Orbitals, atomic molecular

A basis set is a set of functions used to describe the shape of the orbitals in an atom. Molecular orbitals and entire wave functions are created by taking linear combinations of basis functions and angular functions. Most semiempirical methods use a predehned basis set. When ah initio or density functional theory calculations are done, a basis set must be specihed. Although it is possible to create a basis set from scratch, most calculations are done using existing basis sets. The type of calculation performed and basis set chosen are the two biggest factors in determining the accuracy of results. This chapter discusses these standard basis sets and how to choose an appropriate one. 

You can interpret results, including dipole moments and atomic charges, using the simple concepts and familiar vocabulary of the Linear Combination of Atomic Orbitals (LCAO)-molecular orbital (MO) theory. 

Antibonding Molecular Orbital. A Molecular Orbital that is andbonding between particular atomic centers. The opposite is a Bonding Molecular Orbital. 

The CPHF equations are linear and can be determined by standard matrix operations. The size of the U matrix is the number of occupied orbitals times the number of virtual orbitals, which in general is quite large, and the CPHF equations are normally solved by iterative methods. Furthermore, as illustrated above, the CPHF equations may be formulated either in an atomic orbital or molecular orbital basis. Although the latter has computational advantages in certain cases, the former is more suitable for use in connection with direct methods (where the atomic integrals are calculated as required), as discussed in Section 3.8.5. 

Mueller, C. R., J. Chem. Phys. 19, 1498, Scmilocalized orbitals. II. A comparison of atomic, molecular and semilocalized orbital methods for diatomic hydrogenfluoride. ... 

There are two complementary lines of approach to examining the part played by 3d orbitals in molecular orbital theory and to appreciating current doubts as to their role. On the one hand, there is the question of 3d orbitals in relation to the basic formulation of molecular orbitals by overlapping atomic orbitals on the other hand, there is the question of the effect of including or excluding 3d functions in molecular orbital calculations, particularly of the ab initio type. We shall consider each of these briefly in turn. 

Orbitals, atomic, see Atomic orbitals Orbitals, molecular, see Molecular orbitals Orbital steering mechanism, 220-221 Oxyanion intermediates, 172,181,185,210 Oxyanion hole, 181... 

In molecular orbital theory, electrons occupy orbitals called molecular orbitals that spread throughout the entire molecule. In other words, whereas in the Lewis and valence-bond models of molecular structure the electrons are localized on atoms or between pairs of atoms, in molecular orbital theory all valence electrons are delocalized over the whole molecule, not confined to individual bonds. 

Baerends, E.J., Schwarz, W.H.E., Schwerdtfeger, P. and Snijders, J.G. (1990) Relativistic atomic orbital contractions and expansions magnitudes and explanations. Journal of Physics B-Atomic Molecular and Optical Physics, 23, 3225-3240. 

The Orbitron A Gallery of Atomic Orbitals and Molecular Orbitals... 

According to molecular orbital theory the valence p-orbitals of the oxygen atoms combine to form three bonding and three antibonding orbitals in molecular oxygen, as shown in Fig. 1. 

Isolated F-atom Molecular orbitals Isolated P-atom orbitals of three-center bond p orbitals... 

Representation of each molecular orbital as a linear combination of atomic orbitals (atomic basis sets). Atomic basis sets are usually represented as Slater type orbitals or as combinations of Gaussian functions. The latter is very popular, due to a very fast algorithm for the computation of bielectronic integrals. 

Use the symmetry of the atomic orbitals of the central atom to construct (using appropriate hydrogen group orbitals) the molecular orbital diagrams for the following. 

From this wave function, one sees how even in the early beginning of molecular quantum mechanics, atomic orbitals were used to construct molecular wave functions. This explains why one of the first AIM definitions relied on atomic orbitals. Nowadays, molecular ab initio calculations are usually carried out using basis sets consisting of basis functions that mimic atomic orbitals. Expanding the electron density in the set of natural orbitals and introducing the basis function expansion leads to [15]... 

There exists no uniformity as regards the relations between localized orbitals and molecular symmetry. Consider for example an atomic system consisting of two electrons in an (s) orbital and two electrons in a (2px) orbital, both of which are self-consistent-field orbitals. Since they belong to irreducible representations of the atomic symmetry group, they are in fact the canonical orbitals of this system. Let these two self-consistent-field orbitals be denoted by Cs) and (2p), and let (ft+) and (ft ) denote the two digonal hybrid orbitals defined by... 

In the molecular orbital (MO) theory of covalent bonding, atomic orbitals form molecular orbitals that encompass the entire molecule. 

Equations (l)-(6) constitute a remarkable contribution by Oddershede-Sabin to the improvement of the KT in the analysis of atomic and molecular stopping. The partitioning in the stopping contributions from different atomic/molecular orbitals requires the fundamental assumption implied by equation (5) whereby... 

Like atomic orbitals (AOs), molecular orbitals (MOs) are conveniently described by quantum mechanics theory. Nevertheless, the approach is more complex, because the interaction involves not simply one proton and one electron, as in the case of AOs, but several protons and electrons. For instance, in the simple case of two hydrogen atoms combined in a diatomic molecule, the bulk coulombic energy generated by the various interactions is given by four attractive effects (proton-electron) and two repulsive effects (proton-proton and electron-electron cf figure 1.20) ... 

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