Iterative diagonalization is the dominant cost of plane-wave density-functional theory (DFT), with search-space orthogonalization scaling particularly quickly with problem size and the number of target states. We present a randomized block Davidson-type eigensolver that replaces Euclidean orthogonalization with randomized Gram-Schmidt in a sketched inner product, requiring only a single pass over the basis while keeping its conditioning bounded independently of the input vectors. This modification changes only the Rayleigh-Ritz step, which becomes a definite generalized Hermitian eigenproblem. Ritz extraction remains exact, preserving true Ritz pairs and the interlacing property that makes each band energy an upper bound on the true one. The method is implemented in mixed precision for CPUs and GPUs from a single Julia code, interfaces matrix-free with DFTK, and is released in the open-source RandESC library. On sparse test problems with a fixed number of eigenpairs, the sketched solver overtakes its deterministic counterpart beyond matrix dimensions of about $2\times 10^4$ and is $25\%$ faster at $5\times 10^5$. In full self-consistent field DFT calculations, however, both Davidson variants outperform the locally optimal block preconditioned conjugate gradient (LOBPCG) reference only by $5$ to $11\%$ in total time, while the additional benefit of sketching is limited. As the number of requested states grows with system size, orthogonalization savings are offset by the generalized eigenproblem. Therefore, the regime in which sketching pays off is set by how the number of wanted states scales with the problem dimension, not by the eigensolver as such.
Moritz Gubler, Taejun Park, Augustin Bussy et al.· 0 citations
One of the distinguishing aspects of CP2K is its seamless integration of diverse structural and transition-state optimization techniques with advanced sampling approaches including Monte Carlo, molecular dynamics, and metadynamics, enabling the efficient exploration of complex potential- and free-energy landscapes, including rare events. These capabilities are combined with a broad hierarchy of energy and force evaluation methods, ranging from classical and machine-learned interaction potentials and mixed quantum-classical multiscale and semiempirical schemes, to highly accurate quantum-mechanical electronic-structure approaches. At the heart of the latter lies the Gaussian and plane-wave framework, along with its augmented all-electron generalization, which have been described in detail in our previous code review [T. D. K\"uhne et al., J. Chem. Phys. 152, 194103 (2020)]. Building on this foundation, the present work revisits the methods within CP2K that turn electronic structure into dynamics, transport, and spectroscopic response. Particular emphasis is placed on the coupling between static response calculations and nuclear motion: spectra may be evaluated at optimized structures, averaged over thermally sampled configurations, obtained from time-correlation functions along ab-initio or path integral molecular trajectories, or followed in real time together with electronic and nuclear dynamics. The same modular structure also enables equilibrium and biased transport simulations, from Kubo-type linear response to open-boundary approaches under external potentials, highlighting CP2K's unique capability to unify quantum chemistry with quantum and statistical mechanics within a versatile, holistic simulation environment.
Jan Wilhelm, Anna-Sophia Hehn, Hossam Elgabarty et al.· 1 citation· ⚡1