A comparative study of effective core potential and full-electron calculations in Mo compounds. I. An analysis of topological properties of bond charge distribution

Effective core potential (ECP) and full-electron (FE) calculations for MoS₄^?2, MoO₄^?2, and MoOCl₄ compounds were analyzed. Geometry parameters, binding energies, charge distributions, and topological properties of the electronic density were studied for Mo? L bonds (L = S, O, Cl). Results clearly indicate that those approaches that include valence plus 4s and 4p electrons (ECP2 methods) are able to reproduce the topological properties of Mo? L bonds, charge distributions, and geometries with respect to those obtained by FE methods. ECP methods that consider only the 4d and 5s valence electrons (ECP1) fail in the calculation of molecular properties. The use of 5p functions in ECP1 approaches produces a negative Mulliken charge on Mo. Bader's charges give more consistent results than Mulliken's ones. A new parameter for measuring the degree of ionicity is proposed. © 1994 by John Wiley & Sons, Inc.     

Molecular electrostatic potentials and partial atomic charges from correlated wave functions: Applications to the electronic ground and excited states of 3-methylindole

Procedures have been developed to generate molecular electrostatic potentials based on correlated wave function from ab initio or semiempirical electronic structure programs. A new algorithm for point-wise sampling of the potential is described and used to obtain partial atomic charges via a linear, least squares fit between classical and quantum mechanical electrostatic potentials. The proposed sampling algorithm is efficient and promises to introduce less rotational variance in the potential derived partial charges than algorithms applied previously. Electrostatic potentials and fitted atomic charges from ab initio (HF/6–31G* and MP2/6-31G*) and semiempirical (INDO/S; HF, SECI, and SDCI) wave functions are presented for the electronic ground (S₀) and excited (¹L_b, ¹L_a) states of 3-methylindole. © 1992 by John Wiley & Sons, Inc.     

GRECP/5e‐MRD‐CI calculation of the electronic structure of PbH

The correlation calculation of the electronic structure of PbH is carried out with the generalized relativistic effective core potential (GRECP) and multireference single‐ and double‐excitation configuration interaction (MRD‐CI) methods. The 22‐electron GRECP for Pb is used and the outer core 5s, 5p, and 5d pseudospinors are frozen using the level‐shift technique, so only five external electrons of PbH are correlated. A new configuration selection scheme with respect to the relativistic multireference states is employed in the framework of the MRD‐CI method. The [6, 4, 3, 2] correlation spin–orbit basis set is optimized in the coupled cluster calculations on the Pb atom using a recently proposed procedure, in which functions in the spin–orbital basis set are generated from calculations of different ionic states of the Pb atom and those functions are considered optimal that provide the stationary point for some energy functional. Spectroscopic constants for the two lowest‐lying electronic states of PbH (²Π_1/2, ²Π_3/2) are found to be in good agreement with the experimental data. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Time‐Dependent Density Functional Theory Molecular Dynamics Simulations of Liquid Water Radiolysis

The early stages of the Coulomb explosion of a doubly ionized water molecule immersed in liquid water are investigated with time‐dependent density functional theory molecular dynamics (TD–DFT MD) simulations. Our aim is to verify that the double ionization of one target water molecule leads to the formation of atomic oxygen as a direct consequence of the Coulomb explosion of the molecule. To that end, we used TD–DFT MD simulations in which effective molecular orbitals are propagated in time. These molecular orbitals are constructed as a unitary transformation of maximally localized Wannier orbitals, and the ionization process was obtained by removing two electrons from the molecular orbitals with symmetry 1B₁, 3A₁, 1B₂ and 2A₁ in turn. We show that the doubly charged H₂O²⁺ molecule explodes into its three atomic fragments in less than 4 fs, which leads to the formation of one isolated oxygen atom whatever the ionized molecular orbital. This process is followed by the ultrafast transfer of an electron to the ionized molecule in the first femtosecond. A faster dissociation pattern can be observed when the electrons are removed from the molecular orbitals of the innermost shell. A Bader analysis of the charges carried by the molecules during the dissociation trajectories is also reported.     

