research

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quantum chemistry

Simply put, quantum chemistry is concerned with solving the fundamental Schroedinger equation of a molecule consisting of multiple charged nuclei and surrounding electrons which interact via the Coulomb potential.

I develop novel electronic structure methods that defy the exponential scaling of the Hilbert space, but still manage to accurately describe strongly correlated systems, as commonly seen in bond-breaking processes and magnetic systems.

I have made contributions in the recent renaissance of geminal wavefunctions, which can be regarded as a mean-field theory for electron-pairs rather than single electrons, tying in with the Lewis picture of chemical bonding. Opposed to Hartree-Fock theory, full-fledged geminal theory has #P complexity and is therefore intractable for larger systems. In our research, we are developing tractable geminal wavefunction, by borrowing ideas from integrability and coupled-cluster theory. Other methods of interest involve the variational optimization of the 2-body reduced density matrix and methods of symmetry breaking and restoration.

Joint work with: Paul W Ayers, Paul A Johnson, Kasia Boguslawski, Paweł Tecmer, Laurent Lemmens, Patrick Bultinck, Dimitri Van Neck & Diego Alcoba

Selected references

• A New Mean-Field Method Suitable for Strongly Correlated Electrons: Computationally Facile Antisymmetric Products of Nonorthogonal Geminals
  Peter A Limacher, Paul W Ayers, Paul A Johnson, Stijn De Baerdemacker, Dimitri Van Neck, & Patrick Bultinck
  J. Chem. Theory Comp. 9, 1394 (2013)
  [doi:10.1021/ct300902c]

• Efficient description of strongly correlated electrons with mean-field cost
  Katharina Boguslawski, Paweł Tecmer, Paul W Ayers, Patrick Bultinck, Stijn De Baerdemacker, & Dimitri Van Neck
  [doi:10.1103/PhysRevB.89.201106]

• Variational Optimization of the Second-Order Density Matrix Corresponding to a Seniority-Zero Configuration Interaction Wave Function
  Ward Poelmans, Mario Van Raemdonck, Brecht Verstichel, Stijn De Baerdemacker, Alicia Torre, Luis Lain, Gustavo E Massaccesi, Diego R Alcoba, Patrick Bultinck & Dimitri Van Neck
  J. Chem. Theory Comp. 11, 4064 (2015)
  [doi:10.1021/acs.jctc.5b00378]

A large part of quantum chemistry is putting chemical descriptors, such as Lewis bonds, on solid quantum mechanical foundations. The purpose is twofold. It validates those descriptors that have been used for ages in chemistry, and provide possible new building blocks to construct electronic structure methods.

We are developing computational approaches and machine learning algorithms to extract chemical descriptors from exact quantum states at the full Configuration Interaction level.

Joint work with: Guillaume Acke, Niels Billiet, Patrick Bultinck, Farnaz Heidar-Zadeh

Selected references

• Maximum probability domains for Hubbard models
  Guillaume Acke, Stijn De Baerdemacker, Pieter W Claeys, Mario Van Raemdonck, Ward Poelmans, Dimitri Van Neck, & Patrick Bultinck
  Mol. Phys. 114, 1392 (2016)
  [doi:10.1080/00268976.2016.1153742]

• Machine Learning the Hubbard Model
  Niels Billiet
  MSc thesis (Ghent University, 2018)

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