n→π*-Übergänge in Dicarbonylverbindungen Der Einfluss der n,n- und π*, π*-Wechselwirkung

By CNDO-CI calculations we have found that dicarbonyl compounds exhibit only two n → π* transitions in the visible or near UV. region, instead of four as expected from simpler MO-models. The dominant features of the long-wavelength electronic spectra may be characterized by the relative energy of the two n and the two lowest π* orbitals. In general we distinguish between three cases:

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Gaussian vs. Slater representations of d orbitals: An information theoretic appraisal based on both position and momentum space properties

A detailed appraisal of Gaussian-type orbital (GTO) and Slater-type orbital (STO) expansions of 3d orbitals is carried out for the ²S state of copper—a case that should be maximally unfavorable for STOs. The appraisal is based on a wide variety of both position and momentum space properties and utilizes an information theoretic quality assessment technique. It is found that GTO expansions are not as useful as STO expansions for the prediction of 〈p⁸〉, 〈p⁷〉, and 〈r^?6〉 because these properties probe the functional deficiencies of GTOs at small r and large p. On the other hand, GTO expansions can predict accurate values of large r properties like 〈r⁸〉 despite the fact that their position space asymptotic decay is too fast. Unlike the case of s orbitals in helium, there does not seem to be any consistent ordering between accuracy in position space and accuracy in momentum space. The quality measures are found to be very useful for pinpointing the deficiencies of various expansions. This information enables us to construct easily a new GTO and a new STO expansion that are more accurate than any of the others in the literature. It is suggested that one STO is worth no more than two GTOs in the case of d orbitals.     

A systematic preparation of new contracted Gaussian-type orbitals. IX [54/5], [64/5], [64/6], [74/6], [74/7] and MAXI-1–MAXI-5 from Li to Ne

The new contracted Gaussian-type orbitals (CGTO s) for molecular calculations have been developed from Li to Ne. The CGTO s are minimal type, i.e. composed of two s-type CGTO s, s₁, s₂, and one p-type CGTO , p₁. They are new family of CGTO s given by Tatewaki and Huzinaga, and others. In the previous works three primitive GTO s are used for s₂, which is the main part of the 2s orbital, whereas four primitive GTO s are employed in the present work. The sets generated are [54/5], [64/5], [64/6], [74/6], and [74/7]. In almost all the cases the errors in the 2s and 2p orbital energies are smaller than those of DZ . The resulting 2s orbitals are close to the orbitals of the uncontracted GTO sets, (13/n) and (14/n) of Duijneveldt. It is found that the 2s and 2p orbitals given by [64/6], [74/6], and [74/7] are satisfactorily near to those of Hartree–Fock. The basis sets [54/5], [64/6], and [74/7] are applied to the N₂ molecule in the split valence forms of [5211/311], [6211/3111], and [7211/4111]. Adding the d-type polarization functions from one through three, the quality of the basis sets has been examined. All of the three sets show good behavior and the sets augmented with three d-type polarization functions give almost entirely the same results as the very extended basis set.     

Gaussian orbitals optimized for lower bounds of hydrogenic atoms

Various optimization criteria are compared for the hydrogen atom to find orbitals which improve lower bounds computed from the Weinstein, Temple, and Stevenson-Crawford formulas. Minimization of squared energy deviation, “variance,” is recommended because the resulting lower bound orbitals give excellent lower bounds, converge to the exact wave function, are relatively easy to optimize, and are insensitive to the estimated energy eigenvalue. New linear combinations of Gaussian orbitals which minimize the variance are presented for the 1s, 2s, 2p, 3s, 3p, and 3d orbitals. These orbitals are compared with previous linear combinations with regard to their expectation values and local properties.     

9,10‐Diaminoanthracenes Revisited: The Influence of N‐Substituents on Their Electronic States

The electronic and molecular structures of 9,10‐diamino‐substituted anthracenes with different N‐substituents have been re‐examined. In particular, different N‐substituents influence both the electronic and molecular structures of the oxidized species of 9,10‐diaminoanthracenes. The anthrylene moiety of 9,10‐bis(N,N‐di(p‐anisyl)amino)anthracene retains its planarity during the course of two successive one‐electron oxidations, whereas 9,10‐bis(N,N‐dimethylamino)anthracene and 9,10‐bis(N‐p‐anisyl‐N‐methylamino)anthracene undergo a substantial structural change to a butterfly‐like structure through a two‐electron oxidation process. The structural changes observed for the oxidized states are ascribed to significant differences in the frontier molecular orbitals of the above‐mentioned three kinds of 9,10‐diaminoanthracenes due to different extents of mixing between the amine‐localized and anthrylene‐localized orbitals.     

