Fully relativistic calculations of ThF4

Based on the results of first‐principles density functional theory calculations of the electronic structure of ThF₄ in solid state and molecular form, the study of the Th6p, 5f, 6d, 7s and F2s, 2p states was done. We used the fully relativistic cluster discrete variational method with the local exchange‐correlation potential. The hybridization of F2p and Th5f, 6d, 7s, 7p states in the valence molecular orbitals (VMOs) in the region 0–10 eV and of F2s and Th6p states in the inner valence molecular orbitals (IVMOs) in the region 10–50 eV was studied. The results of relativistic cluster calculations are compared with those obtained for ThF₄ molecule. The energies of ionization of VMOs and of IVMOs were evaluated on the basis of the ground‐state and Slater's transition‐state calculations. The MO energy levels provide a satisfactory interpretation of experimental photoelectron spectra. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Exploring the actinide-actinide bond: theoretical studies of the chemical bond in Ac2, Th2, Pa2, and U2

Multiconfigurational quantum chemical methods (CASSCF/CASPT2) have been used to study the chemical bond in the actinide diatoms Ac2, Th2, Pa2, and U2. Scalar relativistic effects and spin-orbit coupling have been included in the calculations. In the Ac2 and Th2 diatoms the atomic 6d, 7s, and 7p orbitals are the significant contributors to the bond, while for the two heavier diatoms, the 5f orbitals become increasingly important. Ac2 is characterized by a double bond with a 3Sigmag-(0g+) ground state, a bond distance of 3.64. A, and a bond energy of 1.19 eV. Th2 has quadruple bond character with a 3Dg(1g) ground state. The bond distance is 2.76 A and the bond energy (D0) 3.28 eV. Pa2 is characterized by a quintuple bond with a 3Sigmag-(0g+) ground state. The bond distance is 2.37 A and the bond energy 4.00 eV. The uranium diatom has also a quintuple bond with a 7Og (8g) ground state, a bond distance of 2.43 A, and a bond energy of 1.15 eV. It is concluded that the strongest bound actinide diatom is Pa2, characterized by a well-developed quintuple bond.     

Octacarbonyl Ion Complexes of Actinides [An(CO)8]+/− (An=Th,U) and the Role of f Orbitals in Metal–Ligand Bonding

The octacarbonyl cation and anion complexes of actinide metals [An(CO)₈]^+/− (An=Th, U) are prepared in the gas phase and are studied by mass-selected infrared photodissociation spectroscopy. Both the octacarbonyl cations and anions have been characterized to be saturated coordinated complexes. Quantum chemical calculations by using density functional theory show that the [Th(CO)₈]⁺ and [Th(CO)₈]⁻ complexes have a distorted octahedral (D_4h) equilibrium geometry and a doublet electronic ground state. Both the [U(CO)₈]⁺ cation and the [U(CO)₈]⁻ anion exhibit cubic structures (O_h) with a ⁶A_1g ground state for the cation and a ⁴A_1g ground state for the anion. The neutral species [Th(CO)₈] (O_h; ¹A_1g) and [U(CO)₈] (D_4h; ⁵B_1u) have also been calculated. Analysis of their electronic structures with the help on an energy decomposition method reveals that, along with the dominating 6d valence orbitals, there are significant 5f orbital participation in both the [An]←CO σ donation and [An]→CO π back donation interactions in the cations and anions, for which the electronic reference state of An has both occupied and vacant 5f AOs. The trend of the valence orbital contribution to the metal–CO bonds has the order of 6d≫5f>7s≈7p, with the 5f orbitals of uranium being more important than the 5f orbitals of thorium.     

Electronic structures and bonding of CeF: a frozen-core four-component relativistic configuration interaction study

We study the electronic structure of the ground and several low-lying states of the CeF molecule using Dirac-Fock-Roothaan (DFR) and four-component relativistic single and double excitation configuration interaction (SDCI) calculations in the reduced frozen-core approximation (RFCA). The ground state and two low-lying excited states are calculated to have (4f)1(5d)1(6s)1 configurations with Omega = 3.5, 4.5, and 3.5, and the resulting excitation energies, T0, are, respectively, 0.319 and 0.518 eV. The experimental configurations for these states are the same, although the experimental T0 values are approximately 0.3 eV smaller than those calculated. Experimentally, the red-degraded band was observed to be 2.181 eV above the ground state, having the configuration (4f)1(5d)1(6p)1 with Omega = 4.5. The calculation for this state gives 2.197 eV and configuration (4f)1.0(5d)1.7(6p)0.3 with Omega = 4.5. We found that Omega, Re, and nu(1-0) obtained by CI agree well with experiment. Bonding between the Ce and the F is highly ionic. The 4f, 5d, and 6s valence electrons are localized at the Ce+ ion, because they are attracted by the Ce4+ ion core, and are excluded from the bonding region because of the electronic cloud around the negatively charged fluoride anion. The bonding in the ground and excited states of the CeF molecule is significantly influenced by the 6s and 5d electron distributions between the Ce and the F.     

