Fast inertial relaxation engine in the CRYSTAL code

In the framework of ab initio simulations, the search for energy minimum atomic structures is the first step to perform in studying the properties of a system. One of the most used and efficient optimization algorithms is a quasi-Newton line-search scheme based on the Broyden–Fletcher–Goldfarb–Shanno (Bfgs) Hessian updating formula. However, recent studies [Bitzek et al., Phys. Rev. Lett. 97, 170201 (2006) and Guénolé et al., Comput. Mater. Sci. 175, 109584 (2020)] suggested that minimization methods based on molecular dynamics concepts, such as the Fast Inertial Relaxation Engine (Fire) algorithm, often exhibit better performance and accuracy in finding local minima than line-search based schemes. In the present work, the implementation of Fire, in the framework of Crystal ab initio quantum mechanical simulation package [Dovesi et al., Wiley Interdiscip. Rev.: Comput. Mol. Sci. 8, e1360 (2018)], has been described. Its efficiency and performance in comparison with Bfgs quasi-Newton scheme have been assessed using Hartree–Fock and density functional theory with Perdew–Burke–Ernzerhof and hybrid functionals to model the potential energy surface. Fire shows good convergence behavior for all the considered systems, well reproducing the minimum energy structures obtained by the Bfgs approach. As regards the computational cost, Fire requires more iterations to converge with respect to Bfgs, but each Fire iteration is faster than the Bfgs one. The overall efficiency of Fire improves as the size of the system increased so that this minimization method seems to be very promising for systems without symmetry (space group P1) with a large number of atoms.