Theoretical study of the reaction of H2 with a Cu2Pt2 cluster

The study of the interaction of a pyramidal tetramer of Cu₂Pt₂ with the H₂ is reported here through ab initio multiconfigurational self-consistent field (MC-SCF) calculations, plus extensive multireference configuration interaction (MR-CI), variational and perturbative calculations. The lowest three electronic states X ¹A′, a ³A′ and a ¹A′ of the bare cluster were considered in order to study this interaction. For the H₂ C_s approaching a Pt vertex, results show that the Cu₂Pt₂ pyramid cluster in its X ¹A′ and a ¹A′ states can spontaneously capture and dissociate the H₂. For the H₂ C_s approaching a Cu vertex, where H₂ is located in the C_s reflecting plane, the Cu₂Pt₂ cluster in its X ¹A′ electronic state shows capture of the hydrogen molecule after surmounting an energy barrier; moreover, in this approach the Cu₂Pt₂ cluster in its a ¹A′ electronic state shows spontaneous capture of the hydrogen molecule. For the H₂ approaching a Cu vertex, where the C_s reflecting plane bisects the H₂ molecule, the Cu₂Pt₂ cluster in its three lowest-lying states is able to capture the hydrogen molecule after surmounting a small barrier. The Cu₂Pt₂+H₂ C_s face-on interactions show a lower H₂ activation than that which was obtained in the equivalent Pt₄+H₂ interactions.     

用能量自洽法研究碱金属双原子分子的势能曲线

用能量自洽法(ECM)研究了碱金属双原子分子一些电子激发态的势能曲线：Na₂ 分子的2¹Π_g,4³Π_g和b³Π< sub>u电子激发态,K₂分子的a³Σ^＋_{u,2¹Πg,B¹Πu和A^{关键词： 能量自洽 双原子分子 势能 碱金属}}     

Low-lying electronic states of LiF molecule with inner electrons correlation

The potential energy curves and dipole moments of the low-lying electronic states of LiF molecule are performed by using highly accurate multi-reference configuration interaction with Awcv5z basis sets. 1s, the inner shell of Li is considered as the closed orbit, which is used to characterise the spectroscopic properties of a manifold of singlet and triplet states. 16 electronic states correlate with two lowest dissociation channels Li(²S)+F(²P) and Li(²P)+F(²P) are investigated. Spectroscopic parameters of the ground state X¹Σ⁺ have been evaluated and critically compared with the available experimental values and the other theoretical data. However, spectroscopic parameters of 1³Π, 1¹Δ, 1¹Σ^?, 1¹Π, 1³Σ⁺, 2³Σ⁺, 1³Δ, 1³Σ^?, 2³Π, 2¹Π, 3³Π, 3¹Π and 3³Σ⁺ states are studied for the first time. These 13 excited states have shallow potential wells, and the dispersion coefficients of these excited states are predicted. In additional, oscillator strengths of excited states at equilibrium distances are also predicted.     

Rydberg states of the HeH+ ion calculated by ab initio methods: potential energies and effective principal quantum numbers

More than 80 excited electronic states of the hydrohelium ion HeH⁺ of ^{1, 3}Σ⁺, ^{1, 3}Π, ^{1, 3}Δ, ^{1, 3}Φ and ^{1, 3}Γ symmetry have been calculated ab initio up to n = 6 for internuclear distances ranging from 0.5 to 100 bohr. The computations involve a configuration interaction (CI) treatment based on a home-made suite of programs that uses special basis sets designed for the representation of molecular Rydberg states. The results are compared with previous computations where these are available (up to n = 4), and it is found that except for the very lowest excited states, the present energies are consistently lower than those obtained previously, with an average lowering corresponding to several hundred cm^?1. It is shown that with the exception of its ground state, HeH⁺ is an effective one-electron system having an overall electronic structure similar to H⁺₂. The interaction of the excited electron with the He⁺ 1s core electron causes small singlet–triplet splittings to appear and ?-mixing interactions to occur, that are not present in H⁺₂.     

