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     

Theoretical electronic structure of the molecule ScBr

The potential energy curves have been investigated for the 23 lowest electronic states in the ^2s+1Λ^± representation of the molecule ScBr via CASSCF and MRCI (single and double excitations with Davidson correction) calculations. Seventeen electronic states have been studied theoretically for the first time. The harmonic frequency ω_e, the internuclear distance r_e, and the electronic energy with respect to the ground state T_e have been calculated. By using the canonical functions approach, the eigenvalues E_v, the rotational constant B_v, and the abscissas of the turning points (R_min, R_max) have been calculated for electronic states up to the vibrational level v = 32. The comparison of these values to the theoretical and experimental results available in the literature shows a good agreement. © 2007 Wiley Periodicalsm Inc. Int J Quantum Chem, 2008     

Theoretical study with vibration–rotation and dipole moment calculations of quartet states of the CrCl molecule

The potential energy curves have been investigated for the 10 lowest quartet electronic states in the ^2s+1Λ^± representation below 30,000 cm^?1 of the molecule CrCl via CASSCF and MRCI (singly and doubly excitation with Davidson correction) calculations. The harmonic frequency ω_e, the internuclear distance r_e, the rotational constant B_e, the electronic energy with respect to the ground state T_e, and the permanent dipole moment μ have been calculated. By using the canonical functions approach, the eigenvalues E_v, the rotational constant B_v, and the abscissas of the turning points r_min and r_max have been calculated for the considered electronic states up to the vibrational level v = 19. Seven electronic states have been studied here theoretically for the first time. The comparison of these values to the theoretical results available in the literature shows a good agreement. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

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.     

Ab initio spectroscopic study for the NaRb molecule in ground and excited states

A wide adiabatic study is performed for NaRb molecule, involving 15¹Σ⁺ electronic states including the ionic state Na^?Rb⁺, as well as 14³Σ⁺, 1–9^1,3Π, and 1–5^1,3Δ states. This investigation is performed using an ab initio approach which involves the effective core potential, the core polarization potential with l‐dependent cut‐off functions. The NaRb system has been treated as a two‐electron system and the full valence configuration interaction is easily achieved. The spectroscopic constants R_e, D_e, T_e, ω_e, ω_ex_e, B_e, and D₀ for all these states are derived. We have also computed the vibrational levels as well their spacing for different values of J. In addition, permanent and transition dipole moments are determined and analyzed. The Dunham coefficients have been used to perform experimental spacing to compare directly with our results. The present calculations on NaRb extend previous theoretical works to numerous electronic excited states in the various symmetries. © 2014 Wiley Periodicals, Inc.     

Theoretical study with rovibrational and dipole moment calculation of sextet states of the CrCl molecule

The potential energy curves have been investigated for the 13 lowest sextet electronic states in the representation below 53,000 cm^?1 of the molecule CrCl via CASSCF and MRCI (single and double excitation with Davidson correction) calculations. The harmonic frequency ω_e, the internuclear distance r_e, the rotational constant B_e, the electronic energy with respect to the ground state T_e, and the permanent dipole moment μ have been calculated. By using the canonical functions approach, the eigenvalues E_v, the rotational constant B_v, and the abscissas of the turning points r_min and r_max have been calculated for the considered electronic states up to the vibrational level v = 16. Nine electronic states have been studied theoretically here for the first time. The comparison of these values with the theoretical and experimental results available in the literature shows a good agreement. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

The origin of energy functional in Roothaan open shell SCF theory

Different methods of averaging of energy over the states of electronic configurations γ^N (n_γ = 1, 2, 3 and N = 1, 2, …, 2n_γ ? 1) leading to Roothaan' energy expression are considered. The consequent values of vector coupling coefficients (VCC ) in energy functionals for various states as well as for average values of energy are presented. It is shown also that in molecular systems of cubic and tetragonal symmetry having electronic configurations t^N (N = 2–4) and e² there exist states for which VCC are dependent on the choice of basis set of degenerate open-shell molecular orbitals. The origin of such “non-Roothaan” terms and peculiarities of its calculation by the restricted Hartree–Fock method are discussed.     

