Molecular Spinors Research Articles

Toward Accurate Spin-Orbit Splittings from Relativistic Multireference Electronic Structure Theory.

Most nonrelativistic electron correlation methods can be adapted to account for relativistic effects, as long as the relativistic molecular spinor integrals are available, from either a four-, two-, or one-component mean-field calculation. However, relativistic multireference correlation methods remain a relatively unexplored area, with mixed evidence regarding the improvements brought by perturbative treatments. We report, for the first time, the implementation of state-averaged four-component relativistic multireference perturbation theories to second and third order based on the driven similarity renormalization group (DSRG). With our methods, named 4c-SA-DSRG-MRPT2 and 3, we find that the dynamical correlation included on top of 4c-CASSCF references can significantly improve the spin-orbit splittings in p-block elements and potential energy surfaces when compared to 4c-CASSCF and 4c-CASPT2 results. We further show that 4c-DSRG-MRPT2 and 3 are applicable to these systems over a wide range of the flow parameter, with systematic improvement from second to third order in terms of both improved error statistics and reduced sensitivity with respect to the flow parameter.

Spin–orbit effects in cluster chemistry: Considerations and applications for rationalization of their properties

Relativistic effects are usually taken into account in heavy-element-containing species, bringing to the scientific community stimulating cases of study. Scalar and spin–orbit effects are required to properly evaluate both the geometrical and electronic structures of such species, where, generally, scalar corrections are included. In order to take into account the spin–orbit term resulting from the interaction between the spatial and spin coordinates, double-valued point groups of symmetry are required, leading to total angular momenta (j) functions and atomic or molecular spinors, instead of pure orbital-angular momenta (l) and atomic or molecular orbitals. Here, we reviewed the role of spin–orbit coupling in bare and ligand-protected metallic clusters, from early to current works, leading to a more comprehensive relativistic quantum chemistry framework. As a result, the electronic structure is modified, leading to a variation in the calculated molecular properties, which usually improves the agreement between theory and experiment, allowing furthering rationalize of experimental results unexpected from a classical inorganic chemistry point of view. This review summarizes part of the modern application of spin–orbit coupling in heavy-elements cluster chemistry, where further treatment on an equal footing basis along with the periodic table is encouraged in order to incorporate such term in the general use vocabulary of both experimental and theoretical chemist and material scientist.

Combinatorial enumeration of relativistic states of actinide dimers

Relativistic effects are quite large for the actinide 5f and 6d open shells, and in the present study we present combinatorial enumeration of $$\upomega {{-}} \upomega $$ states of all 14 actinide (lanthanide) dimers using multinomial symmetric function (S-function) techniques. The techniques presented here enumerate all possible $$\upomega {{-}} \upomega $$ states that arise from relativistic 2-component molecular spinors composed of the 7s, 6d 5f, and possibly 7p shells of the actinide dimers Th2 through Lr2. The combinatorial enumerations techniques reveal that that for Americium dimer (Am2) there are 20,058,300 S-function terms of which only 616,227 terms satisfy the Pauli exclusion principle yielding 401,166,110 $$\upomega {{-}} \upomega $$ states (142.6 MB of output), all of which arise from primarily the 7s/6d/5f shells of Am. Explicit tables are constructed for the relativistic $$\upomega {{-}} \upomega $$ states for Th2 to Am2 with several restrictions imposed on the levels of excitations primarily to reduce the table sizes, and through the electron–hole equivalence $$\upomega {{-}} \upomega $$ states of the remaining dimers of the actinide row are enumerated. The computational and mathematical techniques also enumerate the $$\upomega {{-}} \upomega $$ states of Ce2 to Eu2 and by electron–hole equivalence Gd2 to Tm2, although spin–orbit splittings are smaller for lanthanides. A unique feature of the present combinatorial technique is that it facilitates any number of orbitals and any number of open shells including the possibility of 14 singly-occupied orbitals for actinide and lanthanide dimers, and thus providing for a technique to enumerate $$\upomega {{-}} \upomega $$ states arising from both very high spin open-shell states as well as low spin states exhaustively.