An ab initio investigation of the low-lying electronic states of BeH

Potential energy curves(PECs) for the ground state(X 2 Σ +) and the four excited electronic states(A 2 Π,B 2 Π,C 2 Σ +,4 Π) of a BeH molecule are calculated using the multi-configuration reference single and double excited configuration interaction(MRCI) approach in combination with the aug-cc-pVTZ basis sets.The calculation covers the internuclear distance ranging from 0.07 nm to 0.70 nm,and the equilibrium bond length R e and the vertical excited energy T e are determined directly.It is evident that the X2Σ+,A2Π,B2Π,C2Σ+ states are bound and 4Π is a repulsive excited state.With the potentials,all of the vibrational levels and inertial rotation constants are predicted when the rotational quantum number J is set to be equal to zero(J = 0) by numerically solving the radial Schr¨odinger equation of nuclear motion.Then the spectroscopic data are obtained including the rotation coupling constant ω e,the anharmonic constant ωexe,the equilibrium rotation constant Be,and the vibration-rotation coupling constant αe.These values are compared with the theoretical and experimental results currently available,showing that they are in agreement with each other.     

Accurate theoretical spectroscopic investigations of the 20 Λ-S and 58 Ω states of O2+ cation including the spin–orbit coupling effect

The potential energy curves (PECs) are calculated for the 20 Λ-S states (X²Π_g, A²Π_u, B²Σ^?_g, a⁴Π_u, b⁴Σ^?_g, b′⁴Π_g, c⁴Σ^?_u, 1²Σ⁺_g, 1²Σ⁺_u, 1²Σ^?_u, 1⁴Σ⁺_g, 1⁴Σ⁺_u, 1⁴Δ_g, 1⁴Δ_u, 1⁶Σ⁺_g, 1⁶Σ⁺_u, 1⁶Π_g, 1⁶Π_u, 2⁴Π_g and 2⁴Π_u) of O₂⁺ cation and their corresponding 58 Ω states. Of these 20 Λ-S states, the 1⁶Π_u state is found to be repulsive. The 1²Σ⁺_g, 1⁴Σ⁺_u, c⁴Σ^?_u and 1⁴Δ_u states are found to possess the double well. The b⁴Σ^?_g, 1⁶Σ⁺_g, 1⁴Σ⁺_u, a⁴Π_u, A²Π_u, 1⁶Π_g and 2⁴Π_g states are found to be inverted with the spin–orbit coupling effect included. The b′⁴Π_g, 1⁶Π_g, 1⁶Σ⁺_g, 1⁴Σ⁺_u and 1⁴Δ_u states, and the second well of the 1²Σ⁺_g state are found to be the weakly bound states. The b′⁴Π_g state is found to possess one well with one barrier. The PECs are calculated by the complete active space self-consistent field method, which is followed by the internally contracted multireference configuration interaction approach with the Davidson correction in combination with the aug-cc-pV6Z basis set. The core–valence correlation and scalar relativistic corrections are included. The convergent behaviour of present calculations is discussed with respect to the basis set and theoretical level. The spin–orbit coupling effect is accounted for. The PECs are extrapolated to the complete basis set limit. The spectroscopic parameters are evaluated, and compared with available measurements. It demonstrates that the spectroscopic parameters reported here can be expected to be reliably predicted ones.     

Threshold energy electron impact excitation of carbon dioxide and carbon disulphide

The threshold energy electron impact excitation spectra of CO₂ and CS₂ have been studied using the sulfur hexafluoride scavenger technique. The main results are triplet state excitation and autoionisation of negative ions associated with resonant excited states of the molecules. This confirms previous data concerning diatomic molecules. Furthermore, transitions such as ¹Π_g?X¹Σ_g⁺ and ¹Π_u?X ¹Σ_g⁺ are only weakly induced by low energy electrons, while the corresponding triplet excitations are probably more easily produced. Structures at 5.6, 6.1 and 6.6 eV observed in CS₂ are due to negative ions and/or to ³Π_u, ³Π_g excitation.The autoionisation of CO₂^?(X²Π_u) proceeds also by ejection of a thermal energy electron and leads to highly excited vibrational levels (3–5 eV) of the ground electronic state of CO₂.     

Identification of New Low-Lying Electronic States of the FeF Radical

Dispersed fluorescence studies on the ⁶Π-X⁶Δ and ⁶Φ−X⁶Δ systems of the FeF radical have resulted in the observation of vibrational progressions for transitions to the X⁶Δ state as well as at least two previously unobserved electronic states about 5000 cm⁻¹ above the ground state. The states are assigned as the A⁶Π and B⁶Σ⁺ electronic states. The spin components of both electronic states were found to be heavily perturbed resulting in uneven splittings between them. A third, weak series was also observed but could not be assigned. The (0,0) band of the ⁶Π_7/2−B⁶Σ⁺_5/2 transition at 398 nm was observed in absorption by laser induced fluorescence and its rotational structure was assigned. The spectra obtained were weak because of a poor population of the B⁶Σ⁺ state by the reaction used to form FeF. The levels were found to be markedly perturbed at high J values. Attempts were made to fit the data on the ⁶Π_7/2-B⁶Σ_5/2⁺ system to an effective Hamiltonian, but the presence of perturbations meant that the system is not well described by such a model.     

