Simen Kvaal

• Wozniak, Aleksander P.; Adamowicz, Ludwik; Pedersen, Thomas Bondo & Kvaal, Simen (2024). Gaussians for Electronic and Rovibrational Quantum Dynamics. Journal of Physical Chemistry A. ISSN 1089-5639. 128(18), s. 3659–3671. doi: 10.1021/acs.jpca.4c00364. Fulltekst i vitenarkiv Vis sammendrag

  The assumptions underpinning the adiabatic Born-Oppenheimer (BO) approximation are broken for molecules interacting with attosecond laser pulses, which generate complicated coupled electronic-nuclear wave packets that generally will have components of electronic and dissociation continua as well as bound-state contributions. The conceptually most straightforward way to overcome this challenge is to treat the electronic and nuclear degrees of freedom on equal quantum-mechanical footing by not invoking the BO approximation at all. Explicitly correlated Gaussian (ECG) basis functions have proved successful for non-BO calculations of stationary molecular states and energies, reproducing rovibrational absorption spectra with very high accuracy. In this paper, we present a proof-of-principle study of the ability of fully flexible ECGs (FFECGs) to capture the intricate electronic and rovibrational dynamics generated by short, high-intensity laser pulses. By fitting linear combinations of FFECGs to accurate wave function histories obtained on a large real-space grid for a regularized 2D model of the hydrogen atom and for the 2D Morse potential we demonstrate that FFECGs provide a very compact description of laser-driven electronic and rovibrational dynamics.

• Aurbakken, Einar; Ofstad, Benedicte; Kristiansen, Håkon Emil; Schøyen, Øyvind Sigmundson; Kvaal, Simen & Sørensen, Lasse Kragh [Vis alle 8 forfattere av denne artikkelen] (2024). Transient spectroscopy from time-dependent electronic-structure theory without multipole expansions. Physical Review A (PRA). ISSN 2469-9926. 109(1). doi: 10.1103/PhysRevA.109.013109. Fulltekst i vitenarkiv Vis sammendrag

  Based on the work done by an electromagnetic field on an atomic or molecular electronic system, a general gauge invariant formulation of transient absorption spectroscopy is presented within the semi-classical approximation. Avoiding multipole expansions, a computationally viable expression for the spectral response function is derived from the minimal-coupling Hamiltonian of an electronic system interacting with one or more laser pulses described by a source-free, enveloped electromagnetic vector potential. With a fixed-basis expansion of the electronic wave function, the computational cost of simulations of laser-driven electron dynamics beyond the dipole approximation is the same as simulations adopting the dipole approximation. We illustrate the theory by time-dependent configuration interaction and coupled-cluster simulations of core-level absorption and circular dichroism spectra.

• Ofstad, Benedicte; Wibowo-Teale, Meilani; Kristiansen, Håkon Emil; Aurbakken, Einar; Kitsaras, Marios-Petros & Schøyen, Øyvind Sigmundson [Vis alle 12 forfattere av denne artikkelen] (2023). Magnetic optical rotation from real-time simulations in finite magnetic fields. Journal of Chemical Physics. ISSN 0021-9606. 159(20), s. 1–14. doi: 10.1063/5.0171927. Fulltekst i vitenarkiv Vis sammendrag

  We present a numerical approach to magnetic optical rotation based on real-time time-dependent electronic-structure theory. Not relying on perturbation expansions in the magnetic-field strength, the formulation allows us to test the range of validity of the linear relation between the rotation angle per unit path length and the magnetic-field strength that was established empirically by Verdet 160 years ago. Results obtained from time-dependent coupled-cluster and time-dependent current density-functional theory are presented for the closed-shell molecules H2, HF, and CO in magnetic fields up to 55 kT at standard temperature and pressure conditions. We find that Verdet's linearity remains valid up to roughly 10-20 kT, above which significant deviations from linearity are observed. Among the three current density-functional approximations tested in this work, the current-dependent Tao-Perdew-Staroverov–Scuseria hybrid functional performs the best in comparison with time-dependent coupled-cluster singles and doubles results for the magnetic optical rotation.

