The Crystal program for quantum-mechanical simulations of materials has been bridging the realm of molecular quantum chemistry to the realm of solid state physics for many years, since its first public version released back in 1988. This peculiarity stems from the use of atom-centered basis functions within a linear combination of atomic orbitals (LCAO) approach and from the corresponding efficiency in the evaluation of the exact Fock exchange series. In particular, this has led to the implementation of a rich variety of hybrid density functional approximations since 1998. Nowadays, it is acknowledged by a broad community of solid state chemists and physicists that the inclusion of a fraction of Fock exchange in the exchange-correlation potential of the density functional theory is key to a better description of many properties of materials (electronic, magnetic, mechanical, spintronic, lattice-dynamical, etc.). Here, the main developments made to the program in the last five years (i.e., since the previous release, Crystal17) are presented and some of their most noteworthy applications reviewed.

The implementation of an original Born-Oppenheimer molecular dynamics module is presented, which is able to perform simulations of large and complex condensed phase systems for sufficiently long time scales at the level of density functional theory with hybrid functionals, in the microcanonical (NVE) and canonical (NVT) ensembles. The algorithm is fully integrated in the Crystal code, a program for quantum mechanical simulations of materials, whose peculiarity stems from the use of atom-centered basis functions within a linear combination of atomic orbitals to describe the wave function. The corresponding efficiency in the evaluation of the exact Fock exchange series has led to the implementation of a rich variety of hybrid density functionals at a low computational cost. In addition, the molecular dynamics implementation benefits also from the effective MPI parallelization of the code, suited to exploit high-performance computing resources available on current generation supercomputer architectures. Furthermore, the information contained in the trajectory of the dynamics is extracted through a series of postprocessing algorithms that provide the radial distribution function, the diffusion coefficient and the vibrational density of states. In this work, we present a detailed description of the theoretical framework and the algorithmic implementation, followed by a critical evaluation of the accuracy and parallel performance (e.g., strong and weak scaling) of this approach, when ice and liquid water simulations are performed in the microcanonical and canonical ensembles.

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.

Via density functional theory calculations, we devise a novel strain-engineered GeTe₃/In₃SbTe₂ superlattice to reduce the power consumption of interfacial phase change memories.

Spherical harmonic Gaussian-type orbitals and Slater functions can be expressed using spherical coordinates or linear combinations of the appropriate Cartesian functions. General expressions for the transformation coefficients between the two representations are provided. Values for the transformation coefficients are tabulated up to the quantum number ℓ = 10. The formula is applied to construct the Hartree potential by an arbitrary-order multipole expansion.

We discuss the implementation strategy, numerical accuracy, and computational performance of the acceleration of linear algebra operations through graphics processing units (GPUs) for the self-consistent field driver of the Crystal electronic structure package for solid state density functional theory simulations. Accelerated tasks include matrix multiplication, diagonalization, and inversion, as well as Cholesky decomposition. The scaling of the implemented strategy over multiple accelerating devices is assessed in the range of 1–8 GPUs per node and found to be remarkably regular. Tests are performed on three systems: α-quartz, a microporous zeolitic imidazolate framework (ZIF-8), and a giant mesoporous metal–organic framework (bio-MOF). Scaling with system size is investigated via supercells of increasing size of both α-quartz and ZIF-8 (up to 648 and 2208 atoms per cell, respectively). The bio-MOF model structure has 2808 atoms per cell, with 33 672 basis functions. We test the performance of the accelerated code with both generalized gradient approximation (GGA) and hybrid GGA exchange–correlation functionals. The efficiency of the new accelerated code is compared to the previous central processing unit (CPU)-only parallelization strategies based on MPI or MPI/OpenMP within either replicated or distributed memory (i.e., massively parallel) approaches. Such a comparison highlights how the new GPU-accelerated code enables calculations on large systems at a significantly reduced computational cost relative to CPU-only strategies. For instance, we find that for the bio-MOF system, the computing time of the linear algebra tasks from a single GPU is comparable to that from the reference approach in the range of 512–1024 CPU cores and 4–8 nodes.