Li2分子自旋一致激发态a3Σ+u和b3Πu的分析势能函数的从头算

使用对称性匹配簇-组态相互作用方法首次计算了Li₂分子自旋一致激发态a³Σ⁺_u和b³Π_u的离解能、平衡几何及其谐振频率。使用最小二乘法、利用Murrell-Sorbie函数形式拟合出了Li₂分子三重态的第一激发态a³Σ⁺_u 和第二激发态b³Π_u的完整势能函数，并计算了这两个态的光谱常数 (B_e, α_e, ω_e 和 ω_eχ_e) 和力常数 (f₂, f₃和f₄)。得到了Murrell-Sorbie函数形式既适用于基态、又适用于激发态的结论。将计算得到的激发态（a³Σ⁺_u和b³Π_u）的离解能、平衡几何及其谐振频率与实验结果及其它理论计算结果进行了比较。从比较的结果中可以清楚地看出，本文的计算结果在计算精度方面有很大的改进。     

LiC分子基态及其低电子激发态的多参考组态相互作用方法研究

采用包含Davidson修正的多参考组态相互作用(MRCI+Q)方法结合6-311++G(3df,3pd)基组计算了LiC分子基态(X4Σ-)以及五个低电子激发态(a2Π,b2Δ,c2Σ-,d2Σ+,A4Π)的势能曲线.将得到的势能曲线拟合到Murrell-Sorbie解析势能函数形式,确定了对应态的平衡结构Re、谐振频率ωe和离解能De等光谱数据,计算值与仅有的几个其他结果进行了比较.通过求解核运动的薛定谔方程首次报道了LiC分子几个低电子态在J=0下的振动能级、转动惯量和六个离心畸变常数(Dν,Hν,Lν,Mν,Nν和Oν).     

High-Resolution Survey of the Visible Spectrum of NiF by Fourier Transform Spectroscopy

High-resolution spectra of NiF have been recorded in emission by Fourier transform spectroscopy using a very stable discharge source. The 0-0 bands of 14 electronic transitions have been studied, 6 of them for the first time. This work confirms the presence of 5 low-lying spin components X²Π_3/2, [0.25]²Σ⁺, [0.83]A²Δ_5/2, [1.5]B²Σ⁺, and [2.2]A²Δ_3/2 as known from previous laser-induced fluorescence experiments. Eight electronic states are now identified in the 18 000-24 000 cm⁻¹ range above the ground X²Π_3/2 state. Electronic assignments for these excited states are not always obvious because of violations of the selection rules and unusual fine structure parameters. We think that some of the upper states are spin components of quartet states. In such a congested spectrum, high-resolution spectra are best analyzed in conjunction with an energy level diagram constructed mainly by dispersed low resolution laser-induced fluorescence.     

Rotational distribution in simultaneously excited electronic states of CH

A²Δ, B²Σ^? and C²Σ⁺ states of CH were excited in discharges through flowing C₂H₂ and C₂H₄ and in flames of C₂H₂. The rotational distributions in these states were determined from the measured integrated intensities of rotational lines for bands of A²Δ → X²Π, B²Σ^? → X²Π and C²Σ⁺ → X²Π. The A²Δ state exhibits a non-Maxwellian distribution while the B²Σ^? and C²Σ⁺ states show Maxwellian distributions. The non-Maxwellian distribution of the A²Δ state and the different rotational distributions in the three states are discussed.     

