Lowest electronic states of neutral and ionic LiN

We have investigated the potential energy curves (PECs) of the LiN heteronuclear diatomic molecule, including its ionic species LiN⁺ and LiN⁻, using explicitly correlated multi-reference configuration interaction (MRCI-F12) calculations in conjunction with the correlation consistent quintuple-𝜁 basis set. The effect of core–valence correlation, scalar relativistic effects, and the size of the basis sets has been investigated. A comprehensive set of spectroscopic constants determined based on the above-mentioned calculations are also reported for the lowest electronic states and all systems, including dissociation energies, harmonic and anharmonic vibrational frequencies, and rotational constants. Additional parameters, such as the dipole moments, equilibrium spin-orbit constants, excitation energies, and rovibrational energy levels, are also documented. We found that the three triplet states of LiN, namely, X ³∑⁻, A ³Π, and 2 ³∑⁻, exhibit substantial potential wells in the PEC diagrams, while the quintet states are repulsive in nature. The ground state of the anion also shows a deep potential well in the vicinity of its equilibrium geometry. In contrast, the ground and excited states of the cation are very loosely bound. Charge transfer properties of each of these states are also analyzed to obtain an in-depth understanding of the interatomic interactions. We found that the core–valence correlation has a substantial effect on the calculated spectroscopic constants.     

A MS-CASPT2 study of the low-lying electronic excited states of CH2BrCl

The low-lying singlet excited states of CH₂BrCl have been calculated using multiconfigurational CASSCF, second-order perturbation theory CASPT2 and its multistate extension MS-CASPT2. The CASSCF method shows spurious valence–Rydberg mixing and a wrong order of states. Inclusion of dynamical correlation by single root CASPT2 lowers dramatically the energy of the valences states but does not lead to a complete separation between valence and Rydberg states. This situation is improved by the MS-CASPT2 calculations, which gives two valence states for both A^′ and A″ symmetries below the lowest Rydberg state, corresponding to n(Br)→σ^*(C–Br) and n(Cl)→σ^*(C–Cl) transitions at 6.1 eV (203 nm) and 7.2 eV (173 nm), and being repulsive along C–Br and C–Cl coordinates.     

Theoretical study of the electronic structure of LiX and NaX (X = Rb,Cs) molecules

Adiabatic potential energy, spectroscopic constants, dipole moments, and vibrational levels have been computed for the lowest electronic states of alkali dimers LiX and NaX (X = Rb, Cs). Calculations have been carried with the use of an ab initio approach with core‐potential potentials and full‐valence configuration. Thus, these systems are treated as two‐electron systems. A good agreement is obtained for some lowest states of the molecules studied with available theoretical works. The existence of numerous avoided crossings between electronic states for ¹Σ symmetries is related to the charge‐transfer process in each molecule between its two ionic systems (Li⁺X^?, Li^?X⁺) and (Na⁺X^?, Na^?X⁺). © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Expanded electronic states of the fluorine molecule

Potential curves of electronically excited states of F₂ with an expanded outer orbital have been calculated using a modified frozen core technique: The ionic core has been described with a two-determinant wave function and for the excited states a mixing of configurations with different cores has been employed. An investigation of the valence shell states of F₂ is presented and potential curves for a singly excited as well as a doubly excited V-state of ¹Σ_u⁺ symmetry have been calculated. Further a low lying two-configuration state resulting from simultaneous excitation to a valence and a Rydberg orbital is predicted.     

Accurate spectroscopic constants of the lowest three electronic states in halonitrenes with multireference configuration interaction

Internally contracted multireference configuration interaction (icMRCI) calculations of the ground state (X³Σ⁻), the first excited state (a¹Δ) as well as the second excited state (b¹Σ⁺) have been performed for a series of halogenated nitrenes NXs (X = Cl, Br, and I). Accurate spectroscopic constants of these lowest three electronic states of each NX were obtained in this work using MRCI methods with aug‐cc‐pVXZ (X = T, Q, 5) basis sets and complete basis set (CBS) limit. In addition, various corrections, including the Davidson correction, scalar relativistic effect, core‐valence correlation, and spin‐orbit coupling effect, have been studied in calculating spectroscopic constants, especially for heavy‐atom nitrenes. Comparisons have been made with previous computational and experimental results where available. The icMRCI + Q calculations presented in this work provide a comprehensive series of results at a consistent high level of theory for all of the halogenated nitrenes.     

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.     