The electronic structure of borabenzene: Combination of an aromatic π-sextet and a reactive σ-framework

The electronic structure of borabenzene (C₅H₅B, known also as borinane, borinine, borine) is studied using modern valence bond theory in its spin-coupled (SC) form. Three different types of SC wave functions—with six active π orbitals and with four and eight active σ orbitals—are used to describe the π system of the molecule and the σ-bond framework around the boron atom. It is demonstrated that the SC picture of the π space in borabenzene is very similar to that in benzene: The spins of six distorted nonorthogonal 2p_π orbitals are combined in a spin-coupling pattern involving two dominating Kekulétype and three less important Dewar-type Rumer spin functions. This indicates that it is appropriate to consider the π-electron sextet in borabenzene as aromatic and that the reason for the reactivity of this molecule should lie with its σ framework. The two SC models of the σ bonding around B show that the boron-carbon σ bonds in borabenzene involve orbitals are “bent” to the outer side of the six-membered ring. This creates an orbital “hole” at the boron, which should represent the preferred attachment site for Lewis acids. © 1997 John Wiley & Sons, Inc.     

Structural and electronic properties of PbZrxTi1‐xO3 (x = 0.5, 0.375): A quantum chemical study

The structural and electronic properties of the PZT materials PbZr_0.5Ti_0.5O₃ and PbZr_0.375Ti_0.625O₃ were studied by means of a Hartree–Fock quantum chemical semiempirical method that employs a periodic large unit cell (LUC) model. The atomic relaxation observed upon introduction of the Zr impurities resulted in outward oxygen atom displacements along the 〈100〉 direction for the cubic phases and varied oxygen and lead atom movements for the tetragonal structures. For these materials, the conduction bands (CB) were composed mainly of Pb 6p atomic orbitals with less important contributions of Zr 4d and Ti 3d states. The upper valence band (UVB) for the cubic phases was mostly Pb 6s in nature, with minor contribution of O 2p atomic orbitals. The tetragonal phase on the other hand was formed by Pb 6s with some contribution of admixed O 2p with Zr s atomic orbitals. The optical band gap (ΔSCF method) was found to decrease going from the cubic to the tetragonal phase in both titanates. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 95: 37–43, 2003     

Halogénures Alcalins: Un Modèle Incluant une Délocalisation à Courte Distance Application à la Stabilité Relative des Divers Arrangements Cristallins

The introduction of symmetry-adapted hybrid atomic orbitals on the metallic atoms allows us to divide the crystal into elementary cells which contain 8 valence electrons each. These cells are described by linear combinations of the halogen valence shell s and p orbitals and the hybrid orbitals of the nearest metallic atoms which point to the halogen. The electronic delocalization of the halogen ions is very weak (?0.02) for: LiF, NaF, KF, LiCl, NaCI, and KCI. The cell energy in the crystal is obtained by using a first-order perturbative treatment. In agreement with experiment, the f.c.c. type is found more stable than the b.c.c. or the blende type.     

Relativistic molecular orbitals for the double group D3h

Relativistic symmetry orbitals are given for the double group D_3h. For atomic orbitals at the symmetry center a general expression is presented. The atomic orbitals of the s, p_½, and p_3/2 variety outside the center are also considered. The representation matrices are given in explicit form.     

Calculation of Negative Ions of B,C, N,O and F Using Noninteger n Slater Type Orbitals

Combined Hartree‐Fock‐Roothaan calculations have been performed using noninteger n Slater type orbitals for the ground states of the lowest electron configurations 1s²2s²2pⁿ (2 ≤ n ≤ 6) for negative ions of B, C, N, O and F. These results are compared with the corresponding results obtained from the use of integer n Slater type orbitals. All of the nonlinear parameters are fully optimized. The results of calculation of coupling‐projection coefficients, orbital and total energies and virial ratios are presented. It is shown that the noninteger n Slater type orbitals, in general, improve the orbital energies.     

Recursion formulae for calculation of overlap integrals

Multi-ζ Slater-type orbitals are frequently used in molecular orbital calculations. Master formulae and numerical tables are available in literature for overlap integrals between s, p, and d atomic orbitals up to principal quantum number (n) = 3 and for some other selected quantum numbers. However, no master formula or numerical table is available for quantum numbers n = 5 and above and involving ? orbitals. In this article recursion formulae have been presented for the calculation of the overlap integral between any two s, p, d, and ? atomic orbitals formed by a linear combination of Slater-type orbitals. These formulae, when expanded, would give rise to all the master formulae reported in the literature as well as formulae hitherto unreported.     

Extended Hartree–Fock calculations for the helium ground state

The extended Hartree–Fock (EHF) wave function of an n-electron system is defined (Löwdin, Phys. Rev. 97 , 1509 (1955)) as the best Slater determinant built on one-electron spin orbitals having a complete flexibility and projected onto an appropriate symmetry subspace. The configuration interaction equivalent to such a wavefunction for the ¹S state of a two-electron atom is discussed. It is shown that there is in this case an infinite number of solutions to the variational problem with energies lower than that of the usual Hartree–Fock function, and with spin orbitals satisfying all the extremum conditions. Two procedures for obtaining EHF spin orbitals are presented. An application to the ground state of Helium within a basic set made up of 4(s), 3(p₀), 2(d₀) and 1 (f₀) Slater orbitals has produced 90% of the correlation energy.     

