F atomic orbital

Carbon atoms in free space have spherical symmetry, but a carbon atom in a molecule is a quite different entity because its charge density may well distort from spherical symmetry. To take account of the finer points of this distortion, we very often need to include d, f,. .. atomic orbitals in the basis set. Such atomic orbitals are referred to as polarization functions because their inclusion would allow a free atom to take account of the polarization induced by an external electric field or by molecule formation. 1 mentioned polarization functions briefly in Section 9.3.1. 

A full quantum mechanical calculation of the simplest dimer ion is a formidible task (—e.g., [F—H... H—F] with 21 electrons). We are forced to examine the matter using various approximations. Using a molecular orbital approach we can view the problem as one of five electrons associated with the several atomic cores. For [F—H... H—F], the amplest MO could be built from 2 P orbitals on F and Is orbitals on H, as in Table I. By symmetry, the orbital coefficients for the two F atomic orbitals will be identical in magnitude as will those of the two H atomic orbitals. The orbital coefficients, cit, can thus be chosen to be positive definite if the sign convention in Table I is used. The MO s should be... 

Jensen, F. Atomic orbital basis sets, WIREs Comput. Mol. Set, 2012, 3, 273-295. 

Table 3.11 The spherical (Uj, equations 3.20) and vector surface (Ujjjj ation 3.21) harmonics for central s-, p-, d- and f-atomic orbitals. 

Fig. 3. Representations of the 3 p and 4 f atomic orbitals showing the nodal surfaces (dotted and heavy lines).

Fig. 1.8 Radial distribution functions, A-Kr R rf, for the 3, 3/> and 3

Figure 2.8 (a) The F atomic orbitals, (b) The HF molecular orbitals, (c) The H atomic orbital, (d) Interaction of H I5 orbital with one of the fluorine p orbitals. The overlap of these two orbitals results in a lowering of the energy of the system. The dotted lines joining (6) to (d) emphasize that it is only the fluorine p orbital which overlaps with the H orbital that has a lower energy. The two pairs of unpaired electrons (unshaded lobes) have the same energy in the molecule that they did on the F atom, since these so-called lone pairs are unperturbed by the presence of the hydrogen atom. 

Different from the contracted Gaussian-type basis functions mentioned later, primitive functions usually have a standardized form to save the effort of developing a different computational program for each basis function. The primitive functions corresponding to s, p, d, and f atomic orbitals are represented analogically to the... 

Most transition metal ions can be coordinated into a polymeric structure. These metal ions have empty or unsaturated d or f atom orbitals (receptors) that can accept electrons from ligand molecules (donors) to form coordination bonds. The first-row transition metal ions, such as, Fe +, Co +, Ni +, and Zn +, usually form labile coordination bonds with ligands in coordinating solvents such as water [23], whereas those of the second- and third-row transition metal ions often form irreversible coordination bonds [24], There are also exceptions, such as some lanthanoid... 

Elemental platinum has electrons occupying s, p, d and f atomic orbitals, i Draw the shape of an s orbital and a p orbital, Label the x, y and z axes on each diagram. [2]... 

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