Doubly excited3Se,3De and3Ge states of two-electron atomic systems

Summary Time-dependent perturbation theory has been applied to calculate the doubly excited triplet statesNsns:³S^e,Npnp:³D^e andNdnd:³G^e (N=2, 3, 4,n=N+1, ... ,5) for He, Li⁺, Be²⁺ and B³⁺. A time-dependent harmonic perturbation causes simulataneous excitation of both the electrons with a change of spin state. The doubly excited energy levels have been identified as the poles of an appropriately constructed linearized variational functional with respect to the driving frequency. In addition to the transition energies, effective quantum numbers of these doubly excited states have been calculated and analytic representations of their wave functions are obtained. These are utilized to estimate the Coulomb repulsion term for these states which checks the consistency of the wave functions. These wave functions may also be used for calculating other physical properties of the systems.     

Theoretical studies of organometallic compounds. III. Structures and bond energies of FeCHn and FeCH (n = 1, 2, 3)

The geometries and dissociation energies for the Fe? C and C? H bonds of FeCH_n and FeCH (n = 1, 2, 3) have been calculated by ab initio quantum mechanical methods using different effective core potential models and Møller–Plesset perturbation theory. The HW3 ECP model, which has a configuration [core] (n?1)s², (n?1)p⁶, (n?1)d¹, (n)s^m for the transition metals, is clearly superior to the larger core LANL1DZ ECP model with the configuration [core] (n?1)d¹, (n)s^m. The Fe? C bond energies calculated at correlated levels using the HW3 ECP are in much better agreement with experiment than the LANL1DZ results. This effect is mainly due to the higher number of correlated electrons rather than the inclusion of the outermost core electrons in the Hartree–Fock calculation. At the PMP4/HW3TZ/6-31G(d)//MP2/HW3TZ/6-31G(d) level, the theoretically predicted Fe? C bond energies for FeCH are in the range of 80% of the experimental values and have nearly the same accuracy as all-electron calculations using large valence basis sets and the MCPF method for the correlation energy. © 1992 by John Wiley & Sons, Inc.     

Intramolecular inter-ring haptotropic rearrangement in iridium naphthalene complexes: a DFT study

Quantum chemical simulation of the inter-ring haptotropic rearrangement (IHR) in iridium naphthalene complexes [η⁴-Ir(C₁₀H₈)L₂]⁺ (L = PH₃, PMe₃, PPh₃) involving migration of organometallic group from one of the aromatic ring to the other, was performed using the PBE density functional method with the TZV2p basis set for valence electrons and the relativistic SBK-JC pseudopotentials for the core electrons. The structures of the transition states and intermediates were studied. The IHR proceeds at the periphery of the naphthalene ligand. All transition states have reduced symmetry and hapticity compared with the initial complexes. The calculated thermodynamic parameters of the IHR are in agreement with the NMR data for the related iridium complex of ethylnaphthalene [η⁴-Ir(2-ethylnaphthalene)L₂]⁺A⁻, L = PPh₃, A = SbF₆, k ≈ 6·10⁻⁴ s⁻¹, ΔG ^≠ _{283 K} ≈ 21 kcal mol⁻¹).     

A density functional study of intra- and interring haptotropic η<Superscript>2</Superscript>,η<Superscript>2</Superscript> rearrangements in rhodium,ruthenium, and osmium naphthalene complexes

The density functional theory method was used to perform quantum-chemical modeling of the mechanisms of η²,η²-intraring (Intra-HR) and η²,η²-interring (Inter-HR) haptotropic rearrangements for μ² complexes of naphthalene with rhodium, ruthenium, and osmium. The structure of transition states and intermediates was studied, and the energy parameters of haptotropic rearrangements in these complexes were determined. We used the PBE functional, the TZV2p three-exponential basis set for valence electrons, and the SBK-JC relativistic pseudopotential for core electrons. η²,η² Intra-HR was found to occur inside the aromatic ring of η² naphthalene complexes without going outside it through intermediates and transition states with η ⁿ structures (n = 1, 2). Inter-HR occurred as metal replacements on the periphery of the naphthalene ligand through intermediates and transition states with η ⁿ structures (n = 1, 2, 3) from one ring into another. The calculated activation barriers for η²,μ² Intra-HR and η²,η² Inter-HR in the complexes studied closely agree with their experimental values.     

