Electron pair correlation energies for ZN2+

Pair energies contributing to the correlation energies of the outer-shell electrons (n = 3) as well as for the 1s² and 2s² pairs are computed for the Zn²⁺ closed-shell ion by means of the variational-perturbation method starting with the sum of one-electron Hartree–Fock operators as the zeroth-order Hamiltonian. The results allow an understanding of the electron correlation for pairs of electrons of the p and d type. For 3p3d pairs it has been found that the correlation energy for the singlet pair of ¹D symmetry is lower than for the triplet pair ³D. The 3l-3l′ correlation energies are compared with the MBPT results of Kelly and Ron for Fe. The total correlation energy of the outer shell is ?1.032 a. u.     

Coupling between the convergence behavior of basis set and electron correlation: a quantitative study

The coupling between improvement of the basis set and the valence electron correlation method has been studied quantitatively for the total atomization energies (TAEs) of a number of small molecules, using basis sets of up to [7s6p5d4f3g2h/5s4p3d2f1g] quality. Very significant coupling is found to exist. Using a scaled basis set extrapolation beyond [6s5p4d3f2g/ 4s3p2d1f] at the MP2 or CCSD level, mean absolute errors of 0.18 and 0.15 kcal/mol, respectively, can be obtained for the TAEs of a number of small polyatomic molecules, compared to 0.12 kcal/mol using CCSD(T) throughout. Received: 7 February 1997 / Accepted: 6 May 1997     

Triazènes. Etude XPS. et 1H-RMN. des complexes mercuriques des diaryl-1,3-triazènes

XPS. and ¹H-NMR. spectra of 1,3-diaryltriazenes complexes of Hg(II) The core binding energies C 1s, N 1s, Hg 4f_7/2, Hg 4f_5/2 in 7 symmetrical p-substituted 1,3-diphenyltriazenes complexes of Hg(II) have been measured by XPS. Within the limits of experimental error (± 0.2 eV) only one N 1s signal could be detected. This indicates the equivalence of the 3 N-atoms. Invariance of C 1s, N 1s, Hg 4f_7/2, Hg 4d_5/2 signals with the para substituents on the phenyl ring is explained on the basis of ionic character in the Hg, N bond. These results are corroborated by the ¹H-NMR. spectra.     

Ground state correlation energy of the Be-sequence forZ=4–20 in MCDF approximation

The ground state (J=0) electronic correlation energy of the 4-electron Be-sequence is calculated in the Multi-Configuration Dirac-Fock approximation forZ=4–20. The 4 electrons were distributed over the configurations arising from the 1s, 2s, 2p, 3s, 3p and 3d orbitals. Theoretical values obtained here are in good agreement with experimental correlation energies.     

Study on Pair Correlation Energies of Isoelectronic Systems F^－, HF and H2F^＋

The intrapair and interpair correlation energies of F-, HF and H2F^ systems are calculated and analyzed using MP2-OPT2 method of MELD program with cc-PVSZ^* basis set. From the analysis of pair correlation energies of these isoelectronlc sysoterns, it is found that the 1sF^2 pair correlation energy is trans-ferable in these three isociectronic systems. According to the definition of pair correlation contribution of one electron pair to a system, the pair correlation contribution values of these three systems are calculated. The correlation contribution values of inner electron pairs and H—F bonding electron pair in HF molecule with those in H2F^ system are compared. The results indicate that the bonding effect of a molecule is one of the im-portant factors to influence electron correlation energy of the system. The comparison of correlation energy contributions in-cluding triple and quadruple excitations with those only includ-ing singles and doubles calculated with 6-311 G(d) basis set shows that the higher.excitation correlation energy contribution gives more than 2 % of the total correlation energy for these sys-tems.     

Electronic structure of crystalline uranium nitride: LCAO DFT calculations

The results of electronic structure calculations performed for the first time for crystalline uranium nitride and using a LCAO basis are discussed. For calculations we used the density functional method with the PW91 exchange correlation potential and a variety of relativistic core potentials for the uranium atom. The calculated atomization energy of the crystal agrees well with the experimental data and with the results of calculations with the plane wave basis. It is shown that a chemical bond in crystalline uranium nitride is a metal covalent bond. The metal component of the bond is due to the 5f electrons localized on the uranium atom and having energies near the Fermi level and the bottom of the conduction band. The covalent component of the chemical bond results from an overlap between the uranium 6d and 7s valence orbitals and the nitrogen 2p atomic orbitals. Inclusion of the 5f electrons in the core of the uranium atom introduces relatively minor changes in the calculated binding energy and electron density distribution.     

