Ab initio valence bond calculations. VII. HF,HF+, and H2F+

Ab initio valence bond calculations for the ground and excited states of HF and HF⁺ are presented. Total energies, equilibrium geometries, dissociation energies, dipole moments, and spectroscopic constants for HF and HF⁺ have been calculated. The photoelectron spectrum of HF has been examined and interpreted by means of the valence bond formalism. The ground state of the protonated species H₂F⁺ has been investigated.     

Electronic states and nature of bonding in the molecule YN by all-electron ab initio CASSCF calculations

In the present work, we present results of all-electron ab initio CASSCF calculations of nine electronic states of the molecule YN. Also reported are the spectroscopic constants derived on the basis of the calculated potential energies. The predicted electronic ground state is ¹∑⁺, and this state is found to be separated from the excited states ³∑⁺, ³Π, and ¹Π by 5177, 9290, and 9915 cm^?1, respectively. The chemical bond in the YN molecule is polar with charge transfer from Y to N, giving rise to a dipole moment of 8.19 Debye at 3.3 au in the ¹∑⁺ ground state is basically a double bond composed of two π bonds. The dissociation energy of the YN molecule has been derived as 4.59 eV. © 1993 John Wiley & Sons, Inc.     

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.     

Quasirelativistic valence ab initio calculation of the potential-energy curves for Cd–rare gas atom pairs

The results of large-scale valence ab initio calculations of the potential-energy curves for the ground states and several excited states of Cd–rare gas (RG) van der Waals molecules are reported. In the calculations, Cd²⁰⁺ and RG⁸⁺ cores are simulated by energy-consistent pseudopotentials, which also account for scalar-relativistic effects and spin-orbit interaction within the valence shell. The potential energies of the Cd–RG species in the ΛS coupling scheme have been evaluated by means of ab initio complete-active-space multiconfiguration self-consistent-field (CASSCF)/CAS multireference second-order perturbation theory (CASPT2) calculations with a total 28 valence electrons, but the spin-orbit matrix has been computed in a reduced configuration interaction space restricted to the CASSCF level. Finally, the Ω potential curves are obtained by diagonalization of the modified spin-orbit matrix (its diagonal elements before diagonalization substituted by the corresponding CASPT2 eigenenergies). The calculated potential curves, especially the spectroscopic parameters derived for the ground states and several excited states of the Cd–RG species are presented and discussed in the context of available experimental data. The theoretical results exhibit very good agreement with experiment. Received: 20 April 2000 / Accepted: 1 September 2000 / Published online: 21 December 2000     

Valence electronic states of NH2+ and PH2+ dications

The ab initio second-order effective valence-shell Hamiltonian that is based on the multireference many-body perturbation theory has been applied to determine adiabatic potential energy curves for the valence states of NH²⁺ and PH²⁺ dications. For PH²⁺, three low-lying quasi-bound states (X¹∑⁺, a³ Π, A¹Π) are found and their spectroscopic constants are characterized. In NH²⁺, no quasi-bound states are found. The potential energy curves for NH²⁺ are compared with those for PH²⁺ to understand the difference between these two valence isoelectronic cations. © 1993 John Wiley & Sons, Inc.     

Spectroscopic Parameters of X3∑-, a1△, and A'3△ Electronic States of SO Radical

The potential energy curves (PECs) of three low-lying electronic states (X³∑^-, a¹△, and A^'3△) of SO radical have been studied by ab initio quantum chemical method. The calcula-tions were carried out with the full valence complete active space self-consistent field method followed by the highly accurate valence internally contracted multireference configuration in-teraction (MRCI) approach in combination with correlation-consistent basis sets. Effects of the core-valence correlation and relativistic corrections on the PECs are taken into account. The core-valence correlation correction is carried out with the cc-pCVDZ basis set. The way to consider the relativistic correction is to use the second-order Douglas-Kroll Hamiltonian approximation, and the 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 means of the Davidson modification (MRCI+Q). These PECs are extrapolated to the complete basis set limit by the two-point energy extrapolation scheme. With these PECs, the spectroscopic parameters are determined.     

