Theoretical study of spectroscopic and molecular properties of several low‐lying electronic states of CO molecule

The potential energy curves (PECs) of eight low‐lying electronic states (X¹Σ⁺, a³Π, a′³Σ⁺, d³Δ, e³Σ^?, A¹Π, I¹Σ^?, and D¹Δ) of the carbon monoxide molecule have been studied by an ab initio quantum chemical method. The calculations have been performed using the complete active space self‐consistent field method, which is followed by the valence internally contracted multireference configuration interaction (MRCI) approach in combination with the correlation‐consistent aug‐cc‐pV5Z basis set. The effects on the PECs by the core‐valence correlation and relativistic corrections are included. The way to consider the relativistic corrections is to use the third‐order Douglas–Kroll Hamiltonian approximation at the level of a cc‐pV5Z basis set. Core‐valence correlation corrections are performed using the cc‐pCVQZ basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are corrected for size‐extensivity errors by means of the Davidson modification (MRCI+Q). The spectroscopic parameters (D_e, T_e, R_e, ω_e, ω_ex_e, ω_ey_e, B_e, α_e, and γ_e) of these electronic states are calculated using these PECs. The spectroscopic parameters are compared with those reported in the literature. Using the Breit–Pauli operator, the spin–orbit coupling effect on the spectroscopic parameters is discussed for the a³Π electronic state. With the PECs obtained by the MRCI+Q/aug‐cc‐pV5Z+CV+DK calculations, the complete vibrational states of each electronic state have been determined. The vibrational manifolds have been calculated for each vibrational state of each electronic state. The vibrational level G(ν), inertial rotation constant B_ν, and centrifugal distortion constant D_ν of the first 20 vibrational states when the rotational quantum number J equals zero are reported and compared with the experimental data. Comparison with the measurements demonstrates that the present spectroscopic parameters and molecular constants determined by the MRCI+Q/aug‐cc‐pV5Z+CV+DK calculations are both reliable and accurate. © 2012 Wiley Periodicals, Inc.     

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 of the low‐lying electronic states of the molecular ion KRb+

The potential energy curves of the molecular ion KRb⁺ have been investigated for the 60 lowest molecular states of symmetry ²Σ⁺, ²Π, ²Δ, and Ω = 1/2, 3/2, and 5/2. Using an ab initio method, the calculation has been done in a one active electron approach based on nonempirical pseudopotentials with core valence effects taken into account through parameterized l‐dependent polarization potentials. Using the canonicals functions approach a rovibrational study is done by calculating the eigenvalues E_v, the rotational constants B_v, the centrifugal distortion constants D_v (up to 135 vibrational levels), and the spectroscopic constants ω_e and B_e for the five electronic states (1)²Σ⁺, (3)²Σ⁺, (1)²Π, (1)Ω = 1/2, and (1)Ω = 3/2. No comparison of these values with other results is yet possible because they are given here for the first time. Extensive tables of energy values of E_v, B_v, and D_v are displayed at http://hplasim2.univ‐lyon1.fr/allouche . © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Ab Initio Diabatic energies and dipole moments of the electronic states of RbLi molecule

For all states dissociating below the ionic limit Li^? Rb⁺, we perform a diabatic study for ¹Σ⁺ electronic states dissociating into Rb (5s, 5p, 4d, 6s, 6p, 5d, 7s, 4f) + Li (2s, 2p, 3s). Furthermore, we present the diabatic results for the 1–11 ³σ, 1–8 ^1,3Π, and 1–4 ^1,3Δ states. The present calculations on the RbLi molecule are complementary to previous theoretical work on this system, including recently observed electronic states that had not been calculated previously. The calculations rely on ab‐initio pseudopotential, core polarization potential operators for the core‐valence correlation and full valence configuration interaction approaches, combined to an efficient diabatization procedure. For the low‐lying states, diabatic potentials and permanent dipole moments are analyzed, revealing the strong imprint of the ionic state in the ¹Σ⁺ adiabatic states. The transition dipole moment is used to evaluate the radiative lifetimes of the vibrational levels trapped in the 2 ¹Σ⁺ excited states for the first time. In addition to the bound–bound contribution, the bound–free term has been evaluated using the Franck–Condon approximation and also exactly added to the total radiative lifetime. © 2013 Wiley Periodicals, Inc.     