Theoretical study of LiK and LiK+ in adiabatic representation

The potential energy curves have been calculated for the electronic states of the molecule LiK within the range 3 to 300 a.u., of the internuclear distance R. Using an ab initio method, through a semiempirical spin-orbit pseudo-potential for the Li (1s ²) and K (1s ²2s ²2p ⁶3s ²3p ⁶) cores and core valence correlation correction added to the electrostatic Hamiltonian with Gaussian basis sets for both atoms. The core valence effects including core-polarization and core-valence correlation are taken into account by using an l-dependent core-polarization potential. The molecular orbitals have been derived from self-consistent field (SCF) calculation. The spectroscopic constants, dipole moments and vibrational levels of the lowest electronic states of the LiK molecule dissociating into K (4s, 4p, 5s, 3d, and 5p) + Li (2s, 2p, 3s, and 3p) in ^{1, 3}Σ, ^{1, 3}Π, and ^{1, 3}Δ symmetries. Adiabatic results are also reported for ²Σ, ²Π, and ²Δ electronic states of the molecular ion LiK⁺ dissociating into Li (2s, 2p, 3s, and 3p) + K⁺ and Li⁺ + K (4s, 4p, 5s, 3d, and 5p). The comparison of the present results with those available in the literature shows a very good agreement in spectroscopic constants of some lowest states of the LiK and LiK⁺ molecules, especially with the available theoretical works. The existence of numerous avoided crossing between electronic states of ²Σ and ²Π symmetries is related to the charge transfer process between the two ionic systems Li⁺K and LiK⁺.     

Energies of Sr states with excited valence shell

Singly- and doubly-excited Sr states emerging upon excitation of the valence shell have been investigated. Only states with low values of the principal quantum numbern of the valence electrons have been considered: 5s4d, 5s5p, 5p ², 4d ² and 4d5p. These states have been treated by a perturbation theory based on the Dirac equations with model potential, the valence electrons interaction being considered as a perturbation. The zero-order approximation accounts for the main contributing interactions including the strong core potential screening. The applied calculation method was previously developed for highly-excited Rydberg states but its application also for states with lown was proved to be suitable.     

Visualization of electron correlation in a series of helium S states

Electron correlation has been studied for a series of helium S states represented by a variety of wavefunctions, the best of which are accurate Hylleraas—Kinoshita functions. The states studied are the ground state, the lowest excited ¹S and ³S states, and the (2s)² and (2p)² doubly-excited ¹S states. Primary data is obtained from graphs of the conditional probability density as a function of the radial distance r₂ and the interelectronic angle θ₁₂, given that r₁ is fixed at various distances. Such graphs make clear the extent to which characteristics such as angular and radial correlations, and Fermi and Coulomb holes, are consequences of the relative motion of electrons in two-electron atoms.     

Configuration-Interaction study of lower excited states of O2: Valence and rydberg characters of the two lowest 3Σu − states

Configuration-interaction calculations, with an extended basis, are carried out on the ground and lower excited states of O₂ and O₂⁺ at and near the equilibrium internuclear distance (R = 2.3 a.u.) of the ground state of O₂. Particular attention has been paid to the two lowest ³Σ_u^? states, and the mixing of the valence and Rydberg characters in these states are studied. The lowest ³Σ_u^? state is a Rydberg-type state for R < 2.3 a.u., but becomes valence-type for R ? 2.3 a.u. The second ³Σ_u^? state, which is 1.6 eV above the lowest ³Σ_u^? at R = 2.3 a.u., changes its character from Rydberg to valence, valence to Rydberg, and then to valence again when R increases from 1.9 to 3.1 a.u. Satisfactory agreement between the calculated and experimental vertical excitation energies is obtained.     

Ab initio calculation of the electronic structure of the strontium hydride ion (SrH+)

The potentials, spectroscopic properties and electric dipole moments of SrH⁺ are computed for 63 molecular states dissociating up to Sr²⁺ + H^? using an ab initio approach. The ab initio formalism is based on large basis sets, nonempirical atomic pseudopotential for strontium core, correlation treatment for core valence through the effective core polarization potentials and for valence through full valence configuration interaction. Our theoretical molecular constants match published values very well and a large amount of new results is produced. Unusual potential shapes are found in ¹Σ⁺ states often caused by avoided crossing series between them and imprinted by the ionic state Sr²⁺H^?. The high potential energy curves suggest, it is possible to form H^? or at least to neutralize H⁺ in collisions with strontium. © 2014 Wiley Periodicals, Inc.     