A valence bond study of the oxygen molecule

Ab initio valence bond calculations are performed for the three lowest states of the oxygen molecule (³Σ⁻_g, ¹Δ_g, and ¹Σ⁺_g). One objective of the present study was to make a contribution to previous valence bond discussions about the oxygen “double” bond. Further, we study the origin of a small barrier in the potential energy surface of the ground state. Two compact models are employed to maintain the clear picture that can be offered by the valence bond method. The first model has only the Rumer structures that are essential for bonding and a proper dissociation. The second model, in addition, has structures which represent excited atoms. These prove to be important for the dissociation energies. For both models, the orbitals are fully optimized. The spectroscopic data obtained are significantly better than are the (few) valence bond results on O₂ that have been published and have the quality of multiconfiguration self-consistent field calculations in which the same valence space is used. The “hump” in the potential energy surface of the ground state is shown to arise from a spin recoupling. The free atoms correspond to a spin coupling that is incapable of describing the formation of bonds. Only at short distances, an alternative spin coupling provides bonding and the repulsive curve is converted into an attractive one. Our results on this subject support a valence bond explanation previously given by McWeeny [R. McWeeny, Int. J. Quantum Chem. Symp. 24 , 733 (1990)]. © 1996 John Wiley & Sons, Inc.     

Construction and applications of symmetrized valence bond wave functions

A method constructing symmetry-adapted bonded Young tableau bases is proposed, based on the symmetry properties of bonded tableaus and the projection operator associated with a point group. Several examples including the ground states and π excited states of O₃⁻, O₃, O₃⁺, and C₃⁻ are shown for instruction to construct the symmetrized valence bond (VB) wave function. Excitation energies of transitions from the ground states to π excited states of O₃⁻, C₃H₅, and C₃⁻ are calculated with an optimized symmetrized valence bond wave function in the σ–π separation approximation. Good agreement between the VB and experimental excitation energies is observed. The bonding features of the ground state and the first π excited singlet and triplet states for S₃ are discussed according to bonding populations from VB calculations. Both the singlet-biradical and the dipole structures have significant contributions to the ground state X ¹A₁ of S₃, while the excited state 1 ¹B₂ is essentially composed of the dipole structures, and the 1 ³B₂ excited state is comprised from a triplet-biradical structure. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 1–7, 1998     

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.     

Pseudopotential study of the rare earth monohydrides,monoxides and monofluorides

Nonrelativistic and quasirelativistic energy-adjusted pseudopotentials for fixed 4f subconfigurations of the rare earth elements La through Lu together with corresponding optimized valence basis sets have been used in SCF and CI(SD) calculations to determine the spectroscopic constants for the energetically low lying superconfigurations of the lanthanide monohydrides, monoxides and monofluorides. The experimentally observed trends in dissociation energies, bond lengths and vibrational frequencies for the ground states of the calculated superconfigurations of the monoxides and monofluorides are well reproduced. The results for the monohydrides are mainly predictions.     

Ab-initio study on low-lying states of the TiSi molecule

 The electronic structure of the TiSi molecule was examined using two types of multireference single and double excitation configuration interactions with highly extended basis sets, one including valence correlation and the other including valence and core–valence correlation. A multireference coupled-pair approximation (MRCPA) was further applied to the latter. The calculations suggest a ⁵Δ ground state, and the lowest excited state is ³Π and is only slightly (0.12 eV as estimated by MRCPA) above the ground state. The spectroscopic constants of the low-lying ¹Δ, ³Δ, ¹Π, ⁵Π, and ⁷Σ⁺ states as well as the ⁵Δ ground state and the ³Π excited states were evaluated, and we found that the molecule has only a weak σ bond and that six of the eight valence electrons essentially do not contribute to the bonding. The bonding nature of TiSi in these states is discussed in comparison with the TiC molecule. Received: 7 October 2000 / Accepted: 8 January 2001 / Published online: 3 May 2001     

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.     

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     

CEPA calculations on open-shell molecules. III. Potential curves for the six lowest excited states of He2 in the vicinity of their equilibrium distances

CEPA-PNO and PNO-CI calculations have been performed for the potential energy curves of the He ₂ ⁺ ground state and the six lowest excited states of He₂ in the range of 1.4 a₀ ≤R ≤ 3.5 a₀. The calculated equilibrium distances as well as the spectroscopic constants are in very good agreement with molecular constants as derived experimentally from the rotation-vibration spectrum of He₂ by Ginter, except for thec ³∑ _g ⁺ state. This latter discrepancy is probably due to an “obligatory” hump in thec ³∑ _g ⁺ state occurring at 3.5 a₀ which cannot be properly treated in our calculation. The relative energetic positions of the six lowest states and their ionization energies are reproduced by our calculations with an accuracy of 0–400 cm⁻¹. Extrapolation of our results to infinite basis sets leads to estimates of the dissociation energies of He₂ excited states which cannot be measured spectroscopically because of the humps in all these states.     

