One‐electron pseudopotential study of the alkali hydride cation NaH+: Structure,spectroscopy, transition dipole moments,and radiative lifetimes

The structure and spectroscopic properties of the ground and the lowest excited electronic states of the alkali hydride cation NaH⁺ have been investigated using an ab initio approach. In this approach, a nonempirical pseudopotential for the Na⁺ core has been used and a core–core and a core‐valence correlation corrections have been added. The adiabatic potential energy curves and the molecular spectroscopic constants for numerous electronic states of ²Σ⁺, ²Π, and ²Δ symmetries, dissociating up to Na (4d) + H⁺ and Na⁺ + H (3d), have been calculated. As no experimental data are available, we discuss our results by comparing with the available theoretical calculations. A satisfying agreement has been found for the ground state with previous works. However, a clear disagreement between this study and the model potential work of Magnier (Magnier, J. Phys. Chem. A 2005, 109, 5411) has been observed for several excited states. Numerous avoided crossings between electronic states of ²Σ⁺ and ²Π symmetries have been found and analysed. They are related to the interaction between the potential energy curves and to the charge transfer process between the two ionic systems Na⁺H and NaH⁺. Furthermore, we provide an extensive set of data concerning the transition dipole moments from X²Σ⁺ and the 2²Σ⁺ states to higher excited states of ²Σ⁺ and ²Π symmetries. Finally, the adiabatic potential energy curves of the ground (X²Σ⁺) and the first (2²Σ⁺) excited states and the transition dipole moments between these states are used to evaluate the radiative lifetimes for the vibrational levels of the 2²∑⁺ state for the first time. In addition to the bound–bound contribution, the bound‐free term has been evaluated and added to the total radiative lifetime. © 2012 Wiley Periodicals, Inc.     

Potential energy surfaces for Rh?CO from DFT calculations

We present potential energy surfaces for Rh? CO obtained from density functional theory for two electronic states of Rh? CO. We have performed local spin-density calculations including relativistic as well as gradient corrections. The construction of a reasonably accurate atom–atom potential for Rh? CO is not possible. We were much more successful in constructing the potential energy surfaces by representing the potential as a spherical expansion. The expansion coefficients, which are functions of the distance between the rhodium atom and the carbon monoxide center of mass, can be represented by Lennard-Jones, Buckingham, or Morse functions, with an error of the fit within 10 kJ/mol. The potential energy surfaces, using Morse functions, predict that the electronic ground state of Rh? CO is ²Σ⁺ or ²Δ. This is a linear structure with an equilibrium distance of rhodium to the carbon monoxide center of mass of 0.253 nm. The bonding energy is ?184 kJ/mol. Further, Morse functions predict that the first exicted state is ⁴A′. This is a bent structure (∠Rh? CO = 14°) with an equilibrium distance of rhodium to the carbon monoxide center of mass of 0.298 nm. The bonding energy of this state is ?60 kJ/mol. Both these predictions are in good agreement with the actual density functional calculations. We found 0.250 nm with ?205 kJ/mol for ²Σ⁺ and 0.253 nm with ?199 kJ/mol for ²Δ. For ⁴A′, we found 0.271 nm, ∠Rh? CO = 30°, with ?63 kJ/mol. The larger deviation for ⁴A′ than for ²Σ⁺ or ²Δ is a consequence of the fact that the minimum for ⁴A′ is a very shallow well. © 1994 by John Wiley & Sons, Inc.     

Theoretical prediction on HAlS+ and HSAl+ cations using multiconfiguration second‐order perturbation theory

Some low‐lying states of the HAlS⁺ and HSAl⁺ cations have been studied for the first time by large‐scale theoretical calculations using three methods: complete active space self‐consistent field (CASSCF), complete active second‐order perturbation theory (CASPT2), and density functional theory Becke's three‐parameter hybrid function with the nonlocal correlation of Lee–Yang–Parr (B3LYP) with the contracted atomic natural orbital (ANO‐L) and cc‐pVTZ basis sets. The geometries of all stationary points along the potential energy surfaces (PESs) were optimized at the CASSCF/ANO‐L and B3LYP/cc‐pVTZ levels. The ground and the first excited states of linear HAlS⁺ are predicted to be X²Π and A²Σ⁺ states, respectively. For the linear HSAl⁺ structure, the first excited state is A²Σ⁺. The X²Π state of linear HSAl⁺ is a second‐order saddle point, because it has two imaginary frequencies. Two bent global minima M1 and M2 were found along the 1²A′ and 1²A″ PESs, respectively. The CASPT2/ANO‐L potential energy curves of isomerization reactions were calculated as a function of HAlS bond angle. According to our calculations, the ground‐state HAlS⁺ is linear, whereas the ground‐state HSAl⁺ is bent. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Analysis and predictions of the vibronic spectrum of the ethynyl radical C2H by ab initio methods

