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.     

Pt-Re small cluster interaction with H2

The interaction of small Pt-Re clusters with H₂ is reported here through ab initio multicon-figuration self-consistent field (MC-SCF) calculations, plus extensive multireference configuration interaction (MR-CI), variational and perturbative calculations. These calculations provide a cluster model for the activation of hydrogen by Pt-Re bimetallic catalysts. It was found that the ⁶S(5d⁵6s²) Re atom ground state needs an important activation to induce very weak capture of separated hydrogen atoms, whereas in the lowest excited states the activation energies are small or zero, with a very reasonable depth of well. The four lowest states of Pt-Re were found to be ⁴ Σ⁺, ⁶Π_yz, ^{Σ +} and ⁶Π_xz. Pt-Re interaction with H₂ has been studied from both metal ‘sides’. It was established that Pt-Re with the platinum side in the ground electronic ⁴Σ⁺ state and in the lowest ⁶Π⁺ excited states is able to capture H₂ molecules without activation, whereas in the ⁶Π_yz and ⁶Π_xz excited states there is no capture. The rhenium side of Pt-Re in its four lowest states considered cannot capture the H₂ molecule. The interaction of Pt₂-Re with H₂ was studied also. For the ground ²B₂ electronic state and the low lying ²A₁ electronic state the platinum moiety can spontaneously capture and break H₂. The rhenium side of Pt₂-Re(B₂), however, can capture H₂ only after surmounting a small barrier, and the excited Pt₂-Re(²A₁) can spontaneously capture H₂. For Pt₂-Re in its low lying ⁴A₁ electronic state both metal sides capture and break H₂ after surmounting a small barrier.     

Ab initio study of PN electronic states – a qualitative interpretation of the perturbation and predissociation effects on observed transitions

Valence and high electronic states of PN have been calculated with accurate quantum chemistry methods. The variety of theoretical methods used includes complete active space self-consistent field, multireference configuration interaction and the newly developed explicitly correlated coupled cluster methods. The large correlation-consistent atomic orbitals basis sets AVQZ, AV5Z and AV(5+d)Z are used for the potential energy curves calculations in the bonding and long-range regions. The spectroscopic constants (R_e, B_e, ω_e, ω_ex_e, α_e, D_e, T_e) and the vibrational levels of the bound valence states (X¹Σ⁺, A¹Π, a³Σ⁺, d ³Δ, e³Σ^?, C¹Σ^?, b³Π, D ¹Δ and E¹Σ⁺ and some higher bound states) are determined and compared with experimental findings when available. Significant spin–orbit interactions between triplet states and A¹Π and E¹Σ⁺ excited states are found near the crossing points of the potential energy curves and could explain predissociation phenomena and the perturbations of the vibrational levels experimentally observed for PN in their A¹Π and E¹Σ⁺ states.     

Ab initio calculations on the ground and excited states of InI

Potential energy curves (PECs) of the ground and the low-lying excited states of the InI molecule are computed using the internally contracted multireference singles and doubles configuration interaction with the Davidson correction (ic-MR-CISD + Q) method based on the relativistic effective core potentials (RECPs). The spectroscopic constants are obtained, including the excitation energy (T _e), the equilibrium bond distance (R _e), the dipole moment (μ_e) and the vibrational constants (ω_e and ω_e). Finally, we predict the transition dipole moments, the radiative lifetimes, and the Franc-Condon factors for the transitions of A³Π₀+ ? X¹Σ₀ ⁺ and B³Π^l ? X¹Σ₀ ⁺,. The results reveal that A³Π₀+ and B³Π_l are long-lived states with the lifetimes being of the order of microseconds.     

Theoretical study of low lying electronic states of GdO

Low lying electronic states of GdO have been investigated by complete active space SCF (CASSCF) and multireference singly and doubly excited configuration interaction (MRSDCI) calculations using the model core potential (MCP) method. The 4f electrons of Gd were included explicitly in the valence space. Relativistic effects were incorporated in the MCP and basis sets for Gd at the level of Cowan and Griffin's quasirelativistic Hartree—Fock method. The ⁹Σ^? state (f⁷σ) was the ground state, and excited states, ⁹Δ, ⁹Π, 2⁹Σ^?, ⁷Σ^?, ⁷Δ, ⁷Π, and 2⁷E^?, lay between 0 ～ 22 300 cm^?1. The energy separations for these states agreed well with available experimental values. Calculated GdO bond lengths and vibrational frequencies for these states are in the ranges of 1.81–1.85 Å and of 800–880 cm^?1, respectively. Mulliken population analysis showed that the gross population of the 4f orbitals was 7.1 e for all these states, and that the 4f electrons were strongly localized on Gd atom. The effective charge distribution was approximated to be Gd⁺O^?. The σ and π bonding orbitals were mainly formed by Gd 5d and O 2p orbitals.     

