Theoretical Chemistry for Extended Systems: systematically improvable electronic structure methods
- Arjan Berger (University Paul Sabatier, France)
- Michel Caffarel (University Paul Sabatier, Toulouse, France)
- Thierry Leininger (Laboratoire de Chimie et Physique Quantiques UMR5626 CNRS Université Toulouse 3, France)
- Dirk Andrae (Physikalische und Theoretische Chemie - Institut für Chemie und Biochemie - Freie Universität Berlin, Germany)
- Stefano Evangelisti (Universite Paul Sabatier, France)
Recent years have seen much progress both in Wave-Function (WFT) based and Quantum Monte Carlo (QMC) methods to treat very large or periodic systems. A common theme of the most recent and innovative approaches is the search for fruitful combinations of the best ideas of each world. Most of the standard algorithms of WFT have been revisited in the last five years to optimally exploit new supercomputer architectures and to scale up to an arbitrary number of cores. Important examples include the stochastic MP2 method of Hirata et al. [1-3], the FCI-QMC approach of Alavi and coworkers [4,5], the stochastic coupled-cluster theory , and the stochastic CASSCF method . Quite remarkably the stochastic version has been found on some examples to be capable of surpassing the current limits of the deterministic version. Even in the case of the most standard QMC methods , important effort is currently made  to take full advantage of CI expansions of WFT to construct accurate nodes for the trial wavefunction.
For periodic systems the generalization of WFT and QMC is a crucial step to go beyond the standard DFT, HF, or MP2 levels of theory. This generalization is far from trivial, but some remarkable progress have been recently made. We mention the important work of Ochi and Tsuneyuki  where the standard form of QMC trial wavefunction including an explicitly correlated Jastrow factor is introduced, then is taken into account using a transcorrelated Hamiltonian, and, finally, solved using standard techniques of WFT. The first application of the method to the calculation of optical spectra for solids is very promising. Another important example is the work by Alavi et al. on the extension of FCIQMC to periodic solids . We also mention the recent efforts to combine many-body-perturbation-theory (MBPT) widely used for solids with quantum-chemistry methods, such as coupled cluster theory, in order to describe photoemission spectra of solids .
For these reasons, we think it is timely to bring this new knowledge together in a workshop to assess the problems that are still to be solved, and to learn from each others’ ideas. A major objective will be to compare the emerging approaches of WFT and QMC with the current state-of-the-art tools for calculations of the solid state such as Many-Body Perturbation Theory (MBPT), e.g., Bethe-Salpeter equation  and cumulant expansion .
The aim of this workshop is to bring together experts in WFT, QMC and MBPT from all over the world who are involved in the challenging new developments in the field of large systems and the solid state.
During the workshop, we will try to find answers to the questions mentioned below by having talks of experts in their respective fields and by allowing for ample discussion time between the seminars.
- What are the current capabilities and limits of WFT and QMC approaches to describe large systems and the solid state?
WFT and QMC approaches are known for their great accuracy but their explicit treatment of the Coulomb interaction between electrons makes their application to periodic solids non-trivial. Moreover, WFT and QMC methods are often limited to the calculation of simple observables such as total energies and energy differences, while widely used standard experimental techniques to determine electronic structure, such as photo-emission spectroscopy, have for long been beyond their reach. Therefore, we think it is a good idea to establish the current capabilities and limits of WFT and QMC methods.
- How do the emerging WFT and QMC approaches compare to the state-of-the-art MBPT methods of solid state?
MBPT methods such as GW, and recently also the cumulant expansion, are the state-of-the-art approaches to calculate photo-emission spectra of solids, while the BSE is the state-of-the-art tool for determining their optical absorption spectra. Recently, very promising results for photo-emission and optical spectra have been obtained with WFT and QMC approaches. We think it is important to compare these novel WFT and QMC methods to MBPT and have a discussion on the pros and cons of these different methods.
- What are the similarities and differences between the various approaches? And armed with this knowledge, can we devise a ‘’best-of-both-worlds’’ strategy?
After having established the similarities and in particular the differences between WFT, QMC, and MBPT approaches as well as their respective advantages and disadvantages, it will be interesting to discuss possible combinations of these approaches. What can we learn from each others’ methods and can we combine them to improve precision and comparison with experimental results?
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