PdYH分子的结构与势能函数

用密度泛函理论的B3LYP方法, 对钯和钇原子采用SDD收缩价基函数, 氢原子采用6-311＋＋G**全电子基函数, 对PdY和PdYH体系的结构进行优化. 计算表明: PdY分子的几何构型为C_∞v, 其基态为X²Σ^＋态, 键长R＝0.24168 nm, 离解能为D_e＝2.8261 eV, 谐振频率ω_e＝254.0656 cm^－1, 并拟合得到Murrell-Sorbie势能函数; PdYH分子最稳态为C_s构型, 电子组态为¹A', 平衡核间距R_PdY＝0.24281 nm, R_YH＝0.19824 nm, 键角∠PdYH＝116.7157°, 离解能D_e＝5.6146 eV, 基态简正振动频率: 对称伸缩振动频率ν₁ (a')＝348.2909 cm^－1, 弯曲振动频率ν₂ (a')＝243.3382 cm^－1, 反对称伸缩振动频率ν₃ (a')＝1442.2695 cm^－1. 由微观过程的可逆性原理分析了分子的可能离解极限. 并用多体项展式理论方法分别导出基态PdY和PdYH分子的势能函数, 其等值势能面图准确地再现了PdY和PdYH分子的结构特征和离解能, 由此讨论了Pd＋Y＋H分子反应的势能面静态特征.     

Binding Matter with Antimatter: The Covalent Positron Bond

We report sufficient theoretical evidence of the energy stability of the e⁺?H₂^2? molecule, formed by two H^? anions and one positron. Analysis of the electronic and positronic densities of the latter compound undoubtedly points out the formation of a positronic covalent bond between the otherwise repelling hydride anions. The lower limit for the bonding energy of the e⁺?H₂^2? molecule is 74 kJ mol^?1 (0.77 eV), accounting for the zero‐point vibrational correction. The formation of a non electronic covalent bond is fundamentally distinct from positron attachment to stable molecules, as the latter process is characterized by a positron affinity, analogous to the electron affinity.     

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 calculation of the low-lying sextet electronic states of CrF molecule

The potential energy curves have been investigated for the 12 lowest sextet electronic states in the ^2s+1Λ^(±)${}^{2s+1}{\mathrm{\Lambda }}^{(\pm )}$ representation below 53,000 cm⁻¹ of the molecule CrF via CASSCF and MRCI (single and double excitation with Davidson correction) calculations. Seven electronic states have been studied theoretically for the first time. The harmonic frequency ω_e, the internuclear distance R_e, the rotational constant B_e, the electronic energy with respect to the ground state T_e, and the permanent dipole moment μ have been calculated. By using the canonical functions approach, the eigenvalues E_v, the rotational constant B_v and the abscissas of the turning points R_min and R_max have been calculated for the considered electronic states up to the vibrational level v = 39. The comparison of these values to the theoretical and experimental results available in the literature shows a good agreement.     

Revisiting the nature of the ZnO ground state: Influence of spin–orbit coupling

Relativistic calculations of the low-lying electronic states of the ZnO molecule are performed for the Λ–Σ states, ¹Σ⁺, ¹Π, ¹Δ, ³Π and ³Σ⁻, at the CCSD(T) or MRCI level, using scalar relativistic energy-consistent pseudopotentials, and the EPCISO method for spin–orbit CI coupling. The ZnO ground state is assigned to 0⁺ symmetry and has ¹Σ⁺ character around the equilibrium region. The spectroscopic constants (r_e, ω_e) of the 0⁺ ground state are in good agreement with experimental results. Interpenetration of the vibrational levels of the two lowest 0⁺ states is also shown.     

Diagrammatic perturbation theory: Potential curves for the ground state of the carbon monoxide molecule

Diagrammatic many-body perturbation theory is used to calculate the potential energy function for the X¹ σ+ state of the CO molecule near the equilibrium nuclear configuration. Spectroscopic constants are derived from a number of curves which are obtained from calculations taken through third order in the energy. By forming [2/1] Padé approximants to the constants we obtain: r_e = 1.125 Å (1.128 Å), B_e = 1.943 cm^?1 (1.9312 cm^?1), a^B_e = 0.0156 cm^?1 (0.0175 cm^?1), W_e = 2247 cm^?1 (2170 cm^?1), W_eX_e = 12.16 cm^?1 (13.29 cm^?1), where the experimental values are given in parenthesis.     

Potential energy curves for ground and excited states of NaLi from ab initio calculations with effective core polarization potentials

Sixteen low-lying electronic states of NaLi are investigated by SCF/valence Cl calculations including core polarization effects by means of an effective potential. Spectroscopic constants are obtained with estimated uncertainties of ΔR_e ? 0.01 Å, Δω_e ? 0.6 cm^?1 and ΔD_e ? 80 cm^?1. From a comparison of experimental and theoretical G(υ) values, we suggest a ground-state dissociation energy of 7093 ± 5 cm^?1. Using our rovibrational energies and recently measured excitation lines, we are able to improve the T_e values and dissociation energies of five excited states to an accuracv of ±8 cm^?1.     