• Faulstich, Fabian M.; Kristiansen, Håkon Emil; Csirik, Mihaly Andras; Kvaal, Simen; Pedersen, Thomas Bondo & Laestadius, Andre (2023). The S-diagnostic - an a posteriori error assessment for single-reference coupled-cluster methods. Journal of Physical Chemistry A. ISSN 1089-5639. 127(43), s. 9106–9120. doi: 10.1021/acs.jpca.3c01575. Fulltekst i vitenarkiv Vis sammendrag

  We propose a novel a posteriori error assessment for the single-reference coupled-cluster (SRCC) method called the S-diagnostic. We provide a derivation of the S-diagnostic that is rooted in the mathematical analysis of different SRCC variants. We numerically scrutinized the S-diagnostic, testing its performance for (1) geometry optimizations, (2) electronic correlation simulations of systems with varying numerical difficulty, and (3) the square-planar copper complexes [CuCl4]2-, [Cu(NH3)4]2+, and [Cu(H2O)4]2+. Throughout the numerical investigations, the S-diagnostic is compared to other SRCC diagnostic procedures, that is, the T1, D1, and D2 diagnostics as well as different indices of multi-determinantal and multi-reference character in coupled-cluster theory. Our numerical investigations show that the S-diagnostic outperforms the T1, D1, and D2 diagnostics and is comparable to the indices of multi-determinantal and multi-reference character in coupled-cluster theory in their individual fields of applicability. The experiments investigating the performance of the S-diagnostic for geometry optimizations using SRCC reveal that the S-diagnostic correlates well with different error measures at a high level of statistical relevance. The experiments investigating the performance of the S-diagnostic for electronic correlation simulations show that the S-diagnostic correctly predicts strong multi-reference regimes. The S-diagnostic moreover correctly detects the successful SRCC computations for [CuCl4]2-, [Cu(NH3)4]2+, and [Cu(H2O)4]2+, which have been known to be misdiagnosed by T1 and D1 diagnostics in the past. This shows that the S-diagnostic is a promising candidate for an a posteriori diagnostic for SRCC calculations.

• Kvaal, Simen (2023). Three Lagrangians for the complete-active space coupled-cluster method. Journal of Chemical Physics. ISSN 0021-9606. 158(24). doi: 10.1063/5.0148988.
• Ofstad, Benedicte; Kristiansen, Håkon Emil; Aurbakken, Einar; Schøyen, Øyvind Sigmundson; Kvaal, Simen & Pedersen, Thomas Bondo (2023). Adiabatic extraction of nonlinear optical properties from real-time time-dependent electronic-structure theory. Journal of Chemical Physics. ISSN 0021-9606. 158(15). doi: 10.1063/5.0145521. Fulltekst i vitenarkiv Vis sammendrag

  Real-time simulations of laser-driven electron dynamics contain information about molecular optical properties through all orders in response theory. These properties can be extracted by assuming convergence of the power series expansion of induced electric and magnetic multipole moments. However, the accuracy relative to analytical results from response theory quickly deteriorates for higher-order responses due to the presence of high-frequency oscillations in the induced multipole moment in the time domain. This problem has been ascribed to missing higher-order corrections. We here demonstrate that the deviations are caused by nonadiabatic effects arising from the finite-time ramping from zero to full strength of the external laser field. Three different approaches, two using a ramped wave and one using a pulsed wave, for extracting electrical properties from real-time time-dependent electronic-structure simulations are investigated. The standard linear ramp is compared to a quadratic ramp, which is found to yield highly accurate results for polarizabilities, and first and second hyperpolarizabilities, at roughly half the computational cost. Results for the third hyperpolarizability are presented along with a simple, computable measure of reliability.

• Ofstad, Benedicte; Aurbakken, Einar; Schøyen, Øyvind Sigmundson; Kristiansen, Håkon Emil; Kvaal, Simen & Pedersen, Thomas Bondo (2023). Time-dependent coupled-cluster theory. Wiley Interdisciplinary Reviews. Computational Molecular Science. ISSN 1759-0876. 13(5). doi: 10.1002/wcms.1666. Fulltekst i vitenarkiv Vis sammendrag

  Recent years have witnessed an increasing interest in time-dependent coupled-cluster (TDCC) theory for simulating laser-driven electronic dynamics in atoms and molecules, and for simulating molecular vibrational dynamics. Starting from the time-dependent bivariational principle, we review different flavors of single-reference TDCC theory with either orthonormal static, orthonormal time-dependent, or biorthonormal time-dependent spin orbitals. The time-dependent extension of equation-of-motion coupled-cluster theory is also discussed, along with the applications of TDCC methods to the calculation of linear absorption spectra, linear and low-order nonlinear response functions, highly nonlinear high harmonic generation spectra and ionization dynamics. In addition, the role of TDCC theory in finite-temperature many-body quantum mechanics is briefly described along with a few other application areas.