A purely ab initio study of the vibronic structure of the C₂H spectrum in the region up to 7000 cm^?1, which is complicated by the coupling of theX ²Σ⁺ andA ² II systems, is presented. The potential surfaces for the three lowest-lying electronic states 1² A′, 2² A′ and 1² A″ correlating withX ²Σ⁺ andA ² II at the linear molecular geometry are calculated for the various geometrical distortions by means of the multireference configuration interaction (MRD-CI) method. These adiabatic surfaces are transformed into suitable diabatic counterparts. An approach is developed for a simultaneous treatment of three electronic states coupled via the bending and C-C stretching vibrations. Spin-orbit splitting of the vibronic levels and the vibronically averaged values for the hyperfine coupling constants are computed. The results obtained in this study enable a reliable explanation of the available experimental findings of the C₂H spectrum and predict a number of features to be verified by future experiments.     

Theoretical spectroscopy and metastability of BeS and its cation

Multiconfiguration self-consistent field and multiconfiguration reference interaction including the Davidson’s correction techniques were employed to calculate the potential energy curves (PECs) of the BeS/BeS⁺ electronic states correlating to the 4/5 lowest dissociation limits. After nuclear motion treatment, we deduced reliable spectroscopic data for the neutral and cationic bound states. For BeS, the transition moments and spin-orbit couplings were also evaluated and used later with the PECs to deduce the rovibronic transition probabilities and the radiative lifetimes in the low-lying states, and to investigate the unimolecular decomposition processes of BeS (X¹Σ⁺, A¹Π, ³Σ⁺ and B¹Σ⁺) leading to Be(¹S_g) + S(³P_g). The prominent mechanism is a spin-orbit induced predissociation via the repulsive BeS(1³Σ⁻) state. Finally, we give the single ionization spectrum of BeS (X¹Σ⁺) populating the BeS⁺ (X²Π, 1²Σ⁻, 1²Σ⁺, 1²Δ, 2²Σ⁺, 2²Π and 3²Π) electronic states. The adiabatic ionisation energy of BeS is estimated to be ∼9.15 eV.     

Theoretical study of low‐lying electronic states of the LiRb+ molecular ion: Structure,spectroscopy and transition dipole moments

The electronic structure and the spectroscopic properties for low‐lying electronic states of the LiRb⁺ molecular ion, dissociating into Li (2s, 2p, 3s, 3p, 3d, 4s, and 4p) + Rb⁺ and Li⁺ + Rb (5s, 5p, 4d, 6s, 6p, 5d, and 7s), have been investigated using an ab initio approach based on non‐empirical pseudo potentials for the Li and Rb cores and parametrized l‐dependent polarization potential. We have determined the adiabatic potential energy curves and their spectroscopic constants for many electronic states of ²Σ⁺, ²Π, and ²Δ symmetries. A satisfying agreement, for the spectroscopic constants, has been obtained for the ground and the first excited states with the available theoretical works. Potential energy curves were presented, for the first time, for the higher excited states. In addition, we have localised and analysed the avoided crossings between electronic states of ²Σ⁺ and ²Π symmetries. Their existences can be related to the interaction between the potential energy curves and to the charge transfer process between the two ionic systems Li⁺Rb and LiRb⁺. Moreover, we have determined the transition dipole moments from X²Σ⁺ and 2²Σ⁺ states to higher excited states of ²Σ⁺ and ²Π symmetries. For our best knowledge, no experimental data on the LiRb⁺ molecular ion is available. These theoretical data can help experimentalists to optimize photoassociative formation of ultracold LiRb⁺ molecular ion and their longevity in a trap or in an optical lattice. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Ab initio study of the positronation of the CaO and SrO molecules including calculation of annihilation rates

