DFG Research Grant: Computing Molecular Properties with Controlled Precision Using Multi-Resolution Analysis


The project aims at the accurate description of molecular properties using novel wavelet bases for the wave function. Multi-resolution analysis (MRA) algorithms will be developed that provide a high-quality numerical representation of the correlated molecular wave function.In MRA the basis for each function, i. e. orbital, pair function, or molecular potential, is constructed fully adaptively up to a requested accuracy threshold.This accuracy is maintained throughout the computation and leads to controlled precision in the final results. Orthonormality and compact support of the wavelets avoid several of the drawbacks of conventional wave function representations, such as artificially high scaling with respect to the system size, linear dependencies of the basis functions, basis set incompleteness or basis set superposition error. MRA can be combined with common quantum chemical methods, such as second order perturbation theory (MP2) or the Coupled-Cluster Singles and Doubles (CCSD). By including terms that depend explicitly on the interelectronic distance in the wave function expansion the working equations can be regularized and the numerical stability and performance of the algorithms are improved. The high dimensionality of the wave functions can be overcome by the use of low-rank tensor approximations. Moreover, the removal of the cusps from the wave function also lowers the separation ranks in the tensor approximations. MRA methods are naturally local and low-scaling, which leads to fast algorithms, they fit into modern massively parallel computer architectures, and are thus potentially applicable to large molecules.The objective of the project is to develop correlated quantum chemical methods using MRA, specifically, to develop and implement MRA-CCSD energies, and first order properties for MRA-MP2. Further development of the algorithmic framework will be the second focus of the proposed research. Finally the new methods will be validated and used to investigate physisorption and chemisorption processes of molecules on extended surfaces using a multi-level QM/QM framework.
The project aims at the accurate description of molecular properties using novel wavelet bases for the wave function. Multi-resolution analysis (MRA) algorithms will be developed that provide a high-quality numerical representation of the correlated molecular wave function.In MRA the basis for each function, i. e. orbital, pair function, or molecular potential, is constructed fully adaptively up to a requested accuracy threshold.This accuracy is maintained throughout the computation and leads to controlled precision in the final results. Orthonormality and compact support of the wavelets avoid several of the drawbacks of conventional wave function representations, such as artificially high scaling with respect to the system size, linear dependencies of the basis functions, basis set incompleteness or basis set superposition error. MRA can be combined with common quantum chemical methods, such as second order perturbation theory (MP2) or the Coupled-Cluster Singles and Doubles (CCSD). By including terms that depend explicitly on the interelectronic distance in the wave function expansion the working equations can be regularized and the numerical stability and performance of the algorithms are improved. The high dimensionality of the wave functions can be overcome by the use of low-rank tensor approximations. Moreover, the removal of the cusps from the wave function also lowers the separation ranks in the tensor approximations. MRA methods are naturally local and low-scaling, which leads to fast algorithms, they fit into modern massively parallel computer architectures, and are thus potentially applicable to large molecules.The objective of the project is to develop correlated quantum chemical methods using MRA, specifically, to develop and implement MRA-CCSD energies, and first order properties for MRA-MP2. Further development of the algorithmic framework will be the second focus of the proposed research. Finally the new methods will be validated and used to investigate physisorption and chemisorption processes of molecules on extended surfaces using a multi-level QM/QM framework.


Principal investigators
Bischoff, Florian Dr. (Details) (Theoretical Chemistry)

Duration of project
Start date: 03/2014
End date: 01/2020

Research Areas
Physical Chemistry of Molecules, Liquids and Interfaces, Biophysical Chemistry, Theoretical Chemistry: Electron Structure, Dynamics, Simulation

Last updated on 2022-09-09 at 01:05