Potential energy and dipole moment of the Na2+ ionic molecule

The potential energy curves of 26 electronic states of ²Σ⁺_{g, u}, ²Π_{g, u}, and ²Δ_{g, u} symmetries of the alkali dimer Na₂⁺, dissociating up to Na(4d) + Na⁺, are investigated using an ab initio approach involving a nonempirical pseudopotential for the Na⁺(1s²2s²2p⁶) core and core‐valence correlation corrections. Furthermore, the transition dipole functions between many electronic states and vibrational energy spacings are presented. The spectroscopic constants of these electronic states are extracted and compared with the available theoretical and experimental results. A very good agreement is observed, especially, for the ground and the first excited states. However, the comparison between our study and the model potential (MP) calculations (Magnier and Masnnou‐Seeuws Mol. Phys. 1996, 89, 711) for several states has shown a clear disagreement. The MP well depths of the 3‐4²Σ⁺_g, 1²Π_g, 3‐4²Π_g, and 2²Π_u electronic states are largely underestimated. In addition, the 5‐7²Σ⁺_g, 3‐7²Σ⁺_u, 2²Π_g, 4²Π_g, and 1‐2²Δ_u MP electronic states are repulsive, although in this work, they are attractive with potential well depths of some hundreds of cm^?1. The data presented in this study are very useful for studies on ion–atom interaction and cold collision in the presence of electromagnetic fields. © 2013 Wiley Periodicals, Inc.     

Theoretical study of electronic structure of rhodium mononitride and interpretation of experimental spectra

Potential energy curves of 22 electronic states of RhN have been calculated by the complete active space second‐order perturbation theory method. The X¹Σ₀⁺ is assigned as the ground state, and the first excited state a³Π₀+ is 978 cm^?1 higher. The ¹Δ(I) and B¹Σ⁺ states are located at 9521 and 13,046 cm^?1 above the ground state, respectively. The B¹Σ⁺ state should be the excited state located 12,300 cm^?1 above the ground state in the experimental study. Moreover, two excited states, C¹Π and b³Σ⁺, are found 14,963 and 15,082 cm^?1 above the X¹Σ⁺ state, respectively. The transition C¹Π₁–X¹Σ₀⁺ may contribute to the experimentally observed bands headed at 15,071 cm^?1. There are two excited states, D¹Δ and E¹Σ⁺, situate at 20,715 and 23,145 cm^?1 above the X¹Σ⁺ state. The visible bands near 20,000 cm^?1 could be generated by the electronic transitions D¹Δ₂–a³Π₁ and E¹Σ⁺₀–X¹Σ⁺₀ because of the spin–orbit coupling effect. © 2013 Wiley Periodicals, Inc.     

Ab initio interaction and spectral properties of CO+–He

In this contribution, ab initio methods have been used to study the open-shell CO⁺–He van der Waals (vdW) complex in both the ground and the first Π excited electronic state. Calculations were performed at the UCCSD(T) level of theory in the framework of the supermolecule approach using the cc-pVTZ basis set complemented with a set of standard bond functions in the middle of the vdW bond. Calculations predict a most-stable equilibrium conformation with β e=45°, R _e =2.85 Å and D _e =275 cm^?1 for the ground CO⁺(X²Σ)–He(¹S) state and β e=90°, R _e =2.70 Å and D _e =218 cm^?1 for the excited CO ⁺(A²Π)–He(¹S) state. The dipole moment μ and independent components of the field polarizability α of the CO ⁺–He vdW complex have been studied at the calculated equilibrium geometry of these states. The vertical excitation energies from the ground CO⁺(X ²Σ)–He(¹S) to the excited CO⁺(A²Π)–He (¹S) electronic state and corresponding shifts in the fluorescent spectrum with respect to the isolated CO⁺ molecule are also presented     

Electronic,spectra, and spin orbit interaction for FrAr van der Waals system

The potential energy curves and spectroscopic constants of the ground and many excited states of the FrAr van der Waals system have been determined using a one‐electron pseudopotential approach. The Fr⁺ core and the electron–Ar interactions are replaced by effective potentials. The Fr⁺Ar core–core interaction is incorporated using the accurate CCSD(T) potential of Hickling et al. (Phys. Chem. Chem. Phys. 2004, 6, 4233). This approach reduces the number of active electrons of the FrAr van der Waals system to only one valence electron, which permits the use of very large basis sets for the Fr and Ar atoms. Using this technique, the potential energy curves of the ground and many excited states are calculated at the self consistent field (SCF) level. In addition, the spin–orbit interaction is also considered using the semiempirical scheme for the states dissociating into Fr (7p) and Fr (8p). The FrAr system is not studied previously and its potential interactions, spectroscopic constants and dipole functions are presented here for the first time. Furthermore, we have predicted the X²Σ⁺–A²Π_1/2, X²Σ⁺–AΠ_3/2, X²Σ⁺–B²Σ_1/2⁺, X²Σ⁺–3²Π_1/2, X²Σ⁺–3²Π_3/2, and X²Σ⁺–5²Σ_1/2⁺ absorption spectra. © 2012 Wiley Periodicals, Inc.     

