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)     

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.}     

分子部分电子态的高阶振动能级和离解能的精确研究

鉴于K₂分子电子态的振动能谱和分子离解能D_e在实际研究和应用中的重要性,应用Sun,Ren等人提出的基于微扰理论的代数方法(AM)和基于AM的代数能量方法(AEM)研究了K₂分子的X¹Σ⁺_g,a³Σ⁺_u,0^-_g,B¹Π_{u< 关键词： 2}分子')" href="#">K₂分子 代数方法 高阶振动能级 离解能     

Theoretical determination of the vibrational levels of NH+ 3 and its isotopomers

The vibrational levels associated with the electronic ground state X²A₂″ of NH⁺ ₃ have been determined up to 5000 cm^?1 by perturbation and variational calculations with full dimensionality of the molecule. For the variational part a new version of MULTIMODE was used which uses the ab initio electronic energy and its first derivative to define the potential energy function. These quantities were generated by the B97-1 density functional and RCCSD(T) approaches. For ND⁺ ₃, ND₂H⁺ and NDH⁺ ₂ the vibrational levels were calculated only by perturbation theory. The rotational constants for all the isotopomers were determined and the first transition dipole moments for NH⁺ ₃ and ND⁺ ₃ were plotted. A critical comparison of the perturbation and variational techniques suggests a possible further modification to the MULTIMODE algorithm for large systems.     

AsO+同位素离子X2∑+和A2∏电子态的多参考组态相互作用方法研究

采用包含Davidson修正多参考组态相互作用(MRCI)方法结合价态范围内的最大相关一致基As/aug-cc-pV5Z和O/aug-cc-pV6Z, 计算了AsO⁺ (X²∑⁺)和AsO⁺(A²∏)的势能曲线. 利用AsO⁺离子的势能曲线在同位素质量修正的基础上, 拟合出了同位素离子⁷⁵As¹⁶O⁺和⁷⁵As¹⁸O⁺的两个电子态光谱常数. 对于X²∑⁺态的主要同位素离子⁷⁵As¹⁶O⁺, 其光谱常数R_e, ω_e, ω_ex_e, B_e和α_e分别为 0.15770 nm, 1091.07 cm^-1, 5.02017 cm^-1, 0.514826 cm^-1和0.003123 cm^-1; 对于A²∏态的主要同位素离子⁷⁵As¹⁶O⁺, 其T_e, R_e, ω_e, ω_ex_e, B_e和α_e分别为5.248 eV, 0.16982 nm, 776.848 cm^-1, 6.71941 cm^-1, 0.443385 cm^-1和0.003948 cm^-1. 这些数据与已有的实验结果均符合很好. 通过求解核运动的径向薛定谔方程, 找到了J=0时AsO⁺(X²∑⁺)和AsO⁺(A²∏)的前20个振动态. 对于每一振动态, 还分别计算了它的振动能级、转动惯量及离心畸变常数, 并进行了同位素质量修正, 得到各同位素离子的分子常数. 这些结果与已有的实验值非常一致. 本文对于同位素离子⁷⁵As¹⁶O⁺(X¹∑⁺), ⁷⁵As¹⁸O⁺(X¹∑⁺), ⁷⁵As¹⁶O⁺(A¹∏)和⁷⁵As¹⁶O⁺(A¹∏)的光谱常数和分子常数属首次报导.     

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 potential energy function and spectroscopic study of the X^2∑＋, A^2П and B^2∑＋ states of the CP radical