Ab initio multireference single‐ and double‐excitation configuration interaction calculations have been performed to compute potential curves for ground and excited states of the CaO and SrO molecules and their positronic complexes, e⁺CaO, and e⁺SrO. The adiabatic dissociation limit for the ²Σ⁺ lowest states of the latter systems consists of the positive metal ion ground state (M⁺) and the OPs complex (e⁺O^?), although the lowest energy limit is thought to be e⁺M + O. Good agreement is found between the calculated and experimental spectroscopic constants for the neutral diatomics wherever available. The positron affinity of the closed‐shell X ¹Σ⁺ ground states of both systems is found to lie in the 0.16–0.19 eV range, less than half the corresponding values for the lighter members of the alkaline earth monoxide series, BeO and MgO. Annihilation rates (ARs) have been calculated for all four positronated systems for the first time. The variation with bond distance is generally similar to what has been found earlier for the alkali monoxide series of positronic complexes, falling off gradually from the OPs AR value at their respective dissociation limits. The e⁺SrO system shows some exceptional behavior, however, with its AR value reaching a minimum at a relatively large bond distance and then rising to more than twice the OPs value close to its equilibrium distance. © 2012 Wiley Periodicals, Inc.     

The potential energy curves and probability density distributions of the X1Σ+ and A1Σ+ states of RBH

The potential energy curves PMO—RKR—van der Waals of the electronic A¹Σ⁺ and X₁Σ⁺ states of RbH have been determined. The potentials obtained are self-consistent with the experimental data because they have been tested by direct numerical solution of the radial Schrödinger equation. From exact vibrational eigenfunctions probability density distributions and Franck—Condon factors have been calculated over the range of vibrational levels observed. It is observed that the anomalous behaviour of the A¹Σ⁺ state arises in the υ′ = 1, 2 and 3 levels with probability density functions similar to those of a harmonic oscillator.     

The potential energy surfaces of the ground and excited states of carbon dioxide molecule

Potential energy surfaces (PESs) of the ¹A_l(¹Σ _g ⁺ ), ¹B₂ and ³B₂ electronic states of CO₂ have been computed as a function of the two bond distances and the bond angle. The calculations were based on the complete active space self consistent field (CASSCF) and multiconfigurational second-order perturbation theory (CASPT2) electronic structure models. From our calculations no crossing point between ¹B₂ and ³B₂ states was found, but there is a crossing point located between ¹B₂ and ³A₂ state on the PESs. The energy of the crossing point is lie 0.23 eV above the CO + O (³P), which is in agreement with the value of 0.27 eV on the experiment. This implies that the mechanism of the recombination of an oxygen atom with a carbon monoxide molecule: CO(X ¹Σ⁺, ν) + O(³P)→³CO₂*→¹CO₂*→CO(X ¹Σ⁺, ν = 0) + O(¹ D) may occur through the ³A₂ state crossing the ¹B₂ state. The equilibrium geometries and adiabatic excitation energies of ^1,3B₂, ^1,3A₂ states of CO₂ were reported and discussed in this paper, too.     

OH自由基的高精度量子化学研究

采用内收缩MRCI方法(Internally Contracted Multiconfiguration-Reference Configuration Interaction)研究了OH自由基, 计算得到其基态稳定构型的键长是0.09708 nm, 对应的实验值是0.096966 nm, 第一激发态的键长是0.10137 nm,实验值是0.10121 nm. 同时得到势能曲线PECs (Potential Energy Curve), 再分别由Murrell-Sorbie势能函数拟合计算和POLFIT程序计算得到OH自由基在基态X²Π和第一激发态A²Σ⁺时的光谱数据：平衡振动频率ω_e, 非谐性常数ω_eχ_e以及高阶修正ω_eY_e, 平衡转动常数B_e, 振转耦合系数α_e, 解离能D₀和垂直跃迁能量ν₀₀. 这些理论计算结果与最新的实验值非常吻合, 精确度比前人也有很大提高. 其中我们计算得到基态OH(X²Π)的解离能D₀＝35568.86 cm^－1, 第一激发态OH (A²Σ⁺)的解离能D₀＝18953.93 cm^－1, 从第一激发态A²Σ⁺ (ν＝0)到基态X²Π (v＝0)的垂直跃迁能ν₀₀＝32496.42 cm^－1.     