• Schrader, Simon Elias & Kvaal, Simen (2023). Accelerated coupled cluster calculations with Procrustes orbital interpolation. Journal of Chemical Physics. ISSN 0021-9606. 158(11). doi: 10.1063/5.0141145. Fulltekst i vitenarkiv
• Teale, Andrew Michael; Helgaker, Trygve; Savin, Andreas; Adamo, Carlo; Aradi, Balint & Arbuznikov, Alexei V. [Vis alle 70 forfattere av denne artikkelen] (2022). DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science. Physical Chemistry, Chemical Physics - PCCP. ISSN 1463-9076. doi: 10.1039/d2cp02827a. Fulltekst i vitenarkiv
• Adamowicz, Ludwik; Kvaal, Simen; Lasser, Caroline & Pedersen, Thomas Bondo (2022). Laser-induced dynamic alignment of the HD molecule without the Born-Oppenheimer approximation. Journal of Chemical Physics. ISSN 0021-9606. 157(14). doi: 10.1063/5.0101352. Fulltekst i vitenarkiv Vis sammendrag

  Laser-induced molecular alignment is well understood within the framework of the Born-Oppenheimer (BO) approximation. Without the BO approximation, however, the concept of molecular structure is lost, making alignment hard to define precisely. In this work, we demonstrate the emergence of alignment from the first-ever non-BO quantum dynamics simulations, using the HD molecule exposed to ultrashort laser pulses as a few-body test case. We extract the degree of alignment from the non-BO wave function by means of an operator expressed in terms of pseudo-proton coordinates that mimics the BO-based definition of alignment. The only essential approximation, in addition to the semiclassical electric-dipole approximation for the matter-field interaction, is the choice of time-independent explicitly correlated Gaussian basis functions. We use a variational, electric-field-dependent basis-set construction procedure, which allows us to keep the basis-set dimension low whilst capturing the main effects of electric polarization on the nuclear and electronic degrees of freedom. The basis-set construction procedure is validated by comparing with virtually exact grid-based simulations for two one-dimensional model systems: laser-driven electron dynamics in a soft attractive Coulomb potential and nuclear rovibrational dynamics in a Morse potential.

• Kristiansen, Håkon Emil; Ofstad, Benedicte; Hauge, Eirill Strand; Aurbakken, Einar; Schøyen, Øyvind Sigmundson & Kvaal, Simen [Vis alle 7 forfattere av denne artikkelen] (2022). Linear and Nonlinear Optical Properties from TDOMP2 Theory. Journal of Chemical Theory and Computation. ISSN 1549-9618. 18(6), s. 3687–3702. doi: 10.1021/acs.jctc.1c01309. Fulltekst i vitenarkiv
• Kvaal, Simen; Laestadius, Andre; Tellgren, Erik Ingemar & Helgaker, Trygve (2021). Lower Semicontinuity of the Universal Functional in Paramagnetic Current-Density Functional Theory. The Journal of Physical Chemistry Letters. ISSN 1948-7185. 12(5), s. 1421–1425. doi: 10.1021/acs.jpclett.0c03422. Fulltekst i vitenarkiv
• Pedersen, Thomas Bondo; Kristiansen, Håkon Emil; Bodenstein, Tilmann; Kvaal, Simen & Schøyen, Øyvind Sigmundson (2021). Interpretation of Coupled-Cluster Many-Electron Dynamics in Terms of Stationary States. Journal of Chemical Theory and Computation. ISSN 1549-9618. 17(1), s. 388–404. doi: 10.1021/acs.jctc.0c00977. Fulltekst i vitenarkiv Vis sammendrag