This paper calculates the equilibrium internuclear separations, the harmonic frequencies and the potential energy curves of the X^2∑＋, A^2П and B^2∑＋ states of the CP radical by the highly accurate valence internally contracted multireference configuration interaction method with correlation-consistent basis sets （aug-cc-pV6Z for C atom and aug-cc-pVQZ for P atom）. The potential energy curves are all fitted with the analytic potential energy function by the least-square fitting. Employing the analytic potential energy function, we determine the spectroscopic constants （Be, αe and ωeχe） of these states. For the X2∑＋ state, the obtained values of De, Be, αe, ωeχe, Re and ωe are 5.4831 eV, 0.792119 cm-1, 0.005521 cm-1, 6.89653 cm-1, 0.15683 nm, 12535.11 cm-1, respectively. For the A2H state, the present values of De, Be,αe, ωeχe, Re and We are 4.586 eV, 0.703333 cm-1, 0.005458 cm-1, 6.03398 cm-1, 0.16613 nm, 1057.89 cm-1, respectively. For the B2E＋ state, the present values of De, Be, αe, ωeχe, Re and We are 3.506 eV, 0.677561 cm-1, 0.00603298 cm-1, 5.68809 cm-1, 0.1696 nm, 822.554 cm-1, respectively. For these states, the vibrational states with the rotational quantum number J equals zero （J = 0） are studied by solving the radial nuclear Schr6dinger equation using the Numerov method. For each vibrational state, the vibrational level, the classical turning points, the rotational inertial and the centrifugal distortion constants are calculated. Comparison is made with recent theoretical and experimental results.     

First high-resolution analysis of the 4ν1+ν3 band of nitrogen dioxide near 1.5 μm

The high-resolution absorption spectrum of the 4ν₁+ν₃ band of the ¹⁴N¹⁶O₂ molecule was recorded by CW-Cavity Ring Down Spectroscopy between 6575 and 6700 cm⁻¹. The assignments involve energy levels of the (4,0,1) vibrational state with rotational quantum numbers up to K_a=8 and N=48. A large majority of the spin-rotation energy levels were reproduced within their experimental uncertainty using a theoretical model which takes explicitly into account the Coriolis interactions between the spin-rotational levels of the (4,0,1) vibrational state and those of the (4,2,0) and of (0,9,0) dark states, the anharmonic interactions between the (4,2,0) and (0,9,0) states together with the electron spin-rotation resonances within the (4,0,1), (4,2,0) and (0,9,0) states. Precise vibrational energies, rotational, spin-rotational, and coupling constants were determined for the {(4,2,0), (0,9,0), (4,0,1)} triad of interacting states. Using these parameters and the value of the transition dipole-moment operator determined from a fit of a selection of experimental line intensities, the synthetic spectrum of the 4ν₁+ν₃ band was generated and is provided as Supplementary Material.     

Rotational and vibrational temperatures of electronically excited BiN radicals in a chemiluminescent flame

Rotational and vibrational temperatures of electronically excited BiN radicals in a low-pressure Bi_x+N/N₂*/N₂+Ar chemiluminescent flame have been deduced from high-resolution Fourier-transform emission spectra. Bands of three electronic transitions, a³Σ⁺(a₁1)→X¹Σ⁺(X0⁺), b⁵Σ⁺(b₁0⁺)→X¹Σ⁺(X0⁺), and b⁵Σ⁺(b₁0⁺)→a ³Σ⁺(a₁1), were analysed to determine the optical temperatures in the a³Σ⁺(a₁1) and b⁵Σ⁺(b₁0⁺) states. The rotational temperatures characterising the rotational populations in the a₁1, v=0 and 1 states were determined from the a₁→X, 0-2, 0-3, 0-4, 1-1, and 1-2 bands. The b₁→X, 0-8 and 0-11 bands, and the b₁→a₁, 0-0 bands served to determine the rotational temperature of the radicals in the b₁0⁺, v=0 state. The temperatures derived from the various bands and transitions were well consistent and the mean rotational temperature was determined to be 353±18 K, which is close to the translational temperature of the gas.Vibrational temperatures of the radicals in the a₁1 and b₁0⁺ states were derived from band intensities of the a₁→X and from the b₁→X as well as b₁→a₁ systems, respectively. The Franck-Condon factors needed were calculated with RKR potentials deduced from literature values of the rotational and vibrational constants in the three states involved. The a₁1 vibrational temperature (336±21 K) was close to the rotational temperature, while the b₁0⁺ vibrational temperature (438±36 K) differed, likely due to the previously observed perturbation of the b₁0⁺ state.     