Ionic bonding of lanthanides,as influenced by d‐ and f‐atomic orbitals,by core–shells and by relativity

Lanthanide trihalide molecules LnX₃ (X = F, Cl, Br, I) were quantum chemically investigated, in particular detail for Ln = Lu (lutetium). We applied density functional theory (DFT) at the nonrelativistic and scalar and SO‐coupled relativistic levels, and also the ab initio coupled cluster approach. The chemically active electron shells of the lanthanide atoms comprise the 5d and 6s (and 6p) valence atomic orbitals (AO) and also the filled inner 4f semivalence and outer 5p semicore shells. Four different frozen‐core approximations for Lu were compared: the (1s²–4d¹⁰) [Pd] medium core, the [Pd+5s²5p⁶ = Xe] and [Pd+4f¹⁴] large cores, and the [Pd+4f¹⁴+5s²5p⁶] very large core. The errors of Lu? X bonding are more serious on freezing the 5p⁶ shell than the 4f¹⁴ shell, more serious upon core‐freezing than on the effective‐core‐potential approximation. The Ln? X distances correlate linearly with the AO radii of the ionic outer shells, Ln³⁺‐5p⁶ and X^?‐np⁶, characteristic for dominantly ionic Ln³⁺‐X^? binding. The heavier halogen atoms also bind covalently with the Ln‐5d shell. Scalar relativistic effects contract and destabilize the Lu? X bonds, spin orbit coupling hardly affects the geometries but the bond energies, owing to SO effects in the free atoms. The relativistic changes of bond energy BE, bond length R_e, bond force k, and bond stretching frequency v_s do not follow the simple rules of Badger and Gordy (R_e～BE～k～v_s). The so‐called degeneracy‐driven covalence, meaning strong mixing of accidentally near‐degenerate, nearly nonoverlapping AOs without BE contribution is critically discussed. © 2015 Wiley Periodicals, Inc.     

Bound state energies for the exponential cosine screened Coulomb potential

The energy eigenvalues of bound states of an electron in the general exponential cosine screened Coulomb potential are obtained using the shifted 1/N expansion method. The energies for the states from 1s to 8k are calculated from six to eight significant figures. The energy eigenvalues for the 1s, 2s – 2p, 3s – 3d, and 4s – 4f states are also presented as a function of the screening parameter λ. Results are compared with the ones obtained by other workers. The agreement reduces roughly for large λ. It is also observed that the convergence of the expansion series increases remarkably asl increases.     

A theoretical determination of the dissociation energy of the nitric oxide dimer

Summary Multi-reference CI methods have been applied to determine the dissociation energy and structure of thecis-N₂O₂ molecule. The convergence of the theoretical result has been checked with respect to a systematic expansion of the one-electron basis set and the multi-reference CI wave function. The best calculated value, 13.8 kJ/mol, is in agreement with the experimental value, 12.2 kJ/mol. It has been obtained with an extended ANO-type basis set [6s5p3d2f], including the effect of the basis set superposition error (BSSE) in the geometry optimization, and additional effects, such as the electron correlation of core electrons and relativistic corrections, using the average coupled pair functional (ACPF) approach. The optimal geometry computed at this level was found to be:r(NN)=2.284 Å,r(NO)=1.149 Å, and s5p3d2f] basis set, the BSSE was found to be 2 kJ/mol.     

