Light or photons can excite electrons in a molecule, leading to creation of electronically excited states. Such processes are ubiquitous in nature, such as, vision, photo-protection of DNA/RNA nucleobases, light harvesting, energy and charger transfer etc. This photoexcitation induces nuclear motion on the excited states, leading the excess energy to dissipate either non-radiatively via internal conversion back down to the ground state, isomerization, and dissociation, or radiatively via fluorescence and phosphorescence. In this dissertation, we investigate the non-radiative processes in organic chromophores that ensue in an ultrafast manner, mediated via conical intersections (CoIn). Description of such excited state processes generally require multi-reference treatment because of quasi-degeneracy near CoIns. Hence, most insight about these processes is typically gained by constructing potential energy surface (PES) using multi-reference electronic structure methods along important reaction coordinates. Nonetheless, the aforementioned static treatment fails to provide any dynamical information, such as, excited state lifetime, state populations, branching ratio, quantum yield etc. In this dissertation, we have gone beyond the static treatment by undertaking computationally expensive non-adiabatic excited state molecular dynamics simulations employing trajectory surface hopping (TSH) methodology on PESs created on-the-fly using multi-reference electronic structure methods. This allows us to compare theoretical results to experimental observables, when possible, strengthening the explanations underlying those processes. Our goal is to examine the effect of structure, and of electronic structure methods on the excited state dynamics. We have examined the non-adiabatic excited state dynamics of cis,cis-1,3-cyclooctadiene (cc-COD), a cyclic diene, in an effort to systematically compare and contrast the dynamics of cc-COD to that of other well studied conjugated molecules. Such exploration is very significant, since the majority of the molecules involved in natural photoexcited processes, include an ethylenic double bond or alternating double bonds creating conjugation. Our calculations have revealed ultrafast sub-ps decay for cc-COD, and have illustrated that the internal conversion dynamics is facilitated by CoIns, dominated by twisting of one of the double bonds and pyramidalization of one of the carbons of that double bond, similar to trans-1,3-butadiene and unlike 1,3-cyclohexadiene (CHD). Our high-level electronic structure calculations have also explained the features in the experimental time-resolved photoelectron spectrum of cc-COD. Another molecule of biological importance, uracil, was also investigated using TSH simulations, by systematically increasing dynamical correlation. We have found that the inclusion of dynamical correlation for uracil leads to an almost barrierless PES on S2, leading to a faster decay and no population trap on this state. Uracil also contains a double bond and the simulations have revealed that the ultrafast relaxation is dominated by an ethylenic twist and pyramidalization of a carbon of that bond, increasing importance of such nuclear motion in photoexcited molecular dynamics. A comparison of the molecules studied have illustrated that the rigid molecules, such as uracil, CHD, have a very local CoIn seam space, whereas cc-COD, which is flexible having many low frequency degrees of freedom, has a non-local or extended CoIn seam space. Overall, the work performed in this dissertation, elucidates the significance of structure and conjugation, in the photoinduced coupled electron-nuclear dynamics in organic molecules. / Chemistry