Highly efficient time-domain quantum chemistry algorithms

Lead Research Organisation: University of Oxford
Department Name: Oxford e-Research Centre

Abstract

The current state of Theoretical and Computational Chemistry is a paradox -- the fundamental equations governing physical reality in the chemical energy range (1-100 eV) are known completely, yet their exact solutions are in most cases far too complex to be computed: the best we can currently do, even with the largest modern supercomputers, is about the size of the benzene molecule.

This basic computational problem is solved using physical approximations: calculating a given property to a given accuracy is often a much simpler task than obtaining the full molecular wavefunction. Computational Chemistry currently employs a large array of such approximations -- from the crudest (molecular dynamics) to medium accuracy (semi-empirics and density functional theory) to high accuracy (configuration interaction and high-order preturbation theory) to extreme precision (full configuration interaction). The primary parameter that makes an approximation computable is known as "scaling": polynomial (ideally linear) scaling makes an approximation computationally acceptable, whereas exponential scaling generally means that further theoretical work is required before meaningful calculations can be performed.

This project will enable knowledge transfer between three sub-disciplines of Computational Chemistry -- time-domain electronic structure theory, spin dynamics and density matrix renormalization group (DMRG) -- that will bring some of the exponentially scaling computation stages down to polynomial scaling. Specifically, the latest DMRG algorithms will be adopted for dissipative spin dynamics (Cornell --> Oxford, Edinburgh), the state space restriction algorithms from spin dynamics will be adopted for time-domain electronic structure theory (Oxford, Edinburgh --> Stanford, Bristol) and the tensor factorization algorithms used in electronic structure theory will be applied to spin dynamics (Bristol, Cornell, Cardiff --> Edinburgh, Oxford). The six research groups (two US groups and four UK groups) involved in this project have extensive independent publication records on the subjects listed above, and view the possibility of joining forces on the computational scaling problem as a crucial opportunity in the ongoing effort towards improving the efficiency of Quantum Chemistry algorithms.

Faster and more accurate simulation algorithms benefit all application areas of Quantum Chemistry -- computational drug design, biomolecular structure determination, MRI contrast agent design, metabolomics, magnetic resonance and optical spectroscopy, materials chemistry, etc. Our primary objective is to lift the (presently rather low) ceiling of what is possible to accurately compute using Quantum Chemistry techniques.

Planned Impact

Just as computation in general has become the cornerstone of scientific discovery, Computational Chemistry has become critical for a broad range of applications from biomolecular systems, to nanotechnology and new materials. The impact goes beyond scientific discovery to include both economic and social impact - increasingly, new technological schemes are evaluated in silico, environmental impact assessments are assisted by modelling, and money is saved whilst animal lives are spared by theoretical pre-screening of molecules before running a pharmaceutical experiment.

This is a low-risk, high-impact project - the basic physics is done, tested and published, the various software prototypes were shown to work well in their respective applicaion areas, and we now seek to amplify their usefulness by adopting them in the adjacent areas of Computational Chemistry. As with any improvement in simulation technology, it is likely that the results of this research will yield patentable and commercially exploitable technology. Our current plan, however, is to release the findings into the public domain without patenting (as open-source software and academic papers), so as to maximize their positive impact on the relevant scientific and technological areas. The software that will be developed in this project can be described as basic theoretical infrastructure that will benefit the whole of Chemistry and related areas of research.

Publications

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Edwards LJ (2014) Quantum mechanical NMR simulation algorithm for protein-size spin systems. in Journal of magnetic resonance (San Diego, Calif. : 1997)

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Edwards LJ (2013) Grid-free powder averages: on the applications of the Fokker-Planck equation to solid state NMR. in Journal of magnetic resonance (San Diego, Calif. : 1997)

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Edwards LJ (2014) Simulation of coherence selection by pulsed field gradients in liquid-state NMR using an auxiliary matrix formalism. in Journal of magnetic resonance (San Diego, Calif. : 1997)

 
Description The transatlantic research network that we sought to establish with EPSRC support has been created. Joint research is currently ongoing between Kuprov group (UK) and Chan group (US) on the Density Matrix Renormalization Group technique in Quantum Chemistry and Magnetic Resonance; a joint review is being written (and will be submitted for publication by Easter 2013) by Leimkuhler group (UK) and Kuprov group (UK) on highly efficient time domain simulation methods for Magnetic Resonance systems; the following research visits have taken place with the purpose of knowledge transfer, joint investigations and initiation of collaborative research projects:



1. Kuprov group (UK) to Chan group (US) -- on DMRG techniques;

2. Leimkuhler group (UK) to Martinez group (US) -- on time-domain Quantum Chemistry;

3. Kuprov group (UK) to Martinez group (US) -- on time-domain Quantum Chemistry;

4. Leimkuhler group (UK) to Kuprov group (UK) -- on Magnetic Resonance simulations;

5. Manby group (UK) to Kuprov group (UK) -- on time-domain Quantum Chemistry;

6. Kuprov group (UK) to Knowles group (UK) -- on time-domain Quantum Chemistry.



As per the original Research objectives:



1. Chebyshev propagation methods developed by Leimkuhler group have been adopted and implemented into the Spinach software package by Kuprov group. The package has been released as Open Source by Kuprov group (http://spindynamics.org). The above mentioned literature review refers to this topic.



2. DMRG method was evaluated for use in Magnetic Resonance by Kuprov group and Chan group, a DMRG module for the Spinach library has been written and released as Open Source by Kuprov group (http://spindynamics.org). Research in this direction continues and will likely lead to a fully fledged joint application for research support on this topic.



3. Time-domain spin dynamics simulation techniques developed by Kuprov group were evaluated by Martinez group for Quantum Chemistry systems and found to yield some improvements to the calculation efficiency. Research in this direction continues.



4. Adaptive basis shaping techniques were evaluated by all project participants. Significant similarities were found in the approaches developed independently by the Magnetic Resonance and Quantum Chemistry communities. A decision was made to implement the Multiple Spawning method from Martinez Group for Magnetic Resonance systems and evaluate its performance -- this is presently in progress.



5. A detailed presentation of calculation methods relying on the dissipative nature of Magnetic Resonance dynamics was made by Kuprov group (UK) to Martinez group (US) and Chan group (US). Chan group is presently evaluating the method for spin dynamics simulations using Density Matrix Renormalization Group.



6. Parallel time propagation algorithms for Magnetic Resonance simulations were implemented into the Spinach software library and released as Open Source by Kuprov group (http://spindynamics.org).



In summary, the transatlantic knowledge exchange, research coordination and cross-pollination activities envisaged in the original proposal have been fully realized. The network has been created and is presently busy conducting joint research with the ultimate purpose of delivering joint academic publications and (if necessary) applying for full-scale research funding to both NSF and EPSRC.
Exploitation Route The software and algorithms that came out of this work are being used by other researchers in the area.
Sectors Chemicals,Education

URL http://spindynamics.org
 
Description The algorithms created have been incorporated into Spinach software package (http://spindynamics.org) and published in academic journals.
First Year Of Impact 2014
Sector Chemicals,Digital/Communication/Information Technologies (including Software),Education
Impact Types Cultural,Societal,Economic

 
Title Spin dynamics simulation package 
Description The algorithms resulting from this project have been implemented into the open source simulation package, called Spinach, maintained by Kuprov group (http://spindynamics.org). 
Type Of Technology Software 
Year Produced 2012 
Open Source License? Yes  
Impact See the published papers 
URL http://spindynamics.org