The X-ray photoelectron spectra of inorganic molecules: VI. Compounds containing rhenium-oxygen and rhenium-halogen bonds: rhenium 4f,chlorine 2p and oxygen 1s binding energies and their co

Rhenium 4f, chlorine 2p and oxygen 1s binding energies have been recorded for a series of coordination complexes of rhenium(V) and rhenium(VII) containing rhenium-oxygen bonds. Related studies on the rhenium(III) acetates Re₂(OAc)₄X₂(X = Cl, Br) and on several adducts of the rhenium chlorides (Re 4f and Cl 2p binding energies only) are also reported. Chemical shift data are related where possible to the molecular structures of the complexes. Correlations between rhenium 4f binding energies and oxidation state are of diagnostic value only in distinguishing the high oxidation state species (rhenium(V) and (VII)). Differences in rhenium 4f_{$\text{7}\text{2}$} and oxygen 1s binding energies [δ(O1s, Re 4f_{$\text{7}\text{2}$})] may be useful in probing the nature of the rhenium-oxygen bonds.     

TiCl, TiH, and TiH+ bond energies: a test of a correlation-consistent Ti basis set

Correlation-consistent basis sets are developed for the Ti atom. The polarization functions are optimized for the average of the ³F and ⁵F states. One series of correlation-consistent basis sets is for 3d and 4s correlation, while the second series includes 3s and 3p correlation as well as 3d and 4s correlation. These basis sets are tested using the Ti ³F–⁵F separation and the dissociation energies of TiCl X⁴Φ, TiH X⁴Φ, and TiH⁺ X³Φ. The CCSD(T) complete basis set limit values are determined by extrapolation. The Douglas–Kroll approach is used to compute the scalar relativistic effect. Spin-orbit effects are taken from experiment and/or are computed at the CASSCF level. The Ti³F–⁵F separation is in excellent agreement with experiment, while the TiCl, TiH, and TiH⁺ bond energies are in good agreement with experiment. Extrapolation with the valence basis set is consistent with other atoms, while including 3s and 3p correlation appears to make extrapolation more difficult. Received: 20 January 1999 / Accepted: 26 February 1999 / Published online: 7 June 1999     

Energy-adjusted pseudopotentials for the rare earth elements

Nonrelativistic and quasirelativistic energy-adjusted pseudopotentials and optimized (7s6p5d)/[5s4p3d]-GTO valence basis sets for use in molecular calculations for fixed f-subconfigurations of the rare earth elements, La through Lu, have been generated. Atomic excitation and ionization energies from numerical HF, as well as SCF pseudopotential calculations using the derived basis sets, differ by less than 0.1 eV from numerical HF all-electron results. Corresponding values obtained from CI(SD), CEPA-1, as well as density functional calculations using the quasirelativistic pseudopotentials, are in reasonable agreement with experimental data.     

Ab initio calculations on sulfur-containing compounds. II. One-electron properties of H2S

Closed-shell RHF one-electron properties are calculated for H₂S using a total of 41 different s, p basis sets and two polarized basis sets (6–31G* and 6–31G**). Total energies and geometries alone are not a comprehensive criteria for selecting the best basis sets. It is shown here that the comparison of a number of one-electron properties can serve as an excellent criteria for testing basis sets. The quality or reliability of a basis set is taken as being its agreement with a large uncontracted s, p basis set (s, p limit).     

Lifetime measurements of some TmI odd parity levels

Eleven new lifetimes of odd parity excited energy levels in four configurations: 4f ¹² 5d 6s6p, 4f ¹² 6s² 6p, 4f ¹³ 5d6s and 4f ¹³ 6s7s of atomic thulium have been mesured with atomic-beam laser spectrocopy. Two pulsed dye lasers are used for stepwise excitation and the time-resolved fluorescence decay was used to determine lifetime values. The accuracy of the measurements is about 10%.     

Collisionally activated dissociation of 2,4,6-triphenylpyridinium cations

Thresholds for the appearance of fragment ions allowed the estimation of threshold fragmentation energies (TFE) for the collisionally activated dissociation (CAD) in the gas phase of laser-desorbed pyridine-ring substituted N-benzylpyridinium cations to form pyridine and a carbocation. p-Methylbenzylpyridinium cation underwent an alternative CAD into pyridinium cation and the p-quinodimethane. The TFE are discussed in comparison with the energy differences (ΔΔH_f = ΔH_f(Py) + ΔH_f(R⁺) ? ΔH_f(Py ⁺R) calculated by the AM1 method to provide strong evidence for benzyl to tropylium cation rearrangement in an ion-molecule pair.     

