In this chapter, we demonstrate how graphics processing units (GPUs) can be used to accelerate large-scale semiempirical quantum-chemical calculations on hybrid CPU-GPU platforms. We examine the computational bottlenecks using a series of calculations on eight proteins with up to 3558 atoms and outline how relevant operations are parallelized and ported to GPUs, making use of multiple devices where possible. Significant speedups are achieved that enable simulations on large systems with thousands of atoms. As an example we present results for geometry optimizations of three representative proteins with α-helix, β-sheet, and random coil structures using several common semiempirical Hamiltonians.
IntroductionSemiempirical quantum chemical methods are cost-effective tools for chemists to study the structure, stability, and spectroscopy of molecules as well as chemical reactions [1] (see also Chapter 3). They are based on the Hartree-Fock method commonly used in ab initio molecular orbital (MO) theory [2]. The different semiempirical models simplify the Hartree-Fock procedure by introducing distinct approximations to the Hamiltonian, neglecting many integrals to speed up computations by several orders of magnitude [3]. The remaining integrals are modeled using empirical functions with adjustable parameters that are calibrated against a large number of accurate experimental or high-level theoretical reference data to make semiempirical methods as reliable and general as possible. These features make semiempirical models well suited to many research areas in chemistry, and enabled a large number of semiempirical applications already in the 1970s and 1980s. Since the 1990s, density functional theory (DFT) has become the major workhorse in computational chemistry [4]. However, considering that semiempirical methods are ∼1000× faster than standard DFT approaches [5], they are still valuable computational tools nowadays, for example, for screening large numbers of drug