Relativistic calculations of AuSi+ and AuSi−

Theoretical calculations of the electronic structure of the ground state and a series of excited states of the AuSi⁺ and AuSi⁻ molecules are presented. The calculations were carried out with the spin-free relativistic infinite-order two-component (IOTC) method and high-level complete active space self-consistent field/complete active space perturbation theory correlated methods. The spin-orbit (SO) coupling was introduced via the restricted active space state interaction method with the use of the atomic mean-field SO integrals. The work presents the spectroscopic parameters of calculated states and full potential energy curves of the ionic AuSi⁺ and AuSi⁻ structures for the first time. Electrostatic potential maps projected on the electron density surface illustrate the significant relativistic effects on going from nonrelativistic to scalar relativistic treatments.     

Electronic structures of NbGen−/0/+ (n = 1–3) clusters from multiconfigurational CASPT2 and density matrix renormalization group-CASPT2 calculations

Density functional theory and multiconfigurational CASPT2 and density matrix renormalization group DMRG-CASPT2 have been employed to study the low-lying states of NbGe_n^−/0/+ (n = 1–3) clusters. With the DMRG-CASPT2 method, the active spaces are extended to a size of 20 orbitals. For most of the states, the CASPT2 relative energies are comparable with the DMRG-CASPT2 results. The leading configuration, bond distances, vibrational frequencies, and relative energies of the low-lying states of these clusters were calculated. The ground states of these clusters were computed to be ³Δ, ⁴Φ, and ⁵Φ of NbGe^−/0/+; ³A₂, ⁴B₁, and ³B₁ of cyclic-NbGe₂^−/0/+; and ¹A′, 1²A″ and 1²A′′ (²E), and ³A″ of tetrahedral-NbGe₃^−/0/+ isomers. For NbGe cluster, our calculations proposed that the ⁶∑ is almost degenerate with the ⁴Φ with the CASPT2 and DMRG-CASPT2 relative energies of 0.05 and 0.06 eV. The adiabatic detachment energies of NbGe_n⁻ (n = 1–3) clusters were estimated to be 1.46, 1.55, and 2.18 eV by the CASPT2 method. The relevant detachment energies of the anionic ground state and the ionization energies of the neutral ground states are evaluated at the CASPT2 level.     

Theoretical study of low-lying electronic states of Mn2 using a newly developed relativistic model core potential

We investigated the electronic structure of low-lying electronic states of Mn₂ using a newly developed relativistic model core potential (spdsMCP). Calculations were performed at complete active space self-consistent field (CASSCF) and second-order multiconfiguration quasidegenerate perturbation theory (MCQDPT2) levels. The MCQDPT2 calculations reveal that the 1Σg⁺ state is the ground state. Calculated spectroscopic constants are very similar to the results of recent all-electron calculations and experimental values, indicating that the spdsMCP works well for Mn₂, which requires a highly correlated calculation. The wave functions of low-lying states are also analyzed at the CASSCF level.     

Heavier alkali-metal monosulfides (KS, RbS, CsS, and FrS) and their cations

The heavier alkali-metal monosulfides (KS, RbS, CsS, and FrS) have been studied by high-level ab initio calculations. The RCCSD(T) method has been employed, combined with large flexible valence basis sets. All-electron basis sets are used for potassium and sulfur, with effective core potentials being used for the other metals, describing the core electrons. Potential-energy curves are calculated for the lowest two neutral and cationic states: all neutral monosulfide species have a (2)Pi ground state, in contrast with the alkali-metal monoxide species, which undergo a change in the electronic ground state from (2)Pi to (2)Sigma(+) as the group is descended. In the cases of KS, RbS, and CsS, spin-orbit curves are also calculated. We also calculate potential-energy curves for the lowest (3)Sigma(-) and (3)Pi states of the cations. From the potential-energy curves, spectroscopic constants are derived, and for KS the spectroscopic results are compared to experimental spectroscopic values. Ionization energies, dissociation energies, and heats of formation are also calculated; for KS, we explore the effects of relativity and basis set extrapolation on these values.     

A theoretical investigation of electronic reorganizations accompanying core and valence ionization in simple hydrogen bonded systems

Non-empirical LCAO MO SCF calculations have been carried out on the ground state and core ionized states of some hydrogen bonded dimers, and in the particular case of H₂O the trimer has also been investigated. Comparison of absolute and relative binding energies and relaxation energies with respect to the corresponding monomers reveals that substantial changes occur in going to the associated species. The relaxation energies for a given core hole are shown to increase on going from monomer to dimer indicating that intermolecular contributions to relaxation energies are of the same sign irrespective of the sign for the shift in core binding energy. Creation of a core hole in the dimer species is shown to give rise to substantial changes in hydrogen bond energies compared with the neutral species. In the particular case of valence holes dominantly of 2s and 2p character it is shown that trends in shifts and relaxation energies parallel those for the core hole states.