Since the conventional Haber-Bosch process for ammonia synthesis confronts with a considerable carbon footprint and high energy consumption, various alternatives are being sought to perform environmentally friendly nitrogen reduction under ambient conditions [1]. One of the promising alternatives is photocatalytic ammonia synthesis and titanium dioxide (TiO$_2$) as a promising photocatalyst due to its enticing properties, such as low price, non-toxicity and high photocatalytic activity [1,2]. In this study, we investigated the nitrogen reduction mechanism on pristine and Ru- loaded TiO$_2$ cluster photocatalysts in the ground state and excited state, respectively.

Density functional theory (DFT) calculations were performed in GPAW using the implemented projector- augmented wave method (PAW) [3], the plane wave basis set, and the PBE functional. To account for van der Waals interactions, the Grimme-D3 correction was also included. Saddle points were determined using the nudged elastic band method (NEB) and confirmed by climbing NEB or a dimer method. Excited state calculations were performed with the maximum overlap method (MOM) [4] and direct optimization (DO) [5] as implemented in GPAW.

Based on the calculated electronic properties of pristine and Ru-doped (TiO$_2$)$_{1--12}$ clusters and the determined adsorption modes of N$_2$, NH$_3$, H and 2H, the Ru-(TiO$_2$)$_3$ cluster was selected as a promising candidate for ammonia synthesis. The adsorption modes showed favorable end-on adsorption of the nitrogen molecule on the clusters, so the focus was on determining the nitrogen reduction mechanism (NRR) via a distal or alternating associative pathway in the ground state and lowest excited state.

[1] K. Ithisuphalap; H. Zhang; L. Guo; Q. Yang; H. Yang; G. Wu Small Methods., 2018, 3, 1800352.

[2] I. Ali; M. Suhail; Z. A. Alothman; A. Alwarthan {RSC} Adv., 2018, 8, 30125--30147.

[3] J. J. Mortensen; L. B. Hansen; K. W. Jacobsen Phys. Rev. B - Condens. Matter Mater. Phys., 2005, 71, 1--11.

[4] A. T. B. Gilbert; N. A. Besley; P. M. W. Gill J. Phys. Chem. A., 2008, 112, 13164--13171.

[5] A. V. Ivanov; G. Levi; E. Jónsson; H. Jónsson J. Chem. Theory Comput., 2021, 17, 503--5049.