  We demonstrate theoretically and numerically that laser-driven many-electron dynamics, as described by bivariational time-dependent coupled-cluster theory, may be analyzed in terms of stationary-state populations. Projectors heuristically defined from linear response theory and equation-of-motion coupled cluster theory are proposed for the calculation of stationary-state populations during interaction with laser pulses or other external forces, and conservation laws of the populations are discussed. Numerical tests of the proposed projectors, involving both linear and nonlinear optical processes for the He and Be atoms, and for the LiH, CH+, and LiF molecules, show that the laser-driven evolution of the stationary-state populations at the coupled-cluster singles-and-doubles (CCSD) level is very close to that obtained by ful configuration-interaction theory provided all stationary states actively participating in the dynamics are sufficiently well approximated. When double-excited states are important for the dynamics, the quality of the CCSD results deteriorate. Observing that populations computed from the linear-response projector may show spurious small-amplitude, high-frequency oscillations, the equation-of-motion projector emerges as the most promising approach to stationary-state populations.

• Bodenstein, Tilmann & Kvaal, Simen (2020). A state-specific multireference coupled-cluster method based on the bivariational principle. Journal of Chemical Physics. ISSN 0021-9606. 153(2). doi: 10.1063/5.0009429. Fulltekst i vitenarkiv
• Kvaal, Simen; Laestadius, Andre & Bodenstein, Tilmann (2020). Guaranteed convergence for a class of coupled-cluster methods based on Arponen's extended theory. Molecular Physics. ISSN 0026-8976. 118(19-20). doi: 10.1080/00268976.2020.1810349. Fulltekst i vitenarkiv
• Kristiansen, Håkon Emil; Schøyen, Øyvind Sigmundson; Kvaal, Simen & Pedersen, Thomas Bondo (2020). Numerical stability of time-dependent coupled-cluster methods for many-electron dynamics in intense laser pulses. Journal of Chemical Physics. ISSN 0021-9606. 152. doi: 10.1063/1.5142276. Fulltekst i vitenarkiv
• Faulstich, Fabian Maximilian; Laestadius, Andre; Legeza, Örs; Schneider, Reinhold & Kvaal, Simen (2019). Analysis of the Tailored Coupled-Cluster Method in Quantum Chemistry . SIAM Journal on Numerical Analysis. ISSN 0036-1429. 57(6), s. 2579–2607. doi: 10.1137/18M1171436. Fulltekst i vitenarkiv
• Faulstich, Fabian Maximilian; Máté, Mihály; Laestadius, Andre; Csirik, Mihály András; Veis, Libor & Antalik, Andrej [Vis alle 11 forfattere av denne artikkelen] (2019). Numerical and Theoretical Aspects of the DMRG-TCC Method Exemplified by the Nitrogen Dimer. Journal of Chemical Theory and Computation. ISSN 1549-9618. 15(4), s. 2206–2220. doi: 10.1021/acs.jctc.8b00960. Vis sammendrag

  In this article, we investigate the numerical and theoretical aspects of the coupled-cluster method tailored by matrix-product states. We investigate formal properties of the used method, such as energy size consistency and the equivalence of linked and unlinked formulation. The existing mathematical analysis is here elaborated in a quantum chemical framework. In particular, we highlight the use of what we have defined as a complete active space-external space gap describing the basis splitting between the complete active space and the external part generalizing the concept of a HOMO–LUMO gap. Furthermore, the behavior of the energy error for an optimal basis splitting, i.e., an active space choice minimizing the density matrix renormalization group-tailored coupled-cluster singles doubles error, is discussed. We show numerical investigations on the robustness with respect to the bond dimensions of the single orbital entropy and the mutual information, which are quantities that are used to choose a complete active space. Moreover, the dependence of the ground-state energy error on the complete active space has been analyzed numerically in order to find an optimal split between the complete active space and external space by minimizing the density matrix renormalization group-tailored coupled-cluster error.

• Laestadius, Andre; Tellgren, Erik; Penz, Markus; Ruggenthaler, Michael; Kvaal, Simen & Helgaker, Trygve (2019). Kohn–Sham Theory with Paramagnetic Currents: Compatibility and Functional Differentiability. Journal of Chemical Theory and Computation. ISSN 1549-9618. 15(7), s. 4003–4020. doi: 10.1021/acs.jctc.9b00141.
• Pedersen, Thomas Bondo & Kvaal, Simen (2019). Symplectic integration and physical interpretation of time-dependent coupled-cluster theory. Journal of Chemical Physics. ISSN 0021-9606. 150. doi: 10.1063/1.5085390. Fulltekst i vitenarkiv Vis sammendrag