Electronic,spectra, and spin orbit interaction for FrAr van der Waals system

The potential energy curves and spectroscopic constants of the ground and many excited states of the FrAr van der Waals system have been determined using a one‐electron pseudopotential approach. The Fr⁺ core and the electron–Ar interactions are replaced by effective potentials. The Fr⁺Ar core–core interaction is incorporated using the accurate CCSD(T) potential of Hickling et al. (Phys. Chem. Chem. Phys. 2004, 6, 4233). This approach reduces the number of active electrons of the FrAr van der Waals system to only one valence electron, which permits the use of very large basis sets for the Fr and Ar atoms. Using this technique, the potential energy curves of the ground and many excited states are calculated at the self consistent field (SCF) level. In addition, the spin–orbit interaction is also considered using the semiempirical scheme for the states dissociating into Fr (7p) and Fr (8p). The FrAr system is not studied previously and its potential interactions, spectroscopic constants and dipole functions are presented here for the first time. Furthermore, we have predicted the X²Σ⁺–A²Π_1/2, X²Σ⁺–AΠ_3/2, X²Σ⁺–B²Σ_1/2⁺, X²Σ⁺–3²Π_1/2, X²Σ⁺–3²Π_3/2, and X²Σ⁺–5²Σ_1/2⁺ absorption spectra. © 2012 Wiley Periodicals, Inc.     

Development and testing of a compact basis set for use in effective core potential calculations on rhodium complexes

We present a set of effective core potential (ECP) basis sets for rhodium atoms which are of reasonable size for use in electronic structure calculations. In these ECP basis sets, the Los Alamos ECP is used to simulate the effect of the core electrons while an optimized set of Gaussian functions, which includes polarization and diffuse functions, is used to describe the valence electrons. These basis sets were optimized to reproduce the ionization energy and electron affinity of atomic rhodium. They were also tested by computing the electronic ground state geometry and harmonic frequencies of [Rh(CO)₂μ‐Cl]₂, Rh(CO)₂ClPy, and RhCO (neutral and its positive, and negative ions) as well as the enthalpy of the reaction of [Rh(CO)₂μ‐Cl]₂ with pyridine (Py) to give Rh(CO)₂ClPy, at different levels of theory. Good agreement with experimental values was obtained. Although the number of basis functions used in our ECP basis sets is smaller than those of other ECP basis sets of comparable quality, we show that the newly developed ECP basis sets provide the flexibility and precision required to reproduce a wide range of chemical and physical properties of rhodium compounds. Therefore, we recommend the use of these compact yet accurate ECP basis sets for electronic structure calculations on molecules involving rhodium atoms. © 2012 Wiley Periodicals, Inc.     

Nonrelativistic and quasirelativistic model potential calculations on AgH and Ag2

The major relativistic effects are included into the model potential (MP) method of Bonifacic and Huzinaga. The effects are incorporated on the level of Cowan and Griffin's relativistic Hartree–Fock (RHF) method. The model potential parameters are determined using the results of nonrelativistic Hartree–Fock (NHF) and RHF calculations. A new scheme of selection of the basis functions for use in atomic and molecular MP calculations is proposed. To obtain agreement with the Hartree–Fock calculations on AgH and Ag₂, the 4p shell has to be included explicitly in the MP calculations. The explicit treatment of the 4p electrons and the resulting reduction of the core size are necessary in order to overcome difficulties with approximate representation of the large 4p–4d core-valence interactions on the MP level.     

Enhancing Photoactivity of TiO2(B)/Anatase Core–Shell Nanofibers by Selectively Doping Cerium Ions into the TiO2(B) Core

Cerium ions (Ce³⁺⁾ can be selectively doped into the TiO₂(B) core of TiO₂(B)/anatase core–shell nanofibers by means of a simple one‐pot hydrothermal treatment of a starting material of hydrogen trititanate (H₂Ti₃O₇) nanofibers. These Ce³⁺ ions (≈0.202 nm) are located on the (110) lattice planes of the TiO₂(B) core in tunnels (width≈0.297 nm). The introduction of Ce³⁺ ions reduces the defects of the TiO₂(B) core by inhibiting the faster growth of (110) lattice planes. More importantly, the redox potential of the Ce³⁺/Ce⁴⁺ couple (E°(Ce³⁺/Ce⁴⁺)=1.715 V versus the normal hydrogen electrode) is more negative than the valence band of TiO₂(B). Therefore, once the Ce³⁺‐doped nanofibers are irradiated by UV light, the doped Ce³⁺ ions—in close vicinity to the interface between the TiO₂(B) core and anatase nanoshell—can efficiently trap the photogenerated holes. This facilitates the migration of holes from the anatase shell and leaves more photogenerated electrons in the anatase nanoshell, which results in a highly efficient separation of photogenerated charges in the anatase nanoshell. Hence, this enhanced charge‐separation mechanism accelerates dye degradation and alcohol oxidation processes. The one‐pot treatment doping strategy is also used to selectively dope other metal ions with variable oxidation states such as Co^2+/3+ and Cu^+/2+ ions. The doping substantially improves the photocatalytic activity of the mixed‐phase nanofibers. In contrast, the doping of ions with an invariable oxidation state, such as Zn²⁺, Ca²⁺, or Mg²⁺, does not enhance the photoactivity of the mixed‐phase nanofibers as the ions could not trap the photogenerated holes.     

