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Spatially extended hybrid methods: a review.

ABSTRACT: Many biological and physical systems exhibit behaviour at multiple spatial, temporal or population scales. Multiscale processes provide challenges when they are to be simulated using numerical techniques. While coarser methods such as partial differential equations are typically fast to simulate, they lack the individual-level detail that may be required in regions of low concentration or small spatial scale. However, to simulate at such an individual level throughout a domain and in regions where concentrations are high can be computationally expensive. Spatially coupled hybrid methods provide a bridge, allowing for multiple representations of the same species in one spatial domain by partitioning space into distinct modelling subdomains. Over the past 20 years, such hybrid methods have risen to prominence, leading to what is now a very active research area across multiple disciplines including chemistry, physics and mathematics. There are three main motivations for undertaking this review. Firstly, we have collated a large number of spatially extended hybrid methods and presented them in a single coherent document, while comparing and contrasting them, so that anyone who requires a multiscale hybrid method will be able to find the most appropriate one for their need. Secondly, we have provided canonical examples with algorithms and accompanying code, serving to demonstrate how these types of methods work in practice. Finally, we have presented papers that employ these methods on real biological and physical problems, demonstrating their utility. We also consider some open research questions in the area of hybrid method development and the future directions for the field.

SUBMITTER: Smith CA

PROVIDER: S-EPMC5832735 | biostudies-literature | 2018 Feb

REPOSITORIES: biostudies-literature

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Spatially extended hybrid methods: a review.

Smith Cameron A CA Yates Christian A CA

Journal of the Royal Society, Interface 20180201 139

Many biological and physical systems exhibit behaviour at multiple spatial, temporal or population scales. Multiscale processes provide challenges when they are to be simulated using numerical techniques. While coarser methods such as partial differential equations are typically fast to simulate, they lack the individual-level detail that may be required in regions of low concentration or small spatial scale. However, to simulate at such an individual level throughout a domain and in regions whe ...[more]

PMID: 29491179

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Project description:Time-dependent density functional theory has become state-of-the-art for describing photophysical and photochemical processes in extended materials because of its affordable cost. The inclusion of exact exchange was shown to be essential for the correct description of the long-range asymptotics of electronic interactions and thus a well-balanced description of valence, Rydberg, and charge-transfer excitations. Several approaches for an efficient treatment of exact exchange have been established for the ground state, while implementations for excited-state properties are rare. Furthermore, the high computational costs required for excited-state properties in comparison to ground-state computations often hinder large-scale applications on periodic systems with hybrid functional accuracy. We therefore propose two approximate schemes for improving computational efficiency for the treatment of exact exchange. Within the auxiliary density matrix method (ADMM), exact exchange is estimated using a relatively small auxiliary basis and the introduced basis set incompleteness error is compensated by an exchange density functional correction term. Benchmark results for a test set of 35 molecules demonstrate that the mean absolute error introduced by ADMM is smaller than 0.3 pm for excited-state bond lengths and in the range of 0.02-0.04 eV for vertical excitation, adiabatic excitation, and fluorescence energies. Computational timings for a series of covalent-organic frameworks demonstrate that a speed-up of at least 1 order of magnitude can be achieved for excited-state geometry optimizations in comparison to conventional hybrid functionals. The second method is to use a semiempirical tight binding approximation for both Coulomb and exchange contributions to the excited-state kernel. This simplified Tamm-Dancoff approximation (sTDA) achieves an accuracy comparable to approximated hybrid density functional theory when referring to highly accurate coupled-cluster reference data. We find that excited-state bond lengths deviate by 1.1 pm on average and mean absolute errors in vertical excitation, adiabatic excitation, and fluorescence energies are in the range of 0.2-0.5 eV. In comparison to ADMM-approximated hybrid functional theory, sTDA accelerates the computation of broad-band excitation spectra by 1 order of magnitude, suggesting its potential use for large-scale screening purposes.

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Spatially extended hybrid methods: a review.

Publications

Spatially extended hybrid methods: a review.

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