Valence-only model potential calculations on copper hydride molecule

Different sets of one-electron functions obtained according to the strong-orthogonal geminal theory (GEM) [1], the Generalized Molecular Orbital (GMO) method [2] and the exchange maximization between virtual and occupied orbitals (EVO) [3], are tested as basis for CI calculations. The efficiency of the three procedures is discussed investigating the electronic structure of the CuH molecule using an effective-core potential. The values computed for the bond length, the dissociation energy and the vibrational frequency of the ground electronic state are compared with the experimental ones. The charge distribution is examined to estimate the contribution of the d electrons to the Cu-H bond. Comparisons are made with the results obtained by other theoretical works in which the copper atom is treated as a one valence electron atom.     

Optical oscillator strengths for isoelectronic ions of nitrogen

An analytic atomic active electron model potential adjusted to experimental single-particle energy levels is used to generate wave functions for the valence and excited states of O¹⁺, F²⁺, Ne³⁺, Na⁴⁺, and Mg⁵⁺. Using these wave functions in conjunction with the Born approximation and the LS-coupling scheme, we calculate optical oscillator strengths for excitations from the 1s²2s²2p³(⁴S_3/2) ground state. The results are compared to experimental data and other calculations. Systematic trends along the isoelectronic sequence are discussed.     

Influence of Fine Ligand Substitution Modification of the Isocyanidometal Bridge on Metal-to-Metal Charge Transfer Properties in Class II–III Mixed Valence Complexes

The synthesis and characterization of Class II–III mixed valence complexes have been an interesting topic due to their special intermediate behaviour between localized and delocalized mixed valence complexes. To investigate the influence of the isocyanidometal bridge on metal-to-metal charge transfer (MMCT) properties, a family of new isocyanidometal-bridged complexes and their one-electron oxidation products cis-[Cp(dppe)Fe−CN−Ru(L)₂-NC−Fe(dppe)Cp][PF₆]_n (n=2, 3) (Cp=1,3-cyclopentadiene, dppe=1,2-bis(diphenylphosphino)ethane, L=2,2’-bipyridine (bpy, 1[PF₆]_n ), 5,5’-dimethyl-2,2’-bipyridyl (5,5’-dmbpy, 2[PF₆]_n ) and 4,4’-dimethyl-2,2’-bipyridyl (4,4’-dmbpy, 3[PF₆]_n )) have been synthesized and fully characterized. The experimental results suggest that all the one-electron oxidation products may belong to Class II–III mixed valence complexes, supported by TDDFT calculations. With the change of the substituents of the bipyridyl ligand on the Ru centre from H, 5,5’-dimethyl to 4,4’-dimethyl, the energy of MMCT for the one-electron oxidation complexes changes in the order: 1³⁺ < 2³⁺ < 3³⁺ , and that for the two-electron oxidation complexes decreases in the order 1⁴⁺ > 3⁴⁺ > 2⁴⁺ . The potential splitting (ΔE_1/2(2)) between the two terminal Fe centres for N[PF₆]₂ are the largest potential splitting for the cyanido-bridged complexes reported so far. This work shows that the smaller potential difference between the bridging and the terminal metal centres would result in the more delocalized mixed valence complex.     

Application of an ion-fitted pseudopotential to HF,H2O,NH3, BeO,and HCl in a Gaussian lobe basis

The core potentials for atoms of atomic numer 1–18 fitted to ion spectra by Chang, Habitz, Pittel, and Schwarz have been extended to the molecular case in a Gaussian lobe basis by using a six-Gaussian (6G-POT ) representation for the exponential factors of the atomic core potentials. In a (9s/5p/1d) basis the 6G-POT one-electron energies, dipole moments, and Mulliken charges are improved over a one-Gaussian potential form for HF, NH₃, and H₂O; BeO also yields good agreement within 2.6% of the experimental bond length. For HCl, the core potential shows larger errors in the dipole moment (7%) and one-electron eigenvalues (2%), but a 75% saving in computer time is realized for HCl compared with only about 35% for first-row systems using the 6G-POT core potentials. Analytical expressions are given to extend the 6G-POT method up to s, p, d, f, and g valence shells.     

A first-principle pseudopotential calculation of the (ns) energy levels of the K atom. II.