相对论赝势的从头计算法研究铀酰离子电子结构

用相对论赝势的从头算法研究了铀酰离子的几何构型和电子结构.得到了与实验数据较一致的键长、键角和IR振动频率.铀氧间以U5f与O2p相互作用为主,U6d与O2p间的键合较小;同时,U6p、U7s、U6d和Usd杂化轨道与O2s间也有强的相互作用.不同自旋多重度时对铀酰离子总能量计算结果表明,UO22+的基态为1∑g+的可能性更大.     

Isolation of a Perfectly Linear Uranium(II) Metallocene

Reduction of the uranium(III) metallocene [(η⁵‐C₅ⁱPr₅)₂UI] ( 1 ) with potassium graphite produces the “second‐generation” uranocene [(η⁵‐C₅ⁱPr₅)₂U] ( 2 ), which contains uranium in the formal divalent oxidation state. The geometry of 2 is that of a perfectly linear bis(cyclopentadienyl) sandwich complex, with the ground‐state valence electron configuration of uranium(II) revealed by electronic spectroscopy and density functional theory to be 5f³ 6d¹. Appreciable covalent contributions to the metal‐ligand bonds were determined from a computational study of 2 , including participation from the uranium 5f and 6d orbitals. Whereas three unpaired electrons in 2 occupy orbitals with essentially pure 5f character, the fourth electron resides in an orbital defined by strong 7s‐6d mixing.     

Electronic structure of the GdF molecule by frozen-core four-component relativistic configuration interaction calculations

The electronic structure of GdF is calculated based on frozen-core four-component relativistic configuration interactions. The resulting excitation energies are fairly close to experiment and correctly designate the excited states. For instance, the existence of the experimentally inferred state at 0.55 eV above the ground state is confirmed, having Omega=132 with (4f(7)5d(+) (1)6s(+) (1)); it is 0.58 eV above the ground state according to the present calculation.     

Systematically convergent correlation consistent basis sets for molecular core-valence correlation effects: the third-row atoms gallium through krypton

The family of correlation consistent polarized valence basis sets has been extended in order to account for core-core and core-valence correlation effects within the third-row, main group atoms gallium through krypton. Construction of the basis sets is similar to that of the atoms boron through argon, where either the difference between core-correlated and valence-only correlation energies were calculated via configuration interaction (CISD) computations on the ground electronic states of the atoms (named cc-pCVnZ) or the sets were optimized with respect to the core-valence correlation energy and a small weight of core-core correlation energy (cc-pwCVnZ). Due to the correlation of 3d orbitals, added shells of higher angular momentum exponents compared to the valence sets are necessary to describe the core region. The pattern of added core-correlating functions is (1s1p1d1f) for double-zeta, (2s2p2d2f1g) for triple-zeta, (3s3p3d3f2g1h) for quadruple-zeta, and (4s4p4d4f3g2h1i) for quintuple-zeta. Atomic and molecular results show good convergence to the CBS limit, with the cc-pwCVnZ sets showing improved convergence compared to the cc-pCVnZ ones for molecular core-valence correlation effects. After testing the basis sets on the homonuclear diatomics Ga2-Kr2 with coupled cluster wave functions, it is concluded that a treatment of core-valence correlation effects is essential for high-accuracy ab initio investigations of third-row-containing molecules. Though the basis sets are optimal for 3s3p3d correlation, preliminary atomic and molecular results show the basis sets to be efficient with respect to 3d-only correlation, and these potentially could be used with 3d-only correlation for more qualitative studies on larger species.     

Even-tempered Roothaan-Hartree-Fock wave functions for the third- and fourth-row atoms

Summary Roothaan-Hartree-Fock wave functions composed of 12s8p6d, 12s10p6d, and 12s10p8d even-tempered (ET) Slater-type functions (STFs), respectively, are reported for the atoms K-Zn, Ga-Kr, and Rb-Xe in their ground state. Despite the limited variational freedom in the Et method, the resultant atomic energies are found to compare well with fully-optimized wave functions of similar sizes. In particular, the present ET results reproduce almost completely the fully-optimized Sekiya-Tatewaki energies with the same basis set size for the atoms K-Zn. All the present energies are also lower than the Clementi-Roetti ones with slightly smaller but fully-optimized basis sets. A generalized even-tempered scheme is suggested and shown to give good results for Xe.     

