2.2 EPR simulation
The EPR parameters of L-α-Ala radicals in acidic and alkaline solutions are computed by extracting a sufficient number of representative frames. The computed parameters are averaged and are compared with the experimental data recorded in solution [27-28]. 200 snapshots were extracted along the MD simulations in order to calculate theg -tensor and the hyperfine coupling constants (HFCCs) using the gauge-including projector augmented plane wave (GIPAW) approach [40] as implemented in the QE software packages [40].
In the framework of density functional theory (DFT), the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional has been used for the present calculations [36]. GIPAW pseudopotentials are used and Kohn-Sham wave functions are expanded in a basis of plane waves up to a kinetic cutoff of 50 Ry [41]. Considering the perturbation theory, the g-tensor can be expressed as [42]
(1)
where ge is value for the free-electron (ge = 2.0023193). and are introduced as relativistic mass and gauge corrections respectively which have weak contributions to the g -tensor so that their contributions can be ignored [43]. The main reason for the inclusion of the term in Eq. 1 is to account for the coupling of the orbital Zeeman (OZ) and the spin-orbit coupling (SOC) which is given by [44]:
(2)
where is Bohr magneton; is the spin angular momentum of nucleus , define the position of electron i with respect to the position of nucleus , is the proton number of nuclei; is the spin angular momentum vector of electron j; and are the unperturbed wave-function of the ground state and the n th excited state associated with the energies and respectively.
The HFCC tensor, describing the interaction between spins of unpaired electron and with neighboring nuclear-dipole moments can be divided into two main categories: The isotropic Fermi contact interaction and the anisotropic dipole-dipole interactions. Since, anisotropic part of the HFCC tensor in the dilute and homogenous solution can be neglected, only the isotropic Fermi contact term is considered. The contribution from the Fermi-contact HFCC operator is given by [45]:
(3)
where the quantities and describe g factor and magneton of the nucleus, respectively.
To decouple the effect of solvation, calculations in the solvent (capturing the effects of hydrogen bonding with the water molecules and dynamic solvation on the g -tensor components and HFCCs) are compared with gas-phase calculations. This has been repeated for isolated and radicals in the gas phase, but a stable radical could not be obtained in the gas phase using our level of theory.