
Kristiansen, Håkon Emil; Ofstad, Benedicte Sverdrup; Hauge, Eirill Strand; Aurbakken, Einar; Schøyen, Øyvind Sigmundson & Kvaal, Simen
[Show all 7 contributors for this article]
(2022).
Correction to “Linear and Nonlinear Optical Properties from TDOMP2 Theory”.
Journal of Chemical Theory and Computation.
ISSN 15499618.
18(9),
p. 5755–5757.
doi:
10.1021/acs.jctc.2c00830.

Kvaal, Simen
(2022).
Tie evolution using linear combinations of gaussians.

Bodenstein, Tilmann & Kvaal, Simen
(2020).
A multireference coupledcluster method based on the bivariational principle.

Faulstich, Fabian Maximilian; Máté, Mihály; Laestadius, Andre; Csirik, Mihály András; Veis, Libor & Antalik, Andrej
[Show all 11 contributors for this article]
(2019).
Mathematical and numerical aspects of the coupledcluster method tailored by tensor network states.

Faulstich, Fabian Maximilian; Máté, Mihály; Laestadius, Andre; Csirik, Mihály András; Veis, Libor & Antalik, Andrej
[Show all 11 contributors for this article]
(2019).
Numerical and theoretical aspects of the DMRGTCC method exemplified by the nitrogen dimer.

Laestadius, Andre; Penz, Markus; Tellgren, Erik; Ruggenthaler, Michael; Kvaal, Simen & Helgaker, Trygve
(2019).
Guaranteed convergence of a regularized KohnSham iteration in finite dimensions.
Show summary
Guaranteed convergence of a regularized KohnSham iteration in finite dimensions
M. Penz2, A. Laestadius1, E. Tellgren1, M. Ruggenthaler2, S. Kvaal1, T. Helgaker1
1. University of Oslo, Department of Chemistry, Oslo, Germany
2 .Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany
The iterative KohnSham scheme [1] has to date not been rigorously shown to converge to the correct groundstate density. This talk addresses the recent result of Penz et al. [2] that demonstrates the convergence of the exact MoreauYosida regularized theory in a finitedimensional setting. This builds on previous work [3], where a similar iterative scheme was proposed that proved a weak type of convergence following an idea by Wagner et al. [4,5]. To obtain the desired convergence in both densities and potentials, the MoreauYosida regularization is key for the convergence proof in [2]. This ensures differentiability of the universal Lieb functional [6] and was introduced in densityfunctional theory (DFT) by Kvaal et al. [7]. It has also recently been successfully applied to paramagnetic current DFT [8].
References
[1] W. Kohn and L.J. Sham, Phys. Rev. 140, A1133 (1965).
[2] M. Penz, A. Laestadius, E.I. Tellgren, and Michael Ruggenthaler, Phys. Rev. Lett. 123, 037401 (2019).
[3] A. Laestadius, M. Penz, E.I. Tellgren, M. Ruggenthaler, S. Kvaal, and T. Helgaker, J. Chem. Phys. 149, 164103 (2018).
[4] L.O. Wagner, E. M. Stoudenmire, K. Burke, and S.R. White, Phys. Rev. Lett. 111, 093003 (2013).
[5] L.O. Wagner, T. E. Baker, E. M. Stoudenmire, K. Burke, and S.R. White, Physical Review B 90, 045109 (2014).
[6] E.H. Lieb, Int. J. Quantum Chem. 24, 243 (1983).
[7] S. Kvaal, U. Ekström, A.M. Teale, and T. Helgaker, J. Chem. Phys. 140, 18A518 (2014).
[8] A. Laestadius, M. Penz, E.I. Tellgren, M. Ruggenthaler, S. Kvaal, and T. Helgaker, J. Chem. Theory Comput. 15, 4003 (2019).

Faulstich, Fabian Maximilian; Laestadius, Andre; Legeza, Örs; Schneider, Reinhold & Kvaal, Simen
(2018).
Quadratic error bounds for the coupledcluster method tailored by tensornetwork states.

Faulstich, Fabian Maximilian; Laestadius, Andre; Legeza, Örs; Schneider, Reinhold & Kvaal, Simen
(2018).
Mathematical analysis of the coupledcluster method tailored by tensornetwork states.

Pedersen, Thomas Bondo & Kvaal, Simen
(2018).
Electron Dynamics with CoupledCluster Theory.

Pedersen, Thomas Bondo & Kvaal, Simen
(2018).
TimeDependent CoupledCluster Theory.

Laestadius, Andre; Faulstich, Fabian Maximilian; Kvaal, Simen; Legeza, Örs & Schneider, Reinhold
(2018).
Analysis of The CoupledCluster Method Tailored by
TensorNetwork States in Quantum Chemistry.