The ground and first excited states of HoS studied by four-component relativistic KR-MCSCF and KRCI

The X18.5 ground state and the W17.5 first excited state of the HoS molecule are studied by the four-component Kramers-restricted multiconfiguration self-consistent field (KR-MCSCF) method, with an active space of (4f, 6s)11, and then by the Kramers-restricted configuration interaction method with 27 electrons in Ho(5s), (5p), (4f), (6s), S(3s), and S(3p) correlated. For the X18.5 state, Re, ωe, ΔG1/2, and D0 are calculated as 4.310 au, 477.385 cm−1, 477.72 cm−1, and 3.775 eV, respectively. The values of Re and ΔG1/2 agree well with the observed values of 4.301 au and 463.8811 cm−1, respectively. The dominant configuration state function (CSF) is |(4f5/2)6 (4f7/2,7/2)1 (4f7/2,5/2)1 (4f7/2,3/2)1 (4f7/2,1/2)1 (6s1/2,1/2)1|. This corresponds to the formal charge of Ho2+(5I8)S2−, representing ionic bonding where two electrons, one from [6s] and the other from [4f], are moved from Ho to S. In the doubly occupied S(3p) KR-MCSCF molecular spinors, hybridizations exist between S[3p] atomic spinors and Ho polarization functions [5d*] through which electrons are moved from S to Ho, resulting in covalent bonding. Consequently, ionic bonding is mixed with covalent bonding and 11 electrons of (4f, 6s) move outside the Ho13+([Xe])S2− ion core. The gross atomic charge of Ho is + 0.77 at the CI level. The excitation energy to the W17.5 state is calculated as 0.027 eV, close to the experimental value of 0.031 eV.

Enumeration of relativistic states for superheavy and transactinide dimers in the periodic table

We have employed combinatorial techniques based on multinomial symmetric function (S-function) techniques for exhaustive enumeration and generation of relativistic (ω–ω states) states originating from relativistic 2-component molecular spinors for the seventh row superheavy dimers (Nh2-Ts2), transactinide dimers (Rf2-Rg2) and Ac2. The multinomial generators are so powerful that the complete set of relativistic states of all seventh row superheavy dimers or transactinide dimers are enumerated and constructed in a single generating function. We have computed and constructed the enumeration tables for all valence ω–ω states for the 7p-block and 6d-block dimers (Nh2-Ts2, Rf2-Rg2). Our results show that there are 6455 S-function terms giving rise to 102,830 valence ω–ω states- all arising only from the 6d shells of Bh2. Extension of the developed techniques to relativistic 4-component and 4-spinors arising from fermionic spin-3/2 particles are also suggested with potential applications NMR spectroscopy.

Electronic spectra of DyF studied by four-component relativistic configuration interaction methods.

The electronic states of the DyF molecule below 3.0 eV are studied using 4-component relativistic CI methods. Spinors generated by the average-of-configuration Hartree-Fock method with the Dirac-Coulomb Hamiltonian were used in CI calculations by the KRCI (Kramers-restricted configuration interaction) program. The CI reference space was generated by distributing 11 electrons among the 11 Kramers pairs composed mainly of Dy [4f], [6s], [6p] atomic spinors, and double excitations are allowed from this space to the virtual molecular spinors. The CI calculations indicate that the ground state has the dominant configuration (4f(9))(6s(2))(Ω = 7.5). Above this ground state, 4 low-lying excited states (Ω = 8.5, 7.5, 7.5, 7.5) are found with dominant configurations (4f(10))(6s). These results are consistent with the experimental studies of McCarthy et al. Above these 5 states, 2 states were observed at T0 = 2.39 eV, 2.52 eV by McCarthy et al. and were named as [19.3]8.5 and [20.3]8.5. McCarthy et al. proposed that both states have dominant configurations (4f(9))(6s)(6p), but these configurations are not consistent with the large Re's (∼3.9 a.u.) estimated from the observed rotational constants. The present CI calculations provide near-degenerate states of (4f(10))(6p3/2,1/2), (4f(10))(6p3/2,3/2), and (4f(9))(6s)(6p3/2,1/2) at around 3 eV. The former two states have larger Re (3.88 a.u.) than the third, so that it is reasonable to assign (4f(10))(6p3/2,1/2) to [19.3]8.5 and (4f(10))(6p3/2,3/2) to [20.3]8.5.