Determining relative f and d orbital contributions to M-Cl covalency in MCl6(2-) (M = Ti, Zr, Hf, U) and UOCl5(-) using Cl K-edge X-ray absorption spectroscopy and time-dependent density functional theory

Chlorine K-edge X-ray absorption spectroscopy (XAS) and ground-state and time-dependent hybrid density functional theory (DFT) were used to probe the electronic structures of O(h)-MCl(6)(2-) (M = Ti, Zr, Hf, U) and C(4v)-UOCl(5)(-), and to determine the relative contributions of valence 3d, 4d, 5d, 6d, and 5f orbitals in M-Cl bonding. Spectral interpretations were guided by time-dependent DFT calculated transition energies and oscillator strengths, which agree well with the experimental XAS spectra. The data provide new spectroscopic evidence for the involvement of both 5f and 6d orbitals in actinide-ligand bonding in UCl(6)(2-). For the MCl(6)(2-), where transitions into d orbitals of t(2g) symmetry are spectroscopically resolved for all four complexes, the experimentally determined Cl 3p character per M-Cl bond increases from 8.3(4)% (TiCl(6)(2-)) to 10.3(5)% (ZrCl(6)(2-)), 12(1)% (HfCl(6)(2-)), and 18(1)% (UCl(6)(2-)). Chlorine K-edge XAS spectra of UOCl(5)(-) provide additional insights into the transition assignments by lowering the symmetry to C(4v), where five pre-edge transitions into both 5f and 6d orbitals are observed. For UCl(6)(2-), the XAS data suggest that orbital mixing associated with the U 5f orbitals is considerably lower than that of the U 6d orbitals. For both UCl(6)(2-) and UOCl(5)(-), the ground-state DFT calculations predict a larger 5f contribution to bonding than is determined experimentally. These findings are discussed in the context of conventional theories of covalent bonding for d- and f-block metal complexes.     

6‐31G* basis set for third‐row atoms

Medium basis sets based upon contractions of Gaussian primitives are developed for the third‐row elements Ga through Kr. The basis functions generalize the 6‐31G and 6‐31G* sets commonly used for atoms up to Ar. A reexamination of the 6‐31G* basis set for K and Ca developed earlier leads to the inclusion of 3d orbitals into the valence space for these atoms. Now the 6‐31G basis for the whole third‐row K through Kr has six primitive Gaussians for 1s, 2s, 2p, 3s, and 3p orbitals, and a split‐valence pair of three and one primitives for valence orbitals, which are 4s, 4p, and 3d. The nature of the polarization functions for third‐row atoms is reexamined as well. The polarization functions for K, Ca, and Ga through Kr are single set of Cartesian d‐type primitives. The polarization functions for transition metals are defined to be a single 7f set of uncontracted primitives. Comparison with experimental data shows good agreement with bond lengths and angles for representative vapor‐phase metal complexes. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 976–984, 2001     

Improved valence basis sets for divalent lanthanide 4f-in-core pseudopotentials

Improved energy-optimized (6s5p4d) and (7s6p5d) primitive valence basis sets have been derived for energy-consistent scalar-relativistic 4f-in-core pseudopotentials of the Stuttgart-Cologne variety modeling divalent lanthanides with a $4\hbox{f}^{n+1}$ occupation (n = 0?C13 for La?CYb). Segmented contracted basis sets covering the range of polarized double-, triple-, and quadruple-zeta quality, augmented by 2f1g correlation sets, were created for use in molecular calculations. The basis sets contain smaller (4s4p3d) and (5s5p4d) primitive subsets, which are designed in particular for solid state calculations of crystals containing divalent lanthanide ions. Hartree?CFock, density functional theory and coupled cluster results obtained with the new basis sets for lanthanide atomic ionization potentials as well as of geometry optimizations of various test molecules, i.e. selected lanthanide mono- and dihydrides, mono- and difluorides, and monooxides, show a satisfactory agreement with experimental data as well as with corresponding scalar-relativistic all-electron results. Core-polarization potentials are found to improve the results, especially for the atomic first and second ionization potentials.     

Soft x-ray spectroscopy of Ba24Ge100: electronic phase transition and Ba-atom rattling

The electronic states of Ba24Ge100 are studied by soft x-ray photoelectron spectroscopy (XPS) at a high-energy photon factory. A large reduction in the density of states (DOS) at the Fermi level is clearly shown before and after the electronic phase transition at 200 K. The changes in the spectrum widths and the fine structures of the core-level Ba 4d spectra give a very reasonable indication of the Ba-atom rattlings in the clathrate polyhedra. On-resonance experiments using the excitation from Ba 3d to 4f levels display that the wave functions of Ba 5d and 6s orbitals give only a small contribution to make a Fermi surface through the hybridization with the Ge20 cluster orbitals. Importantly, reliable values of the DOS at the Fermi level NEF are successfully deduced, using two data sets of DOS obtained from high-resolution XPS and the total magnetic susceptibilities by a superconducting quantum interference device, to be 0.149 and 0.0427 states eV(-1) (Ge atom)(-1) for a high-temperature and for a low-temperature phase.     

