Computational Study of the Photochemical Fragmentation of Hydantoin

The mechanism of the photochemical fragmentation reaction is investigated theoretically using the model system, hydantoin, using the CAS(22,16)/6-31G(d) and MP2-CAS-(22,16)/6-311G(d)//CAS(22,16)/6-31G(d) methods. The model investigation demonstrates that the preferred reaction route for the photofragmentation reaction is as follows: hydantoin → Franck-Condon region → conical intersection → fragment photoproducts (i.e., CO, isocyanic acid, and methylenimine). The theoretical finding additionally sug - gests that no organic radicals exist during the fragmentation reaction. Moreover, due to the high activation energy, the theoretical evidences suggest that it would be difficult to yield the three fragments under the thermal reaction. All the above theoretical observations are consistent with the available experimental results.


Introduction
Hydantoins (or 2,4-imidazolidinediones, 1) are known to be useful chemicals in various pharmaceutical and agrochemical fields [1].In order to examine the electronic structure, infrared spectrum, and unimolecular UV-induced photochemistry of the parent hydantoin monomer, Ildiz and co-workers recently reported that upon irradiation at λ = 230 nm, photochemical transformation of matrix-isolated 1 took place leading to formation of CO, isocyanic acid, and methylenimine (Scheme 1) [2].However, since then neither experimental nor theoretical work has been devoted to the study of the photofragmentation mechanism of such five-membered ring heterocyclic molecule.In order to obtain more understanding of the photochemical behaviors of the transformation of hydantoin and their related heterocyclics to various photoproducts, the potential energy surfaces on its both singlet ground state and singlet excited state were investigated by CASSCF and MP2-CAS calculations.It will be shown below that the conical intersection (CI) [3][4][5][6][7][8], whose geometrical structure is fragments-like, plays a crucial role in the unimolecular photochemistry of hydantoin.
It is well established that most photochemical reactions begin from an excited potential surface and then cross over to a lower surface along the reaction route.They subsequently arrive on the ground state surface through a series of radiationless transitions (i.e., CIs).Eventually, they generate the photoproducts on the ground state surface [3][4][5][6][7][8].That is to say, it is the presence of minima and transition states on the ground and excited state that controls the photochemical reactions [3][4][5][6][7][8].

Methodology
The theoretical results of the ab initio complete active space multiconfiguration self-consistent field (CASSCF) level of theory were achieved using the Gaussian 09 software package [9].In this work, six σ, six π, and four nonbonding orbitals were selected as active orbitals.In addition, the optimization of CIs was achieved in the (f-2)-dimensional intersection space using the method of Robb et al. implemented in the Gaussian 09 program [9].As a result, the 22 electrons in 16 orbitals CASSCF method was utilized with the 6-31G(d) basis sets (CAS(22,16)/6-31G(d)) for geometrical optimization.