Application of a planar superatom model on [Hg5(C(CF3)2)]. Bonding and magnetic response considerations into a five-fold d10–d10 metal cycle

Application of the planar superatom model to describe the electronic structure, and to gain insights into the stabilization of metal macrocycles supporting closed-shell d(10)-d(10) interactions, is studied through analysis of the membered ring composed by Hg(ii) atoms, namely, [Hg(C(CF3)2)]5. Its electronic structure resembles the level sequence given for a planar jellium model, revealing an electronic configuration given by 1s(2) 1p(4)x,y 1d(4)xy,x(2)-y(2). The analysis of the population of each level of the Hg5core, denotes a slight net bonding into the [Hg(C(CF3)2)]5 ring. However, stabilization is mainly supported by the balance given by a similar population of the jellium levels, which is suggested to be a different scheme for stabilizing d(10) macrocyclic clusters with metallophilic interactions, in the category of long d(10)-d(10) contacts. The extension of the planar jellium model to the relativistic case, including spin-orbit coupling considering the D5h* point group, denotes the consequent splitting for levels with l ≠ 0, namely, 1px,y and 1dxy,x(2)-y(2). In this framework, the electronic configuration is given by 1s1/2(2) 1p3/2(2) 1p1/2(2) 1d5/2(2) 1d3/2(2), which contribute to the analysis of the electronic structure of planar clusters in terms of spin-orbit coupling, involving molecular spinors (j = l ± s) instead of molecular orbitals (pure l).

Variation of Zr-L2,3 XANES in tetravalent zirconium oxides

Zr-L2,3 XANESs of tetravalent zirconium oxides with different coordination numbers and local symmetries are systematically investigated by ab initio multiplet calculations using fully relativistic molecular spinors for model clusters. Experimental Zr-L2,3 XANESs are obtained for SrZrO3, m-ZrO2 (monoclinic) and t-ZrO2 (tetragonal). The theoretical spectra are in good agreement with the experimental data. The multiplet effects are found to play essential roles in determining the peak shape. The shapes of L3- and L2-edges are systematically different. The intensity ratios of the doublet peaks at both L3- and L2-edges are found to be sensitive to the coordination number of Zr. The ratio can therefore be used to estimate the coordination number of Zr in such oxides.

KPACK: Relativistic Two-component Ab Initio Electronic Structure Program Package

E-mail: yslee@kaist.eduReceived October 9, 2012, Accepted October 28, 2012We describe newly developed software named KPACK for relativistic electronic structure computation ofmolecules containing heavy elements that enables the two-component ab initio calculations in Kramersrestricted and unrestricted formalisms in the framework of the relativistic effective core potential (RECP). Thespin-orbit coupling as relativistic effect enters into the calculation at the Hartree-Fock (HF) stage and hence, istreated in a variational manner to generate two-component molecular spinors as one-electron wavefunctionsfor use in the correlated methods. As correlated methods, KPACK currently provides the two-componentsecond-order Moller-Plesset perturbation theory (MP2), configuration interaction (CI) and complete-active-space self-consistent field (CASSCF) methods. Test calculations were performed for the ground states ofgroup-14 elements, for which the spin-orbit coupling greatly influences the determination of term symbols. Acategorization of three procedures is suggested for the two-component methods on the basis of spin-orbitcoupling manifested in the HF level.Key Words : Electronic structure program, Relativistic quantum chemistry, Two-component method, Relativ-istic effective core potential, Group-14 elementsIntroductionThere has been growing interest in the variational treat-ment of spin-orbit (SO)-coupling in ab initio calculations,especially at the self-consistent field (SCF) level.

A simple scheme for magnetic balance in four-component relativistic Kohn–Sham calculations of nuclear magnetic resonance shielding constants in a Gaussian basis

We report the implementation of nuclear magnetic resonance (NMR) shielding tensors within the four-component relativistic Kohn-Sham density functional theory including non-collinear spin magnetization and employing London atomic orbitals to ensure gauge origin independent results, together with a new and efficient scheme for assuring correct balance between the large and small components of a molecular four-component spinor in the presence of an external magnetic field (simple magnetic balance). To test our formalism we have carried out calculations of NMR shielding tensors for the HX series (X = F, Cl, Br, I, At), the Xe atom, and the Xe dimer. The advantage of simple magnetic balance scheme combined with the use of London atomic orbitals is the fast convergence of results (when compared with restricted kinetic balance) and elimination of linear dependencies in the basis set (when compared to unrestricted kinetic balance). The effect of including spin magnetization in the description of NMR shielding tensor has been found important for hydrogen atoms in heavy HX molecules, causing an increase of isotropic values of 10%, but negligible for heavy atoms.

