Potential energy surfaces of OsCO

Potential energy surfaces for the low-lying states of osmium carbon monoxide (OsCO) have been studied using the complete active space multi-configuration self-consistent field (CAS-MCSCF) followed by multireference singles+doubles configuration interaction (MRSDCI). Additionally, spin–orbit effects were included through the relativistic configuration interaction method. It is found that the ground state of OsCO is an 0⁺ spin–orbit state which is a mixture of ³Σ⁻ and ¹Σ⁺. Spin–orbit coupling not only splits the various electronic states of OsCO but also mixes different electronic states.     

Calculations of electronic structure of the UF<Subscript>6</Subscript> molecule and the UO<Subscript>2</Subscript> crystal with a relativistic pseudopotential

The influence of relativistic effects on the properties of uranium hexafluoride was considered. Detailed comparison of the spectrum of one-electron energies obtained in the nonrelativistic (by the Hartree-Fock method), relativistic (by the Dirac-Fock method), and scalar-relativistic (using a relativistic potential of the uranium atom core) calculations was carried out. The methods of optimization of atomic basis in the LCAO calculations of molecules and crystals are discussed which make it possible to consider distortion of atomic orbitals upon the formation chemical bonds. The influence of the atomic basis optimization on the results of scalar-relativistic calculations of the molecule UF₆ properties is analyzed. Calculations of the electronic structure and properties of UO₂ crystals with relativistic and nonrelativistic pseudopotentials are fulfilled.     

Bonding trends in MCH2 systems: Simple orbital interpretation and evidence for double bonds

MCH₂ systems, where M is a metal from 4th up to 7th period, are studied at DFT level using B3LYP functional and small-core quasirelativistic pseudopotential or fully relativistic four-component methodology. We obtained structural data for 44 elements, M, and our results can be used to infer double-bond lengths for these elements. Our results also suggest that the bonding of these MCH₂ systems can be understood by a simple pictorial approach, even when spin–orbit effects are present.     

Spin–orbit corrections to the indirect nuclear spin–spin coupling constants in XH4 (X=C, Si, Ge, and Sn)

Summary.  Using the quadratic response function at the ab initio SCF level of approximation we have calculated the relativistic corrections from the spin–orbit Hamiltonian, H ^SO, to the indirect nuclear spin–spin coupling constants of XH₄ (X=C, Si, Ge, and Sn). We find that the spin–orbit contributions to J _X–H are small, amounting only to about 1% for J _Sn–H. For the geminal H–H coupling constants the relativistic corrections are numerically smaller than for J _X–H, but in some cases relatively larger compared to the actual magnitude of J _H–H. We also investigate the use of an effective one-electron spin–orbit Hamiltonian rather than the full H ^SO in the calculation of these corrections. Received July 12, 1996 / Final revision received September 12, 1996 / Accepted September 17, 1996     

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).     

Quantum relativistic investigation about the coordination and bonding effects of different ligands on uranyl complexes

The coordination and bonding effects of equatorial ligands such as fluoride (F⁻), chloride (Cl⁻), cyanide (CN⁻), isocyanide (NC⁻), and carbonate (CO₃⁻²) on uranyl dication (UO₂²⁺) has been studied using relativistic density functional theory. The ZORA Hamiltonian was applied for the inclusion of relativistic effects taking into account all the electrons for the optimization and the explicit inclusion of spin–orbit coupling effects. Geometry optimizations including the counterions and frequencies analysis were carried out with PW91 and PBE functional. Solvents effects were considered by using the conductor like screening model (COSMO) for water and acetonitrile. The Time-Dependent Density Functional Theory (TDDFT) was used to calculate the excitation energies with GGA SAOP functional and the electronic transitions were analyzed using double group irreducible representations. The theoretical results are in a good agreement with experimental IR, Raman and EXAFS spectra and previous theoretical results. New information about the effect of different (donor and acceptors) ligands on the bonding of uranyl ion and on the electronic transitions involved in these complexes is provided with a possible impact on the understanding of the uranyl coordination chemistry.     