On the choice and definition of atomic-orbital bases. I. General considerations; promotion and hybridization; electric dipole moments

After a brief discussion of the physical significance of the choice of the basis in molecular calculations, the nature and definition of an atomic-orbital basis for use in limited calculations is discussed, in view of the possibility of replacing, say, ordinary 2s and 2p Slater orbitals by appropriate hybridized-promoted atomic orbitals. It is indicated that, if the orbitals must be defined in connection with a given interpretation scheme for the behavior of molecules, hybridization and promotion may be necessary. The two kinds of conditions one may wish to impose on a restricted atomic-orbital set are explicitly considered. The first is that the atomic orbitals should be hybrids directed along the bonds and at the same time satisfy the maximum overlap criterion; the other is the requirement that the atomic orbitals should be such that the electric dipole moment of a polyatomic molecule described in terms of a semiempirical bond-orbital scheme should be expressed as the dipole moment of the system of bond charges located at the nuclei. The latter condition is treated in detail, showing that it implies a cancellation of atomic and overlap moments. The equations defining the atomic orbitals satisfying the condition in question are given. In the course of the mathematical treatment some general results concerning the expression of the dipole moment of a molecule and the definition of net atomic charges are given, showing that, for systems where overlap integrals are low, the atomic populations can be taken as sums of the squares of the coefficients of orthogonalized atomic orbitals. Applications of the results will be presented in part II.     

Hulthén and slater type 2d functions in some excited configurations of sulphur and phosphorus

It is shown that a substantial energy improvement is gained by the variational use of Hulthén orbitals, instead of single Slater orbitals, in the 3d shells of some excited configurations of sulphur and phosphorus. The energies obtained are close to those attained with two-term Slater functions. In some cases the radial distribution functions from Hulthén orbitals are as good an approximation of SCF radial distributions as those from two-term Slater orbitals. Single term 2d functions with only one parameter are found to give almost identical energies and radial distribution functions as those obtained from two-parameter Hulthén orbitals. It is shown that the relationship between one-term 2d orbitals and Hulthén orbitals gives a method of enforcing nuclear cusp conditions on the former with little effect on the energy.     

Ab initio study of the transition-metal carbene cations

The geometries and bonding characteristics of the first-row transition-metal carbene cations MCH_2~ were investigated by ab initio molecular orbital theory (HF/LANL2DZ). All of MCH_2~ are coplanar. In the closed shell structures the C bonds to M with double bonds; while in the open shell structures the partial double bonds are formed, because one of the σ and π orbitals is singly occupied. It is mainly the π-type overlap between the 2p_x orbital of C and 4p_x, 3d_(xz), orbitals of M~ that forms the π orbitals. The dissociation energies of C—M bond appear in periodic trend from Sc to Cu. Most of the calculated bond dissociation energies are close to the experimental ones.     

The bonding in the ozone molecule: From a different perspective

A new qualitative treatment of the bonding in ozone is presented. It is based upon a combination of several simple concepts: the nonparticipation of the pairs of electrons tightly held in the atomic 2s orbitals; simple overlap of the 2p orbitals to form sigma bonds; interaction of three 2p orbitals to yield bonding and nonbonding pi molecular orbitals that are populated by electron pairs; and van der Waals repulsion between the two terminal oxygen atoms forcing these atoms apart to yield the bond angle of 117° as a compromise. Both the assumptions and the resulting bonding picture are in accord with the photoelectron spectroscopic data, the results from sophisticated molecular orbital calculations, and the common physical properties of ozone.     

Synthesis and nuclear magnetic resonance spectroscopic studies of 1‐arylpyrroles

A series of m‐ and p‐substituted 1‐phenyl, 1‐benzyl, 1‐benzoyl, and 1‐(2‐phenylethyl)pyrroles was prepared and their ¹H and ¹³C nmr spectroscopic characteristics were examined. In general, good correlations were observed between the chemical shift values of the β? H and the β? C of pyrroles [except 1‐(2‐phenylethyl)pyrroles] and the Hammettt σ. The observation may be explained in terms of the electronic effects of the substituents which are transmitted through bonds and through space by interaction of the p orbitals between β? Cs of the pyrrole ring and m‐ and p? Cs of the phenyl ring. Substituent constants of 1‐pyrrolyl, 1‐pyrrolylmethyl, and 1‐pyrroloyl groups for the ¹H and ¹³C chemical shifts of phenyl ring are also presented.     

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.