Semidiffuse states of diatomic molecules: Configuration interaction studies of the lowest 2Σ+ and 2Δ states of NS,SiF, and CCl

It has been shown by ab initio configuration-interaction methods that the lowest ²Σ⁺ states of NS and SiF are ‘semidiffuse’ states, like the B ²Σ⁺ state of PO. The lowest ²Σ⁺ state of CCl also appears to be semidiffuse, although here the situation is not so clear. Semidiffuse states require diffuse orbitals in the wavefunction, but they are not Rydberg states. The second ²Σ⁺ state of each molecule is shown to be the lowest ns Rydberg state, whereas the third ²Σ⁺ state is a valence state for NS and CCl, and a 4po Rydberg state for SiF. The lowest ²δ state of each molecule derives from the 7σ → 3π valence configuration. Comparison with available experimental information shows, in general, good agreement.     

Spectroscopic constants and molecular properties of the X2Π and a4Σ− electronic states of the SiF radical

The potential energy curves (PECs) of the X²Π and a⁴Σ^? electronic states of the SiF radical have been studied by an ab initio quantum chemical method. The calculations have been made using the complete active space self‐consistent field (CASSCF) method, which is followed by the valence internally contracted multireference configuration interaction (MRCI) approach in combination with several correlation‐consistent basis sets. 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 relativistic corrections are made at the level of cc‐pV5Z basis set. The core‐valence correlation corrections are performed using the cc‐pCV5Z 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). These PECs are extrapolated to the complete basis set limit by the total‐energy extrapolation scheme. Using these PECs, the spectroscopic parameters are determined and compared with those reported in the literature. With these PECs obtained by the MRCI+Q/CV+DK+56 calculations, the vibrational levels, inertial rotation, and centrifugal distortion constants of the first 20 vibrational state of each electronic state are calculated when the rotational quantum number J equals zero. Comparison with the Rydberg‐Klein‐Rees (RKR) data shows that the present results are reliable and accurate. The molecular constants of the X²Π and a⁴Σ^? electronic states determined by the MRCI+Q/CV+DK+56 calculations should be good prediction for future laboratory experiment. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

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.     

Chromatographic separation of inorganic ions on specially prepared calcium sulphate sticks

It has been shown⁶ that specially prepared calcium sulphate sticks are suitable as adsorbent bodies in the chromatographic separation of inorganic ions. With the help of these sticks separations of Cu⁺² — Sb⁺³, Bi⁺³ — Sb⁺³, Cd⁺² — Sb⁺³, Cd⁺² — Sn⁺², Hg⁺² — AS⁺³, Hg⁺² — Sb⁺³, Cu⁺² — As⁺³, Bi⁺³ — As⁺³, Hg⁺² — Cu⁺², Cu⁺² — Fe⁺³ have been effected.     

Spectroscopic constants and molecular properties of A3Σu+, B3Πg,W3Δu,and B′3Σu− electronic states of the N2 molecule

The potential energy curves (PECs) of A³Σ, B³Π_g, W³Δ_u, and B^′3Σ electronic states of the N₂ molecule have been studied for internuclear separations from 0.05 to 2.0 nm using the full valence complete active space self‐consistent‐field method followed by the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach in conjunction with the correlation‐consistent basis sets. Effects on the PECs by the core–valence correlation and relativistic corrections are taken into account. The way to consider the relativistic correction is to use the second‐order Douglas‐Kroll Hamiltonian approximation. The core–valence correlation correction is made with the 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 the Davidson modification (MRCI+Q). These PECs are extrapolated to the complete basis set limit. The spectroscopic parameters of ¹⁴N₂, ¹⁴N¹⁵N, and ¹⁵N₂ isotopologs have been evaluated and compared with those reported in the literature. Excellent agreement has been found between the present results and the Rydberg‐Klein‐Rees (RKR) data. With the PECs obtained by the MRCI+Q/CV+DK+56 calculations, the first 30 vibrational states for three species are computed for each electronic state. And for each electronic state of each species, the vibrational level G(ν), inertial rotation constant B_ν, and centrifugal distortion constant D_ν have been determined, which agree well with the RKR data. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Intruder state avoidance multireference Møller-Plesset perturbation theory