Astatine Facing Janus: Halogen Bonding vs. Charge-Shift Bonding

The nature of halogen-bond interactions was scrutinized from the perspective of astatine, potentially the strongest halogen-bond donor atom. In addition to its remarkable electronic properties (e.g., its higher aromaticity compared to benzene), C₆At₆ can be involved as a halogen-bond donor and acceptor. Two-component relativistic calculations and quantum chemical topology analyses were performed on C₆At₆ and its complexes as well as on their iodinated analogues for comparative purposes. The relativistic spin–orbit interaction was used as a tool to disclose the bonding patterns and the mechanisms that contribute to halogen-bond interactions. Despite the stronger polarizability of astatine, halogen bonds formed by C₆At₆ can be comparable or weaker than those of C₆I₆. This unexpected finding comes from the charge-shift bonding character of the C–At bonds. Because charge-shift bonding is connected to the Pauli repulsion between the bonding σ electrons and the σ lone-pair of astatine, it weakens the astatine electrophilicity at its σ-hole (reducing the charge transfer contribution to halogen bonding). These two antinomic characters, charge-shift bonding and halogen bonding, can result in weaker At-mediated interactions than their iodinated counterparts.     

Vibronic effects accelerate the intersystem crossing processes of the through-space charge transfer states in the triptycene bridged acridine–triazine donor–acceptor molecule TpAT-tFFO

Quantum chemical studies employing combined density functional and multireference configuration interaction methods suggest five excited electronic states to be involved in the prompt and delayed fluorescence emission of TpAT-tFFO. Three of them, a pair of singlet and triplet charge transfer (CT) states (S₁ and T₁) and a locally excited (LE) triplet state (T₃), can be associated with the (Me → N) conformer, the other two CT-type states (S₂ and T₂) form the lowest excited singlet and triplet states of the (Me → Ph) conformer. The two conformers, which differ in essence by the shearing angle of the face-to-face aligned donor and acceptor moieties, are easily interconverted in the electronic ground state whereas the reorganization energy is substantial in the excited singlet state, thus explaining the two experimentally observed time constants of prompt fluorescence emission. Forward and reverse intersystem crossing between the singlet and triplet CT states is mediated by vibronic spin–orbit interactions involving the LE T₃ state. Low-frequency vibrational modes altering the distance and alignment of the donor and acceptor π-systems tune the S₁ and T₃ states (likewise S₂ and T₃) into and out of resonance. The enhancement of intersystem crossing due to the interplay of vibronic and spin–orbit coupling is considered a general feature of organic through-space charge-transfer thermally activated delayed fluorescence emitters.

DFT/MRCI quantum chemical studies suggest five excited electronic states to be involved in the prompt and delayed fluorescence emission of TpAT-tFFO.     

Dirac-Fock one-centre calculations. The model systems TiH4, ZrH4, HfH4 and (104)H4

Relativistic and non-relativistic Hartree-Fock calculations including np and np and (n-1)d orbitals in the valence MO's are reported for the tetrahedral model systems TiH₄, ZrH₄, HfH₄ and (104)H₄. About 50%p and 50%d character is found, making the relativistic effects on the bond lengths and strengths one order of magnitude smaller than for the groups Ib, IIIb or IVb. This probably explains the close chemical similarity between Zr and Hf. The Ti---H bond length agrees with experiment. Inverted spin—orbit splitting is found to TiH₄.     

Solvent effects on optically detected magnetic resonance in triplet spin labels

We have calculated solvent effects on the zero-field splitting (ZFS) constants induced by electron spin–spin coupling (SSC) in the low-lying triplet states of azaaromatic molecules in solutions using multiconfiguration self-consistent-field wave functions and the polarizable continuum model. The second-order spin–orbit coupling (SOC) contribution to the splitting of the ^3* states is found to be almost negligible, and the calculations therefore provide a good estimate of the ZFS parameters and their solvent dependence based only on the electron spin–spin coupling expectation values. The correlation between the shift in the ZFS and the phosphorescence frequency that has been observed in optically detected magnetic resonance experiments in low-temperature glasses is supported by our direct SSC calculations without taking SOC into account. This makes it possible to distinguish between the two theories that earlier were proposed to explain the inhomogeneous broadening of triplet state spectra, and discard the one that is exclusively based on the SOC-induced mixing of the singlet and triplet states.Contribution to the Jacopo Tomasi Honorary IssueAcknowledgments. This work was supported (B. M.) by the Swedish Royal Academy of Science (KVA). This work was also supported by the Norwegian Research Council through a grant of computer time from the Program for Supercomputing. We are grateful to B. Schimmelpfenning for his valuable assistance in the computations.     