MRCI study on spectroscopic parameters and molecular constants of the ground state of AsP(X1Σ+) molecule

The potential energy curve (PEC) for the ground state of AsP(X¹Σ⁺) has been investigated by the highly accurate valence internally contracted multireference configuration interaction method in the Molpro2008 program package with the correlation consistent basis set. The PEC is fitted to the analytic Murrrell–Sorbie function (M–S function) from which the spectroscopic constants are determined. The present D_e, B_e, α_e, ω_eχ_e, R_e, and ω_e values are of 4.2823 eV, 0.188622 cm^?1, 0.000749 cm^?1, 1.984427 cm^?1, 2.0194 Å, and 598.60 cm^?1, respectively. In addition, by numerically solving the radial Schrödinger equation of nuclear motion in the adiabatic approximation, the total of 96 vibration states is predicted when the rotational quantum number J = 0. The complete vibration levels, classical turning points, inertial rotation, and centrifugal distortion constants are reproduced. Comparison has been made with recent theoretical and experimental data. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

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.     

基态PuOH分子的多体展式分析势能函数

Using the density functional method B3LYP with relativistic effective core potential(RECP)for Pu atom,thelow-lying excited states(~4Σ~ ,~6Σ~ ,~8Σ~ )for three structures of PuOH molecule were optimized.The results showthat the ground state is X~6Σ~ of the linear Pu-O-H(C_(∞v)),its corresponding equilibrium geometry and dissociationenergy are R_(Pu-O)=0.20595 nm,R_(O-H)=0.09581 nm and —8.68 eV,respectively.At the same time,two other me-tastable structures [PuOH(C_s)and H-Pu-O(C_(∞v)] were found.The analytical potential energy function has alsobeen derived for whole range using the many-body expansion method.This potential energy function represents theconsiderable topographical features of PuOH molecule in detail,which is adequately accurate in the whole potentialsurface and can be used for the molecular reaction dynamics research.     

Calculations of D‐wave bound states and resonance states of the screened helium atom using correlated exponential wave functions

We have investigated the effects of screened Coulomb (Yukawa) potentials on the bound ^1,3D states and the doubly excited ^1,3 D^e resonance states of helium atom using highly correlated exponential basis functions. The Density of resonance states are calculated using stabilization method. Highly correlated exponential basis functions are used to consider the correlation effect between the charged particles. A total of 18 resonances (nine each for ¹ D^e and ³ D^e states) below the n = 2 He ⁺ threshold has been calculated. For each spin states, this includes four members in the 2pnp series, three members in the 2snd series, and two members in 2pnf series. The resonance energies and widths for various screening parameters ranging from infinity to a small value for these ^1,3 D^e resonance states are reported along with the bound‐excited 1s3d ^1,3 D state energies. Overall behavior of the spectral profile of 1s3d ¹D state of helium atom due to electron‐electron and electron‐nucleus screening are also presented. Accurate resonance energies and widths are also reported for He in vacuum. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Theoretical description of nuclear quadrupole coupling in light diatomic molecules

A practical procedure for calculation of nuclear quadrupole coupling constants for light diatomic molecules is discussed. The procedure is based on a molecular wave function that explicitly describes nuclear motion. The approach is capable of yielding quadrupole coupling constants for excited rovibrational levels of diatomic molecules in their ground and excited electronic states. An application of the procedure to the X¹Σ⁺_g and B¹Σ⁺_u states of HD and D₂ is presented.     