We have calculated the energies of the (7s) and (8s) states of the valence electron in the K atom by making use of a pseudopotential based on recently obtained variational solutions of the Thomas–Fermi (TF) equation for neutral atoms, and positive ions. We have chosen trial wave functions, with appropriate parameters, for the valence electron and then minimized the energies of the respective states using the pseudoHamiltonian. The exchange interaction between the K⁺ core and the valence electron has also been considered as a perturbation. Comparison of the calculated (7s) and (8s) energies with the experimental values shows an agreement of about 6% for the former one and of about 5% for the latter one, respectively. With the exchange correction both of these discrepancies are reduced to less than 2%. We conclude that the procedure outlined here is a promising one in dealing with problems involving a highly excited electron outside of a closed-shell ion core, a system for which a more exact quantum-mechanical treatment would be much more difficult.     

Substituent effects in second-row molecules: Basis set performance in calculations of normal valency phosphorus and sulfur compounds

Ab inito molecular orbital calculations of the phosphorus- and sulfur-containing series PH₂X, PH₃X⁺, SHX, and SH₂X⁺ (X = H, CH₃, NH₂, OH, F) have been carried out over a range of Gaussian basis sets and the results (optimized geometrical structures, relative energies, and electron distributions) critically compared. As in first-row molecules there are large discrepancies between substituent interaction energies at different basis set levels, particularly in electron-rich molecules; use of basis sets lower than the supplemented 6-31G basis incurs the risk of obtaining substituent stabilizations with large errors, including the wrong sign. Only a small part of the discrepancies is accounted for by structural differences between the optimized geometries. Supplementation of low level basis sets by d functions frequently leads to exaggerated stabilization energies for π-donor substituents. Poor performance also results from the use of split valence basis sets in which the valence shell electron density is too heavily concentrated in diffuse component of the valence shell functions, again likely to occur in electron-rich molecules. Isodesmic reaction energies are much less sensitive to basis set variation, but d function supplementation is necessary to achieve reliable results, suggesting a marginal valence role for d functions, not merely polarization of the bonding density. Optimized molecular geometries are relatively insensitive to basis set and electron population analysis data, for better-than-minimal bases, are uniform to an unexpected degree.     

Orbitalexponenten von einfachen analytischen Wellenfunktionen der Atome bis zur Kernladungszahl 30

Zusammenfassung Die Orbitalexponenten von einfachen analytischen Atomfunktionen werden über die Bedingung errechnet, daß der Erwartungswert der Einelektronenenergie bezüglich eines effektiven Einelektronenoperators möglichst gleich wird dem Erwartungswert bezüglich desHartree-Fock-Operators. Von den untersuchten Ansätzen geben orthogonalisierteSlater-Funktionen die beste Übereinstimmung mit experimentellen Werten für die Einelektronen- und Gesamtenergien sowie für die Überlappung mitSCF-Funktionen. Diese orthogonalisiertenSlater-Funktionen sind als Linearkombination von (n-l)-Slater-Funktionen angesetzt und enthalten für jede (nl)-Gruppe nur einen einzigen Variationsparameter. Sie erfüllen das Virialtheorem bezüglich eines effektiven Einelektronenpotentials, das auch für mehrgliedrige Funktionen durch eine einzige effektive Kernladung gekennzeichnet ist.

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Orbital exponents of simple analytic wave functions for atoms with atomic numbers up to 30

The orbital exponents of simple analytic atomic functions have been calculated by imposing the condition, that the expectation value of the one-electron energy with respect to an effective one-electron operator should be close to the expectation value with respect to theHartree-Fock-operator. Of the investigated functions, orthogonalizedSlater functions give the best agreement with experimental values for the one-electron and total energies as well as for the overlap withSCF-functions. These orthogonalizedSlater functions are constructed as a linear combination of (n-l)-Slater type orbitals and each (nl) group contains only one variation parameter. These functions fulfill the virial theorem with respect to an effective one-electron potential, which is characterized by a single effective nuclear charge even when the orthogonalizedSlater functions contain more than one term.

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Herrn Prof. Dr. Dr. h. c.H. Nowotny gewidmet.     

