Chem-notes-beyond-alvl 2
Atomic structure and bonding
Chemical Structure and bonding
Definition: Valence electrons typically refer to electrons with the highest
principle quantum number in an atom; i.e. electrons in the electron shell with
the highest energy level in the atom.
Definition: Lone pairs refer to valence electrons in an atom that does not
participate in the bonding in a molecule.
We all know that atoms in molecules form covalent bonds between one another.
Lewis Structure
To explain bonding in molecules before the formulation of the quantum mechanical model of an
atom, scientist Gilbert Lewis proposed the Lewis Structure. This theory explains that during covalent
bonding, atoms come together to share their electrons and each atom seeks to gain a stable octet
(duet for hydrogen) electronic configuration in which all atoms of the molecule has 8 (or 2 for
hydrogen) valence electrons. Covalent bonds are formed when atoms share their electrons and are
represented by straight lines in a Lewis Structure. Lone pairs are represented by dots.
VSEPR theory
After determining the molecule from Lewis Structure, one then can find out the geometry (i.e. shape)
of the molecule through VSEPR theory. VSEPR theory stands for Valence Shell Electron Pair
Repulsion theory. It determines the geometry of the molecule based on the number of σ bonds and
the number of lone pairs in the molecule.
The AXE method is commonly used in electron counting to determine the geometry of the molecule
from VSEPR theory.
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A represents the central atom of the molecule.
X represents the number of σ bonds in the molecule. Please note that double bonds and triple
bonds only contain 1 σ bond and thus are counted as 1.
E represents the number of lone pairs of the central atom.
Steric number is the sum of the number of σ bonds and the number of lone pairs.
Below is a table that shows how the steric number and the number of lone pairs correspond to the
geometry of the molecule.
Note that in the table, the overall 3D shape of the molecule is being drawn.
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The thin straight lines represent the bonds that are in the plane of the paper.
The bold lines represent the bonds that coming out of the plane of the paper.
The dashed lines represent the bonds that are going into the plane of the paper.
Quantum Mechanical Model
However, although these two theories appear to be able to predict the shapes of molecules very
well, there were still many flaws to these two theories. Especially after the quantum model of an
atom was formulated.
Firstly, the theories were unable to explain the geometry of the molecule from the electronic
configuration of the constituent atoms. The VSEPR theory predicts the geometry of the molecule
with regards to the central atom but is unable to explain the shape of the molecule. Moreover, the
introduction of quantum mechanics into the picture has further distorted the view.
The quantum mechanical model of an atom is modification of the Bohr model of an atom. The Bohr
model puts electrons neatly into specified orbitals. The quantum model is developed from the
Heisenberg’s uncertainty principle. According to this principle, we are unable to determine the
position of an electron, but can only predict the probability of finding an electron within a given
space. Thus, the orbitals in Bohr’s model were redefined in the quantum model to be the regions of
space where electrons were most likely to be found. Thus, the s, p, d, f… orbitals were born to define
the specific shapes of the orbitals within the energy shells defined by Bohr. Also, note that the
shapes of s, p, d, f… orbitals were gotten from solving the Schrödinger equation for different atoms.
The simple names s orbital, p orbital, d orbital and f orbital refer to orbitals with angular momentum
quantum number l = 0, 1, 2 and 3 respectively. These names indicate the orbital shape and are used
to describe the electron configurations. They are derived from the characteristics of their
spectroscopic lines: sharp, principal, diffuse, and fundamental, the rest being named in alphabetical
order (omitting j)
Below is a table showing the shapes of orbitals.
Validation of Atomic Orbitals Model
(Copied from Wikipedia)
Under quantum mechanics, each quantum state has a well-defined energy. When applied to atomic
orbitals, this means that each state has a specific energy, and that if an electron is to move between
states, the energy difference is also very fixed.
Consider two states of the Hydrogen atom:
State 1) n=1, l=0, ml=0 and s=+1⁄2
State 2) n=2, l=0, ml=0 and s=+1⁄2
By quantum theory, state 1 has a fixed energy of E1, and state 2 has a fixed energy of E2 with E2 > E1.
This is obvious as state 1 is in the 1s orbital and state 2 is in the 2s orbital and it is given that the 2s
orbital is in a electron shell of higher energy (n=1 vs. n=2).
Now, what would happen if an electron in state 1 were to move to state 2? For this to happen, the
electron would need to gain an amount of energy of exactly E2 - E1. If the electron receives energy
that is less than or greater than this value, it cannot jump from state 1 to state 2 as the electron
cannot jump to somewhere between these two states.
Now, suppose we irradiate the atom with a broad-spectrum of light. Photons that reach the atom
that contain energy of exactly E2 - E1 will be absorbed by the electron in state 1, and that electron
will jump to state 2. However, photons that are greater or lower in energy cannot be absorbed by
the electron, because the electron can only jump to one of the orbitals; i.e. it cannot jump to a state
between orbitals.
The result is that only photons of a specific frequency will be absorbed by the atom. This creates a
line in the spectrum, known as an absorption line, which corresponds to the energy difference
between states 1 and 2.
The atomic orbital model thus predicts the existence of the absorption line, which has been
observed experimentally. This is one of the main validations of the atomic orbital model.
The atomic orbital model is nevertheless an approximation to the full quantum theory, which
recognizes many electron states. The predictions of line spectra are qualitatively useful but are not
quantitatively accurate for atoms and ions other than those containing only one electron.