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Schrader, Simon Elias; Kristiansen, Håkon Emil; Pedersen, Thomas Bondo & Kvaal, Simen
(2023).
Time evolution of the Hydrogen atom in a strong laser field using Rothe's method.
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Schrader, Simon Elias; Kristiansen, Håkon Emil; Pedersen, Thomas Bondo & Kvaal, Simen
(2023).
Time evolution of the Hydrogen atom in a strong laser field using Rothe's method.
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Kvaal, Simen; Pedersen, Thomas Bondo; Lasser, Caroline & Adamowicz, Ludwik
(2022).
No need for a grid: Gaussians for the time-dependent Schrödinger equation.
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Kvaal, Simen; Pedersen, Thomas Bondo; Lasser, Caroline & Adamowicz, Ludwik
(2022).
Time evolution using linear combinations of gaussians.
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Kvaal, Simen
(2022).
Tie evolution using linear combinations of gaussians.
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Bodenstein, Tilmann & Kvaal, Simen
(2020).
A multireference coupled-cluster method based on the bivariational principle.
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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 coupled-cluster method tailored by tensor network states.
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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 DMRG-TCC method exemplified by the nitrogen dimer.
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Laestadius, Andre; Penz, Markus; Tellgren, Erik; Ruggenthaler, Michael; Kvaal, Simen & Helgaker, Trygve
(2019).
Guaranteed convergence of a regularized Kohn-Sham iteration in finite dimensions.
Show summary
Guaranteed convergence of a regularized Kohn-Sham 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 Kohn-Sham scheme [1] has to date not been rigorously shown to converge to the correct ground-state density. This talk addresses the recent result of Penz et al. [2] that demonstrates the convergence of the exact Moreau-Yosida regularized theory in a finite-dimensional 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 Moreau-Yosida regularization is key for the convergence proof in [2]. This ensures differentiability of the universal Lieb functional [6] and was introduced in density-functional 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).
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Faulstich, Fabian Maximilian; Laestadius, Andre; Legeza, Örs; Schneider, Reinhold & Kvaal, Simen
(2018).
Quadratic error bounds for the coupled-cluster method tailored by tensor-network states.
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Faulstich, Fabian Maximilian; Laestadius, Andre; Legeza, Örs; Schneider, Reinhold & Kvaal, Simen
(2018).
Mathematical analysis of the coupled-cluster method tailored by tensor-network states.
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Pedersen, Thomas Bondo & Kvaal, Simen
(2018).
Electron Dynamics with Coupled-Cluster Theory.
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Pedersen, Thomas Bondo & Kvaal, Simen
(2018).
Time-Dependent Coupled-Cluster Theory.
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Laestadius, Andre; Faulstich, Fabian Maximilian; Kvaal, Simen; Legeza, Örs & Schneider, Reinhold
(2018).
Analysis of The Coupled-Cluster Method Tailored by
Tensor-Network States in Quantum Chemistry.
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Laestadius, Andre; Faulstich, Fabian Maximilian; Kvaal, Simen; Legeza, Örs & Schneider, Reinhold
(2018).
The Study of Coupled-Cluster Methods Using Strong Monotonicity.
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Laestadius, Andre & Kvaal, Simen
(2018).
ANALYSIS OF THE EXTENDED COUPLED-CLUSTER METHOD IN QUANTUM
CHEMISTRY.
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Laestadius, Andre; Penz, Markus; Tellgren, Erik; Ruggenthaler, Michael; Kvaal, Simen & Helgaker, Trygve
(2018).
Generalized Kohn-Sham iteration on Banach Spaces.
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Faulstich, Fabian Maximilian; Laestadius, Andre; Legeza, Örs; Schneider, Reinhold & Kvaal, Simen
(2017).
Mathematical aspects of the coupled-cluster method tailored by tensor-network states in quantum chemistry.
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Laestadius, Andre & Kvaal, Simen
(2016).
Analysis of the Extended Coupled-Cluster Method.
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Kvaal, Simen & Laestadius, Andre
(2016).
The extended coupled-cluster method and its rigorous analysis.
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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.
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Kvaal, Simen
(2014).
Bivariational approximations & the orbital-adaptive coupled-cluster method.