Spin–orbit effects on a gold-based superatom: a relativistic Jellium model

The inclusion of relativistic effects always brings to the scientific community great and stimulating surprises. To consider the spin-orbit term, which accounts for the interaction between the spatial and spin coordinates, requires the use of double point groups of symmetry in order to solve the Dirac equation or the two component approximation to it, leading to total angular momenta (j) functions, atomic or molecular spinors, instead of pure orbital angular momenta (l), atomic or molecular orbitals. Large and small components, derived from the Dirac treatment, depict wavefunctions corresponding to fermions, electrons, which are described for the first time for a superatom case. In addition, their behavior is revisited in order to clarify the effects of the inclusion of the spin-orbit coupling into the electronic structure calculations, which can be extended to other superatoms, clusters, molecules and atoms.

Understanding the Electronic Structure of 4d Metal Complexes: From Molecular Spinors to L-Edge Spectra of a di-Ru Catalyst

L(2,3)-edge X-ray absorption spectroscopy (XAS) has demonstrated unique capabilities for the analysis of the electronic structure of di-Ru complexes such as the blue dimer cis,cis-[Ru(III)(2)O(H(2)O)(2)(bpy)(4)](4+) water oxidation catalyst. Spectra of the blue dimer and the monomeric [Ru(NH(3))(6)](3+) model complex show considerably different splitting of the Ru L(2,3) absorption edge, which reflects changes in the relative energies of the Ru 4d orbitals caused by hybridization with a bridging ligand and spin-orbit coupling effects. To aid the interpretation of spectroscopic data, we developed a new approach, which computes L(2,3)-edges XAS spectra as dipole transitions between molecular spinors of 4d transition metal complexes. This allows for careful inclusion of the spin-orbit coupling effects and the hybridization of the Ru 4d and ligand orbitals. The obtained theoretical Ru L(2,3)-edge spectra are in close agreement with experiment. Critically, existing single-electron methods (FEFF, FDMNES) broadly used to simulate XAS could not reproduce the experimental Ru L-edge spectra for the [Ru(NH(3))(6)](3+) model complex nor for the blue dimer, while charge transfer multiplet (CTM) calculations were not applicable due to the complexity and low symmetry of the blue dimer water oxidation catalyst. We demonstrated that L-edge spectroscopy is informative for analysis of bridging metal complexes. The developed computational approach enhances L-edge spectroscopy as a tool for analysis of the electronic structures of complexes, materials, catalysts, and reactive intermediates with 4d transition metals.

Ab initiocharge transfer multiplet calculations on theL2,3XANES and ELNES of3dtransition metal oxides

The ${L}_{2,3}$ x-ray absorption near-edge structures (XANES) and electron energy loss near-edge structures (ELNES) of $3d$ transition metal (TM) oxides are systematically calculated by the ab initio charge transfer multiplet (CTM) method using fully relativistic molecular spinors on the basis of density-functional theory. The electronic excitation from molecular spinors mainly composed of O-$2p$ to those of TM-$3d$, that is, charge transfer, is included by considering additional electronic configurations in the configuration interactions. The effects of the covalency and charge transfer on the TM-${L}_{2,3}$ XANES are investigated in detail. The power of the ab initio CTM method to quantitatively reproduce the spectra is demonstrated. Meanwhile, limitations of the application of the method are discussed.

General implementation of the relativistic coupled-cluster method

We report the development of a general order relativistic coupled-cluster (CC) code. Our implementation is based on Kramers-paired molecular spinors, utilizes double group symmetry, and is applicable with the full Dirac-Coulomb and several approximate relativistic Hamiltonians. The available methods include iterative and perturbative single-reference CC approaches with arbitrary excitations as well as a state-selective multi-reference CC ansatz. To illustrate the performance of the new code, benchmark calculations have been performed for the total energies, bond lengths, and vibrational frequencies of the monoxides of Group IVa elements. The trends due to the simultaneous inclusion of relativity as well as higher-order electron correlation effects are analyzed. The newly developed code significantly widens the scope of the ab initio relativistic calculations, for both molecules and atoms alike, surpassing the accuracy and reliability of the currently available implementations in the literature.