Theoretical investigation of the molecular structure and transition dipole moments of the NaK low lying electronic states

The electronic structure and the spectroscopic constants of the low lying electronic states of the NaK⁺ ionic molecule have been determined through using an ab initio approach involving a non-empirical pseudopotential for the Na and K cores and core valence correlation correction. The potential energy of nearly 26 electronic states of ²Σ⁺, ²Π, and ²Δ symmetries has been calculated up to their dissociation limit Na(4d) + K⁺ and Na⁺ + K(6s). Their spectroscopic constants (R_e, D_e, T_e, ω_e, ω_eχ_e, and B_e) are derived and compared with the few available theoretical studies. A good agreement has been found for the ground state and few excited states with previous works. New potential energy curves were presented, for the first time, for the higher excited states. Numerous avoided crossing between electronic states of ²Σ⁺, ²Π symmetries have been localized and analyzed. Their existences are related to the charge transfer between the two ionic molecules Na⁺K and NaK⁺. Furthermore, we have determined the transition dipole moments for several states and analyzed the avoided crossings related to charge transfer between alkaline atoms.     

Electronic and vibrational spectroscopy of the low-lying states of potassium mono-sulphide KS,and comparison in the series of MS (M = Li,Na, K,Rb, Cs)

ABSTRACT

Potential energy curves (PECs) of the lowest electronic states of the potassium mono-sulphide KS have been determined with highly correlated ab initio calculations, using internally contracted multi reference interaction configuration methods including Davidson correction (MRCI?+?Q) with and without considering spin-orbit effects. For the three low-lying bound states, we report a set of spectroscopic parameters including equilibrium distances, dissociation energies, vibrational and rotational constants. The effects of spin-orbit-induced changes on these parameters are also discussed. An analysis of the properties of the three bound states, X²Π, 1²Σ⁺ and 2²Π, illustrates the common characteristics of the whole series of compounds in the MS family (M?=?Li, Na, K, Rb, Cs). Indeed, the shapes of the PECs of these bound states are strongly affected by the interactions between the two ionic states, ²Σ⁺ and ²Π, correlating at large internuclear separations (R_MS) to the first ionic dissociation limit [M⁺?+?S^?] and the electronic states correlating to the three/four lowest dissociation limits. The spectroscopy of these low-lying electronic states and the lifetime of their vibrational levels are thus affected by the spin-orbit interactions which are mainly related to the S atom and consequently common to all alkali-metal mono-sulphides.     

Rydberg states of carbon dioxide and carbon disulfide

The electronic absorption spectra of carbon dioxide and carbon disulfide have been reexamined. Model potential calculations have been used to calculate the energies of excited states in Rydberg approximation, and (npσ) and (npπ) Rydberg series have been assigned. For both molecules, the lowest excited ¹Π_g and ¹Π_u states are identified as Rydberg states. The lowest ${}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ state is mainly Rydberg for CO₂, but contains some valence character for CS₂, There is no evidence for transitions to additional valence states of these symmetries.It is shown that $\text{LCAO}\text{MO}$ predictions about excited states can be misleading because of near-linear dependencies which arise in multicenter expansions. A consideration of the united atom orbitals for CO₂ and CS₂ predicts that there should be only the number of low-energy excited states which are found from the spectral analysis.     

Ab initio configuration interaction study on the electronic structure of the X2Σ+, B2Σ+ and 32Σ+ states of SiO+

The energy levels and electronic structure of the X²Σ⁺, B²Σ⁺ and 3²Σ⁺ states of SiO⁺ are studied using ab initio configuration interaction (CI) calculations at and around their equilibrium internuclear distances R _e. Spectroscopic constants and the vertical excitation energy from the SiO⁺ X²Σ⁺ state are predicted for the 3²Σ⁺ state. Based on the calculated CI wavefunctions, avoided crossings of the potential energy curve for the 3²Σ⁺ state and a near-degeneracy effect in the avoided crossing region are examined. The effects of the mixing of excited configuration state functions in the total electronic wavefunctions for the 1–3 ²Σ⁺ states are investigated by analysing correlation energies in terms of the contributions from classes of excited configurations. The importance of both the near-degeneracy effect and the correlation energy effect in describing correctly the electronic structure of the 3 ²Σ⁺ state in the neighbourhood of its R _e is discussed.     

Spontaneous radiative dissociation in molecular hydrogen

The spontaneous radiative dissociations of the discrete vibrational levels of the B¹Σ⁺_u electronic states of H₂, HD and D₂ of the C¹Π_u electronic state of H₂ into the vibrational continuum of the ground X¹Σ⁺_g state are calculated as a function of the emission wavelength. The fluorescent spectra of HD in the Lyman system and of H₂ in the Werner system resulting from an excitation source uniform in wavelength are predicted. The vibrational radiative lifetimes are tabulated as are the fractions of radiative decays that lead to dissociation. The effects of centrifugal distortion are discussed briefly. An appendix describes a sum rule used to check the numerical accuracy of the calculations.     