Relativity and the chemistry of UF6: A molecular Dirac—Hartree—Fock—CI study

The electronic structure and bonding of UF₆ and UF₆⁻ are studied within a relativistic framework using the MOLFDIR program package. A stronger bonding but more ionic molecule is found if one compares the relativistic with the nonrelativistic results. The first peak in the photoelectron spectrum of Karlsson et al. is assigned to the 12γ_8u component of the 4t_1u orbital, in agreement with other theoretical and experimental results. Good agreement is found between the experimental and theoretical 5f spectrum UF₆⁻. Some properties, like the dissociation energy and electron affinity, are calculated and the necessity of a fully relativistic framework is shown. The Breit interaction has an effect on the core spinors and the spin-orbit splitting of these spinors but the influence on the valence spectrum is negligible. © 1996 John Wiley & Sons, Inc.     

The Heat of Formation of the Uranyl Dication: Theoretical Evaluation Based on Relativistic Density Functional Calculations

By using a set of model reactions, we estimated the heat of formation of gaseous UO₂²⁺ from quantum‐chemical reaction enthalpies and experimental heats of formation of reference species. For this purpose, we performed relativistic density functional calculations for the molecules UO₂²⁺, UO₂, UF₆, and UF₅. We used two gradient‐corrected exchange‐correlation functionals (revised Perdew–Burke–Ernzerhof (PBEN) and Becke–Perdew (BP)) and we accounted for spin‐orbit interaction in a self‐consistent fashion. Indeed, spin‐orbit interaction notably affects the energies of the model reactions, especially if compounds of U^IV are involved. Our resulting theoretical estimates for Δ_f (UO₂²⁺), 365±10 kcal mol^?1 (PBEN) and 370±12 kcal mol^?1 (BP), are in quantitative agreement with a recent experimental result, 364±15 kcal mol^?1. Agreement between the results of the two different exchange‐correlation functionals PBEN and BP supports the reliability of our approach. The procedure applied offers a general means to derive unknown enthalpies of formation of actinide species based on the available well‐established data for other compounds of the element in question.     

Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory

Strong electron correlation plays an important role in transition-metal and heavy-metal chemistry, magnetic molecules, bond breaking, biradicals, excited states, and many functional materials, but it provides a significant challenge for modern electronic structure theory. The treatment of strongly correlated systems usually requires a multireference method to adequately describe spin densities and near-degeneracy correlation. However, quantitative computation of dynamic correlation with multireference wave functions is often difficult or impractical. Multiconfiguration pair-density functional theory (MC-PDFT) provides a way to blend multiconfiguration wave function theory and density functional theory to quantitatively treat both near-degeneracy correlation and dynamic correlation in strongly correlated systems; it is more affordable than multireference perturbation theory, multireference configuration interaction, or multireference coupled cluster theory and more accurate for many properties than Kohn–Sham density functional theory. This perspective article provides a brief introduction to strongly correlated systems and previously reviewed progress on MC-PDFT followed by a discussion of several recent developments and applications of MC-PDFT and related methods, including localized-active-space MC-PDFT, generalized active-space MC-PDFT, density-matrix-renormalization-group MC-PDFT, hybrid MC-PDFT, multistate MC-PDFT, spin–orbit coupling, analytic gradients, and dipole moments. We also review the more recently introduced multiconfiguration nonclassical-energy functional theory (MC-NEFT), which is like MC-PDFT but allows for other ingredients in the nonclassical-energy functional. We discuss two new kinds of MC-NEFT methods, namely multiconfiguration density coherence functional theory and machine-learned functionals.

This feature article overviews recent work on active spaces, matrix product reference states, treatment of quasidegeneracy, hybrid theory, density-coherence functionals, machine-learned functionals, spin–orbit coupling, gradients, and dipole moments.     

Relativistic electronic structure of cadmium(II) multidecker phthalocyanine compounds

Cadmium phthalocyanines (Pc) give rise to multilayered compounds, which may have potential application in material science. The Cd(II) single macrocycle (1) (C_4v), double decker [CdPc₂] (2) (D₄), triple decker [Cd₂Pc₃] (3) (D_4h) and quadruple decker [Cd₃Pc₄] (4) (D_4d), are already characterized experimentally. The electronic structures of the multidecker compounds were compared against the single macrocycle (1) which is used as benchmark. Relativistic electronic structure were carried out via DFT calculations using the two components ZORA Hamiltonian including both scalar and spin–orbit effects. Double point groups were used to take into account the inclusion of the spin–orbit coupling, and their group correlation is shown. The calculations show that the quadruple decker is the most reactive and behaves like a one-dimensional molecular metal.     

