Absolute rotational assignment of the origin band of the à 2Π u ↔ [Xtilde] 2Π g transition of the diacetylene cation

The rotational analysis of the origin bands of the à ²Π _u -[Xtilde] ²Π _g transition of diacetylene and dideuterodiacetylene cations is considered. Although an analysis for diacetylene cation was made in 1956 by Callomon, some ambiguity remained concerning the absolute numbering and hence led to uncertainty in the derived constants. This situation has now been resolved by recording the emission spectra of this transition of the two isotopic cationic species rotationally cooled to ≈ 10 K in a supersonic free jet, as well as their rotationally resolved laser excitation spectra. By comparison of the Q-branch locations in the emission spectra, which only become discernible at such low temperatures, with those predicted using the two possible sets of constants, the rotational numbering is established. Consequently, the correct spectro-scopic constants of diacetylene and dideutero-diacetylene cations in their [Xtilde] ²Π _g and à ²Π _u electronic states are presented.     

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.     

Characterization of the [Xtilde] 1Σ+ à 3Π and à 1Π electronic states of BBO

The three lowest-lying electronic states, [Xtilde] ¹Σ⁺, à ³II and à ¹II, of the linear BBO molecule have been systematically investigated using ab initio electronic structure theory. The equilibrium structures and physical properties including dipole moments, vibrational frequencies and associated infrared intensities, Renner parameters and energetics for the three states of BBO have been determined employing SCF, CISD, CCSD and CCSD(T) levels of theory and a wide range of basis sets. The ground state of BBO presents a degenerate real bending frequency, while the à ³II and à ¹II states show two distinct real bending frequencies due to the Renner-Teller interaction. The bending motion of the à ¹II state was analysed using the equation-of-motion (EOM)-CCSD and EOM-CC3 techniques in order to avoid possible variational collapse to a lower-lying state. The [Xtilde] ¹Σ⁺-à ³II separation was predicted to be T ₀ = 16.6 kcal mol^?1 (5800 cm^?1, 0.719 eV) at the cc-pVQZ CCSD(T) level of theory. With the cc-pVQZ EOM-CC3 method the [Xtilde] ¹Σ⁺-à ¹II splitting was predicted to be T ₀ = 48.0 kcal mol^?1 (16 800 cm^?1, 2.08 eV), which is in good agreement with the experimental value of T ⁰ = 46.6 kcal mol^?1 (16 300 cm^?1, 2.02 eV). The Renner parameters and averaged harmonic frequencies of the bending mode were determined to be ? = 0.184 and ω₂ = 363 cm^?1 for the à ³II state, and ? = 0.246 and ω₂ = 383cm^?1 for the à ¹II state. The theoretical [Xtilde] ¹Σ⁺ state harmonic B-B stretching frequency ω₃ = 636 cm^?1 is somewhat higher than the experimental estimate of 582 cm^?1 and the predicted à ¹II state harmonic B-B stretching frequency ω₃ = 861 cm^?1 is significantly higher than the experimental estimate of 440 cm^?1     

Outer vibrational turning points near dissociation in the B(3Π0u +) state of Br2 and Cl2

A [1, 0] Padé approximant to the long-range interaction energy is used to describe the outer limb of the Rydberg-Klein-Rees curve of the state B (³Π_0u ⁺) of Br₂ and Cl₂. Empirical values of C ₅ and C ₆ are obtained.     

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.     

Radiative lifetime measurements of vibrational levels of Cl2 + A 2Π u

The radiative lifetimes of several vibrational levels of Cl₂ ⁺ A ²Π _u are measured by a novel technique. A uniform electric field extracts the ions from the observation region of a spectrometer, and the decrease of fluorescence signal as a function of the electric field strength is measured to obtain the radiative lifetime. Measurements are made on 20 different vibronic bands of the Cl₂ ⁺ A ²Π _u -X ²Π _g system, and the results are compared with other methods. An attempt is made to correlate the results with the highly perturbed spectroscopic nature of the A ²Π _u electronic state.     

Transition Moments betweenΔg,Πg, andΠuStates of the H2Molecule

Electronic transition moments are computed for dipole transitions between theCandD¹Π_u,IandR¹Π_gandJandS¹Δ_gstates of the hydrogen molecule for internuclear distancesR∈ [1, 15] bohr. The character of the wavefunctions at large internuclear distances is investigated. It is shown that in theDandRstates the asymptotic configurations are strongly mixed forR≤ 15 bohrs. TheSstate has mixed character even atR= 40 bohr.     

Electron resonance studies of the renner effect

The gas phase electron resonance spectra of NCO in its ground ²Π_3/2 vibronic state and in two excited vibronic states are described. Theoretical analysis of the spectra yields effective g values for the three states. In additon the ¹⁴N magnetic hyperfine and electric quadrupole coupling constants and the electric dipole moment are determined. The theory of the Renner coupling of electronic and vibrational motion is extended, and shown to account for anomalous contributions to the g values. The theory also shows that these contributions are closely related to the Renner coupling constant.     

Reanalysis of the C1Πu state of Na2 based on ultraviolet argon ion laser fluorescence

Six uv lines of an argon ion laser (CR-18 UV) are used to excite the C¹Π_u state of the Na₂ molecule. There are nine fluorescence series observed, two of which are excited from a fairly high vibrational level (v″ ≥ 11) in the ground state. A careful study of the intensities of these transitions reveals that the previous vibrational assignments of the energy levels in the C¹Π_u state are incorrect (too high by 2). A new analysis for this state was carried out and resulting molecular parameters are presented.     

