Symmetry Analysis of Water (H2O) Practice Flashcards

A set of vocabulary flashcards covering the systematic approach to molecular orbital symmetry for water using Group Theory, characters, and SALCs.

Basis Set (H2O Symmetry Analysis)

The set consisting of the two Hydrogen $1s$ orbitals, denoted as ($s_1$, $s_2$), which are physically identical and used as the foundation for determining molecular orbital symmetry.

Unchanged Orbital Shortcut

A method used to find the characters ($\chi$) for a reducible representation by counting how many basis functions remain in their original position after a symmetry operation.

Identity ($E$) Character (H 1s)

For the $s_1$ and $s_2$ basis, both orbitals stay put under identity, resulting in a character of $\chi = 1 + 1 = 2$.

Rotation ($C_2$) Character (H 1s)

In water symmetry, this operation causes $s_1$ and $s_2$ to swap positions, resulting in a character of $\chi = 0 + 0 = 0$.

Reflection ($\sigma_{xz}$) Character (H 1s)

The character for the perpendicular plane reflection where $s_1$ and $s_2$ swap positions, resulting in $\chi = 0 + 0 = 0$.

Reflection ($\sigma_{yz}$) Character (H 1s)

The character for the molecular plane reflection where both $s_1$ and $s_2$ stay put, resulting in $\chi = 1 + 1 = 2$.

Reducible Representation ($\Gamma_{H1s}$)

The combined set of characters for the Hydrogen basis set across all symmetry operations in the $C_{2v}$ group, which is $(2, 0, 0, 2)$.

Order of the Group ($h$)

The total number of symmetry operations in the point group; for the $C_{2v}$ group of water, $h = 4$.

Reduction Formula

A calculation used to decompose a reducible representation into its irreducible components (irreps), defined as $n_{\Gamma} = \frac{1}{h} \sum [ \chi^{\Gamma}(R) \times \chi(R) ]$.

Irreducible Representation (Irreps) for H 1s

The specific symmetry labels that make up the reducible representation of water's hydrogen orbitals, determined to be $A_1 \oplus B_2$.

Projection Formula

A formula used to determine the mathematical shape of symmetry-adapted combinations, defined as $\text{SALC} = \sum [ \chi^{\Gamma}(R) \times (R \times s_1) ]$.

SALC

An acronym for Symmetry Adapted Linear Combination, describing any symmetry-consistent mathematical combination of atomic orbitals.

$A_1$ Symmetry Combination

An in-phase combination of orbitals simplified to $s_1 + s_2$, which bonds with Oxygen $2s$ and $2p_z$ orbitals.

$B_2$ Symmetry Combination

An out-of-phase combination of orbitals simplified to $s_1 - s_2$, which bonds with the Oxygen $2p_y$ orbital.

Oxygen $2p_x$ ($B_1$) Orbital

An orbital that remains non-bonding in the water molecule because it has no matching symmetry in the Hydrogen basis set.