Ab initio study of low-lying electronic states of the FNO2 molecule

Ab initio electronic structure calculations are reported for low-lying electronic states, ¹A₁, ¹A₂, ³A₂, ¹B₁, ³B₁, ¹B₂, and ³B₂ of the FNO₂ molecule. Geometric parameters for the ground state ¹A₁ are predicted by MRSDCI calculations with a double-zeta plus polarization basis set. The vertical excitation energies for these electronic states are determined using MRSDCI/DZ+P calculations at the ground-state equilibrium conformation. The oscillator strengths and radiative lifetimes for some electronic states are calculated based on the MRSDCI wave functions. © 1993 John Wiley & Sons, Inc.     

He++N2 Charge Transfer Reaction: An Ab initio Analysis

An ab initio analysis on the involved potential energy surfaces is presented for the investigation of the charge transfer mechanism for the He⁺+N₂ system. At high collision energy, as many as seven low-lying electronic states are observed to be involved in the charge transfer mechanism. Potential energy surfaces for these low-lying electronic states have been computed in the Jacobi scattering coordinates, applying multireference configuration interaction level of theory and aug-cc-pVQZ basis sets. Asymptotes for the ground and various excited states are assigned to mark the entrance (He⁺+N₂) and charge transfer channels (He+N₂⁺). Nonadiabatic coupling matrix elements and quasi-diabatic potential energy surfaces have been computed for all seven states to rationalize the available experimental data on the charge transfer processes and to facilitate dynamics studies.     

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.     

Hartree-Fock cluster study of interstitial transition metals in silicon

Results are presented of a Hartree-Fock cluster study of interstitial Ti, V, Cr, and Mn impurities in silicon. A Si₁₀ cluster models the nearest Si atoms around a tetrahedral interstitial site in crystalline Si. The dangling bonds of the Si atoms are saturated by hydrogens. The effect of the Si core electrons is represented by an effective potential. Characteristic for the electronic structure of the low-lying states of the neutral, singly positive, and doubly positive ions in silicon is the presence of fairly delocalized but still predominantly transition-metal (3d)-like orbitals of t₂ and e symmetry. For all ions the energy of the weighted average of the terms belonging to a configuration is lowest for the configuration with maximum occupation of the t₂ orbitals. Ground states with maximum spin multiplicity are found for all ions, except Ti⁰.     

Vibrational analysis of the electronic spectrum of ethylene based onab initio SCF-CI calculations

Ab initio calculations for CH₂ twisting and CC stretching vibrational wavefunctions and energy levels are reported for various electronic states of ethylene C₂H₄. Electronic transition moments between these states are also obtained to allow a calculation of the oscillator strengths for vibrational transitions involved in various electronic band systems; from this study it is concluded that thevertical electronic energy differenceΔE _e may differ significantly from the energy of the absorption maximumΔE _max with which it is often equated. In particular it is found in the case of theπ→π ^* singlet-singlet excitation of ethylene that theΔE _e value overestimates the most probable vibrational transition energy (7.89 eV) by some 0.4 eV, thereby offering an explanation for the fact that previous attempts to predict the location of theV-N Franck-Condon absorption maximum have consistently obtained substantially higher results than the 7.66 eV value actually observed. Similar calculations for various Rydberg species and for theN-T transition are also found to obtain a quite consistent representation of the electronic spectrum of this system.     

Molecular electric properties in electronic excited states: multipole moments and polarizabilities of H2O in the lowest1 B 1 and3 B 1 excited states

Summary The dipole and quadrupole moments and the dipole polarizability tensor components are calculated for the¹ B ₁ and³ B ₁ excited states of the water molecule by using the complete active space (CAS) SCF method and an extended basis set of atomic natural orbitals. The dipole moment in the lowest¹ B ₁ (0.640 a.u.) and³ B ₁ (0.416 a.u.) states is found to be antiparallel to that in the ground electronic state of H₂O. The shape of the quadrupole moment ellipsoid is significantly modified by the electronic excitation to both states investigated in this paper. All components of the excited state dipole polarizability tensor increase by about an order of magnitude compared to their values in the ground electronic state. The present results are used to discuss some aspects of intermolecular interactions involving molecules in their excited electronic states.