b) wave functions. The calculations of intensities and polarization of Zeeman patterns is presented for transitions between doublet states with arbitrary spin-orbit (if Λ≠ 0) or spin-rotation (if Λ = 0) interaction, and for case (a)-case (a) transitions of any multiplicity. These calculations are in good agreement with observations.     

Adequate representation of the dipole moment function for diatomic molecules and the matrices of vibration-rotation transition moments

An exponential representation of perturbations is used as a basis of the perturbed Morse oscillator approach which is applied, in a matrix form, for calculating the radial matrix elements for diatomic molecules. An analytic procedure is developed to deduce an exponential-power series expansion for the dipole moment function M(r) from experimental spectral intensities. It is shown that for real anharmonic molecules, the series expansion in powers of e^ar (α being the Morse parameter) is an adequate form for representing transition operators, just as the usual series expansion in powers of internuclear distance r is adequate for the case of a harmonic oscillator, and it is equivalent to a series expansion in vibrational wavefunctions. An exponential-power series expansion is derived as well for a model dipole moment function which has a correct long-range dependence and limit. To exemplify the accuracy and efficiency of the technique proposed, the (40 × 40) matrices of vibration-rotation transition moments 〈vJ|M(r)|v′J′〉(v, v′ = 0, 1, …, 39) have been calculated for the ground state of CO. Typical results of these computations are presented (up to v = 35, J = 100, and v′ ? v = 1–4) to illustrate the dependence of vibration-rotation interaction functions on the vibrational and rotational quantum numbers.     

Theoretical study of the electronic states and transition dipole moments of the LiK molecule

The adiabatic potential energy, the spectroscopic constants and the transition dipole moments of the lowest electronic states of the LiK⁺ molecule, dissociating into Li(2s, 2p, 3s, 3p, 3d, 4s, and 4p) + K⁺ and Li⁺ + K(4s, 4p, 5s, 3d, 5p, 4d, and 6s), have been investigated. We have used an ab initio approach involving a non-empirical pseudopotential for the Li (1s²) and K (1s²2s²2p⁶3s²3p⁶) cores and core valence correlation correction. A very good agreement has been obtained for the ground state for the spectroscopic constants with the available theoretical works. The transition dipole moment from X²Σ, 2²Σ, 3²Σ, and 4²Σ states to higher excited states have been determined. Numerous avoided crossing between electronic states of ²Σ and ²Π symmetries, have been localised and analysed. Their existences are related to the charge transfer process between the two ionic systems Li⁺K and LiK⁺.     

On Λ-type doubling in multiplet states of diatomic molecules

Explicit expressions valid in the neighborhood of Hund's case (a) and (b) are obtained for the width of Λ-type doubling of multiplet Π terms up to septet multiplicity. Moreover, a relation between the constants occurring in the expressions of Hund's cases (a) and (b) is given.     

用杂化CIS-DFT方法研究外电场对乙烯激发态的影响

采用杂化CIS-DFT方法研究了外电场对乙烯分子基态和激发态性质的影响,结果表明外电场对分子几何结构,总能量,偶极矩,极化率,振子强度和激发能有显著影响.CIS-DFT的优点在于能确定外场下分子的对称性,给出正确的激发顺序以及分子轨道的电子组态,由此导出乙烯分子的激发态,结果与实验一致.首次研究了乙烯分子的外电场效应.与其他从头算方法相比,杂化CIS-DFT方法计算精确和效率相对较高,可用于研究大分子体系.     

双原子分子激发态转动传能量子干涉效应模型

物质波的干涉是由于微观粒子具有波的特性而产生的干涉现象.对于双原子分子单三重混合态转动传能过程具有波动特性,两个通道间存在量子干涉效应.基于玻恩近似的微扰理论,本文利用各向异性相互作用势和直线轨迹近似给出了包含干涉相位角的干涉表达式,建立了新的量子干涉模型,并讨论了此模型中利用的近似理论.     