Electronic structure and molecular spectroscopic constants of ScN and ScP investigated by several quantum chemistry methods

The electronic structure of the ScN and ScP molecules is a subject of controversy and turns out to be a challenging problem in quantum chemistry. We show that the ground-state electronic structure for both molecules depends critically on the choice of methods used which incorporate different ways of accounting for electron correlation. A parallel ab initio, DFT and TD-DFT study is performed for this purpose and uses sufficiently flexible basis sets able to reproduce accurate electronic structures, as well as correct spectroscopic constants.

In the ab initio methodology, results have been obtained with methods such as Hartree-Fock (HF), M?ller-Plesset perturbation theory (MPn), direct configuration interaction (CI), quadratic configuration interaction (QC), coupled cluster configuration interaction (CC), complete active space self-consistent field (CASSCF) and multireference configuration interaction (CIPSI) methods. In the DFT methodology, various ‘pure’ and ‘hybrid’ density functionals are used and the corresponding results are compared to sophisticated ab initio methods and to available experimental data.

All the methods used show that the ground state of both molecules is ¹Σ⁺, but two electronic structure natures, ¹Σ⁺ open-shell or ¹Σ⁺ closed-shell, are competitive and depend on the method employed. All the ab initio methods based on a single determinant wavefunction suffer seriously in predicting clearly the exact nature of the ground state or its correct structural and spectroscopic parameters. However, the ab initio methods based on a multiconfigurational wavefunction appear to be successful in describing correctly, within one shot, the electronic structure and the molecular spectroscopic constants. The ground state, particularly for the ScN molecule, presents an unusual electronic structure: the presence of degenerate determinants, quasidegeneracy with other states and one avoided crossing in the region around the equilibrium distances. The bonding of the ground state is a two open-shell ¹Σ⁺ state described as a π double bond and a Σ dative bond; the real triple bond ¹Σ⁺ state, i.e. closed-shell state, is found to lie higher in energy. The potential energy curves of the lowlying electronic states, the derived electronic structures and various molecular spectroscopic constants are presented and discussed for each method employed.     

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}}     

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.     

Excited states of HCl

Ab initio CI calculations are presented for potential curves for the valence states of HCl, for the vertical electronic spectrum and for the potential curve for the B ¹Σ⁺ state. The valence ¹Π, ³Π and ³Σ⁺ states are found to be repulsive. Calculated vertical excitation energies are in good agreement with experiment. The B ¹Σ⁺ curve is predicted to have a double minimum.     

Electronic states of SiF and SiF+: Configuration-interaction studies

For SiF, low-lying ²Π, ⁴Π, ²Σ⁺, ⁴Σ⁺, ²Σ⁻, ⁴Σ⁻, ²Δ, and ⁴Δ states were studied by configuration-interaction methods, using a double-zeta plus polarization basis set with 4s, 4pσ, 4pπ, and 5pπ Rydberg orbitals. Potential energy curves and spectroscopic constants for 17 stable valence and Rydberg states are given. The lowest ²Σ⁻ state is repulsive. There is good agreement with known spectroscopic constants. Besides A²Σ⁺, another semidiffuse state, 1⁴Π, is predicted. For the isoelectronic PO molecule, 2π → 3π valence excitations lie below Rydberg excitations, such that 2²Π of PO derives from 2π → 3π, whereas 2²Π of SiF derives from 3π → 4pπ. Dipole moments of X²Π and A²Σ⁺ at their respective R_e, and the radiative lifetime of A²Σ⁺ were calculated. For SiF⁺, many electronic states were investigated, but only two, the X¹Σ⁺ ground state and 1³Π are found to be stable. The ionization energy of SiF is calculated to be 6.87 eV (adiabatic) and 7.05 eV (vertical).     

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.     