Feasibility study of laser cooling of InF molecule

By employing ab initio quantum chemistry method, we investigate the feasibility of laser cooling InF molecule. Four low-lying electronic states (X¹Σ⁺, C¹Π, ³Π and 2³Π) of InF have been calculated using the multi-reference configuration interaction (MRCI) method. The spin-orbit coupling effects are also taken into account in the electronic structure computation at the MRCI level. The highly diagonal Franck-Condon factors for C¹Π → X¹Σ⁺ transitions are estimated. The radiative lifetime of the C¹Π (v′ = 0) state is about 2.22 ns, which is found to be enough short for rapid laser cooling. Though the cooling wavelength of InF is located in the short-wavelength ultraviolet light (UVC), a frequency quadrupled Ti: sapphire laser (189–235 nm) could be capable of generating laser transition wavelength of InF. Furthermore, the C¹Π → X¹Σ⁺ transitions perhaps can be followed by the B³Π₁ → X¹Σ⁺_0⁺ transitions to attain a lower Doppler temperature. Meanwhile, for achieving quasi-closed transition cycle of InF molecule, we investigate the hyperfine structure of the lowest state X¹Σ⁺. Overall, the present results indicate the possibility of laser cooling InF molecules.     

Spectroscopic and molecular properties of 14 selected electronic states of Si2 molecule

The potential energy curves (PECs) of the X³Σ_g⁻, D³Π_u, a¹Δ_g, b¹Π_u, H′³Σ_u⁻, K³Σ_u⁻, 1³Σ_u⁺, 1³Π_g, 2³Σ_u⁺, 2³Π_g, 3³Π_g, 3³Σ_u⁺, 2³Π_u and 2³Σ_g⁻ electronic states of the Si₂ molecule are investigated using the complete active space self-consistent field (CASSCF) method followed by the valence internally contracted multireference configuration interaction (MRCI) approach with the correlation-consistent basis sets of Dunning and co-workers. The effects on the PECs by the core-valence correlation and relativistic corrections are included. The way to consider the relativistic correction is to use the third-order Douglas-Kroll Hamiltonian approximation. The core-valence correlation correction is made with the aug-cc-pCV5Z basis set. And the relativistic correction is performed at the level of cc-pV5Z basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are also corrected for size-extensivity errors by means of the Davidson modification (MRCI+Q). The PECs of all these electronic states are extrapolated to the complete basis set limit by the total-energy extrapolation scheme. Using the PECs, the spectroscopic parameters are determined and compared with those reported in the literature. With these PECs determined by the MRCI+Q/CV+DK+56 calculations, the vibrational levels and inertial rotation constants of the first 20 vibrational states are evaluated and compared with the RKR data for these electronic states when the rotational quantum number J equals zero. On the whole, as expected, the most accurate spectroscopic parameters and molecular constants of the Si₂ molecule are determined by the MRCI+Q/CV+DK+56 calculations. And the spectroscopic parameters of the 1³Σ_u⁺, 1³Π_g, 2³Σ_u⁺, 2³Π_g, 3³Π_g, 3³Σ_u⁺, 2³Π_u and 2³Σ_g⁻ electronic states obtained by the MRCI+Q/CV+DK+56 calculations should be good prediction for future laboratory experiment.     

Calculation of potential energy curves for Rb2 including relativistic effects

All-electron relativistic calculations have been performed on the Rb₂ molecule. The molecular orbitals are optimized within a spin-free no-pair Hamiltonian formalism and spin-orbit coupling is treated using quasi-degenerate perturbation theory. Potential curves of the ground state and several excited states are calculated, and the spectroscopic constants T _e, D _e, R _e and ω_e are in good agreement with experimental values. The spin-orbit splittings at the 5p and 6p asymptotic limits are found to be underestimated by about 30%. Large perturbations in the spectra from the 1¹Σ⁺ _u(A) state are predicted due to an avoided crossing with a 1 ³Π_ub state caused by spin-orbit interaction. The predissociation dynamics of the 2 ¹Π_uC and 3 ¹Π_uD states is discussed. The calculations support the observation that a (1) ³ Δ_u state causes the fast predissociation of the ^{3 1}Π_uD state but rule out the (2)³Σ⁺ _u state as causing the slow predissociation at the lower part of the 3 ¹Π_uD potential energy curve.