Atomic orbital chemical bonds

The electron is the lightweight particle that "orbits" outside of the atomic nucleus. Chemical bonding is essentially the interaction of electrons from one atom with the electrons of another atom. The magnitude of the charge on an electron is equal to the charge on a proton. Electrons surround the atom in pathways called orbitals. The inner orbitals surrounding the atom are spherical but the outer orbitals are much more complicated. 

In the recent years, the traditional discussion of chemical bonding in terms of the canonical orbitals has been challenged [1-3]. In fact, in general SCF theory, the definition of orbitals remains ambiguous [4-6] and several localization procedures have been introduced by suitable unitary transformations of the set of canonical orbitals in order to provide a more rigorous mathematical meaning to chemical concepts such as bonded atoms, reactants, chemical bonds, electron shells, and lone electron pairs [7-9]. Yet, the realization that theoretical partitionings are not unique casts a shadow of mistmst over certain definitions [10]. 

Elemental boron exists in a number of allotropic forms of which four (two rhombohedral forms and two tetragonal forms) are well established (Table 5). The structures of all of these allotropic forms of boron are based on various ways of joining B12 icosahedra using the external orbitals on each boron atom. The chemical bonding topology in these B12 icosahedra appears to be exactly analogous to that found in the discrete Bi2Hi2 anion, so that elemental boron provides an example of three-dimensional aromaticity in a refractory material. 

Quantum-mechanical theory describes the behavior of electrons in atoms. Since chemical bonding involves the transfer or sharing of electrons, quantum-mechanical theory helps us understand and describe chemical behavior. As we saw in Chapter 7, electrons in atoms exist within orbitals. An electron configuration for an atom shows the particular orbitals that electrons occupy for that atom. For example, consider the ground state—or lowest energy state—electron configuration for a hydrogen atom ... 

So far, we have assumed that the overlapping orbitals that form chemical bonds are simply the standard p, or d atomic orbitals. Valence bond theory treats the electrons in a molecule as if they occupied these standard atomic orbitals, but this is a major oversimplification. The concept of hybridization in valence bond theory is essentially a step toward recognizing that the orbitals in a molecule are not necessarily the same as the orbitals in an atom. Hybridization is a mathematical procedure in which the standard atomic orbitals are combined to form new atomic orbitals called hybrid orbitals that... 

Covalent bonds are characterized by shared electrons between atoms. Sigma bonds are the strongest type of covalent bonds and are formed by overlapping between atomic orbitals. Pi bonds are weaker covalent chemical bonds where two lobes of an atomic orbital overlap two lobes of another atomic orbital. 

Boranes are typical species with electron-deficient bonds, where a chemical bond has more centers than electrons. The smallest molecule showing this property is diborane. Each of the two B-H-B bonds (shown in Figure 2-60a) contains only two electrons, while the molecular orbital extends over three atoms. A correct representation has to represent the delocalization of the two electrons over three atom centers as shown in Figure 2-60b. Figure 2-60c shows another type of electron-deficient bond. In boron cage compounds, boron-boron bonds share their electron pair with the unoccupied atom orbital of a third boron atom [86]. These types of bonds cannot be accommodated in a single VB model of two-electron/ two-centered bonds. 

A is a parameter that can be varied to give the correct amount of ionic character. Another way to view the valence bond picture is that the incorporation of ionic character corrects the overemphasis that the valence bond treatment places on electron correlation. The molecular orbital wavefimction underestimates electron correlation and requires methods such as configuration interaction to correct for it. Although the presence of ionic structures in species such as H2 appears coimterintuitive to many chemists, such species are widely used to explain certain other phenomena such as the ortho/para or meta directing properties of substituted benzene compounds imder electrophilic attack. Moverover, it has been shown that the ionic structures correspond to the deformation of the atomic orbitals when daey are involved in chemical bonds. 