  The formulation of the time-dependent Schrödinger equation in terms of coupled-cluster theory is outlined, with emphasis on the bivariational framework and its classical Hamiltonian structure. An indefinite inner product is introduced, inducing physical interpretation of coupled-cluster states in the form of transition probabilities, autocorrelation functions, and explicitly real values for observables, solving interpretation issues which are present in time-dependent coupled-cluster theory and in ground-state calculations of molecular systems under the influence of external magnetic fields. The problem of the numerical integration of the equations of motion is considered, and a critical evaluation of the standard fourth-order Runge–Kutta scheme and the symplectic Gauss integrator of variable order are given, including several illustrative numerical experiments. While the Gauss integrator is stable even for laser pulses well above the perturbation limit, our experiments indicate that a system-dependent upper limit exists for the external field strengths. Above this limit, time-dependent coupled-cluster calculations become very challenging numerically, even in the full configuration interaction limit. The source of these numerical instabilities is shown to be rapid increases of the amplitudes as ultrashort high-intensity laser pulses pump the system out of the ground state into states that are virtually orthogonal to the static Hartree-Fock reference determinant.

• Laestadius, Andre; Penz, Markus; Tellgren, Erik; Ruggenthaler, Michael; Kvaal, Simen & Helgaker, Trygve (2018). Generalized Kohn-Sham iteration on Banach spaces. Journal of Chemical Physics. ISSN 0021-9606. 149(16), s. 1–9. doi: 10.1063/1.5037790. Fulltekst i vitenarkiv
• Laestadius, Andre & Kvaal, Simen (2018). Analysis of the Extended Coupled-Cluster Method in Quantum Chemistry. SIAM Journal on Numerical Analysis. ISSN 0036-1429. 56(2), s. 660–683. doi: 10.1137/17M1116611. Fulltekst i vitenarkiv
• Tellgren, Erik; Laestadius, Andre; Helgaker, Trygve; Kvaal, Simen & Teale, Andrew Michael (2018). Uniform magnetic fields in density-functional theory. Journal of Chemical Physics. ISSN 0021-9606. 148(2), s. 1–19. doi: 10.1063/1.5007300.
• Kvaal, Simen & Helgaker, Trygve (2015). Ground-state densities from the Rayleigh-Ritz variation principle and from density-functional theory. Journal of Chemical Physics. ISSN 0021-9606. 143(18). doi: 10.1063/1.4934797.
• Jarlebring, Elias; Kvaal, Simen & Michiels, Wim (2014). An inverse iteration method for eigenvalue problems with eigenvector nonlinearities. SIAM Journal on Scientific Computing. ISSN 1064-8275. 36(4), s. A1978–A2001. doi: 10.1137/130910014.
• Kvaal, Simen; Ekström, Ulf Egil; Teale, Andrew Michael & Helgaker, Trygve (2014). Differentiable but exact formulation of density-functional theory. Journal of Chemical Physics. ISSN 0021-9606. 140(18). doi: 10.1063/1.4867005.
• Tellgren, Erik; Kvaal, Simen & Helgaker, Trygve (2014). Fermion N -representability for prescribed density and paramagnetic current density. Physical Review A. Atomic, Molecular, and Optical Physics (PRA). ISSN 1050-2947. 89(1). doi: 10.1103/PhysRevA.89.012515. Fulltekst i vitenarkiv
• Kvaal, Simen (2013). Variational formulations of the coupled-cluster method in quantum chemistry. Molecular Physics. ISSN 0026-8976. 111(9-11), s. 1100–1108. doi: 10.1080/00268976.2013.812254.
• Kvaal, Simen (2012). Ab initio quantum dynamics using coupled-cluster. Journal of Chemical Physics. ISSN 0021-9606. 136(19). doi: 10.1063/1.4718427.
• Halvorsen, Tore Gunnar & Kvaal, Simen (2012). Manifestly gauge invariant discretizations of the Schrodinger equation. Physics Letters A. ISSN 0375-9601. 376(12-13), s. 1107–1114. doi: 10.1016/j.physleta.2012.02.028.
• Tellgren, Erik; Kvaal, Simen; Sagvolden, Espen; Ekström, Ulf Egil; Teale, Andrew Michael & Helgaker, Trygve (2012). Choice of basic variables in current-density-functional theory. Physical Review A. Atomic, Molecular, and Optical Physics (PRA). ISSN 1050-2947. 86(6). doi: 10.1103/PhysRevA.86.062506. Fulltekst i vitenarkiv
• Jarlebring, Elias; Kvaal, Simen & Michiels, Wim (2011). Computing all Pairs (lambda, mu) Such That lambda is a Double Eigenvalue of A + mu B. SIAM Journal on Matrix Analysis and Applications. ISSN 0895-4798. 32, s. 902–927. doi: 10.1137/100783157. Fulltekst i vitenarkiv
• Kvaal, Simen (2011). Multiconfigurational time-dependent Hartree method to describe particle loss due to absorbing boundary conditions. Physical Review A. Atomic, Molecular, and Optical Physics (PRA). ISSN 1050-2947. 84(2). doi: 10.1103/PhysRevA.84.022512.
• Selstø, Sølve; Birkeland, Tore; Kvaal, Simen; Nepstad, Raymond & Førre, Morten (2011). A master equation approach to double ionization of helium. Journal of Physics B: Atomic, Molecular and Optical Physics. ISSN 0953-4075. 44(21). doi: 10.1088/0953-4075/44/21/215003.
• Kvaal, Simen; Jarlebring, Elias & Michiels, Wim (2011). Computing singularities of perturbation series. Physical Review A. Atomic, Molecular, and Optical Physics (PRA). ISSN 1050-2947. 83(3). doi: 10.1103/PhysRevA.83.032505.
• Pedersen Lohne, Magnus; Hagen, Gaute; Hjorth-Jensen, Morten; Kvaal, Simen & Pederiva, Francesco (2011). Ab initio computation of the energies of circular quantum dots. Physical Review B. Condensed Matter and Materials Physics. ISSN 1098-0121. 84. doi: 10.1103/PhysRevB.84.115302. Vis sammendrag