Force field for computation of conformational energies,structures, and vibrational frequencies of aromatic polyesters

A CFF93¹ all-atom force field for aromatic polyesters based on ab initio calculations is reported. The force field parameters are derived by fitting to quantum mechanical data which include total energies, first and second derivatives of the total energies, and electrostatic potentials. The valence parameters and the ab initio electrostatic potential (ESP) derived charges are then scaled to correct the systematic errors originating from the truncation of the basis functions and the neglect of electron correlation in the HF/6-31G* calculations. Based on the force field, molecular mechanics calculations are performed for homologues of poly(p-hydroxybenzoic acid) (PHBA) and poly(ethylene terephthalate) (PET). The force field results are compared with available experimental data and the ab initio results. © 1994 by John Wiley & Sons, Inc.     

The extended Koopmans' theorem Fock operator and the generalized overlap amplitude one-electron operator

The wave function of a system may be expanded in terms of eigenfunctions of the N −1 electron Hamiltonian times one-particle functions known as generalized overlap amplitudes (GOAS). The one-electron operator whose eigenfunctions are the GOAS is presented, without using an energy-dependent term as in the one-particle Green function or propagator approach. It is shown that this operator and the extended Koopmans' theorem (EKT) one-electron operator are of similar form, but perform complementary roles. The GOA operator begins with one-electron densities and total energies of N −1 electron states to generate the two-matrix and total energy of an N-electron state. The EKT operator begins with the two-matrix of an N-electron state to generate one-electron densities and ionization potentials (or approximations thereto) for N −1 electron states. However, whereas the EKT orbitals must be linearly independent, no such restriction applies to the GOAS. © 1996 John Wiley & Sons, Inc.     

Core polarization and relativistic effects competition in the first ionization potentials for some systems in the Cu,Ag, and Au isoelectronic sequences

Single-configuration relativistic Hartree–Fock values of the first ionization potentials for Cu through Kr⁷⁺, Ag through I⁶⁺, and Au through Pb³⁺ are computed in “frozen” and “relaxed core” approximations with and without allowance for core polarization. Effects of polarization of the atomic core by the valence electron are included by introducing a polarization potential in the one-electron Hamiltonian of the valence electron. The core polarization potential depends on two parameters, the static dipole polarizability of the core α and the cut-off radius r₀, which are chosen independently of the ionization potential data. It is demonstrated that by including the core polarization potential with α and r₀ parameters, which are simply chosen instead of being empirically fitted, it is still possible to account, on the average, for at least 70% of the discrepancy between the single-configuration relativistic Hartree–Fock ionization potentials and the experiment, a discrepancy usually ascribed to the contribution of valence-core electron correlations, and to bring the theoretical ionization potentials to an average agreement with experiment of around 1%. It can be concluded from this study that for low and medium Z elements the core polarization dominates for neutral systems or systems in low ionization stages, whereas for highly ionized systems the relativistic effects prevail. For heavy elements, however, the core polarization influence is comparable to the relativistic one only for neutral systems, whereas for ions the relativistic effects are overwhelmingly predominant.     

Theoretical study of the valence π → π* excited states of polyacenes: anthracene and naphthacene

The valence π → π ^* excited states of anthracene and naphthacene are studied with multireference perturbation theory with complete active space self-consistent field reference functions. The predicted spectra provide a consistent assignment of all one- and two-photon spectra and T-T spectra of low-lying valence π → π ^* excited states of anthracene and naphthacene. The present theory predicts the valence π → π ^* excitation energies with an accuracy of 0.15 eV for anthracene and of 0.25 eV or better for naphthacene. The excited states of anthracene and naphthacene are compared with those of benzene and naphthalene studied previously. The present calculations predict that, going from anthracene to naphthacene, there is a symmetry reversal of the two lowest singlet state transitions, but not for the triplet, just as indicated by the experimental data. Some general trends of polyacene excited states are discussed based on the calculated results for benzene to naphthacene. Conclusive results obtained for anthracene and naphthacene can be used as a model for understanding the excited states of larger polyacenes. Received: 22 April 1998 / Accepted: 6 July 1998 / Published online: 28 September 1998     

Determination of the local structure and parameters of the one-electron potential from XANES data (inverse problem of XANES theory)

A method of obtaining complex information on the structure of polyatomic systems using experimental data for one-electron quasistationary state (shape resonance) is developed. The method involves the equation for S-matrix poles in the muffintin (MT) approximation. The parameters of the model (intemuclear distances, valence angles, and potential characteristics) are fitted in such a way that the S-matrix poles in a complex energy plane be maximally close to {E-iГ/2}, where E and Fare the energies and widths of the XANES maxima of one-electron origin. Testing the method on a number of objects shows that it determines internuclear distances with an accuracy of 1% and valence angles with an accuracy of 3%. Among the potentials of this type, the empirical potentials obtained are the best for describing shape resonances. The suggested scheme is applicable in determining the microstructure and in the cases where the diffraction methods of structural analysis do not work (unordered systems, molecular adsorption on the surface of solids, etc.). Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 6, pp. 1013–1017, November–December, 1998.     

