Why is Beta-Carotene Orange?

Beta-carotene is the plant pigment that is responsible for giving carrots their notorious orange hue, but how does this work? When carefully examining beta-carotene, scientists can observe and analyze its chemical structure containing a long chain of alternating carbon-carbon single and double bonds. This formation can be described as a system of conjugated carbon atoms that have delocalized π electrons in 22 unhybridized p-orbitals, which lower the molecule’s overall energy, thus increasing its stability. What exactly does a conjugated system refer to in this case? Within beta-carotene’s structure, carbons 5-26 are considered conjugated, meaning they are a part of an alternating double bond structure in which the p-orbitals overlap with each other across interfering sigma bonds. This occurrence is also known as a conjugative chain, allowing the molecule to absorb light in the visible region of the electromagnetic spectrum.

As electrons gain energy from wavelengths of light causing them to jump across levels, colors are produced that correspond with their ground and excited states. In particular, beta-carotene absorbs wavelengths that are within the range of 450-500 nanometers, meaning it falls in the blue portion of the spectrum. Since white light consists of two complementary colors, human eyes will perceive it as orange, as the reflected orange light directly compliments the blue absorbed light.

According to valence bond theory, all of the carbon atoms in beta-carotene are considered sp3 or sp2 hybridized because of their electron geometry with 4 and 3 domains. Since these bonds are right next to each other, they constructively interfere and form the π system with 22 unpaired electrons and 21 π bonds in-between each unhybridized p-orbital. As a result, the highest occupied molecular orbital (HOMO) for beta-carotene will be half of the amount of the 22 unhybridized electrons because each orbital can hold 2 electrons. Keeping this information in mind, beta-carotene’s HOMO will result in n=11 while the lowest unoccupied molecular orbital (LUMO) is n=12 because it is one energy level higher. These values of HOMO and LUMO can help scientists calculate the wavelength of light required to excite an electron in beta-carotene from n=11 to n=12 using the particle in a box method. First, the Schrodinger’s Equation for particle in a box is used to find (n^2)(h^2)/8(m)(L^2) where m = the mass of one electron (9.109*10^-31), h = Planck’s Constant (6.626*10^-34), and L = the bond length of the structure multiplied by the number of bonds between carbons 5-26 (21*139 = 2919 pm). Then, convert the L value into 2.919*10^-9 m and plug in all values for both energy levels of n. After subtracting n-initial by n-final, we are left with 1.626*10^-9 J which can be used to find the wavelength with the equation E = hc/lambda where c = speed of light (2.998*10^8 m/s). Calculating this value gives us a wavelength of 1.221*^10-6 m or 1221 nm.

The electromagnetic spectrum reveals that 1221 nm falls under the infrared region, but this greatly differs from the predicted experimental wavelength of absorption for beta-carotene. How is this possible? This inconsistency is caused because the particle in a box model is too simple, leading to conjugational error, which makes it insufficient for this type of problem.

Based on this information, we can also compare beta-carotene with a similar structure, vitamin A, to determine its color from its wavelength. Since vitamin A is significantly smaller than beta-carotene and the particle’s box is shorter, it requires a higher band gap, which corresponds with a smaller wavelength value that is needed to excite electrons. Instead of being orange, vitamin A is closer to the ultraviolet portion of the electromagnetic spectrum, meaning it appears colorless and does not absorb the same complementary wavelength as beta-carotene. Despite both beta-carotene and vitamin A having similar chemical structures, they have contrasting energies and wavelengths which reveal their place on the electromagnetic spectrum, thus exposing their different colors.

Works Cited:

“Beta Carotene.” Beta-Carotene, https://www.drugfuture.com/chemdata/beta-carotene.html.

Bradaschia, Filippo. “Components of Electromagnetic Spectrum.” Radio2Space, 9 Dec. 2019, https://www.radio2space.com/components-of-electromagnetic-spectrum/.

Mark Occhipinti, Ph.D. “The Science of Orange-Colored Fruits and Vegetables.” Health, Fitness & Nutrition Certifications and Courses, https://www.afpafitness.com/blog/the-science-of-orange-colored-fruits-and-vegetables.

Newman, Tim. “Vitamin A: Health Benefits and Risks.” Medical News Today, MediLexicon International, https://www.medicalnewstoday.com/articles/219486.