Overlap, atomic orbitals

In valence-bond theory, we assume that bonds form when unpaired electrons in valence-shell atomic orbitals pair the atomic orbitals overlap end to end to form cr-bonds or side by side to form ir-bonds. 

When N atomic orbitals overlap, they form N molecular orbitals. 

When N valence atomic orbitals overlap, they form N molecular orbitals. The ground-state electron configuration of a molecule is deduced by using the building-up principle to accommodate all the valence electrons in the available molecular orbitals. The bond order is the net number of bonds that hold the molecule together. 

Explain the relevance of atomic orbital overlap and of molecular orbital filling to the strength of the bond formed between two atoms. 

Each atom in a bar of sodium has the same outer 3s orbital containing one electron. The individual atomic orbitals overlap, creating a huge number of molecular orbitals among which the electrons can move freely. This gives sodium and the other metals... 

Summary Ab initio calculated bond dissociation energies of silicon compounds will be discussed by means of atomic ionization energies and atomic orbital overlap. Ring strain energies of C- as well as Si-rings are estimated by homodesmotic reactions. The hybridization concept is critically examined in the case of silicon compounds. From the most important results a set of basic rules will be presented. 

Bond strengths are essentially controlled by valence ionization potentials. In the well established extended Hiickel theory (EHT) products of atomic orbital overlap integrals and valence ionization potentials are used to construct the non-diagonal matrix elements which then appear in the energy eigenvalues. The data in Table 1 fit our second basic rule perfectly. 

A cr orbital can be formed either from two s atomic orbitals, or from one s and one p atomic orbital, or from two p atomic orbitals having a collinear axis of symmetry. The bond formed in this way is called a a bond. A n orbital is formed from two p atomic orbitals overlapping laterally. The resulting bond is called a n bond. For example in ethylene (CH2=CH2), the two carbon atoms are linked by one a and one n bond. Absorption of a photon of appropriate energy can promote one of the n electrons to an antibonding orbital denoted by n. The transition is then called Ti —> 7i. The promotion of a a electron requires a much higher energy (absorption in the far UV) and will not be considered here. 

If many atoms are bound together, for example in a crystal, their atomic orbitals overlap and form energy bands with a high density of states. Different bands may be separated by gaps of forbidden energy for electrons. The calculation of electron levels in the periodic potential of a crystal is a many-electron problem and requires several approximations for a successful solution. 

You know that a covalent bond involves the sharing of a pair of electrons between two atoms each atom contributes one electron to the shared pair. In some cases, such as the hydronium ion, HsO", one atom contributes both of the electrons to the shared pair. The bond in these cases is called a co-ordinate covalent bond. In terms of the quantum mechanical model, a co-ordinate covalent bond forms when a filled atomic orbital overlaps with an empty atomic orbital. Once a co-ordinate bond is formed, it behaves in the same way as any other single covalent bond. The next Sample Problem involves a polyatomic ion with a co-ordinate covalent bond. 

The formation of bonding molecular orbitals by an overlap of atomic orbitals applies not only to the Is orbitals of hydrogen, but also to other atomic orbitals. When the atomic orbitals overlap along the axis of the bond, a covalent bond, called a sigma (a) bond, results. This is normally referred to as end-on overlap. Some examples of the formation of a bonds from overlapping atomic orbitals are shown in the diagrams. 

The atomic orbitals overlap laterally or side-on and form a pi (ti) bond. 

When two atomic orbitals overlap end-on along the axis of the bond, a tr molecular orbital forms. Atomic orbitals that overlap side-on form x molecular orbitals. 

As we have already seen, two molecular orbitals form when two atomic orbitals overlap - a bonding molecular orbital and an antibonding molecular orbital. End-on overlap of atomic orbitals along the axis of the bond results In cr and cr molecular orbitals forming. Slde-on overlap of atomic orbitals at an angle perpendicular to the axis of the bond results In the formation of n and molecular orbitals. 