Ab initio investigation of the electronic and vibrational properties for the (CaLi)+ ionic molecule

A wide adiabatic study has been performed for numerous electronic states of CaLi⁺ molecular ion. The adiabatic potential energy curves and their spectroscopic constants (R_e, D_e, ω_e and T_e) have been calculated using an ab initio approach including a nonempirical pseudo-potential for the Ca and Li cores with the core polarisation potentials operator through full configuration interaction (FCI). Thereafter, the energies of vibrational levels and their spacing for all these states have been reported. In addition, the electric dipole moment curves have been investigated for the (1-19) Σ, (1-12) Π and (1-8) Δ electric states. Moreover it lets us check the extreme transition dipole moments (TDM). These behaviours of TDM are more accustomed to estimate the radiative lifetimes for all vibrational levels in 2¹Σ⁺ and 3¹Σ⁺ states. Also, the bound-bound and the bound-free contribution have been calculated precisely and by employing a Franck–Condon (FC) approximation.     

New high-resolution analysis of the {ν1 + ν3} band of the NO2 isotopomer of nitrogen dioxide: Line positions and intensities

The high-resolution Fourier transform absorption spectrum of an isotopic sample of nitrogen dioxide, ¹⁵N¹⁶O₂, was recorded in the 3.4 μm region. Starting from the results of a previous study [Y. Hamada, J. Mol. Struct. 242 (1991) 367-377] a new analysis of the ν₁ + ν₃ band located at 2858.7077 cm⁻¹ has been performed. This new assignment concerns (1 0 1) energy levels involving rotational quantum numbers up to K_a = 10 and N = 54. Using a theoretical model which accounts for both the electron spin-rotation resonances within each vibrational state and the Coriolis interactions between the (1 2 0) and (1 0 1) vibrational states, the spin-rotation energy levels of the (1 0 1) vibrational state could be reproduced within their experimental uncertainty. In this way, the precise vibrational energy, rotational, spin-rotation, and coupling constants were achieved for the {(1 2 0), (1 0 1)} interacting states of ¹⁵N¹⁶O₂. Using these parameters and the transition moment operator which was obtained for the main isotopic species, ¹⁴N¹⁶O₂, a comprehensive list of the line positions and intensities was generated for the ν₁ + ν₃ band of ¹⁵N¹⁶O₂.     

Vibrational and rotational energy transfer of CH+ in collisions with 4He and 3He

A quantum mechanical investigation of vibrational and rotational energy transfer in cold and ultra cold collisions of CH⁺ with ³He and ⁴He atoms is presented. Ab initio potential energy calculations are carried out at the BCCD(T) level and a global 3D potential energy surface is obtained using the Reproducing Kernel Hilbert Space (RKHS) method. Close coupling scattering calculations using this surface are performed at collision energy ranging from 10^-6 to 2000 cm^-1. In the very low collision energy limit, the vibrational and rotational quenching cross sections of CH⁺ in collisions with He are found to be of the same order of magnitude. This unusual result is attributed to the large angular anisotropy of the intermolecular potential and to the unusually small equilibrium value of the Jacobi R coordinate of the He–CH⁺ complex. As for the He–N₂ ⁺ collision, we also find a strong isotope effect in the very low collision energy range which is analyzed in terms of scattering length and the differences between these two collisions are also discussed.     

The absorption spectrum of 12C2H2 between 12800 and 18500cm−1 II. Rotational analysis

The rotational structure of the vibrational bands of ¹²C₂H₂ is investigated in three spectral energy regions not previously systematically explored at high resolution, 12800–13500 cm^?1, 14000–15200 cm^?1 and 16500–18360 cm^?1, on the basis of new spectral data recorded by intracavity laser absorption spectroscopy. The rotational analysis of 17 new absorption bands arising from the ground state is reported (11 Σ_u ⁺ ? Σ_g ⁺ bands and 6Π_u ? Σ_g ⁺ bands). Four bands in the range studied show strong perturbations affecting both the line positions and intensities. Their detailed analysis is performed in order to determine the nature of the coupling schemes, the vibrational species and the rotational constants of the perturber states. Altogether, the vibration-rotation parameters of 21 newly observed vibrational states are derived.     