Accurate ab initio study of low-lying electronic states of phosphorus nitride radical

This paper employs the highly accurate valence internally contracted multireference configuration interaction method to investigate the potential energy curves (PECs) for the ground state (X 1 Σ +) and two low-lying excited states (A 1 Π and D 1 of phosphorus nitride (PN) radical with the correlation-consistent basis set,aug-cc-pV6Z,in the valence range.Relativistic effects are considered in these calculations.The spectroscopic constants of the X 1 Σ + and A 1 Π states are calculated based on the PECs,and the results are in good accord with the available experimental data.The first 30 vibrational states for the X 1 Σ + state and the first 40 vibrational states for theA 1 Π state are determined when J=0.For each vibrational state,molecular constants G(υ),B(υ) and D(υ) are also attained.     

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.     

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.     

N2O+离子A2Σ+电子态高振动能级的转动结构分析

利用一束波长为36055nm的激光,通过(3+1)共振多光子电离方法制备纯净的且处于X²Π_1/2,3/2(000)态的N₂O⁺离子,用另一束激光激发所制备的离子到第一电子激发态A²Σ⁺的不同振动能级,然后解离,通过检测解离碎片NO⁺强度随光解光波长的变化,得到了转动分辨的N₂ 关键词： 2O⁺离子A²Σ⁺电子态')" href="#">N₂O⁺离子A²Σ⁺电子态 共振增强多光子电离 光解碎片激发光谱 光谱常数     

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。     

The electronic states of carbon monofluoride: Rydberg states

Hartree-Fock and multiconfiguration Hartree-Fock calculations are reported on some low-lying Rydberg states of CF and the ground state of CF⁺. For the CF⁺ ground state, ¹Σ⁺, the calculations give a bond length of 1.55 Å, a fundamental frequency of 1821 cm^?1, and a dissociation energy of 6.9 eV. Many interactions between the valence and Rydberg state manifolds are revealed. Also a strong mixing of the 3dσ and 4sσ components due to an accidental degeneracy is described.     

The electronic spectrum of AgBr2: Ab initio benchmark vs. DFT calculations on the lowest ligand-field states including spin-orbit effects

The X²Π_g, ²Σ_g⁺ and ²Δ_g states of AgBr₂ have been studied through benchmark ab initio CASSCF + Averaged Coupled Pair Functional (ACPF) and DFT calculations using especially developed valence basis sets to study the transition energies, geometries, vibrational frequencies, Mulliken charges and spin densities. The spin-orbit (SO) effects were included through the effective hamiltonian formalism using the |ΛSΣ〉 ACPF energies as diagonal elements. At the ACPF level, the ground state is ²Π_g, in contradiction with ligand-field theory and Hartree-Fock results. The ACPF adiabatic excitation energies of the ²Σ_g⁺ and ²Δ_g states are 3825 and 20 152 cm⁻¹, respectively. The inclusion of the SO effects leads to a pure Ω = 3/2 (²Π_g) ground state, a Ω = 1/2 (97% ²Π_g + 3% ²Σ_g⁺) A state, a Ω = 1/2 (3% ²Π_g + 97% ²Σ_g⁺) B state, a Ω = 5/2 (²Δ_g) C state and a Ω = 3/2 (99% ²Δ_g) D state. The B97, B3LYP and PBE0 functionals, which were shown to yield accurate transition energies for CuCl₂, overestimate the X²Π_g-²Σ_g⁺ T_e by around 25% but provide a qualitative energetic ordering in agreement with CASSCF and ACPF results. The nature of the bonding in the X²Π_g ground state is different from that of AgCl₂ since the Mulliken charge on the metal is 0.95 while the spin density is only 0.39. DFT strongly delocalizes the spin density providing even smaller values of around 0.13 on Ag not only for the ground state, but also for the ²Σ_g⁺ state.     

The electronic structure of the low lying sextet and quartet states of CrF and CrCl

The electronic structure of CrF and CrCl in X ⁶Σ⁺, ⁶Π, ⁶Δ, A⁶Σ⁺, ⁴Σ⁺, ⁴Π, and ⁴Δ states that correlate with the low lying ⁶S, ⁶D, and ⁴D states of Cr⁺ have been studied, using large atomic natural orbital (ANO) basis sets and a variety of ab initio methods, including multi-reference configuration interaction (MRCI) and coupled cluster with perturbative triples (RCCSD(T)). We include scalar relativistic effects perturbatively and also explore the consequence of correlating the 3s and 3p electrons on the transition metal. We report T _e, R _e,ω_e, as well as dipole moments, bond energies, and charge distributions and compare with the available experimental data as well as previous theoretical results.