双原子分子激发态转动传能量子干涉效应模型

物质波的干涉是由于微观粒子具有波的特性而产生的干涉现象。对于双原子分子单三重混合态转动传能过程具有波动特性,两个通道间存在量子干涉效应。基于玻恩近似的微扰理论,本文利用各向异性相互作用势和直线轨迹近似给出了包含干涉相位角的干涉表达式,建立了新的量子干涉模型,并讨论了此模型中利用的近似理论。     

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.     

Kinetics of dipole moments of polyatomic molecules

The relations that link the time dependences of the dipole moments of the ground and excited states of a molecular system whose charge distribution is nonstationary with the correlation functions of the shift of the absorption and emission spectra of this system are derived on the basis of of the well-known equations of solvatochromism. The calculated dependences of the kinetics of the dipole moments of the excited singlet states of dimethylaminobenzonitrile and 4-dimethylamino-4′-cyanostilbene in some polar solvents are presented.     

Ab initio calculation of transition dipole moments for transitions between valence states in oxygen molecules

Results of ab initio calculations of potential-energy curves for 20 singlet and 20 triplet valence states of oxygen with configuration interaction taken into account in the 6-31G basis are presented. Transition dipole moments of triplet-triplet (1³Π_g ← B ³Σ _u ^? , 1³Π_g ← A ³Σ _u ⁺ , 1³Π_g ← A′ ³Δ_u, B ³Σ _u ^? ← X ³Σ _g ^? , 2³Π_u ← 1³Π _g, 2³Σ _g ^? ← B ³Σ _u ^? , 1³Π_u ← X ³Σ _g ^? , 2³Π_u ← X ³Σ _g ^? , 2³Π _g ← A′³Δ_u, 3³Π_g ← A′ ³Δ _u, 2³Δ_u ← 2³Π_g, 3³Π_g ← B ³Σ _u ^? , and 2³Π_g ← A ³Σ _u ⁺ ) and singlet-singlet (2¹Σ _g ⁺ ← 2¹Π_u, 2¹Π_u ← 1¹Π ^g, ¹Π_u ← 2¹Δ_g, 1¹Π_g ← c ¹Σ _u ^? , ¹Π_u ← b ¹Σ _g ⁺ , 1¹Δ _u ← a ¹Δ_g, 2¹Π_u ← a ¹Δ_g, 2¹Δ_g ← 1¹Δ_u, ¹Π _u ← a ¹Δ _g, 1¹Π_u ← b ¹Σ _g ⁺ , 2¹Π_g ← 1¹Π_u, 2¹Π _g ← c ¹Σ _u ^? , 1¹Δ _u ← 1¹Π _g, f′Σ _u ⁺ ← b ¹Σ _g ⁺ , 2¹Σ _g ⁺ ← f ′¹Σ _u ⁺ , 3¹Π_g ← 1¹Δ_u) radiative transitions are calculated as functions of internuclear separation. The possibility of observing these transitions under experimental conditions is discussed.     

Electronic transition dipole moments and excited-state alignment in linear molecules,with application to diatomic rare gas halides

The relationship between the direction of transition dipoles and the symmetry of electronic wavefunctions is investigated. In the case of $\text{Ω}\text{=}\text{1}\text{2}\text{?}\text{Ω′}\text{=}\text{1}\text{2}$ transitions, the dipole direction is not determined by symmetry alone. However, in all other cases the directions (parallel or perpendicular) are specified by simple selection rules based upon $\text{ΔΩ}$. In $\text{Ω}\text{=}\text{1}\text{2}\text{Ω′}\text{=}\text{1}\text{2}$ transitions, the transition dipole may accidentally have spherical symmetry, in which case a linearly polarized plane wave photon beam produces an unaligned excited-state distribution. These results are applied to the ultraviolet charge transfer transitions of the diatomic rare gas halides.     

Calculations of diatomic molecules with the LCTCO method. Doubly excited states of the H2 molecule

Nonempirical calculations of 20 autoionizing states of the H₂ molecule are performed in a two-center orbital basis and for two values of the internuclear distance. Results obtained are compared with other results known from the literature.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 31–34, July, 1986.