Hund's rules and the interpretation and common misinterpretation of energy differences

With a Z expansion formalism which is exact in non-relativistic quantum mechanics it has been shown that for multiplets of neutral atoms and of many positive ions the state of the highest energy has the lowest expectation value for the interelectronic repulsion energy. This reversed order of the repulsion energy occurs for cases which obey Hund's first rule as well as for cases which obey the second of Hund's rules. It can be shown that the energy differences are in all cases dominated by the difference in electron nuclear attraction energy and not by the difference in electron repulsion energy.

The lowest ¹Π _u and ³Π _u states of the H₂ molecule have similar features. At many internuclear distances, including the equilibrium ones, the ¹Π _u state has the highest energy but the lower kinetic energy and electron repulsion energy but again the higher electron nuclear attraction energy. These results contradict clearly the usual theories for energy differences between spectroscopic states in atoms and molecules.     

Study of the covalent and triplet ionic-pairing states of the fluorine molecule with the MRDCI method

The results of nonempirical calculations of the electronic structure, spectroscopic constants, and potential-energy curves for the covalent and triplet ionic-pairing states of the F₂ molecule are presented. It is shown that the covalent 1³Π_u state is weakly bound, with the depth of the potential well of this state being of about 0.05–0.2 eV. The effect of the spin-orbital interaction on the ionic-pairing states, which can result in the perturbation of the Ω=0⁺ and Ω=1 components of the ³Σ _u ^? and ³Π_u states, is analyzed. It is demonstrated that the lasing observed at λ ≈ 157 nm is caused by the transitions between the ionic-pairing state 2³Π_g and the weakly bound covalent state 1³Π_u.     

The rotational dependence of the Renner-Teller interaction: a new term in the effective Hamiltonian for linear triatomic molecules in Π electronic states

An additional term in the effective Hamiltonian for a molecule in a ^2S+1Π state subject to a small Renner—Teller effect is derived. It takes the form of a rotational dependence of the Renner—Teller operator and is assigned the parameter ?ω_2,D . This term reproduces two characteristics of the spin—rotational levels of Renner—Teller molecules, both of which are well documented by experimental examples but are not explicable in terms of the previous effective Hamiltonian. These are the small difference between the B values of different vibronic components of the same bending vibrational level and the anomalously strong dependence of the spin—rotation parameter γ on ν₂ for molecules with S > 0. These effects have been explained by previous workers using perturbation theory but in a less general and more complicated fashion.     

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}}     

Analytical potential energy functions for the ground and some excited states of N2

The analytical potential energy functions have been calculated for the ground state X¹Σ⁺_g and four excited electronic states a¹Π_g, A³Σ⁺_u, B′³Σ^?_u and B³Π_g of N₂ molecule using the algebraic and energy-consistent methods (AM-ECM). Based on our previously published full AM vibrational energies and spectroscopic constants, the low-lying force constants f_n, the expansion coefficients a_n and the variational parameters λ in the AM–ECM potentials are determined for these states. The computed AM–ECM potential energy curve of each state is in excellent agreement with the experimental data and better than other analytical potentials.     

Electronic transition dipole moment functions and difference potentials for transitions among low-lying states of Li2 and Na2

Electronic transition dipole moment functions based on ab initio multiconfiguration self-consistent field wavefunctions are computed for the transitions ¹Σ_u⁺-¹Σ_g⁺, ³Σ_g⁺-³Σ_u⁺, ¹Π_u-¹Σ_g⁺, ³Π_g-³Σ_u⁺, ¹Σ_u⁺-¹Π_g, ³Σ_g⁺-³Π_u, ¹Π_u-¹Π_g, and ³Π_g-³Π_u in Li₂ and Na₂. (In each case the states are the lowest lying of their symmetry.) We also calculate the matrix element 〈³Σ_u⁺|i(L_x - iL_y)|³Π_u〉 for the predissociation of the ³Π_u state by the ³Σ_u⁺ state. Several unobserved spectral features are predicted.     

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.     

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.     

Observation of the 5pΠu Rydberg state of Li2

Some weak, collisionally induced transitions in ⁷Li₂ have been recorded by Fourier transform spectrometry in the near infrared, following excitation of the 5d¹Π_g state by optical-optical double resonance. They have been assigned as transitions to the 1 ¹Δ_g state from levels v=0 and 1 of a new ungerade Rydberg state, 5p¹Π_u. Quantum defect considerations indicate that the principal quantum number for this new state is 5, and that the assignment to 5p is compatible with a Rydberg series of which the lowest members would be the B¹Π_u and C¹Π_u states.     

S2分子B″3Πu态的势能函数和光谱常数的理论研究

推导了S₂分子B″³Π_u态的合理离解极限.用Gaussian 94 QCISD(T)方法和6-311++G^**基组计算了S₂分子B″³Π_u以及X³Σ^-_g态的势能曲线.给出了S₂分子B″³Π_u态的Murrell-Sorbie势能函数和光谱常数.B″³Π_u与B³Σ^-_u态在排斥支重叠范围大；同时，B″³Π_u与X³Σ^-_g态有相同离解极限，因而，在吸引支有重叠.讨论了B″³Π_u与B³Σ^-_u和X³Σ^-_g态相互作用的特征. 关键词：