Laestadius, Andre; Faulstich, Fabian Maximilian; Kvaal, Simen; Legeza, Örs & Schneider, Reinhold
(2018).
The Study of CoupledCluster Methods Using Strong Monotonicity.

Laestadius, Andre & Kvaal, Simen
(2018).
ANALYSIS OF THE EXTENDED COUPLEDCLUSTER METHOD IN QUANTUM
CHEMISTRY.

Laestadius, Andre; Penz, Markus; Tellgren, Erik; Ruggenthaler, Michael; Kvaal, Simen & Helgaker, Trygve
(2018).
Generalized KohnSham iteration on Banach Spaces.


Faulstich, Fabian Maximilian; Laestadius, Andre; Legeza, Örs; Schneider, Reinhold & Kvaal, Simen
(2017).
Mathematical aspects of the coupledcluster method tailored by tensornetwork states in quantum chemistry.

Laestadius, Andre & Kvaal, Simen
(2016).
Analysis of the Extended CoupledCluster Method.

Kvaal, Simen & Laestadius, Andre
(2016).
The extended coupledcluster method and its rigorous analysis.

Tellgren, Erik; Teale, Andrew Michael; Ekström, Ulf Egil; Kvaal, Simen; Sagvolden, Espen & Helgaker, Trygve
(2015).
Current density functional theory for molecular systems in strong magnetic fields.

Kvaal, Simen
(2014).
Bivariational approximations & the orbitaladaptive coupledcluster method.


Helgaker, Trygve; Kvaal, Simen; Ekström, Ulf Egil & Teale, Andy
(2014).
Differentiable but Exact Formulation of DensityFunctional Theory.

Helgaker, Trygve; Kvaal, Simen; Ekström, Ulf Egil & Teale, Andrew Michael
(2014).
Differentiable but Exact Formulation of DensityFunctional Theory.

Helgaker, Trygve; Kvaal, Simen; Teale, Andrew Michael; Ekström, Ulf Egil; Jørgensen, Poul & Olsen, Jeppe
(2014).
Differentiable but Exact Formulation of DensityFunctional Theory.

Helgaker, Trygve; Kvaal, Simen; Teale, Andrew Michael & Ekström, Ulf Egil
(2014).
Differentiable but Exact Formulation of DensityFunctional Theory.

Sagvolden, Espen; Tellgren, Erik; Kvaal, Simen; Ekström, Ulf Egil; Teale, Andrew Michael & Helgaker, Trygve
(2013).
Building blocks of Current Density Functional Theory.

Sagvolden, Espen; Tellgren, Erik; Kvaal, Simen; Ekström, Ulf Egil; Teale, Andrew Michael & Helgaker, Trygve
(2013).
Building blocks of Current Density Functional Theory.

Ekström, Ulf Egil; Kvaal, Simen; Borgoo, Alex; Helgaker, Trygve; Sagvolden, Espen & Tellgren, Erik
(2013).
MoreauYosida regularization of DFT.

Kvaal, Simen
(2013).
Abels Tårn.
[Radio].
NRK P2.

Kvaal, Simen; Ekström, Ulf Egil; Tellgren, Erik; Borgoo, Alex; Helgaker, Trygve & Sagvolden, Espen
(2013).
MoreauYosida regularization of DFT.

Kvaal, Simen
(2013).
Ab initio dynamics using the coupled cluster method.

Selstø, Sølve; Kvaal, Simen; Birkeland, Tore; Nepstad, Raymond & Førre, Morten
(2012).
Double ionization with absorbers.
EurophysicsNews.
ISSN 05317479.
43(1),
p. 15–16.

Kvaal, Simen; Jarlebring, Elias & Michiels, Wim
(2010).
A numerical method for computing the radius of convergence of Rayleigh Schroedinger Perturbation theory without the need for the terms in the series.

Kvaal, Simen
(2010).
Timedependent coupledcluster approach to manybody quantum dynamics.

Kvaal, Simen
(2010).
Timedependent Coupled Cluster for ManyBody Quantum Dynamics.

Kvaal, Simen
(2010).
Variational Principles for CoupledCluster Methods.

Kvaal, Simen
(2010).
Adaptive timedependent coupled cluster method for wavepacket propagation of manyfermion systems.

Selstø, Sølve & Kvaal, Simen
(2010).
Absorbing boundary conditions for dynamical manyparticles systems.

Selstø, Sølve; Førre, Morten; Kvaal, Simen; Nepstad, Raymond & Birkeland, Tore
(2010).
Describing double photoionization of helium bymeans of absorbing boundaries.

Selstø, Sølve; Kvaal, Simen; Nepstad, Raymond & Førre, Morten
(2010).
Nonsequential double ionization of helium: Extracting the cross section.