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Helgaker, Trygve; Kvaal, Simen; Ekström, Ulf Egil & Teale, Andy
(2014).
Differentiable but Exact Formulation of Density-Functional Theory.
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Helgaker, Trygve; Kvaal, Simen; Ekström, Ulf Egil & Teale, Andrew Michael
(2014).
Differentiable but Exact Formulation of Density-Functional Theory.
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Helgaker, Trygve; Kvaal, Simen; Teale, Andrew Michael; Ekström, Ulf Egil; Jørgensen, Poul & Olsen, Jeppe
(2014).
Differentiable but Exact Formulation of Density-Functional Theory.
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Helgaker, Trygve; Kvaal, Simen; Teale, Andrew Michael & Ekström, Ulf Egil
(2014).
Differentiable but Exact Formulation of Density-Functional Theory.
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Sagvolden, Espen; Tellgren, Erik; Kvaal, Simen; Ekström, Ulf Egil; Teale, Andrew Michael & Helgaker, Trygve
(2013).
Building blocks of Current Density Functional Theory.
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Sagvolden, Espen; Tellgren, Erik; Kvaal, Simen; Ekström, Ulf Egil; Teale, Andrew Michael & Helgaker, Trygve
(2013).
Building blocks of Current Density Functional Theory.
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Ekström, Ulf Egil; Kvaal, Simen; Borgoo, Alex; Helgaker, Trygve; Sagvolden, Espen & Tellgren, Erik
(2013).
Moreau-Yosida regularization of DFT.
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Kvaal, Simen
(2013).
Abels Tårn.
[Radio].
NRK P2.
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Kvaal, Simen; Ekström, Ulf Egil; Tellgren, Erik; Borgoo, Alex; Helgaker, Trygve & Sagvolden, Espen
(2013).
Moreau-Yosida regularization of DFT.
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Kvaal, Simen
(2013).
Ab initio dynamics using the coupled cluster method.
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Selstø, Sølve; Kvaal, Simen; Birkeland, Tore; Nepstad, Raymond & Førre, Morten
(2012).
Double ionization with absorbers.
EurophysicsNews.
ISSN 0531-7479.
43(1),
p. 15–16.
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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.
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Kvaal, Simen
(2010).
Time-dependent coupled-cluster approach to many-body quantum dynamics.
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Kvaal, Simen
(2010).
Time-dependent Coupled Cluster for Many-Body Quantum Dynamics.
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Kvaal, Simen
(2010).
Variational Principles for Coupled-Cluster Methods.
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Kvaal, Simen
(2010).
Adaptive time-dependent coupled cluster method for wave-packet propagation of many-fermion systems.
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Selstø, Sølve & Kvaal, Simen
(2010).
Absorbing boundary conditions for dynamical many-particles systems.
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Selstø, Sølve; Førre, Morten; Kvaal, Simen; Nepstad, Raymond & Birkeland, Tore
(2010).
Describing double photo-ionization of helium bymeans of absorbing boundaries.
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Selstø, Sølve; Kvaal, Simen; Nepstad, Raymond & Førre, Morten
(2010).
Non-sequential double ionization of helium: Extracting the cross section.
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Selstø, Sølve & Kvaal, Simen
(2010).
Absorbing boundaries for more than one particle.
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Kvaal, Simen
(2009).
Usynlig Verden.
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Kvaal, Simen & Halvorsen, Tore Gunnar
(2009).
One gauge to rule them all -- Gauge-invariant grid discretizations.
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Hjorth-Jensen, Morten & Kvaal, Simen
(2007).
Similarity Transformations, Flow Equations and Many-Body Perturbation Theory: Role of Many-Body Forces.
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Ofstad, Benedicte Sverdrup & Kvaal, Simen
(2023).
Time-domain quantum dynamics: Optical properties from time-dependent electronic-structure theory.
University of Oslo, Faculty of Mathematics and Natural Sciences, Department of Chemistry.
ISSN 1501-7710.
2023(2689).
