Interpolating wavelets in Kohn-Sham electronic structure calculations

In many biology, chemistry and physics applications quantum mechanics is used to study material and process properties. The methods applied are however expensive in terms of computational as well as memory requirements and scale poorly. In this work we describe an alternative method based on wavelets with better scaling properties. We show how the Kohn-Sham equations, both spin polarized and spin unpolarized, are solved and give a description of pseudopotentials and a preconditioned conjugate gradient method to solve the Hartree potential and the Schrödinger equation. Example calculations for small molecules are given to show the validity of the method

Interpolating wavelets in Kohn-Sham electronic structure calculations

In many biology, chemistry and physics applications quantum mechanics is used to study material and process properties. The methods applied are however expensive in terms of computational as well as memory requirements and scale poorly. In this work we describe an alternative method based on wavelets with better scaling properties. We show how the Kohn-Sham equations, both spin polarized and spin unpolarized, are solved and give a description of pseudopotentials and a preconditioned conjugate gradient method to solve the Hartree potential and the Schrödinger equation. Example calculations for small molecules are given to show the validity of the method

Towards hybrid molecular simulations

In many biology, chemistry and physics applications molecular simulations can be used to study material and process properties. The level of detail needed in such simulations depends on the application. In some cases quantum mechanical simulations are indispensable. However, traditional ab-initio methods, usually employing plane waves or a linear combination of atomic orbitals as a basis, are extremely expensive in terms of computational as well as memory requirements. The well-known fact that electronic wave functions vary much more rapidly near the atomic nuclei than in inter-atomic regions calls for a multi-resolution approach, allowing one to use low resolution and to add extra resolution only in those regions where necessary, so limiting the costs. This is provided by an alternative basis formed of wavelets. Using such a wavelet basis, a method has been developed for solving electronic structure problems that has been applied successfully to 2D quantum dots and 3D molecular systems. In other cases, it suffices to use effective potentials to describe the atomic interaction instead of the use of the electronic structure, enabling the simulation of larger systems. Molecular dynamics simulations with such effective potentials have been used for a systematic study of surface wettability influence on particle and heat flow in nanochannels, showing that the effects at the solid-gas interface are crucial for the behavior of the whole nanochannel. Again in other cases even coarse grained models can be used where the average behavior of several atoms is combined into a single particle. Such a model, refraining from as much detail as possible while maintaining realistic behavior, has been developed for lipids and with this model the dynamics of membranes and vesicle formation have been studied in detail. A disadvantage of molecular dynamics simulations with effective potentials is that no reactions are possible. Therefore a new method has been developed, where molecular dynamics is coupled with stochastic reactions. Using this method, both unilamellar and multilamellar vesicle formation, and vesicle growth, bursting, and healing are shown. Still larger systems can be simulated using other methods, like the direct simulation Monte Carlo method. However, as shown for nanochannels, these methods are not always accurate enough. But, exploiting again that the finest level of detail is often only needed in part of the domain, a hybrid method has been developed coupling molecular dynamics, where needed for accuracy, and direct simulation Monte Carlo, where possible in order to speed up the calculation. Further development of such hybrid simulations will further increase molecular simulation’s scientific role