A strongly stabiliztng interaction between two atoms in which certain of their atomic orbitals overlap, thereby resulting in a region of high electron density. This sharing of two electrons in the orbital by the two bonded atoms describes a molecular orbital. 

In summary, the electron density for HF as described by Eq. (3.15) includes the effects of charge transfer between atoms, atomic orbital overlap, and preferential population of lone-pair orbitals, which are neglected in the independent-atom scattering formalism. 

In the formaldehyde molecule, H2CO, a double bond exists between the carbon and oxygen atoms, (a) What type of hybridization is involved (b) The molecule is found to be planar one bond between the C and O atoms is a cr bond, and the other is a rr bond. With a simple sketch, show the atomic orbital overlap that is responsible for the tt bond. 

Pi bond When atomic orbitals overlap side to side in such away that the resulting molecular orbital is symmetric with the bond axis in only one plane, chemists say that a 7t bond (pi bond) is formed. 

Figure 3.5 Orbital envelope diagrams showing the formation of the bonding and anti-bonding molecular orbitals when two 1s atomic orbitals overlap...

The band of molecular orbitals formed by the 2s orbitals of the lithium atoms, described above, is half filled by the available electrons. Metallic beryllium, with twice the number of electrons, might be expected to have a full 2s band . If that were so the material would not exist, since the anti-bonding half of the band would be fully occupied. Metallic beryllium exists because the band of MOs produced from the 2p atomic orbitals overlaps (in terms of energy) the 2s band. This makes possible the partial filling of both the 2s and the 2p bands, giving metallic beryllium a greater cohesiveness and a higher electrical conductivity than lithium. 

Covalent bonds are formed when atomic orbitals overlap. The overlap of atomic orbitals is called hybridization, and the resulting atomic orbitals are called hybrid orbitals. There are two types of orbital overlap, which form sigma (cr) and pi (tt) bonds. Pi bonds never occur alone without the bonded atoms also being joined by a ct bond. Therefore, a double bond consists of a O bond and a tt bond, whereas a triple bond consists of a ct bond and two tt bonds. A sigma overlap occurs when there is one bonding interaction that results from the overlap of two s orbitals or an s orbital overlaps a p orbital or two p orbitals overlap head to head. A tt overlap occurs only when two bonding interactions result from the sideways overlap of two parallel p... 

When N atomic orbitals overlap, they form N molecular orbitals. In molecular hydrogen, where we are building LCAO-MOs from two atomic orbitals, we expect two molecular orbitals. In the second molecular orbital, the two atomic orbitals interfere destructively where they overlap. This orbital has the form... 

The S matrix is the overlap matrix, whose elements are overlap integrals Sy which are a measure of how well pairs of basis functions (roughly, atomic orbitals) overlap. Perfect overlap, between identical functions on the same atom, corresponds to Su = 1, while zero overlap, between different functions on the same atom or well-separated functions on different atoms, corresponds to Sy = 0. 

Baetzold used extended Hiickel and complete neglect of differential overlap (CNDO) procedures for computing electronic properties of Pd clusters (102, 103). It appeared that Pd aggregates up to 10 atoms have electronic properties that are different than those of bulk palladium. d-Holes are present in small-size clusters such as Pd2 (atomic configuration 4dw) because the diffuse s atomic orbitals overlap strongly and form a low-energy symmetric orbital. In consequence, electrons occupy this molecular orbital, leaving a vacant d orbital. For a catalytic chemist the most important aspect of these theoretical studies is that the electron affinity calculated for a 10-atom Pd cluster is 8.1 eV. This value, compared to the experimental work function of bulk Pd (4.5 eV), means that small Pd clusters would be better than bulk metal as electron acceptors. 

A covalent bond is formed between two atoms together in a molecular structure. It is formed when atomic orbitals overlap to produce a molecular orbital. For example, the formation of a hydrogen molecule (H2) from two hydrogen atoms. Each hydrogen atom has a half-filled Is atomic orbital and when the atoms approach each other, the atomic orbitals interact to produce two MOs (the number of resulting MOs must equal the number of original atomic orbitals) ... 

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