First-principles and experimental analysis offn−fn−1d1absorption spectra and multiplet energy levels ofPr3+,Nd3+, andU3+inLiYF4

We performed experimental and theoretical investigation of the ${f}^{n}\text{\ensuremath{-}}{f}^{n\text{\ensuremath{-}}1}{d}^{1}$ transitions of ${\text{Pr}}^{3+}$, ${\text{Nd}}^{3+}$, and ${\text{U}}^{3+}$ in ${\text{LiYF}}_{4}$. The $4{f}^{2}\text{\ensuremath{-}}4{f}^{1}5{d}^{1}$ absorption spectra for ${\text{Pr}}^{3+}$ in ${\text{LiYF}}_{4}$ and the $4{f}^{3}\text{\ensuremath{-}}4{f}^{2}5{d}^{1}$ absorption spectra for ${\text{Nd}}^{3+}$ in ${\text{LiYF}}_{4}$ were measured using a synchrotron radiation light source at several different temperatures while the $5{f}^{3}\text{\ensuremath{-}}5{f}^{2}6{d}^{1}$ absorption spectra for ${\text{U}}^{3+}$ in ${\text{LiYF}}_{4}$ referred to report of Hubert et al. The multiplet energy levels and ${f}^{n}\text{\ensuremath{-}}{f}^{n\text{\ensuremath{-}}1}{d}^{1}$ absorption spectra were calculated by a first-principles four-component relativistic configuration-interaction method. For all calculations of ${\text{Nd}}^{3+}$ and ${\text{U}}^{3+}$ in ${\text{LiYF}}_{4}$, we used the Dirac-Coulomb-Breit Hamiltonian and the molecular spinors obtained from the relativistic Vosko-Wilk-Nusair potential. The overall features of the theoretical absorption spectra of both ${\text{Nd}}^{3+}$ and ${\text{U}}^{3+}$ in ${\text{LiYF}}_{4}$ reproduced the experimental features well. The origins of the experimental absorption spectra were clarified by performing a configuration analysis based on the many-electron wave functions. The splitting between peaks were affected by both spin-orbit interaction of $f$ orbitals and crystal-field splitting of $d$ orbitals. We found that the oscillator strengths of the $4{f}^{3}\text{\ensuremath{-}}4{f}^{2}5{d}^{1}$ transition for ${\text{Nd}}^{3+}$ in ${\text{LiYF}}_{4}$ are slightly larger than those of the $5{f}^{3}\text{\ensuremath{-}}5{f}^{2}6{d}^{1}$ transition for ${\text{U}}^{3+}$ in ${\text{LiYF}}_{4}$. The experimental absorption spectra for ${\text{Nd}}^{3+}$ in ${\text{LiYF}}_{4}$ measured at nine different temperatures indicated that the $4{f}^{3}\text{\ensuremath{-}}4{f}^{2}5{d}^{1}$ absorption spectra for ${\text{Nd}}^{3+}$ in ${\text{LiYF}}_{4}$ have no significant temperature dependence. For ${\text{Pr}}^{3+}$ in ${\text{LiYF}}_{4}$, we performed more detailed investigations. The lattice relaxation effects due to the substitution of ${\text{Y}}^{3+}$ by ${\text{Pr}}^{3+}$ were estimated using a first-principles density-functional calculation. Structural optimization calculations indicated that the local structure of the ${\text{Pr}}^{3+}$ site was slightly distorted. Overall, the theoretical $4{f}^{2}\text{\ensuremath{-}}4{f}^{1}5{d}^{1}$ absorption spectra reproduced the experimental spectra. The experimental absorption spectra were investigated by configuration analysis based on the many-electron wave functions. The theoretical calculations indicated that the temperature dependence of the experimental spectra was due to both thermal excitation and phonon effects. In addition, we also investigated the effects of the exchange-correlation interaction and the Breit term by comparing the results from six different Hamiltonians.

Electronic structure of LaO based on frozen-core four-component relativistic multiconfigurational quasidegenerate perturbation theory

The electronic structure of the LaO molecule is studied using frozen-core four-component multiconfigurational quasidegenerate perturbation theory. The ground state and nine experimentally observed excited states are examined. The ground state is (2)Sigma(1/2)(+) and its gross atomic orbital population is La(5p(5.76)6s(0.83)6p(0.14)p(*(0.21) )d(*(1.17) )f(*(0.26) )) O(2p(4.63)), where p*, d*, and f* are the polarization functions of La that form molecular spinors with O 2ps. We found that it is not necessary to consider the excitation from the O 2p electrons when analyzing the experimental spectra. This validates the foundation of the ligand field theory on diatomic molecules, including the La atom where only one electron is considered. The spectroscopic constants R(e), omega(e), and T(0) calculated for the ground state and low-lying excited states A'((2)Delta(3/2)), A'((2)Delta(5/2)) A((2)Pi(1/2)), and A((2)Pi(3/2)) are in good agreement with the experimental values.