A new perturbation approach is proposed that enhances the low‐order, perturbative convergence by modifying the zeroth‐order Hamiltonian in a manner that enlarges any small‐energy denominators that may otherwise appear in the perturbative expansion. This intruder state avoidance (ISA) method can be used in conjunction with any perturbative approach, but is most applicable to cases where small energy denominators arise from orthogonal‐space states—so‐called intruder states—that should, under normal circumstances, make a negligible contribution to the target state of interests. This ISA method is used with multireference Møller–Plesset (MRMP) perturbation theory on potential energy curves that are otherwise plagued by singularities when treated with (conventional) MRMP; calculation are performed on the 1³Σ state of O₂; and the 2¹Δ, 3¹Δ, 2³Δ, and 3³Δ states of AgH. This approach is also applied to other calculations where MRMP is influenced by intruder states; calculations are performed on the ³Π_u state of N₂, the ³Π state of CO, and the 2¹A′ state of formamide. A number of calculations are also performed to illustrate that this approach has little or no effect on MRMP when intruder states are not present in perturbative calculations; vertical excitation energies are computed for the low‐lying states of N₂, C₂, CO, formamide, and benzene; the adiabatic ¹A₁–³B₁ energy separation in CH₂, and the spectroscopic parameters of O₂ are also calculated. Vertical excitation energies are also performed on the Q and B bands states of free‐base, chlorin, and zinc–chlorin porphyrin, where somewhat larger couplings exists, and—as anticipated—a larger deviation is found between MRMP and ISA‐MRMP. © 2002 Wiley Periodicals, Inc. J Comput Chem 10: 957–965, 2002     

Geometries,vibrational frequencies,and excitation energies of a series of fluorine‐substituted carbenes,FCX (X = H,F, Cl,Br, and I): A high‐level multireference configuration interaction study

High‐level calculations using internally contracted multireference configuration interaction including Davidson correction (icMRCI+Q) method have been carried out for the ground singlet states, the first excited states, and the lowest triplet states of a series of fluorine‐substituted carbenes FCX (X = H, F, Cl, Br, and I). Equilibrium geometries and vibrational frequencies of the three electronic states, adiabatic transition energy of the first excited singlet state, as well as the ground singlet—lowest triplet energy gap (S‐T gap) of each of FCX carbenes have been obtained. Effects of the basis set of icMRCI+Q calculation on the geometries and energies have been investigated. In addition, various corrections, including the scalar relativistic effect, spin‐orbit coupling, and core‐valence correlation, have been studied in calculating the transition energies and the S‐T gaps, especially for heavy‐atom carbenes. This results have been compared with previous calculations using a variety of methods. Our icMRCI+Q results are in very good agreement with the high‐resolution laser‐based spectroscopic results where available. Some structure and spectroscopic constants of the fluorine‐substituted carbenes which are void in the literature have been provided with consistent high‐level calculations. © 2013 Wiley Periodicals, Inc.     

Multiconfigurational perturbation theory (CASPT2) applied to the study of the low-lying singlet and triplet excited states of cyclopropene

The electronic spectrum of cyclopropene has been studied using multiconfigurational second-order perturbation theory (CASPT2) with extended ANO-type basis sets. The calculation comprises two valence states and the 3s, 3p, 3d members of the Rydberg series converging to the π and σ ionization limits. A total of twenty singlet and twenty triplet excited states have been analyzed. The results confirm the valence nature of the lowest energy singlet-singlet band and yield a conclusive assignment: the first dipole-allowed transition in cyclcopropene is due to absorption to a (σ → π*) state. The (π → π*) (V) state is interleaved among a number of Rydberg states in the most intense band of the system. The remaining spectral bands are due to Rydberg transitions of higher energy. The two lowest singlet-triplet transitions involve the same valence states. The results are in agreement with available experimental data and provide a number of new assignments of the experimental spectra.     

Valence ab initio calculation of the potential-energy curves for the Ca<Subscript>2</Subscript> dimer

The electronic structure of the Ca₂ molecule has been investigated by use of a two-valence-electron semiempirical pseudopotential and applying the internally contracted multireference configuration interaction method with complete-active-space self-consistent-field reference wave functions. Core–valence correlation effects have been accounted for by adding a core-polarization potential to the Hamiltonian. The ground-state properties of the Ca₂ and Ca₂⁺ dimers have also been studied at the single-reference coupled-cluster level with single and double excitations including a perturbative treatment of triple excitations. Good agreement with experiment has been obtained for the ground-state potential curve and the only experimentally known A¹_u⁺ excited state of Ca₂. The spectroscopic parameters D_e and R_e deduced from the calculated potential curves for other states are also reported. In addition, spin–orbit coupling between the singlet and triplet molecular states correlating, respectively, with the (4p)¹P and (4p)³P Ca terms has been investigated using a semi-empirical two-electron spin–orbit pseudopotential. Acknowledgement.This work was supported by grant 5 P03B 082 21 from the Polish State Committee for Scientific Research (KBN).