  We perform coupled-cluster and diffusion Monte Carlo calculations of the energies of circular quantum dots up to 20 electrons. The coupled-cluster calculations include triples corrections and a renormalized Coulomb interaction defined for a given number of low-lying oscillator shells. Using such a renormalized Coulomb interaction brings the coupled-cluster calculations with triples correlations in excellent agreement with the diffusion Monte Carlo calculations. This opens up perspectives for doing ab initio calculations for much larger systems of electrons.

• Hjorth-Jensen, Morten; Dean, David Jarvis; Hagen, G. & Kvaal, Simen (2010). Many-body interactions and nuclear structure. Journal of Physics G: Nuclear and Particle Physics. ISSN 0954-3899. 37(6). doi: 10.1088/0954-3899/37/6/064035.
• Selstø, Sølve & Kvaal, Simen (2010). Absorbing boundary conditions for dynamical many-body quantum systems. Journal of Physics B: Atomic, Molecular and Optical Physics. ISSN 0953-4075. 43(6). doi: 10.1088/0953-4075/43/6/065004. Fulltekst i vitenarkiv
• Kvaal, Simen (2009). Harmonic oscillator eigenfunction expansions, quantum dots, and effective interactions. Physical Review B. Condensed Matter and Materials Physics. ISSN 1098-0121. 80(4). doi: 10.1103/PhysRevB.80.045321.
• Kvaal, Knut; Kucheryavski, Sergei V; Halstensen, Maths; Kvaal, Simen; Flø, Andreas Svarstad & Minkkinen, Pentti [Vis alle 7 forfattere av denne artikkelen] (2008). eAMTexplorer: a software package for texture and signal characterization using Angle Measure Technique. Journal of Chemometrics. ISSN 0886-9383. 22(11-12), s. 717–721. doi: 10.1002/cem.1160. Vis sammendrag

  Texture characterization plays an important role in image analysis as do signal complexity characterization for one-dimensional arrays (time series a.o.). One of the most effective approaches for this task is Angle Measure Technique (AMT) which simultaneously describes the complexity of images or signals at all scales. This approach is not widespread yet, first of all because of the absence of universal software with a user-friendly interface, which implements the general AMT algorithm together with the many necessary pre- and post-processing techniques. In this paper, we propose a comprehensive software package for analysis of textures and one-dimensional signals with the AMT - The eAMTexplorer is an implementation of the two optimal algorithms as well as other application options suggested during the 10 years history of the AMT. eAMTexplorer is designed to be a user friendly, graphically oriented visual data analysis facility, implemented in Delphi 2006 and Borland C++. We here describe the specific implementation concepts and give a short introduction to the potentials of systematic use of this new software. Copyright (C) 2008 John Wiley & Sons, Ltd.