Relativistic calculations on the ground and excited states of AgH and AuH in cylindrical harmonic confinement

The relativistic ground and low-lying excited state potential energy curves of AgH and AuH in the presence of a cylindrical harmonic confining potential were calculated using the multi-state multi-reference perturbation theory with the spin-free no-pair Hamiltonian obtained via the third-order Douglas–Kroll transformation, incorporated with the full two-electron Breit–Pauli spin–orbit operator. The spectroscopic parameters were obtained for both the scalar- and quasi-relativistic potentials. The spin–orbit coupling constants were calculated for several strengths of the confining potential, and the effects of the applied potential on the coupling constants were analyzed using configuration interaction. This paper is dedicated to Serafín Fraga—colleague, mentor, and friend.     

Electric properties of hydrogen iodide: Reexamination of correlation and relativistic effects

The electric dipole moment and the static dipole polarizability of the hydrogen iodide molecule were studied using sophisticated correlated and relativistic methods. Both scalar and spin–orbit relativistic effects were carefully accounted for. We conclude that the large differences between the theoretical and experimental dipole moment, the dipole moment derivative and the polarizability cannot be reconciled by improved account of electron correlation and relativistic effects. The most striking difference between theory and experiment is observed for the polarizability anisotropy. We believe that experimental data, namely the experimental dipole moment (the most recent value is 0.176 au as compared to our best theoretical estimate, 0.154±0.003 au), the parallel polarizability (44.4 and 38.47±0.05 au) and the anisotropy (11.4 and 2.33±0.05 au) must be inaccurate. Experimental and theoretical perpendicular polarizability components (33.0 and 36.14±0.05 au,) and the mean polarizability (36.8 and 36.92±0.05 au) agree better. Our vibrationally corrected relativistic CCSD(T) results represent the most sophisticated predictions of electric properties of HI obtained so far.Contribution to the Björn Roos Honorary Issue     

Relativistically parameterized extended hückel calculations. IX. An iterative version with applications to some xenon,thorium and uranium compounds

A charge-consistent version of the relativistic extended Hückel method REX is presented. The diagonal matrix elements are corrected for occupations of individual orbitals on the same atom using derivatives from atomic Dirac-Slater calculations and for external charges. The method is applied to systems containing the heavy atoms Xe, Th and U. For the XeF_n series (n = 2, 4, 6) the charge distributions improved compared to the non-iterative version of REX and the new results are close to non-relativistic ab initio SCF results. Bonding in the uranyl ion is discussed. The EHT-level explanations for the linear geometry by Tatsumi and Hoffmann nd by Pyykkö and Lohr are shown to be identical. The effect of secondary ligands is discussed. The role of the 6p AOs in actinoid nuclear quadrupole coupling in the actinyls is pointed out. The XPS of UF₆ is explained by different amounts of 5f character in the split components of the t_1u HOMO.     

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.     

The accuracy of hyperfine integrals in relativistic NMR computations based on the zeroth-order regular approximation

The accuracy of the hyperfine integrals obtained in relativistic NMR computations based on the zeroth–order regular approximation (ZORA) is investigated. The matrix elements of the Fermi contact operator and its relativistic analogs for s orbitals obtained from numerical nonrelativistic, ZORA, and four–component Hartree–Fock–Slater calculations on atoms are compared. It is found that the ZORA yields very accurate hyperfine integrals for the valence shells of heavy atoms, but performs rather poorly for the innermost core shells. Because the important observables of the NMR experiment—chemical shifts and spin–spin coupling constants—can be understood as valence properties it is concluded that ZORA computations represent a reliable tool for the investigations of these properties. On the other hand, absolute shieldings calculated with the ZORA might be substantially in error. Because applications to molecules have so far exclusively been based on basis set expansions of the molecular orbitals, ZORA hyperfine integrals obtained from atomic Slater-type basis set computations for mercury are compared with the accurate numerical values. It is demonstrated that the core part of the basis set requires functions with Slater exponents only up to 10⁴ in the case where errors in the hyperfine integrals of a few percent are acceptable.