# UV Light Absorption

Electrons are excited by ultraviolet light absorption. Woodward-Fieser rules are used to estimate the wavelength of maximum absorbance, $\lambda_{\rm max}$.

The highest occupied molecular orbital (HOMO) is the highest energy level that is occupied by electrons. The lowest unoccupied molecular orbital (LUMO) is the lowest energy level that is not occupied by electrons. LUMO is the lowest energy orbital available to accept a HOMO electron. The number of molecular orbitals is equal to the number of atomic orbitals used to create them. Ultraviolet (UV) light causes an excitation of an electron from the HOMO to the LUMO in conjugated dienes and carbonyls. When the electron is excited into the LUMO, the energy level becomes the HOMO* (pronounced, HOMO-star). Compounds containing two double bonds are known as dienes. A conjugated diene is a diene consisting of two double bonds that are separated by one single bond. In conjugated dienes, the energy gap is smaller, and the wavelength is longer, compared to nonconjugated dienes. In a more conjugated system, the HOMO-LUMO gap or distance between the molecular orbitals is smaller.

Conjugated dienes and carbonyls have a smaller gap between the HOMO and LUMO than an isolated alkene, a nonconjugated alkene. Therefore, conjugated dienes and carbonyls require less energy to excite an electron from the HOMO to the LUMO. Conjugation reduces the HOMO-LUMO gap and shifts ultraviolet absorption to longer wavelengths. As the conjugated system becomes larger, the HOMO-LUMO energy gap narrows, and the wavelength of absorbed light becomes longer. Oxygen (O2) and nitrogen (N2) in the atmosphere, along with isolated alkenes, absorb light at less than 200 nanometers (nm). So, ultraviolet radiation of less than 200 nm is seldom used.

#### HOMO and LUMO Energy States

The Woodward-Fieser rules are a set of empirically derived rules that predict the wavelength of the absorption maximum ($\lambda_{\rm max}$) in an ultraviolet–visible spectrum of a given substance. Each type of conjugated diene or unsaturated carbonyl system has fixed values at which absorption takes place, called the parent or base value. Alkyl and polar substituents add to the base value to obtain the absorption maximum. The $\lambda_{\rm max}$ of the molecule is calculated using the formula:
${\lambda_{\rm max}}=\text{Base Value}+\Sigma\;{\text{Substituent Contributions}}+\;\Sigma\;{\text{Other Contributions}}$

### Sample Conjugated Dienes Base Values for Woodward-Fieser Rules

Structure Description Base Value (nm)
acyclic open chain 214
heteroannular ring conjugated double bonds in different rings 214
homoannular ring conjugated double bonds in the same ring 235

Each structure has a base absorption value.

### Sample Substituent Contributions for Woodward-Fieser Rules

Structure Description Substituent Contribution (nm)
alkyl CnH2n+1 5
ring residues carbon-containing group in a ring that is attached directly to a carbon of the conjugated system 5
exocyclic double bond double bond in which one carbon is part of a ring and the other is not part of the same ring 5
halide ${-}{\rm{Cl}}$, ${-}{\rm{Br}}$ 5
ether ${-}{\rm{OR}}$ 6
thioether ${-}{\rm{SR}}$ 30
double bond extending conjugation ${=}{\rm{C}{-}}$ (with or without substituents) attached to the conjugated system so that it extends the system 30
acetoxy group ${-}{\rm{OCOCH}_3}$ 60

The absorption maximum $\lambda_{\rm max}$ of a structure is the sum of the base absorption value and each substituent contribution multiplied by the number of that type of substituent.

For example, an acyclic diene with two alkyls has ${\lambda_{\rm max}}=214\;\rm{nm}+2(5\;\rm{nm)}=224\;\rm{nm}$. A homoannular ring with three alkyls and a double bond extending conjugate has ${\lambda_{\rm max}}=235\;\rm{nm}+3(5\;\rm{nm)} +30\;\rm{nm}=280\;\rm{nm}$. Cis- or trans- conformation will affect the absorption maximum. For example, cis-1,3-pentadiene has a ${\lambda_{\rm max}}=223\;\rm{nm}$, and trans-1,3-pentadiene has a ${\lambda_{\rm max}}=223.5\;\rm{nm}$.