Molecular Orbital Theory, Hybridization, and Chemical Bonding

Practice vocabulary flashcards covering the molecular orbital model, valence bond theory, orbital hybridization, bond order calculations, magnetic properties, and second-row homonuclear diatomic molecules.

Valence Bond (VB) Model

A bonding model that describes covalent bonds in terms of localized hybrid atomic orbitals and directional $2e^-$ pairs, consistent with molecular geometry determined by crystallography.

Molecular Orbital (MO) Model

A bonding model that describes electrons as delocalized over the geometry of the entire molecule through linear combinations of atomic orbitals (LCAO), consistent with electronic energy levels determined by molecular spectroscopy.

Limitations of the Localized Electron Model

Theoretical shortcomings including the incorrect assumption that electrons are strictly localized, the necessity of introducing resonance, the inability to effectively handle molecules containing unpaired electrons, and the lack of direct information regarding bond energies.

Molecular Orbitals (MOs)

Mathematical wave functions that share the characteristics of atomic orbitals, can hold a maximum of two electrons with opposite spins, and whose squared wave functions ($\text{WF}^2$) indicate electron probability distributions across a molecule.

Sigma ($\sigma$) Molecular Orbital

A molecular orbital whose electron probability distribution is rotationally symmetric and centered directly along the internuclear axis passing through the two bonded nuclei.

Bonding Molecular Orbital

A molecular orbital that is lower in energy than the atomic orbitals from which it is constructed, concentrating electron probability between the nuclei and favoring bond formation.

Antibonding Molecular Orbital

A molecular orbital, denoted by an asterisk ($*$), that is higher in energy than the parent atomic orbitals, with electron probability concentrated outside the internuclear region, favoring separated atoms.

Conservation of Molecular Orbitals

The quantum mechanical principle dictating that the number of molecular orbitals formed must always equal the number of atomic orbitals used to construct them.

Bond Order

A quantitative indicator of bond strength defined by the formula: $\text{Bond order} = \frac{\text{Number of bonding electrons} - \text{Number of antibonding electrons}}{2}$.

$H_2^-$ Ion Bond Order

A bond order of $\frac{1}{2}$, calculated as $\frac{2 - 1}{2}$ because the ion contains two bonding electrons in $\sigma_{1s}$ and one antibonding electron in $\sigma_{1s}^*$.

Paramagnetism

The magnetic phenomenon wherein a substance is attracted into an inducing magnetic field due to the presence of unpaired electrons.

Diamagnetism

The magnetic phenomenon wherein a substance is not attracted into (or is repelled by) an inducing magnetic field due to all of its electrons being paired.

Net Paramagnetism

The magnetic state observed in any chemical substance that contains both paired and unpaired electrons, where the effect of the unpaired electrons dominates.

Paramagnetism of $B_2$

The magnetic property of the diboron molecule explained by its molecular orbital diagram, in which two valence electrons occupy separate, degenerate $\pi_{2p}$ molecular orbitals with parallel spins.

Instability of $Ne_2$

The nonexistence of the dineon molecule explained by its 16 valence electrons filling both bonding and antibonding orbitals equally, producing a bond order of $\frac{8 - 8}{2} = 0$.

Pi ($\pi$) Bond

A covalent chemical bond formed by the sidewise overlap of two parallel $p$ atomic orbitals, resulting in electron density located above and below the internuclear axis.

$sp$ Hybridization

The combination of one $s$ and one $p$ atomic orbital to produce two equivalent linear hybrid orbitals oriented at an angle of $180^\circ$, as seen in molecules such as $C_2H_2$ and $BeCl_2$.

$sp^2$ Hybridization

The combination of one $s$ and two $p$ atomic orbitals to produce three equivalent trigonal planar hybrid orbitals oriented at angles of $120^\circ$, adopted by atoms in species such as $BH_3$, $C_2H_4$, and the carbonyl carbon in 3-buten-2-one.

$sp^3$ Hybridization

The combination of one $s$ and three $p$ atomic orbitals to produce four equivalent tetrahedral hybrid orbitals with bond angles of approximately $109.5^\circ$, producing four $\sigma$ bonds in saturated hydrocarbons such as $CH_4$ and $C_2H_6$.

Benzene ($C_6H_6$) Pi Electrons

A total of $6$ delocalized electrons that occupy the continuous $\pi$ system formed by overlapping unhybridized $p$ orbitals across the carbon ring.

Bond Strength, Energy, and Length Relationship

The principle that as bond strength decreases, the magnitude of the bond dissociation energy decreases and the bond length increases.

Combination of Hydrogen $1s$ Atomic Orbitals Diagram

The formation of molecular orbitals from two atomic $1s$ orbitals, showing that subtraction ($1s_A - 1s_B$) generates the higher-energy antibonding orbital ($MO_2$) and addition ($1s_A + 1s_B$) generates the lower-energy bonding orbital ($MO_1$).

Period 2 Homonuclear Diatomic MO Summary

A comparative table outlining the valence electron orbital occupancies, magnetism, bond orders ($1$ to $3$), bond dissociation energies ($154\,\text{kJ/mol}$ to $942\,\text{kJ/mol}$), and bond lengths ($110\,\text{pm}$ to $159\,\text{pm}$) for $B_2$, $C_2$, $N_2$, $O_2$, and $F_2$.