Discussion
The central feature of the photochemical mechanism of 1 is the location of CI in the ground and excited electronic states.In this work, we shall use the molecular orbital (MO) model as presented in Figure 1 as a basis for the interpretation of the phototransformation mechanism  At the beginning, 1 is promoted to its excited singlet state by a vertical excitation as shown in the left-hand side of Figure 2. Our MP2-CAS vertical excitation energy to the lowest excited S 1 state of 1 was computed to be 127 kcal/mol.However, according to the available experimental report shown in Scheme 1, the experimental wavelength λ = 230 nm (=124.3kcal/mol in energy) [2] is somewhat lower than our computational data.Nevertheless, it is believed that the present calculations should provide a good estimate of the relative energies for the parent hydantoin (1) system.As seen in Figure 2, after the vertical excitation process, 1 is located on the excited singlet surface but still possesses the S 0 (ground state) geometry (FC).From the point reached by the vertical excitation, 1 relaxes to reach an S 1 /S 0 CI, where the photoexcited system decays nonradiatively to S 0 .Examining the geometrical structure of CI given in Figure 2, it is noteworthy that its N 1 ─C 2 , C 2 ─N 3 , and C 4 ─C 5 bond distances were calculated to be 1.439, 3.375, and 1.893 Å, respectively, which strongly imply that these chemical bonds are easily broken due to the node planes appeared between these atoms in the LUMO, as already schematically illustrated in Figure 1.The computational results predicted that the energy of S 1 /S 0 CI lies 106 kcal/mol above 1 and 21 kcal/mol below FC at the MP2-CAS level of theory.Funneling through S 1 /S 0 CI, different reaction pathways on the ground state surface may be anticipated by following the derivative coupling vector or the gradient difference vector directions. 2 Figure 2 shows that the derivative coupling vector is mainly related to the N 1 C 2 , C 2 N 3 , and C 4 C 5 stretching modes that give three kinds of fragment products (i.e., CO, isocyanic acid, and methylenimine) on the S 0 surface.On the other hand, gradient difference vector gives the asymmetric C 2 N 1 C 5 C 4 bending motion that may lead to a vibrationally hot 1-S 0 species.It has to be noted that this photoreaction path is a one-step process (the direct mechanism), which only involves the S 1 /S 0 CI point.Besides, this work predicts that the reaction pathway for the photofragmentation of 1 should be a barrierless route.In consequence, the process of the photochemical reaction path can be represented as follows (Figure 2): This work also examined the thermal reaction (Scheme 1) on the ground state (S 0 ) potential energy surface using the same levels of theory.In spite of the fact that photoexcitation elevates 1 into an excited electronic state, it was already emphasized that the products of the photochemical reaction are influenced by the S 0 potential surface [2].If one searches for transition states on the S 0 surface near the structure of S 1 /S 0 CI, one may obtain TS.From Figure 2, the energy of the TS connecting 1 and Pro on the S 0 surface lies about 20 kcal/mol below that of the S 1 /S 0 CI.It should be mentioned here that the calculated results reveal the energy barriers for 1 → Pro and Pro → 1 are estimated to be 86 and 6.0 kcal/mol, respectively.This theoretical evidence indicates that it would be difficult to generate the three fragments (i.e., CO, isocyanic acid, and methylenimine) under the thermal (dark) reaction, which agrees well with the experimental observations [2].
Besides these, one may argue that it is possible to have radical formation in such a photofragmentation reaction.In fact, the CAS(22,16)/6-31G(d) method has been used to calculate the energies of some radicals (such as HN═C═O• and CO•).Their relative energies, however, are higher than that of the CI (121 kcal/mol, at most 133 kcal/mol).Therefore, the radical mechanism is not considered in this work.

Conclusion
In conclusion, the present theoretical computations demonstrate that upon absorption of a photon of light, the hydantoin (1) is excited vertically to S 1 (FC) via a 1 (π → π*) transition.
Subsequently, the excited 1 can enter an extremely efficient channel.From the CI point, 1 continues its development on the ground state potential surface to yield the photoproduct through either the radiationless path or return to 1 at the singlet ground state.Additionally, the theoretical examinations suggest that no other radicals exist in such a photofragmentation reaction.Also, the theoretical findings indicate that under the thermal procedures, the fragmentation reaction of 1 should be failed.All these theoretical findings can give successful explanations for the available experimental finding [2].

Figure 2
Figure 2 contains all the relative energies of the key points with respect to the energy of the reactant, 1.Moreover, the geometrical structures of these points on the possible mechanistic pathway of Figure 2 are demonstrated in the same figure.

Figure 2 .
Figure 2. Potential energy surfaces for the fragmentation reaction of hydantoin (1).The abbreviations FC, TS, CI, and Pro stand for Franck-Condon, transition state, conical intersection, and products, respectively.The relative energies were obtained at the MP2-CAS-(22,16)/6-311G(d)//CAS(22,16)/6-31G(d) and CAS(22,16)/6-31G(d) (in parentheses) levels of theory.The selected geometrical parameters (Å) of CASSCF optimized structures of the stationary points are also given.Hydrogen is omitted for clarity.The heavy arrows in the TS indicate the main atomic motions in the transition state eigenvector.For more information, see the text.