High resolution laser excitation spectroscopy of barium monosulfide

High-resolution spectra of BaS were recorded using laser excitation spectroscopy. BaS molecules were synthesized in a Broida-type oven. The observed rotationally-resolved spectrum of BaS in the 12 100–12 765 cm^?1 spectral range contains the 2-1, 3-1, 3-2, 4-2, 5-2, 5-3 vibrational bands of the A′¹Π–X¹Σ⁺ transition and the 4-1, 5-1, 5-2 vibrational bands of the a³Π₁–X¹Σ⁺ transition. Approximately 1000 lines of the A′¹Π–X¹Σ⁺ transition and 600 lines of the a³Π₁–X¹Σ⁺ transition for the main isotopologue ¹³⁸Ba³²S (67.5% natural abundance) were measured. Rotational and vibrational parameters were derived for the A′¹Π and a³Π₁ states.     

Spectroscopic study of an rf discharge in nitrogen

The absolute populations of the vibrational levels of the B³Πg and C³Π_u states in an rf nitrogen discharge are calculated from the quantum yields of the 1⁺ and 2⁺ systems in the discharge, and the “excitation temperature” of these states is measured. Emission spectroscopic methods are used to determine the vibrational and rotational temperatures of the C³Π_u state, as well as the vibrational temperature of the B³Π_g state. These data are used to estimate the vibrational temperature of the X′∑ _g ⁺ state and the stored energy in the activated nitrogen, and to examine the mechanism by which translational-vibrational degrees of freedom are excited in nitrogen molecules in the discharge.     

A symmetry adapted approach to vibrational excitations in atomic clusters

An algebraic method especially suited to describe the strongly anharmonic vibrational spectra in molecules may be an appropriate framework to study the vibrational spectra of Na _n ⁺ clusters, where nearly flat potential energy surfaces and the appearance of close lying isomers have been reported. As an illustration we describe the model and apply it to the Be₄, H ₃ ⁺ , Be₃ and Na ₃ ⁺ clusters. Presented by A. Frank at the International Conference on “Atomic Nuclei and Metallic Clusters”, Prague, September 1–5, 1997. This work was supported in part by the European Community under contract No. CI1*-CT94-0072, DGAPA-UNAM under project IN101997 and Spanish DGCYT under project PB92-0663.     

Dissociative excitation of HD+, D2+ , and DT+ by electron impact

In the framework of the Multi-Channel Quantum Defect Theory (MQDT), a theoretical study of the dissociative excitation is presented. Numerical results for the dissociative excitation cross sections of HD ⁺, D ₂⁺, and DT ⁺ with electrons of energy between 2 and 12 eV are reported. The contribution of the vibrational continua of the two lowest electronic states as explicit ionization channels has been considered. Within a quasi-diabatic representation of the molecular electronic states, the Born expansion of second order is done in the K-matrix evaluation.     

A refined potential energy function for the electronic ground state of H2Se

The potential energy surface for the electronic ground state of the hydrogen selenide molecule has been determined previously by Jensen and Kozin [J. Mol. Spectrosc. 160 (1993) 39] in a fitting to experimental data by means of the MORBID computer program. We report here a further refinement of this surface, also made with the MORBID program. With the refined potential surface, we can make predictions of rotation-vibration transition wavenumbers for H₂Se, D₂Se, and HDSe, and with these predictions we can assign weak spectra of these molecules. We assign here two very weak bands of HD⁸⁰Se, ν₁+ν₂+ν₃ and 2ν₁+ν₃. The refinement of the potential energy surface was made possible because (1) the number of vibrational states characterized experimentally for various isotopomers of H₂Se has approximately doubled since 1993, and (2) we now have access to larger computers with which we can fit energy spacings of states with J?8, whereas Jensen and Kozin could only use J?5. In the present work, we fitted rotation-vibration energy spacings associated with 24 vibrational states of H₂⁸⁰Se with v₁?6, v₂?3, and v₃?2; 11 vibrational states of D₂⁸⁰Se with v₁?2, v₂?3, and v₃?2, and 17 vibrational states of HD⁸⁰Se with v₁?3, v₂?3, and v₃?3. The input data set comprised 3611 energy spacings. In the fitting, we could usefully vary 29 potential energy parameters. The standard deviation of the fitting was 0.12 cm⁻¹ and the root-mean-square deviation for 49 vibrational term values was 0.59 cm⁻¹.