Theoretical study on low‐lying states of HAlO+ and HOAl+ cations

Some low‐lying states of HAlO⁺ and HOAl⁺ cations have been studied using the complete‐active‐space self‐consistent field (CASSCF) and multiconfiguration second‐order perturbation theory (CASPT2) methods with the contracted atomic natural orbital (ANO) basis sets. The geometries of all stationary points along the potential energy surfaces were optimized at the CASSCF/ANO and CASPT2/ANO levels. The ground and the first excited states of HAlO⁺ are predicted to be X²Π and A²Σ⁺ states, respectively. It was predicted that the ground state of HOAl⁺ is X²Σ⁺ state. The A²Π state of HOAl⁺ has unique imaginary frequency. A bent local minimum M1 was found along the 1²A″ potential energy surface, and the A²Π state of HOAl⁺ should be the transition state of the isomerization reactions for M1 ? M1. The CASPT2/ANO potential energy curves of isomerization reactions were calculated as a function of HAlO bond angle. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Spectroscopic properties and potential energy curves of some low-lying electronic states of AlO,AlO+, LaO,and LaO+: An ab initio CASSCF study

Results of CASSCF state-averaged calculations on the lowest electronic states of LaO and LaO⁺ are reported in this work. For comparison, some low-lying electronic states of AlO and AlO⁺ are also reported. The ground state of LaO was found to be the X²Σ⁺ (R_e = 1.987 Å, ω_e = 794 cm^?1) with a low-lying A²Δ excited state. Five more excited states below 26000 cm^?1 were found. The first ionization potential (IP ) is found at 5.16 eV, resulting in an X¹Σ⁺ ground state for the LaO⁺ diatom, in opposition to AlO⁺ for which an X³ Π ground state has been found. Analysis of the wave functions, dipole moments, and Mulliken populations reveal that the bonding is quite ionic in both systems. © 1994 John Wiley & Sons, Inc.     

Ab initio calculations on low-lying electronic states of PdH

Potential energy curves for the low-lying electronic states of PdH have been calculated using the MRCI method with scalar relativistic and spin-orbit corrections, and all electronic states correlating to the 4d¹⁰ (¹S), 4d⁹ 5s¹ (³D), 4d⁹ 5s¹ (¹D) and 4d⁸ 5s² (³F) states of Pd were included. Potential energy curves for the individual Ω states have been obtained, and the experimentally observed spectra of both PdH and PdD isotopologues have been assigned appropriately based on the ab initio results. Einstein A coefficients were calculated for other possible transitions from the low-lying electronic states to the X²Σ⁺ ground state. Diagonal and off-diagonal matrix elements of the spin-orbit Hamiltonian were calculated for all vibrational levels of the X²Σ⁺, 1²Δ, 1²Π, 2²Σ⁺ and 3²Σ⁺ states, and it was found from the eigenvectors that the vibrational wavefunctions of the 1²Δ_3/2 and 1²Π_3/2 states are mixed significantly in both PdH and PdD isotopologues.     

Bound vibrational levels of the two lowest 1Σ+ states of LiF

The energies of the vibrational levels of the two lowest ¹Σ⁺ states of LiF corresponding to adiabatic and to diabatic potential energy curves are calculated and compared. The high-lying levels of the ionic adiabatic and diabatic states separating to Li⁺ + F^- are represented by quantum defect formulas.     

High Resolution Laser Excitation Spectra and Franck-Condon Factors of A2Π-X2Σ+ Electronic Transition of MgF

Magnesium monofluoride (MgF) is proposed as an ideal candidate radical for direct laser cooling. Here, the rotationally resolved laser spectra of MgF for the A²Π-X²Σ⁺ electronic transition system were recorded by using laser induced fluorescence technique. The MgF radicals were produced by discharging SF₆/Ar gas mixtures between the tips of two magnesium needles in a supersonic jet expansion. We recorded a total of 19 vibrational bands belonging to three sequences of Δv=0, ±1 in the region of 348-370 nm. Accurate spectroscopic constants for both X²Σ⁺ and A²Π states are determined from rotational analysis of the experimental spectra. Spectroscopic parameters, including the Franck-Condon factors (FCFs), are determined from the experimental results and the Rydberg-Klein-Rees (RKR) calculations. Significant discrepancies between the experimentally measured and RKR-calculated FCFs are found, indicating that the FCFs are nearly independent of the spin-orbit coupling in the A²Π state. Potential energy curves (PECs) and FCFs determined here provide necessary data for the theoretical simulation of the laser-cooling scheme of MgF.     