Electronic Delocalization, Energetics, and Optical Properties of Tripalladium Ditropylium Halides, [Pd3(C7H7)2X3]1− (X = Cl−, Br−, and I−)

Here we report relativistic electronic structure calculations employing all-electron density functional theory (DFT) including scalar and spin-orbit interaction, on the multimetallic sandwich compound [Pd(3)(C(7)H(7))(2)X(3)](1-) (X = Cl(-) (1), Br(-) (2), and I(-) (3)), which can be considered as a [Pd(3)X(3)](3-) fragment flanked by two ring-ligands [(C(7)H(7))(2)](2+). The calculations suggest that the [Pd(3)X(3)](3-)-ligand interaction is mainly arising from electrostatic contributions, where the formally zerovalent Pd atoms allows backdonation of charge from the halide X(1-) atoms to the [(C(7)H(7))(2)](2+) ligands, resulting in a net charge of about +0.4 for each Pd atoms that decreases from 1 to 3. The electronic delocalization estimated via the NICS indexes and the ELF function allows us to describe a significant stabilizing sigma-aromaticity at the center of the Pd(3) triangle, which decreases from [Pd(3)Cl(3)](3-) to [Pd(3)I(3)](3-) (1 to 3) due to the softer character of the iodine counterpart, that donates extra charge to the ligands. The calculated electronic transitions via TD-DFT are in reasonable agreement with the experimental data obtained in CH(2)Cl(2) solution, indicating that the most intense transition involves a core-centered [Pd(3)X(3)](3) transition toward the [(C(7)H(7))(2)](2+) ligands, with mainly X(1-) character in the former molecular spinor that is responsible for the variation of the observed lambda(max) according to the variation of X(1-).

Ab-initio CI calculations for 3d transition metal L2,3 X-ray absorption spectra of TiCl4 and VOCl3

X-ray-absorption near-edge structures (XANES) at the transition metal (TM) L2,3-edge of TiCl4 and VOCl3 are calculated by the all-electron configuration interaction (CI) method using fully-relativistic molecular spinors with density functional theory (DFT). The electronic excitation from molecular spinors mainly composed of ligand p atomic spinors to those of TM-3d spinors, i.e., the charge transfer, is included by taking additional electronic configurations in the CI. The effects of the ligand field and the charge transfer on the TM-L2,3 XANES are investigated by an ab-intio method. The reduction of inter-electron interaction due to the covalent bonding between TM and ligand atoms has been found. The contribution of charge transferred configuration is small at the initial state of TM-L2,3 XANES while the significant amount of charge transferred configuration is found at the final states. The spectral shapes of TM-L2,3 XANES of both TiCl4 and VOCl3 are strongly modified by the charge transfer effects.

Two component calculations of Pt2 with relativistic effective core potential including spin‐orbit operator

AbstractThe Kramers restricted two‐component ab initio calculations were performed for the eight lowest electronic states of Pt2 using the relativistic effective core potential with the spin‐orbit operator at the multireference first‐order configuration interaction level of theory employing two‐component molecular spinors as one‐electron basis. The dominant role of the spin‐orbit effects are mainly accounted for by using two‐component spinors as one‐electron wave function, and the importance of the dynamic and the nondynamic electron correlation effects are shown by employing configuration interaction and coupled cluster methods to obtain reliable spectroscopic data for this molecule. The two‐component molecular spinors were generated from Kramers restricted Hartree–Fock calculations for the average configuration and used in the multireference Kramers restricted configuration interaction method to account for nondynamic correlation effect. Effect of dynamic correlations was investigated with the Kramers restricted coupled‐cluster (KRCC) method. Spectroscopic constants calculated at the KRCC level are in good agreement with the most recent experimental values. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Molecular spinors suitable for four‐component relativistic correlation calculations: Studies of LaF+ and LaF using multiconfigurational quasi‐degenerate perturbation theory

AbstractMulticonfigurational second‐order quasidegenerate perturbation theory (MCQDPT) calculations were performed for the LaF+ molecule, with one LaF2+ and four LaF+ Dirac–Fock–Roothaan (DFR) spinor sets. The best spinor set was that of LaF2+, which gave the lowest total energies and also the best excitation energies for any state considered. The MCQDPT calculations with the cation and neutral molecular spinors were also performed for LaF. The MCQDPT with the cation spinors gave the lowest total energies for all states under consideration, and the calculated excitation energies compared best with experiment. We prefer the LaF+ spinor set to those of LaF. These calculations indicate that the DFR spinor set for the (n−1) electron system is adequate for treating the molecular electronic system having n electrons. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009