GRECP/MRD‐CI calculations of spin‐orbit splitting in ground state of Tl and of spectroscopic properties of TlH

The generalized relativistic effective core potential (GRECP) approach is employed in the framework of multireference single‐ and double‐excitation configuration interaction (MRD‐CI) method to calculate the spin‐orbit splitting in the ²P^o ground state of the Tl atom and spectroscopic constants for the 0⁺ ground state of TlH. The 21‐electron GRECP for Tl is used, and the outer core 5s and 5p pseudospinors are frozen with the help of the level shift technique. The spin‐orbit selection scheme with respect to relativistic multireference states and the corresponding code are developed and applied in the calculations. In this procedure both correlation and spin‐orbit interactions are taken into account. A [4,4,4,3,2] basis set is optimized for the Tl atom and employed in the TlH calculations. Very good agreement is found for the equilibrium distance, vibrational frequency, and dissociation energy of the TlH ground state (R_e=1.870 Å, ω_e=1420 cm⁻¹, D_e=2.049 eV) as compared with the experimental data (R_e=1.872 Å, ω_e=1391 cm⁻¹, D_e=2.06 eV). © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 409–421, 2001     

Ab initio study of the molecular vibrations and electronic structure of the X,B, D and F2Σ+ states of AlO

Molecular vibrations and electronic structure of the X²Σ⁺, B²Σ⁺, D²Σ⁺, and F²Σ⁺ states of AlO are studied by carrying out ab initio configuration interaction calculations and molecular vibration calculations using accurate potential energy functions. An avoided crossing between the D²Σ⁺ and F²Σ⁺ potential energy curves occurs in the neighborhood of 4.0 a₀ and results in irregular vibrational levels of the D and F²Σ⁺ states. The vibrational constants for the F²Σ⁺ state are predicted from the vibrational levels not involved in the irregularity. Configuration mixing is important in describing the B, D, and F²Σ⁺ states. The F²Σ⁺ state at and around its well minimum and the D and F²Σ⁺ states in the avoided crossing region are characterized in terms of their main configurations and dipole moment functions.     

Theoretical electronic structure of the molecule ScI

Theoretical investigation of the 18 lowest electronic states of the molecule ScI in the representation ^2S+1Λ^(±) has been performed via CASSCF and MRCI (single and double excitation with Davidson correction) calculations. To the best of our knowledge these calculated electronic states are the first ones from ab initio methods. Thirteen electronic states between 4,500 cm^?1 and 21,000 cm^?1 have been studied for the first time and have not yet been observed experimentally. The harmonic frequency ω_e, the internuclear distance R_e, the electronic transition energy with respect to the ground state T_e, and the rotational constant B_e have been calculated for the considered electronic states. By using the canonical functions approach the eigenvalues E_υ and the rotational constants B_υ have also been calculated for the six lowest‐lying electronic states. The comparison of these results with the theoretical and the experimental data available in the literature shows a good agreement. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

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.     

Ab initio spectroscopy and thermochemistry of the BN molecule

The lowest¹Σ⁺ and³Π states of the BN molecule have been studied using the quadratic configuration interaction method and (spdf) basis sets. The lowest¹Σ⁺ and³Π states lie extremely closely (T _e≈100 cm^?1) together; it is not clear which is the ground state. The very small separation should form a useful benchmark for basis sets and electron correlation methods. The dissociation energyD ₀ is computed to be 103.9±2 kcal/mol. A self-consistent set of spectroscopic constants is derived from a combination of ab initio and experimental data. JANAF-style thermodynamic functions in the range 100–6000 K, including anharmonic, rovibrational coupling, centrifugal stretching, and spin-orbit coupling effects are computed using direct numerical summation over the 25 lowest electronic states. A modified procedure for the latter is outlined that reduces computer time by one or two orders of magnitude without compromise in accuracy.     

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     

Multireference configuration interaction study on spectroscopic parameters and molecular constants of PO and PO+

The highly accurate valence internally contracted multireference configuration interaction (MRCI) approach has been employed to investigate the potential energy curves (PECs) for the X²Π, b⁴Σ^?, C²Σ^? states of PO and the X¹Σ⁺ state of PO⁺. For these electronic states, the spectroscopic parameters of the isotopes (P¹⁶O, P¹⁸O, P¹⁶O⁺, and P¹⁸O⁺) have been determined and compared with those of the investigations reported in the literature. The comparison shows that excellent agreement exists between the present results and the available experiments. With the PECs determined here, the first 30 vibrational states for P¹⁶O(X²Π, b⁴Σ^?), P¹⁸O(X²Π, b⁴Σ^?), P¹⁶O⁺(X¹Σ⁺), and P¹⁸O⁺(X¹Σ⁺) are computed when the rotational quantum number J equals zero (J = 0). The vibrational level G(υ), inertial rotation constant B_υ and centrifugal distortion constant D_υ are determined when J = 0. All the results of vibrational states except for P¹⁶O (X²Π) are reported for the first time. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011