Show summary
Within the field of nonlinear optics, nonlinear optical properties are defined as frequency-dependent responses. This definition emerged in the frequency domain, as lasers used in these early experiments emitted monochromatic continuous waves. This led to the development of time-dependent electronic-structure theory predominantly in the frequency domain, using perturbation-theory based response theory. However, in recent years, advances in computing power and the advent of ultrashort laser pulses have sparked interest in the time-domain for both electronic-structure theory and nonlinear optics. Time-domain electronic-structure theory provides a time-resolved description of light-matter interaction, closely mimicking experiment. Additionally, they offer the advantage of highly nonlinear responses being straightforward to implement.
This thesis contributes to the field of time-domain time-dependent electronic-structure theory for the description of nonlinear optical properties by: Investigating the potential of dynamic (time-dependent) orbitals for improving the description of nonlinear optical properties, extending a hierarchy of time-domain time-dependent coupled-cluster methods to accommodate strong magnetic fields, and by developing an efficient approach for extracting higher-order response properties.
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Davidov, Aleksandar; Kvaal, Simen & Balcells, David
(2023).
Improving semiempirical quantum chemistry with graph neural networks.
Kjemisk Institutt, Universitetet i Oslo.
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Kristiansen, Håkon Emil; Pedersen, Thomas Bondo; Kvaal, Simen & Ruud, Kenneth
(2022).
Coupled-Cluster Theory for Electron Dynamics.
Department of Chemistry, Faculty of Mathematics and Natural Sciences, University of Oslo.
ISSN 1501-7710.
2022(2507).
Show summary
Coupled-cluster (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 time-dependent electronic structure theory which is then referred to as time-dependent 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 non-Hermitian formulation. For example, there is no fully consistent definition of excited states in CC theory, preventing the calculation of stationary-state populations. Based on equation-of-motion CC (EOMCC) and CC linear response (CCLR) theory, we propose two sets of projection operators that yield time-dependent stationary-state 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 second-order approximation to TDCC theory with dynamic orbitals and applied the method to the description of optical properties in small molecules.
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Hansen, Audun Skau; Pedersen, Thomas Bondo; Helgaker, Trygve & Kvaal, Simen
(2021).
Local correlation methods for infinite systems.
Universitetet i Oslo, Det matematisk-naturvitenskapelige fakultet.
ISSN 1501-7710.
2021(2380).
Full text in Research Archive
Show summary
Quantum Chemistry constitutes an extensive framework for accurately simulating the electronic wavefunction of atoms and molecules. The same framework may in principle be applied to the domain of periodic structures such as crystals, but is in practice severely limited by the infinite nature of these structures in conjunction with the computational complexity of quantum chemical methods. In his thesis, the candidate utilizes a mathematical structure known as bi-infinite block-Toeplitz matrices in order to smoothly transition between the molecular and periodic realm. Furthermore, he extends the divide-expand-consolidate methods originally devised for molecules to the periodic case, and demonstrates that this procedure can reduce the computational scaling of the simulation while retaining systematic control over the error.
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Bore, Sigbjørn Løland; Cascella, Michele & Kvaal, Simen
(2020).
Advances in the Hybrid Particle-Field Approach: Towards Biological Systems.
Matematisk Naturvitenskapelig fakultet, Universitetet i Oslo.
ISSN 1501-7710.
2020(2245).
Show summary
This dissertation aims at advancing the capability of hybrid particle-field simulations of representing various physical phenomena relevant to biological systems. While hybrid particle-field 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 particle-field 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 constant-pressure conditions, and new models for proteins and charged lipids within the hybrid particle-field formalism. The work contained in this thesis thus provides key steps towards large-scale realistic representations of biological systems
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Halvorsen, Tore Gunnar & Kvaal, Simen
(2009).
Manifestly gauge invariant discretizations of the Schrödinger equation.
http://arxiv.org.
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Jarlebring, Elias; Kvaal, Simen & Michiels, Wim
(2009).
Computing all pairs (lambda,mu) such that lambda is a double eigenvalue of A + mu B.
Leuven University Press.
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 two-parameter
eigenvalue problem, which is already studied in the literature. The method,
which we call the method of fixed relative distance (MFRD), involves solving a
two-parameter 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 non-semisimple as well as semisimple
eigenvalues.
The approach is illustrated with one academic example and one application
to a simple problem in computational quantum mechanics.
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