A Fock space coupled cluster study on the electronic structure of the UO(2), UO(2) (+), U(4+), and U(5+) species

The ground and excited states of the UO(2) molecule have been studied using a Dirac-Coulomb intermediate Hamiltonian Fock-space coupled cluster approach (DC-IHFSCC). This method is unique in describing dynamic and nondynamic correlation energies at relatively low computational cost. Spin-orbit coupling effects have been fully included by utilizing the four-component Dirac-Coulomb Hamiltonian from the outset. Complementary calculations on the ionized systems UO(2) (+) and UO(2) (2+) as well as on the ions U(4+) and U(5+) were performed to assess the accuracy of this method. The latter calculations improve upon previously published theoretical work. Our calculations confirm the assignment of the ground state of the UO(2) molecule as a (3)Phi(2u) state that arises from the 5f(1)7s(1) configuration. The first state from the 5f(2) configuration is found above 10,000 cm(-1), whereas the first state from the 5f(1)6d(1) configuration is found at 5,047 cm(-1).     

Molecular structure of diatomic lanthanide compounds

The molecular constants of selected diatomic lanthanide compounds (LaH, LaO, LaF, EuH, EuO, EuF, EuS, GdO, GdF, GdH, YbH, YbO, YbF, YbS, LuH, LuO and LuF) have been calculated by using relativistic small-core pseudopotentials and optimized (14s13p10d8f6g)/ [6s6p5d4f3g] valence basis sets. The results are in good agreement with available experimental data, with exception of YbO and LuF. The reasons for the discrepancies in case of YbO are due to a complicated mixing of configurations in the ground state, whereas in case of LuF the binding energy estimated by experimentalists appears to be too low.     

The low-lying electronic states of nickel cyanide and isocyanide: A theoretical investigation

At different levels of coupled cluster theory optimum structures, energetics, and harmonic vibrational frequencies for several low-lying doublet and quartet electronic states of linear NiCN and NiNC were studied using four contracted Gaussian basis sets, ranging from Ni[6s5p4d2f], CN[4s3p2d] to Ni[8s7p5d3f2g1h], CN[5s4p3d2f1g]. The most reliable predictions were obtained with a relativistic Douglas-Kroll restricted open-shell-based coupled cluster method including singles, doubles, and perturbative triple excitations [DK-R/UCCSD(T)]. This level of theory was used in conjunction with correlation-consistent polarized valence Douglas-Kroll recontracted quadruple-zeta basis sets (cc-pVQZDK). The energetic ordering of the electronic states of NiCN is predicted to be 2delta < 2sigma+ < 2pi < 4delta < 4pi and that of NiNC is 2delta approximately 2sigma+ < 2pi < 4delta < 4pi < 4sigma-. Our theoretical investigation supports the assignment of the ground-state term symbol, the Ni-C stretching frequency, and the bending frequency for the ground electronic state of NiCN by Kingston et al. [J. Mol. Spectrosc. 215, 106 (2002)] and by Sheridan and Ziurys [J. Chem. Phys. 118, 6370 (2003)]. The predicted structure of the 2delta ground state of NiCN, r(e)(Ni-C) = 1.822 angstroms and r(e)(C-N) = 1.167 angstroms, at DK-R/UCCSD(T)/cc-pVQZDK shows excellent agreement with the experimentally determined Ni-C bond length of 1.826 A and less satisfactory agreement for the C-N bond length of 1.153 angstroms [J. Chem. Phys. 118, 6370 (2003)]. It is also concluded that the metal-to-ligand pi back donation is weak or negligible. Additionally, we found that on the 2delta surface the linear cyanide isomer lies lower in energy than the linear isocyanide isomer by 12.2 kcal mol(-1).     

NX(X=F,Cl,Br)分子结构与极化函数f轨道的作用

用密度泛函理论的Becke3LYP方法，计算了NX（X=F，Cl,Br）的激发态b1Σ＋ 和基态X3Σ－，并对比不含f轨道的基集合cc-pvDZ和6-311＋G与含f轨道的基集合6-311＋G(3df)的计算结果，发现极化函数f轨道对NCl和NBr的键长与谐振频率ωe有明显改进作用，即f轨道对成键有贡献，而f轨道对NF的Re和ωe则无明显作用.同时，基于能量共振转移的需要，用NF代替O2-I 红外激光系统的O2是不适宜的，而用NCl和NBr代替则是可能的.