• Kvaal, Simen (2008). Geometry of effective Hamiltonians. Physical Review C. Nuclear Physics. ISSN 0556-2813. 78(4). doi: 10.1103/PhysRevC.78.044330.
• Kvaal, Simen; Hjorth-Jensen, Morten & Nilsen, Halvor Møll (2007). Effective interactions, large-scale diagonalization, and one-dimensional quantum dots. Physical Review B. Condensed Matter and Materials Physics. ISSN 1098-0121. 76. doi: 10.1103/PhysRevB.76.085421. Vis sammendrag

  The widely used large-scale diagonalization method using harmonic oscillator basis functions (an instance of the Rayleigh-Ritz method [S. Gould, Variational Methods for Eigenvalue Problems: An Introduction to the Methods of Rayleigh, Ritz, Weinstein, and Aronszajn (Dover, New York, 1995)], also called a spectral method, configuration-interaction method, or “exact diagonalization” method) is systematically analyzed using results for the convergence of Hermite function series. We apply this theory to a Hamiltonian for a one-dimensional model of a quantum dot. The method is shown to converge slowly, and the nonsmooth character of the interaction potential is identified as the main problem with the chosen basis, while, on the other hand, its important advantages are pointed out. An effective interaction obtained by a similarity transformation is proposed for improving the convergence of the diagonalization scheme, and numerical experiments are performed to demonstrate the improvement. Generalizations to more particles and dimensions are discussed.

Se alle arbeider i Cristin

• 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.
• 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.
• Kvaal, Simen; Pedersen, Thomas Bondo; Lasser, Caroline & Adamowicz, Ludwik (2022). No need for a grid: Gaussians for the time-dependent Schrödinger equation.
• Kvaal, Simen; Pedersen, Thomas Bondo; Lasser, Caroline & Adamowicz, Ludwik (2022). Time evolution using linear combinations of gaussians.
• Kristiansen, Håkon Emil; Ofstad, Benedicte Sverdrup; Hauge, Eirill Strand; Aurbakken, Einar; Schøyen, Øyvind Sigmundson & Kvaal, Simen [Vis alle 7 forfattere av denne artikkelen] (2022). Correction to “Linear and Nonlinear Optical Properties from TDOMP2 Theory”. Journal of Chemical Theory and Computation. ISSN 1549-9618. 18(9), s. 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 coupled-cluster method based on the bivariational principle.
• Faulstich, Fabian Maximilian; Máté, Mihály; Laestadius, Andre; Csirik, Mihály András; Veis, Libor & Antalik, Andrej [Vis alle 11 forfattere av denne artikkelen] (2019). Mathematical and numerical aspects of the coupled-cluster method tailored by tensor network states.
• Faulstich, Fabian Maximilian; Máté, Mihály; Laestadius, Andre; Csirik, Mihály András; Veis, Libor & Antalik, Andrej [Vis alle 11 forfattere av denne artikkelen] (2019). Numerical and theoretical aspects of the DMRG-TCC method exemplified by the nitrogen dimer.
• Laestadius, Andre; Penz, Markus; Tellgren, Erik; Ruggenthaler, Michael; Kvaal, Simen & Helgaker, Trygve (2019). Guaranteed convergence of a regularized Kohn-Sham iteration in finite dimensions. Vis sammendrag

  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).