Selstø, Sølve & Kvaal, Simen
(2010).
Absorbing boundaries for more than one particle.

Kvaal, Simen
(2009).
Usynlig Verden.



Kvaal, Simen & Halvorsen, Tore Gunnar
(2009).
One gauge to rule them all  Gaugeinvariant grid discretizations.

HjorthJensen, Morten & Kvaal, Simen
(2007).
Similarity Transformations, Flow Equations and ManyBody Perturbation Theory: Role of ManyBody Forces.

Kristiansen, Håkon Emil; Pedersen, Thomas Bondo; Kvaal, Simen & Ruud, Kenneth
(2022).
CoupledCluster Theory for Electron Dynamics.
Department of Chemistry, Faculty of Mathematics and Natural Sciences, University of Oslo.
ISSN 15017710.
2022(2507).
Show summary
Coupledcluster (CC) theory, often referred to as the gold standard of quantum chemistry, defines a convergent hierarchy of increasingly accurate methods for the description of molecular properties. The same hierarchy of methods can be extended to timedependent electronic structure theory which is then referred to as timedependent CC theory (TDCC).
TDCC theory can be formulated with static orbitals or with dynamic orbitals. In his thesis, the candidate has developed software implementing both variants. An assessment of the importance of employing dynamic orbitals is given.
A drawback of TDCC theory is the difficulty of interpretation due to the nonHermitian formulation. For example, there is no fully consistent definition of excited states in CC theory, preventing the calculation of stationarystate populations. Based on equationofmotion CC (EOMCC) and CC linear response (CCLR) theory, we propose two sets of projection operators that yield timedependent stationarystate populations as expectation values.
Furthermore, TDCC methods are computationally expensive. To bring reduce the computational cost, approximations to specific orders of the theory can be formulated based on perturbation theory. The candidate has developed a program for a secondorder approximation to TDCC theory with dynamic orbitals and applied the method to the description of optical properties in small molecules.


Bore, Sigbjørn Løland; Cascella, Michele & Kvaal, Simen
(2020).
Advances in the Hybrid ParticleField Approach: Towards Biological Systems.
Matematisk Naturvitenskapelig fakultet, Universitetet i Oslo.
ISSN 15017710.
2020(2245).
Show summary
This dissertation aims at advancing the capability of hybrid particlefield simulations of representing various physical phenomena relevant to biological systems. While hybrid particlefield simulations are computationally efficient and well adapted for studying mesoscale systems with molecular resolution, this approach has so far predominantly been applied to simple polymers. The computational investigation of systems of higher complexity, such as DNA and proteins, requires development of new models and an extension of the hybrid particlefield methodology. To this end, six research papers are presented. The main research output of these papers consists in both new methods for representing electrostatics and constantpressure conditions, and new models for proteins and charged lipids within the hybrid particlefield formalism. The work contained in this thesis thus provides key steps towards largescale realistic representations of biological systems

Halvorsen, Tore Gunnar & Kvaal, Simen
(2009).
Manifestly gauge invariant discretizations of the Schrödinger equation.
http://arxiv.org.

Jarlebring, Elias; Kvaal, Simen & Michiels, Wim
(2009).
Computing all pairs (lambda,mu) such that lambda is a double eigenvalue of A + mu B.
Katholieke Universiteit Leuven.
Full text in Research Archive
Show summary
Double eigenvalues are not generic for matrices without any particular structure. A matrix depending linearly on a scalar parameter, A+ mu B, will however
generically have double eigenvalues for some values of the parameter mu. In this
paper we consider the problem of finding those values. More precisely, we construct
a method to accurately find all scalar pairs (lambda, mu) such that A + mu B has
a double eigenvalue lambda, where A and B are given arbitrary complex matrices.
Before presenting the numerical scheme, we prove some properties necessary
for a problem to be solvable numerically in a reliable way. In particular, we
show that the problem is (under mild assumptions) well conditioned.
The general idea of the globally convergent method is that if mu is close
to a solution then A + mu B has two eigenvalues close to each other. We fix
the relative distance between these two eigenvalues and construct a method to
solve and study it by observing that the resulting problem is a twoparameter
eigenvalue problem, which is already studied in the literature. The method,
which we call the method of fixed relative distance (MFRD), involves solving a
twoparameter eigenvalue problem which returns approximations of all solutions.
It is unfortunately not possible to get full accuracy with MFRD. In order to
compute solutions with full accuracy, we present an iterative method which,
when given a sufficiently good starting value, returns a very accurate solution.
The method returns accurate solutions for nonsemisimple as well as semisimple
eigenvalues.
The approach is illustrated with one academic example and one application
to a simple problem in computational quantum mechanics.
