Atomic orbitals in molecules

In a molecular environment, the effective atom-like orbitals are expected to be modified by two principal physical effects  

As a simple example, let us first consider the hydrogen fluoride (HF) molecule, using the output from a wavefunction calculation that might be obtained as follows (e.g., for Gaussian input)  

For this closed-shell example (as in the F case of Chapter 2), only one main section of NBO output is produced (rather than separate sections for ot and (3 spin), and each orbital refers to a spatial orbital of occupancy 0-2 (rather than a spin-orbital of occupancy 0-1). 

2 Visualizing Atomic Orbital Interactions with PNAOs 

Population invECBion EOOEbd on 9to n f L P0f ul4tL0n invecBjon found on atom H Z 

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On the other hand, researchers have usually confined themselves to trying to find the best approximation for molecular integrals but generally overlooked the possibility that atomic orbitals in molecules might differ widely from those in the isolated atoms. 

The OCT has recently been extended to cover many orbital effects in the chemical bond and reactivity phenomena [38, 68-70]. The orbital communications have also been used to study the bridge bond order components [71, 72] and the multiple probability scattering phenomena in the framework of the probability-amplitude channel [73]. The implicit bond-dependency origins of the indirect (bridge) interactions between atomic orbitals in molecules have also been investigated [74],... 

As an observation, the coefficients of atomic orbitals in (2.126) are the real ones, i.e., those that fix the size of the lobes of atomic orbitals in associated molecular orbital, therefore having the role of describing the population of those atomic orbitals in molecule. 

Attempts at discerning atomic orbitals in molecules have resulted in several published definitions of hybrid orbitals. 4 Applications of other orbital-related concepts, such as circo-lant orbitals, orbital transformation matrices along reaction paths, and so-called internally consistent canonical orbitals, to analysis of electronic wavefunctions have also been documented in the chemical literature. 

Molecular ion (Section 13 22) In mass spectrometry the species formed by loss of an electron from a molecule Molecular orbital theory (Section 2 4) Theory of chemical bonding in which electrons are assumed to occupy orbitals in molecules much as they occupy orbitals in atoms The molecular orbitals are descnbed as combinations of the or bitals of all of the atoms that make up the molecule Molecularity (Section 4 8) The number of species that react to gether in the same elementary step of a reaction mechanism... 

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. 

We briefly recall here a few basic features of the radial equation for hydrogen-like atoms. Then we discuss the energy dependence of the regular solution of the radial equation near the origin in the case of hydrogen-like as well as polyelectronic atoms. This dependence will turn out to be the most significant aspect of the radial equation for the description of the optimum orbitals in molecules. 

Of particular importance in structural chemistry is the concept of hybridization, that is, the construction of linear combinations of atomic orbitals that transform according to the symmetry of the structure. For the present, a simple illustration is provided by the hybridization of atomic orbitals in a molecule or complex ion of trigonal structure. 

Most of what we know about the structure of atoms and molecules has been obtained by studying the interaction of electromagnetic radiation with matter. Line spectra reveal the existence of shells of different energy where electrons are held in atoms. From the study of molecules by means of infrared spectroscopy we obtain information about vibrational and rotational states of molecules. The types of bonds present, the geometry of the molecule, and even bond lengths may be determined in specific cases. The spectroscopic technique known as photoelectron spectroscopy (PES) has been of enormous importance in determining how electrons are bound in molecules. This technique provides direct information on the energies of molecular orbitals in molecules. 

Fig. 2-2. Formation of molecular orbital levels from atomic orbital levels r = distance between X and Y To - stable atom-atom distance in molecule XY AO= atomicorbital BO = bonding orbital ABO = antibonding orbital.

The double degeneracy of NBMOs in m-[8] has nothing to do with the geometrical symmetry of the molecule, but, rather, with the connectivity of the two radical centres, or the phase relationship of the atomic orbitals in the conjugated system. Therefore, the term topological symmetry has been proposed to describe the connectivity of the carbon atoms carrying the n-electrons and the periodicity of the Jt-orbitals in this class of non-Kekule hydrocarbons. 

Molecular Orbital Theory Model. Oxygen and hydrogen atoms in H2O are held together by a covalent bond. According to the quantum molecular orbital theory of covalent bonding between atoms, electrons in molecules occupy molecular orbitals that are described, using quantum mechanical language, by a linear combination of... 

The cross terms (df)0(d,), with i j in Eq. (10.3) do not appear in the case of the isolated atom for which the electron density is the sum of the square of the atomic orbitals. In the molecular case, the cross terms will only be nonzero for orbitals belonging to the same representation of the point group of the molecule, like the eg orbitals in the case of trigonal site symmetry discussed above. In the square-planar point group D4h(4/m mm), the orbitals have alg, blg, b2g, and eg symmetry, and no such mixing occurs. 

Figure 4.1 The c and n orbital overlaps between 2p atomic orbitals in the formation of some diatomic molecules...

The basis of the VSEPR theory is that the shape of a molecule (or the geometry around any particular atom connected to at least two other atoms) is assumed to be dependent upon the minimization of the repulsive forces operating between the pairs of sigma (a) valence electrons. This is an important restriction. Any pi (7t) or delta (8) pairs are discounted in arriving at a decision about the molecular shape. The terms sigma , pi and delta refer to the type of overlap undertaken by the contributory atomic orbitals in producing the molecular orbitals, and are referred to by their Greek-letter symbols in the remainder of the book. 

Classify the atomic orbitals in the valency shell of the central atom with respect to the point group of the molecule. 

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