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Bivariational Approximations in Quantum Mechanics and Applications to Quantum Chemistry

Total Cost €


EC-Contrib. €






Project "BIVAQUM" data sheet

The following table provides information about the project.


Organization address
address: PROBLEMVEIEN 5-7
city: OSLO
postcode: 313

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Norway [NO]
 Project website
 Total cost 1˙499˙572 €
 EC max contribution 1˙499˙572 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2014-STG
 Funding Scheme ERC-STG
 Starting year 2015
 Duration (year-month-day) from 2015-04-01   to  2020-11-30


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITETET I OSLO NO (OSLO) coordinator 1˙499˙572.00


 Project objective

The standard variational principles (VPs) are cornerstones of quantum mechanics, and one can hardly overestimate their usefulness as tools for generating approximations to the time-independent and time-dependent Schröodinger equations. The aim of the proposal is to study and apply a generalization of these, the bivariational principles (BIVPs), which arise naturally when one does not assume a priori that the system Hamiltonian is Hermitian. This unconventional approach may have transformative impact on development of ab initio methodology, both for electronic structure and dynamics.

The first objective is to establish the mathematical foundation for the BIVPs. This opens up a whole new axis of method development for ab initio approaches. For instance, it is a largely ignored fact that the popular traditional coupled cluster (TCC) method can be neatly formulated with the BIVPs, and TCC is both polynomially scaling with the number of electrons and size-consistent. No “variational” method enjoys these properties simultaneously, indeed this seems to be incompatible with the standard VPs.

Armed with the BIVPs, the project aims to develop new and understand existing ab initio methods. The second objective is thus a systematic multireference coupled cluster theory (MRCC) based on the BIVPs. This is in itself a novel approach that carries large potential benefits and impact. The third and last objective is an implementation of a new coupled-cluster type method where the orbitals are bivariational parameters. This gives a size-consistent hierarchy of approximations to multiconfiguration Hartree--Fock.

The PI's broad contact with and background in scientific disciplines such as applied mathematics and nuclear physics in addition to quantum chemistry increases the feasibility of the project.


year authors and title journal last update
List of publications.
2019 Thomas Bondo Pedersen, Simen Kvaal
Symplectic integration and physical interpretation of time-dependent coupled-cluster theory
published pages: 144106, ISSN: 0021-9606, DOI: 10.1063/1.5085390
The Journal of Chemical Physics 150/14 2020-02-05
2018 Andre Laestadius, Markus Penz, Erik I. Tellgren, Michael Ruggenthaler, Simen Kvaal, Trygve Helgaker
Generalized Kohn–Sham iteration on Banach spaces
published pages: 164103, ISSN: 0021-9606, DOI: 10.1063/1.5037790
The Journal of Chemical Physics 149/16 2020-02-05
2019 Fabian M. Faulstich, Andre Laestadius, Örs Legeza, Reinhold Schneider, Simen Kvaal
Analysis of the Tailored Coupled-Cluster Method in Quantum Chemistry
published pages: 2579-2607, ISSN: 0036-1429, DOI: 10.1137/18m1171436
SIAM Journal on Numerical Analysis 57/6 2020-02-05
2018 Andre Laestadius, Erik I. Tellgren
Density–wave-function mapping in degenerate current-density-functional theory
published pages: , ISSN: 2469-9926, DOI: 10.1103/PhysRevA.97.022514
Physical Review A 97/2 2019-11-15
2018 Erik I. Tellgren, Andre Laestadius, Trygve Helgaker, Simen Kvaal, Andrew M. Teale
Uniform magnetic fields in density-functional theory
published pages: 24101, ISSN: 0021-9606, DOI: 10.1063/1.5007300
The Journal of Chemical Physics 148/2 2019-11-15
2018 Andre Laestadius, Simen Kvaal
Analysis of the Extended Coupled-Cluster Method in Quantum Chemistry
published pages: 660-683, ISSN: 0036-1429, DOI: 10.1137/17M1116611
SIAM Journal on Numerical Analysis 56/2 2019-11-15
2018 Rolf H. Myhre
Demonstrating that the nonorthogonal orbital optimized coupled cluster model converges to full configuration interaction
published pages: 94110, ISSN: 0021-9606, DOI: 10.1063/1.5006160
The Journal of Chemical Physics 148/9 2019-11-15

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