Ein einfaches Modell zur Beeinflussung der atomaren Spin—Bahn-Kopplung durch einen Ringstrom, 2. Mitt.

In the simple model introduced in¹ the interaction of a ring current in the ground state with the spin—orbit coupling of an one-electron atom is dicussed now. The electron of the atom is taken like a point charge. In those cases where the atom cannot be placed in the middle of the ring in principle the same results are obtained as described in¹ if one replaces the quantum numbern by (n+1) for an excited ring. Fors functions,l=0, we have no interaction.

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Mit 2 Abbildungen     

Configuration-Interaction study of lower excited states of O2: Valence and rydberg characters of the two lowest 3Σu − states

Configuration-interaction calculations, with an extended basis, are carried out on the ground and lower excited states of O₂ and O₂⁺ at and near the equilibrium internuclear distance (R = 2.3 a.u.) of the ground state of O₂. Particular attention has been paid to the two lowest ³Σ_u^? states, and the mixing of the valence and Rydberg characters in these states are studied. The lowest ³Σ_u^? state is a Rydberg-type state for R < 2.3 a.u., but becomes valence-type for R ? 2.3 a.u. The second ³Σ_u^? state, which is 1.6 eV above the lowest ³Σ_u^? at R = 2.3 a.u., changes its character from Rydberg to valence, valence to Rydberg, and then to valence again when R increases from 1.9 to 3.1 a.u. Satisfactory agreement between the calculated and experimental vertical excitation energies is obtained.     

On the usefulness of generalised quantum chemical valence parameters in monitoring the course of a chemical reaction: A case study of the photochemical decomposition of HNO in excited states

A variant of the orthogonal gradient method of orbital optimization in the INDO-MCSCF framework has been used to study the photochemical decomposition of the HNO molecule into H + NO in the lowest^1.3A″ states. A complete geometry optimization has been carried out at all points of the reaction path which appears to be almost barrierless. The one-electron density matrix extracted from the optimized wavefunction at each point has been used to generate the relevant sets of quantum chemical valence parameters. A sharp transition is noted in the N-H bond order and hydrogen free valence index when plotted as functions of r_NH. This enables us to locate the transition region easily.     

3J(HH)?Pμ,ν correlation for planar 7-membered cyclic π-systems—structural effects on 3J(HH)

It is shown that sterically unperturbed vicinal HH coupling constants in planar 7-membered π-systems correlate linearly with the HMO π-bond order: ³J(HH) = 20.91P_μ,_ν–3.85 (r.m.s. error 0.26 Hz, correlation coefficient =0.988). Systematic deviations from this relationship which most probably originate from valence angle changes are found for fused π-systems containing rings of different size. Model calculations using the CNDO/2 method as well as finite perturbation theory and INDO wave functions support the experimental findings. An improvement of existing ³J(HH)? P_μ,_ν correlations for planar 6-membered rings is possible if CNDO/2 π-bond orders are used instead of HMO or PPP-SCF data.     

Correlation effects to the expectation values of atomic systems

The Hartree-Fock and first natural spin determinants were compared as reference determinants for calculating various one-electron properties such as ρ(0), 〈½?〉, 〈r^?2〉,…, 〈r³〉, and r^?1₁₂〉. Calculations were made on various small atoms and their positive and negative ions. For nearly all the expectation values studied, the first natural spin orbital determinant gave consistently superior results. In particular, the Hartree-Fock functions gave markedly inferior results for some long range properties such as the magnentic susceptibilities of negative ions. The major correlation error in the expectation values is primarily an orbital effect which may be accounted for by including correlation terms in the one-particle Hamiltonian. Such approximate Brueckner or best overlap orbitals should reproduce most one-electron expectation values accurately.