Silymarin is a natural mixture with beneficial properties for health, specifically due to its antiradical characteristics. The major components of this mixture are silybin (SIL), silychristin (SILYC), isosilybin (ISOSIL), silydianin (SILYD), and taxifolin (TAX). In this report, the electronic properties of these substances are investigated using density functional theory calculations, mainly in order to fully understand the free radical scavenger properties of these compounds. Optimized geometries and Raman spectra are reported. These results could be experimentally useful for identifying some of the major components of the mixture. The relative abundance of deprotonated species under physiological conditions is also included. The free radical scavenger capacity is studied in relation to three mechanisms: the single electron transfer (SET), the radical adduct formation (RAF), and the hydrogen atom transfer (HAT). According to this investigation, the HAT mechanism is the most efficient mechanism for scavenging free radicals for these compounds followed by the RAF mechanism where intramolecular hydrogen bonds are formed in order to stabilize the (•)OOH free radical. A particularly important factor is that none of the compounds being studied showed an outstanding antiradical capacity performance compared to the others. In this sense, silymarin is an interesting mixture with antiradical properties and we now know that one single component should be as effective as the mixture.