The geometrical shape and the inherent physical/chemical properties seen in molecules can be attributed to atomic and molecular orbitals. Features of molecular structure can be explained by taking into consideration (1) how orbitals interact within a single atom to form hybrid atomic orbitals and (2) how atomic orbitals between different atoms interact, giving rise to molecular orbitals. This module will serve as a reminder of the fundamental concepts of bonding as they relate to molecular structure, as well as an investigation into the complexities of hybridized atomic orbitals
The Localized Electron Bonding Model
What is a chemical bond? The most elementary way to understand the bonding between two or more atoms is to make use of Lewis dot structures; a structure drawn where each valence electron surrounding an atom is symbolized by a dot and each bonding electron is symbolized by a pair of dots or a dash (Wade p.7). In accordance with the observations of G. N. Lewis, atoms having or sharing 8 valence electrons will tend to be in an arrangement of lowest energy (ACS p.11). A more sophisticated approach to understanding bonding is to consider how atomic orbitals within individual atoms interact with one another forming molecular orbitals and subsequent covalent bonding. A complete understanding of the subject involves knowledge of quantum mechanics, wave functions and molecular symmetry. This module will focus on how atomic orbitals on an individual atom can give rise to hybrid atomic orbitals, which define the geometry of the bond, and how hybrid atomic atoms of different atoms come together to form molecular orbitals, which define the geometry of the molecule.
Why do chemical bonds form? The stability of a covalent bond, the bond formed when atomic orbitals of separate atoms interact to form molecular orbitals, results from there being a large amount of electron density in the region of space between the two nuclei (Wade p.44). This region is known as the bonding region and here the electrons are close to both nuclei, subsequently lowering the overall energy.
The Heisenberg Uncertainty Principle
The Heisenberg Uncertainty Principle rationalizes the inability of chemists and physicists alike to simultaneously determine both the position and momentum of an atomic particle in space. In lieu of this, theoretical chemists had to develop methods of calculating the position of an electron in terms of probabilities rather than assigning electrons fixed location about a nucleus (Barret p.2). These calculations are collectively known as quantum mechanics, with the Schrodinger wave equation (ĤΨ = iħ d/dtΨ) being the quantum mechanic calculation of greatest interest to orbital symmetry. Solving the Schrodinger wave equation gives the shapes of atomic orbitals represented graphically as the probability of finding an electron residing in a region of space about an atom.
Orbitals and Hybridization
Valence Bond theory describes the formation of a chemical bond in terms of overlapping between atomic orbitals. The 1s orbital of hydrogen, for example, can overlap in-phase and combine constructively to form a molecular orbital called a sigma bond.
Furthermore, a 1s orbital is analogous to the fundamental vibration of a guitar string. The wave function is seemingly positive and negative simultaneously. The effect of squaring the wave function gives the distribution of electron density, which can be used to graphically represent the spherical symmetry of an s orbital.
Atomic orbitals can interact to form new molecular orbitals but let us first consider that orbitals within an individual atom can interact amongst themselves giving rise to hybridized atomic orbitals. Yielding a sp hybrid orbital with an electron density predominately concentrated toward one side of the atom. Molecular orbital theory dictates that the number of hybrid orbitals produced must equal the sum of the orbitals that underwent hybridization and be it that we started with one s orbital and one p orbital (for a total of two orbitals) we must finish with a total of two hybrid sp orbitals.
The final result of this hybridization is a pair of directional sp hybrid orbitals pointed in opposite directions, providing enough electron density in the bonding regions to provoke a sigma bond to both the left and the right of the atom. These 2 sp hybrid orbitals generate a bond angle of 180˚, creating a bond formation with linear geometry. Lastly, the degree of orbital hybridization is governed by the number of attachments (ligands) found on a central atom, lone pairs of electrons included. Table 1.1 provides a summary of orbital hybridization wherein the number of ligands attached to a central molecule correlates to the molecules geometry.
Table 1.1 Summary of hybridization
As discussed, molecular orbitals form as a result of constructive & destructive wave overlap of atomic orbitals between different atoms as well as the potential for atomic orbitals contained within an atom can combine amongst themselves giving rise to hybrid atomic orbitals. It becomes prudent then to consider the spatial orientation of atomic orbitals during the interaction of orbitals on different atoms in the formation of chemical bonds.
The chemical bonding of compounds with triple bonds, such as alkynes, can be expounded by sp hybridization. Inspection of the electron configuration of carbon reveals that the electrons in the 2s orbital mix with only one of the three available p orbitals. This results in two hybrid sp orbitals and two unaltered p orbitals. C2H2, for instance, is held together then by the overlap of adjacent/approaching sp-sp hybrid orbitals on each carbon atom. The bond that ultimately forms is a sigma bond complemented by additional pi bonds formed by p-p orbital overlap; triple bonds are actually composed of two different types of bonds, sigma and pi. Each carbon also bonds to a hydrogen by means of a sigma bond formed this time by s-sp orbital overlap.
1. Using the space provided please draw a) an s orbital & all three appropriately labeled p orbitals and b) the product(s) of their hybridization.
2. The constructive overlap between orbitals of Hydrogen forming sigma bonds was discussed. Please describe the sigma* anti-bonding orbital that results from destructive overlap.
3. Please a) draw both the Lewis Dot and VSEPR structure of CO2 labeling the hybridization and bond angle b) draw the orbitals that overlap during bond formation of CO2 c) identify all the symmetry elements.
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