Orbitals and Electronic Structure

Skriver, H. L. (1984). The LMTO Method Muffin-Tin Orbitals and Electronic Structure. Berlin Springer-Verlag. 

Consider atomic hydrogen and its components. In its most common isotopic form, it has one proton and one electron. The mass ratio of these two components is nearly 2000 1. Why are the two parts so different in mass Protons are so massive that they, individually and therefore in assemblages, may be assumed to be stationary. From this the concept of molecular and geometric structure arises bond lengths and angles require fixed positions. The mass of the electron is so low that we should consider electrons inherently delocalized. From this the concept of orbitals and electronic structure unavoidably arises we should not talk about dots and lines that describe fixed electrons. At least as importantly, atoms, molecules, and all the chemical-based reality from legumes to lepidoptera... 

Another example of reduced symmetry is provided by the changes that occur as H2O fragments into OH and H. The a bonding orbitals (ai and b2) and in-plane lone pair (ai) and the a antibonding (ai and b2) of H2O become a orbitals (see the Figure below) the out-of-plane bi lone pair orbital becomes a" (in Appendix IV of Electronic Spectra and Electronic Structure of Polyatomic Molecules, G. Herzberg, Van Nostrand Reinhold Co., New York, N.Y. (1966) tables are given which allow one to determine how particular... 

We have extended the linear combination of Gaussian-type orbitals local-density functional approach to calculate the total energies and electronic structures of helical chain polymers[35]. This method was originally developed for molecular systems[36-40], and extended to two-dimensionally periodic sys-tems[41,42] and chain polymers[34j. The one-electron wavefunctions here are constructed from a linear combination of Bloch functions c>>, which are in turn constructed from a linear combination of nuclear-centered Gaussian-type orbitals Xylr) (in ihis case, products of Gaussians and the real solid spherical harmonics). The one-electron density matrix is given by... 

What Do We Need to Know Already This chapter uses atomic orbitals and electron configurations (Chapter 1). It also extends the concept of Lewis structures introduced in Chapter 2. The discussion of polar molecules develops the material on polar bonds described in Section 2.12. 

As in the case of iron chemistry, most valuable information concerning bond properties (anisotropic electron population of molecular orbitals) and local structure may be extracted from quadrupole-split Ru spectra. This has been... 

A distinguishing feature of electronically excited atoms and molecules is that they have one or a few excited orbitals of an electron. The principal properties of these particles are represented by a high internal energy potential localized on the excited orbitals and the structure of electron shell essentially different from the electron ground state. 

Kleier, D. A., and W. N. Lipscomb. 1977. Molecular Orbital Study of Polypeptides. Conformational and Electronic Structure of Polyglycine. Int. J. Quantum Chem. Quantum Biol. Symp. 4, 73-86. 

Perhaps the most fruitful of these studies was the radiolysis of HCo(C0)4 in a Kr matrix (61,62). Free radicals detected in the irradiated material corresponded to processes of H-Co fission, electron capture, H-atom additions and clustering. Initial examination at 77 K or lower temperatures revealed the presence of two radicals, Co(C0)4 and HCo(C0)4 , having similar geometries (IV and V) and electronic structures. Both have practically all of the unpaired spin-density confined to nuclei located on the three-fold axis, in Co 3dz2, C 2s or H Is orbitals. Under certain conditions, a radical product of hydrogen-atom addition, H2Co(C0)3, was observed this species is believed to have a distorted trigonal bipyramidal structure in which the H-atoms occupy apical positions. 

Suppose that by means of an external cause - for example the metal surface of a catalyst - the otherwise empty antibonding orbital of a molecule becomes partially filled. As a result the bond is weakened and may eventually break. Before we discuss the relation between catalysis and electronic structure, we look at bonding in metals. 

Since the start of high school science courses, you have used the periodic table to help you investigate the composition and behaviour of the elements. Your early experiences with the periodic table were limited largely to the first 20 elements, because you could explain their electron structure without the concepts of orbitals and electron configurations. 

Scheme 16.27. Orbital interactions that determine the geometry and electronic structure of 28 and 99. ...

Such a bond, in which the donor molecule (or anion) provides both bonding electrons and the acceptor cation provides the empty orbital, is called a coordinate or dative bond. The resulting aggregation is called a complex. Actually, any molecule with an empty orbital in its valence shell, such as the gas boron trifluoride, can in principle act as an electron pair acceptor, and indeed BF3 reacts with ammonia (which has a lone pair, NH3) to form a complex H3N ->BF3. Our concern here, however, is with metal cations, and these usually form complexes with from 2 to 12 donor molecules at once, depending on the sizes and electronic structures of the cation and donor molecules. The bound donor molecules are called ligands (from the Latin ligare, to bind), and the acceptor and donor species may be regarded as Lewis acids and Lewis bases, respectively. 

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