Theoretical study on HBO+ and HOB+ cations using multiconfiguration second‐order perturbation theory

The HBO⁺ and HOB⁺ cations have been reinvestigated using the CASSCF and CASPT2 methods in conjunction with the contracted atomic natural orbital (ANO) basis sets. The geometries of all stationary points in the potential energy surfaces were optimized at the CASSCF/ANO and CASPT2/ANO levels. The ground and the first excited states of HBO⁺ are predicted to be X²Π and A²Σ⁺ states, respectively. It was predicted that the ground state of HOB⁺ is X²Σ⁺ state. The A²Π state of HOB⁺ has unique imaginary frequency. A bending local minimum M1 was found for the first time along the 1²A′′ potential energy surface and the A²Π state of HOB⁺ should be the transition state of the isomerization reactions for M1? M1. The CASPT2/ANO potential energy curves (PECs) of isomerization reactions were calculated as functions of the HBO bond angle. Many of the CASSCF and CASPT2 calculated results were different from the previously published QCISD(T) results. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

CASPT2 study on low‐lying states of HMgO and HOMg

The HMgO and magnesium monohydroxide (HOMg) have been reinvestigated using the complete active space self‐consistent field (CASSCF) and multiconfiguration second‐order perturbation theory (CASPT2) methods with the contracted atomic natural orbital (ANO) basis sets. The geometries of all stationary points along the potential energy surfaces (PESs) were optimized at the CASSCF/ANO levels. The ground and the first excited states of HMgO are predicted to be X²Π and A²Σ⁺ states, respectively. It was predicted that the ground state of HOMg is X²Σ⁺ state. The A²Π state of HOMg has unique imaginary frequency. A bent local minimum M1 was found for the first time along the 1²A″ PES and the A²Π state of HOMg should be the transition state of the isomerization reactions for M1 ? M1. The CASPT2/ANO potential energy curves of isomerization reactions were calculated as a function of HMgO bond angle. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

A theoretical ab initio SCF CI investigation of the Na + H2 reaction: The possibility of new photoreactive channels in the 4 eV region

We propose an exploratory study of the behavior of the first Rydberg states ²(4p¹) and ²(4s¹). Semiquantitative calculations (SCF + Limited CI) are used for describing the related PESs. Extended SCF CI (Moller-Plesset CIPSI algorithm) is used to characterize the important points of the reaction coordinate. The feasibility of chemical quenching yielding either NaH + H or NaH₂ starting from Rydberg states is discussed. It is shown that NaH₂ is not likely to be a stable species since the lowest minimum (linear²Σ_g⁺) is found 0.6 eV above the dissociative ²Σ_u⁺ species. Via a series of crossings a cascade from the Rydberg region to the reactive 1 ²B₂ surface is possible. Once the system is provided with the resulting extra energy, it is likely to yield chemical quenching (NaH + H) after passing through a triangular geometry. The crossing between the lowest 1²A₁ and 1²B₂ surfaces is therefore a key point for all the potential reactivity of the system.     

CASPT2 study on low‐lying states of HBN and HNB radicals

In this study, some low‐lying states of the HBN and HNB radicals have been studied using multiconfiguration second‐order perturbation theory. The geometries of all stationary points along the potential energy surfaces (PESs) were optimized at the CASPT2/cc‐pVQZ level. The ground and the first excited states of HBN were predicted to be X²Π and A²Σ⁺ states, respectively. It was predicted that the ground state of HNB is X²Σ⁺ state. The A²Π state of HNB has unique imaginary frequency, which was different from the previously published results. A bending local minimum M1 was found for the first time along the 1²A″ PES, and the A²Π state of HNB should be the transition state of the isomerization reactions for M1 ? M1. The CASPT2/ANO potential energy curves (PECs) of isomerization reactions for HBN ? HNB were calculated as a function of HBN bond angle. By comparing the CASPT2 and CASSCF calculated results, we concluded that the influence of the dynamic electron correlation on HBN ? HNB system is not large. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Theoretical evaluation of the radiative lifetimes of LiCs and NaCs in the A<Superscript>1</Superscript>Σ<Superscript>+</Superscript> state

Calculations of the adiabatic potential energy curves and the transition dipole moments between the ground (A¹Σ⁺) and the first excited (A¹Σ⁺) states have been determined for the LiCs and NaCs molecules. The calculations are performed using an ab initio approach based on non-empirical pseudopotentials for Cs⁺, Li⁺ and Na⁺ cores, parameterized l-dependent polarization potentials and full configuration interaction calculations. The potential energy curves and the transition dipole moment are used to estimate the radiative lifetimes of the vibrational levels of the A⁺Σ⁺ state using the Franck–Condon (FC) approximation and the approximate sum rule method. The radiative lifetimes associated with the A⁺Σ⁺ state are presented here for the first time. These data can help experimentalists to optimize photoassociative formation of ultracold molecules and their longevity in a trap or in an optical lattice.