Solid-State Photochemistry—A Method of Generating Unusual Valence States

High-energy radiation can give rise to pairs of complementary defects in nonmetallic solids by the transfer of electrons between various types of atoms. These “color centers” which are generally paramagnetic, can usually be described as unusual valence states of an element. They are destroyed by heating and in most cases regenerated by renewed irradiation. In a heteropolar solid the formation of color centers usually leads to cancellation of point charges due to foreign ions of other valence or to vacancies. This is shown by the examples of kunzite, brazilianite, smoky quartz, and citrine; the most important methods for the structural elucidation of color centers are also described. Application of the principle of charge balance opens up possibilities for the production of unusual valence states, e.g. Al²⁺, F^2?, Fe⁴⁺, and O^?. Moreover, the type of the color center often permits far-reaching conclusions to be drawn about the defect structure of real crystals, which could hardly be clarified in other ways.     

Synthesis,structures and magnetic properties of a series of polynuclear copper(II)‐lanthanide( III) complexes assembled with carboxylate and hydroxide ligands

Heterometallic copper(II)‐lanthanide(III) complexes have been made with a variety of exclusively O‐donor ligands including betaines (zwitterionic carboxylates) and chloroacetate, which are dinuclear CuLn, tetranuclear Cu₂Ln₂, pentanuclear C_u3Ln₂, and octadecanuclear C_u12 complexes. The results show that subtle changes in both the carboxylates and acidity of the reaction solution can cause drastic changes in the structures of the products. Magnetic studies exhibit that shielding of the Ln³⁺ 4f electrons by the outer shell electrons is very effective to preclude significant coupling interaction between the Ln³⁺ 4f electrons and Cu²⁺ 3d electrons in either a mono‐atomic hydroxide‐bridged, or a carboxylate‐bridged system.     

Enhanced Zintl anions by carbon doping in Al-Na clusters and new magic structure Al6Na4C

This article investigated the low-energy structures of Al₆Na _mC (m = 2, 4, 6, 8) clusters and their electronic structures by using genetic algorithm combined with density functional theory and configuration interaction methods. The computations show that the C atoms prefer sitting at the center, whereas the Na atoms tend to locate at the outside of the clusters. The valence molecular orbitals (MOs) agree well with the prediction of the jellium model. The stronger attraction of the central carbon to the valence electrons will depress the potential energies locally, which makes the 2S level go obviously lower and the 2P and 1D orbitals form a sub-band. The 26 valence electrons in Al₆Na₄C form closed 1S²1P⁶2S²1D¹⁰2P⁶ shells and correspond to a new magic structure. The MOs and electron localization function show that the sodium cores are exposed at the outside of the valence electrons and form naked cations. The contraction of the valence electrons because of the carbon doping enhances the charges on the Al₆C moieties, and the Na⁺ cores on the peripheries are ionically bonded to the Zintl anions (Al₆C)^q−. The Al₆Na₄C has a tetrahedral structure with symmetry T_d, and it may be used as building blocks to synthesize Zintl solid.     

Relativistic Gaussian basis sets for the atoms hydrogen to neon

Gaussian basis sets for use in relativistic molecular calculations are developed for atoms and ions with one to ten electrons. A relativistic radial wavefunction coupled to an angular function of l-symmetry is expanded into a linear combination of spherical Gaussians of the form r ^l exp (–r ²). One set of basis functions is used for all large and small components of the same angular symmetry. The expansion coefficients and the orbital exponents have been determined by minimizing the integral over the weighted square of the deviation between the Dirac or Dirac-Fock radial wavefunctions and their analytical approximations. The basis sets calculated with a weighting function inversely proportional to the radial distance are found to have numerical constants very similar to those of their energy-optimized non-relativistic counterparts. Atomic sets are formed by combining l-subsets. The results of relativistic and non-relativistic calculations based on these sets are analyzed with respect to different criteria, e.g. their ability to reproduce the relativistic total energy contribution and the spin-orbit splitting. Contraction schemes are proposed.Dedicated to Prof. Dr. A. Neckel on occasion of his 60th birthday