In the late 1920s, it was shown that the chemical bond existing between two identical hydrogen atoms in H2 can be described mathematically by taking a linear combination of the Is orbitals [Pg.176]

It is easy to see that the full shape of the orbital is better represented by the sum of these two Gaussians, especially at the tail of the cur ve where chemical bonding takes place, than it is by one Gaussian. When we run an STO-2G ab initio calculation on the hydrogen atom using the GAUSSIAN stored parameters rather than supplying oirr own, the input file is... 

The progression of sections leads the reader from the principles of quantum mechanics and several model problems which illustrate these principles and relate to chemical phenomena, through atomic and molecular orbitals, N-electron configurations, states, and term symbols, vibrational and rotational energy levels, photon-induced transitions among various levels, and eventually to computational techniques for treating chemical bonding and reactivity. 

Molecular orbitals (mos) are formed by combining atomic orbitals (aos) of the constituent atoms. This is one of the most important and widely used ideas in quantum chemistry. Much of chemists understanding of chemical bonding, structure, and reactivity is founded on this point of view. 

Likewise, a basis set can be improved by uncontracting some of the outer basis function primitives (individual GTO orbitals). This will always lower the total energy slightly. It will improve the accuracy of chemical predictions if the primitives being uncontracted are those describing the wave function in the middle of a chemical bond. The distance from the nucleus at which a basis function has the most significant effect on the wave function is the distance at which there is a peak in the radial distribution function for that GTO primitive. The formula for a normalized radial GTO primitive in atomic units is... 

If IS offen convenienf to speak of the valence electrons of an atom These are the outermost electrons the ones most likely to be involved m chemical bonding and reac tions For second row elements these are the 2s and 2p electrons Because four orbitals (2s 2p 2py 2pf) are involved the maximum number of electrons m the valence shell of any second row element is 8 Neon with all its 2s and 2p orbitals doubly occupied has eight valence electrons and completes the second row of the periodic table... 

The molecular orbital approach to chemical bonding rests on the notion that as elec trons m atoms occupy atomic orbitals electrons m molecules occupy molecular orbitals Just as our first task m writing the electron configuration of an atom is to identify the atomic orbitals that are available to it so too must we first describe the orbitals avail able to a molecule In the molecular orbital method this is done by representing molec ular orbitals as combinations of atomic orbitals the linear combination of atomic orbitals molecular orbital (LCAO MO) method... 

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... 

Valence bond theory (Section 2 3) Theory of chemical bond mg based on overlap of half filled atomic orbitals between two atoms Orbital hybridization is an important element of valence bond theory... 

J Chem. Phys., 52, 431 (1970)] is a relatively inexpensive one and can be used for calculations on quite large molecules. It is minimal in the sense of having the smallest number of functions per atom required to describe the occupied atomic orbitals of that atom. This is not exactly true, since one usually considers Is, 2s, and 2p, i.e., five functions, to construct a minimal basis set for Li and Be, for example, even though the 2p orbital is not occupied in these atoms. The 2sp (2s and 2p), 3sp, 4sp, 3d,. .., etc. orbitals are always lumped together as a shell , however. The minimal basis set thus consists of 1 function for H and He, 5 functions for Li to Ne, 9 functions for Na to Ar, 13 functions for Kand Ca, 18 functions for Sc to Kr,. .., etc. Because the minimal basis set is so small, it generally can not lead to quantitatively accurate results. It does, however, contain the essentials of chemical bonding and many useful qualitative results can be obtained. 

Carbon has six electrons around the atomic core as shown in Fig. 2. Among them two electrons are in the K-shell being the closest position from the centre of atom, and the residual four electrons in the L-shell. TTie former is the Is state and the latter are divided into two states, 2s and 2p. The chemical bonding between neighbouring carbon atoms is undertaken by the L-shell electrons. Three types of chemical bonds in carbon are single bond contributed from one 2s electron and three 2p electrons to be cited as sp bonding, double bond as sp and triple bond as sp from the hybridised atomic-orbital model. 

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