- Fridtjof Nansen's Award for Young Scientists (Fridtjof Nansens belønning for yngre forskere), 1985
The Nansen Fund, the Norwegian Academy of Science and Letters
- Odd Hassel Scholarship (Odd Hassel-stipend), 1989
Norwegian Research Council for Science and Humanities (NAVF)
- Golden Spatula (Den gyldne spatel), 1992
Students' Teaching Award, Department of Chemistry, University of Oslo, Norway
- 12th Annual Charles A. Coulson Lecture, 1999
Department of Chemistry, University of Georgia, Athens, USA
- Norwegian Academy of Science and Letters (Det Norske Videnskaps-Akademi), 2004
elected member to the Mathematics and Sciences Class, Chemistry Group
- International Academy of Quantum Molecular Science (IAQMS), 2005
elected member
- Scientific Board of the World Association of Theoretical and Computational Chemists (WATOC), 2005
elected member
- University of Oslo Research Prize (Universitetet i Oslos forskningspris), 2006
University of Oslo, Norway
- Guldberg–Waage Medal (Guldberg–Waage-medaljen), 2007
Norwegian Chemical Society (Norsk Kjemisk Selskap)
- Centenary Prize, 2007/2008
Royal Society of Chemistry (RSC), UK
- Research Excellence Award, 2010
International Conference on Computational Methods in Sciences and Engineering (ICCMSE), Greece
- ERC Advanced Grant (AdG), 2010
European Research Council (ERC), European Commission
- Award for Outstanding Research (Møbius Prize)
(Norges forskningsråds pris for fremragende forskning (Årets Møbius)), 2011
Research Council of Norway (Norges forskningsråd)
- Very Accurate and Large Computations and Applications (VALCA) — Conference in Honour of Trygve Helgaker, 2013
9–12 June 2013, Strand Hotel, Fevik, Norway
- Special Issue of Molecular Physics in Honour of Trygve Helgaker, 2013
Molecular Physics 111, 1061–1629 (2013)
- 16th Annual Ede Kapuy Memorial Lecture, 2016
Institute of Chemistry, Eötvös Loránd University, Hungary
- Board of the International Academy of Quantum Molecular Science (IAQMS), 2018
elected board member
- Fridtjof Nansen Award for Excellence in Science (Fridtjof Nansens belønning for fremragende forskning), 2019
The Nansen Fund, Norwegian Academy of Science and Letters
- Royal Swedish Academy of Sciences (Kungliga Vetenskapsakademien), 2021
elected foreign member to the Class for chemistry