THE RELATIONSHIP BETWEEN CARCINOGENIC ACTIVITIES OF POLYCYCLIC AROMATIC HYDROCARBONS AND THEIR SINGLET, TRIPLET, AND SINGLET-TRIPLET SPLITTING ENERGIES AND PHOSPHORESCENCE LIFETIMES

Abstract— The energies of the lowest excited singlet, E_s, and triplet, E_t, states, and singlet-triplet splitting energies, ΔE_s,t, were determined on 18 carcinogenic and 31 noncarcinogenic polycyclic aromatics. A highly significant correlation was found between carcinogenic activity and the energy of the excited singlet state. Compounds with an E_s < 312 kJ/mol were 4.8 times more likely to be carcinogens than those compounds with E_s 312 kJ/mol (P= 0.015). Compounds whose singlet energies fell within the narrow range of 297 ≤E_s≤ 310 kJ/mol were 22.8 times more likely to be carcinogens than those compounds which fell outside this range (P= 0.00006). A significant correlation between carcinogenic activity and E_t energies was not found, while the correlation involving ΔE_s,t energies was intermediate between the E_s and E_t correlations. The phosphorescence lifetimes, τ_p, of the 18 carcinogenic aromatics and 27 of the noncarcinogenic aromatip were determined, and were shown not to be correlated with carcinogenic activity. When either the E_t or ΔE_s,t energies were plotted as a function of E_s it was found that the carcinogens tended to form in an elliptical cluster. Compounds whose E_s and E_t energies placed them within the ellipse were 9.7 times more likely to be carcinogens than those compounds which fell outside the ellipse (P= 0.002), while with the E_s, ΔE_s,t ellipse, compounds which fell inside were 20.6 times more likely to be carcinogens than those which fell outside (P= 0.0004). E_s, E_t, ΔE_s,t and τ_p values were also determined on 12 carcinogenic and 4 noncarcinogenic alkyl substituted benz[a]anthracenes. There was no significant difference between the carcinogens and noncarcinogens and the “elliptical” correlation predicted both the carcinogens and noncarcinogens to be carcinogenic. The results suggest that either some property(ies) of the lowest excited singlet state, but not its energy, or some molecular property(ies) which runs parallel to singlet state energies may be important in determining carcinogenic activity in polycyclic aromatics.     

Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions

Generally contracted basis sets for the first row transition metal atoms Sc-Zn have been constructed using the atomic natural orbital (ANO) approach, with modifications for allowing symmetry breaking and state averaging. The ANOs are constructed by averaging over the three electronic configurationsd ⁿ ,d ^n–1 s, andd ^n–2 s ² for the neutral atom as well as the ground state for the cation and the ground state atom in an external electric field. The primitive sets are 21s15p10d6f4g. Contraction to 6s5p4d3f2g yields results that are virtually identical to those obtained with the corresponding uncontracted basis sets for the atomic properties, which they have been designed to reproduce. Slightly larger deviations are obtained with the 5s4p3d2f1g for the polarizability, while energetic properties still have only small errors. The design objective has been to describe the ionization potential, the polarizability and the valence spectrum as accurately as possible. The result is a set of well-balanced basis sets for molecular calculations, which can be used together with basis sets of the same quality for the first and second row atoms.     

X-Ray Photoelectron Study of Thorium Silicate ThSiO4 · nH2O and Uranium Silicate USiO4·nH2O

The naturally occurring compounds of thorium ThSiO₄, ThSiO₄· nH₂O, and (Th, Fe)SiO₄ and uranium USiO₄· nH₂O have been studied by X-ray photoelectron spectroscopy in the range of electron binding energies from 0 to 1200 eV. The oxidation state of Th in the natural compounds is close to that in Th(OH)₄; for uranium, it is similar to that in UO₂. Based on the structure of the low-energy electron spectra it is assumed that the electrons of the filled Th6p- and O2s-atomic orbitals take an active part in chemical bonding. Fine structure was observed in the Th(U)6s-, 5d-, 5p-, 4f-, 4d-, and 4p _3/2 electron spectra of all substances under study. Mechanisms of fine structure formation are discussed and the fine structure parameters are correlated with the physicochemical properties of the compounds.