• 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.
• Faulstich, Fabian Maximilian; Laestadius, Andre; Legeza, Örs; Schneider, Reinhold & Kvaal, Simen (2018). Mathematical analysis of the coupled-cluster method tailored by tensor-network states.
• Pedersen, Thomas Bondo & Kvaal, Simen (2018). Electron Dynamics with Coupled-Cluster Theory.
• Pedersen, Thomas Bondo & Kvaal, Simen (2018). Time-Dependent Coupled-Cluster Theory.
• 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.
• Laestadius, Andre; Faulstich, Fabian Maximilian; Kvaal, Simen; Legeza, Örs & Schneider, Reinhold (2018). The Study of Coupled-Cluster Methods Using Strong Monotonicity.
• Laestadius, Andre & Kvaal, Simen (2018). ANALYSIS OF THE EXTENDED COUPLED-CLUSTER METHOD IN QUANTUM CHEMISTRY.
• Laestadius, Andre; Penz, Markus; Tellgren, Erik; Ruggenthaler, Michael; Kvaal, Simen & Helgaker, Trygve (2018). Generalized Kohn-Sham iteration on Banach Spaces.
• Tellgren, Erik; Lange, Kai Kaarvann; Sagvolden, Espen; Kvaal, Simen; Austad, Jon & Reimann, Sarah [Vis alle 9 forfattere av denne artikkelen] (2018). Quantum chemistry for strong magnetic fields.
• 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.
• Laestadius, Andre & Kvaal, Simen (2016). Analysis of the Extended Coupled-Cluster Method.
• Kvaal, Simen & Laestadius, Andre (2016). The extended coupled-cluster 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 orbital-adaptive coupled-cluster method.
• Helgaker, Trygve; Borgoo, Alex; Ekström, Ulf Egil; Furness, James; Hoffmann, Mark & Kvaal, Simen [Vis alle 12 forfattere av denne artikkelen] (2014). Density-Functional Theory in Magnetic Fields.
• Helgaker, Trygve; Kvaal, Simen; Ekström, Ulf Egil & Teale, Andy (2014). Differentiable but Exact Formulation of Density-Functional Theory.
• Helgaker, Trygve; Kvaal, Simen; Ekström, Ulf Egil & Teale, Andrew Michael (2014). Differentiable but Exact Formulation of Density-Functional Theory.
• Helgaker, Trygve; Kvaal, Simen; Teale, Andrew Michael; Ekström, Ulf Egil; Jørgensen, Poul & Olsen, Jeppe (2014). Differentiable but Exact Formulation of Density-Functional Theory.
• Helgaker, Trygve; Kvaal, Simen; Teale, Andrew Michael & Ekström, Ulf Egil (2014). Differentiable but Exact Formulation of 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.
• 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). Moreau-Yosida 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). Moreau-Yosida 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 0531-7479. 43(1), s. 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). Time-dependent coupled-cluster approach to many-body quantum dynamics.
• Kvaal, Simen (2010). Time-dependent Coupled Cluster for Many-Body Quantum Dynamics.
• Kvaal, Simen (2010). Variational Principles for Coupled-Cluster Methods.
• Kvaal, Simen (2010). Adaptive time-dependent coupled cluster method for wave-packet propagation of many-fermion systems.
• Selstø, Sølve & Kvaal, Simen (2010). Absorbing boundary conditions for dynamical many-particles systems.
• Selstø, Sølve; Førre, Morten; Kvaal, Simen; Nepstad, Raymond & Birkeland, Tore (2010). Describing double photo-ionization of helium bymeans of absorbing boundaries.
• Selstø, Sølve; Kvaal, Simen; Nepstad, Raymond & Førre, Morten (2010). Non-sequential 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 (2009). Rigorous analysis of ab initio calculations for parabolic quantum dots. Fulltekst i vitenarkiv
• Hjorth-Jensen, Morten & Kvaal, Simen (2009). Effective interactions and convergence criteria for configuration interaction methods.
• Kvaal, Simen & Halvorsen, Tore Gunnar (2009). One gauge to rule them all -- Gauge-invariant grid discretizations.
• Hjorth-Jensen, Morten & Kvaal, Simen (2007). Similarity Transformations, Flow Equations and Many-Body Perturbation Theory: Role of Many-Body Forces.
• 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). Vis sammendrag

  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.

• Davidov, Aleksandar; Kvaal, Simen & Balcells, David (2023). Improving semiempirical quantum chemistry with graph neural networks. Kjemisk Institutt, Universitetet i Oslo.
• 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). Vis sammendrag

  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.

• 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). Fulltekst i vitenarkiv Vis sammendrag

  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.

• 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). Vis sammendrag

  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

• 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. Leuven University Press. Fulltekst i vitenarkiv Vis sammendrag

  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.

• Kvaal, Simen (2009). Analysis of many-body methods for quantum dots. Det matematisk naturvitenskapelige fakultet.

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