Håkon Emil Kristiansen

• Aurbakken, Einar; Kristiansen, Håkon Emil; Kvaal, Simen; Camper, Antoine Yves Marie Charles & Pedersen, Thomas Bondo (2026). Ultrafast laser-driven quantum dynamics in positronium chloride. Journal of Chemical Physics. ISSN 0021-9606. 165. doi: 10.1063/5.0335998. Full text in Research Archive Show summary

  We present a computational study of the laser-driven quantum dynamics of positronium (Ps), PsH, and PsCl at the time-dependent Hartree–Fock level of theory. To eliminate finite-basis effects and to properly capture continuum dynamics, we use a spherical polar pseudospectral representation. The multicomponent theory and its implementation are described in detail. We find that relative to H− and Cl−, respectively, the presence of the positron delays electron ionization in PsH, while slightly enhancing electron ionization in PsCl. In both cases, the positronic response is faster than that of the electrons. We propose that the formation of PsCl may be directly observed through photopositron spectra in the multiphoton regime, where PsCl peaks are expected at roughly twice the energy of Ps peaks, making PsCl clearly distinguishable from Ps. In the tunneling regime, however, photopositron rescattering peaks may only be distinguishable if the amount of Ps is sufficiently low.

• Krishnan, Aparna; Kristiansen, Håkon Emil; Peyton, Benjamin G.; Crawford, Thomas Daniel & Pedersen, Thomas Bondo (2026). Chemical Interpretation of Time-Dependent Coupled-Cluster Theory. Journal of Physical Chemistry A. ISSN 1089-5639. 130(32), p. 6475–6495. doi: 10.1021/acs.jpca.6c03228. Full text in Research Archive Show summary

  While providing a highly accurate framework for simulating laser-induced many-electron dynamics in atoms and molecules, including linear and nonlinear steady-state and transient absorption spectra, time-dependent coupled-cluster theory does not offer a straightforward interpretation in chemical terms. This should be contrasted with conventional time-independent equation-of-motion coupled-cluster or frequency-dependent response models where a simple eigenvector analysis readily reveals the dominant orbital-excitation character of individual excited states. We fill this gap by expanding the left and right coupled-cluster functions in a Slater-determinant basis, thus allowing for a time-dependent generalization of configuration weights that can be used to track populations throughout a simulation. The same expansions are used to decompose the time-dependent electric-dipole moment and autocorrelation function, providing a computationally straightforward approach to the assignment of absorption peaks to orbital transitions for single-reference systems. At the time-dependent coupled-cluster singles-and-doubles level of theory, we demonstrate the power of the proposed methodology by assigning valence lines in the linear absorption spectra of four ten-electron molecules (HF, H2O, NH3, and CH4) with different point-group symmetries, validating the assignment by comparison with equation-of-motion coupled-cluster singles-and-doubles theory. In addition, core-level excitations are assigned for HF, H2O, and NH3. Finally, the usefulness of time-dependent configuration weights is illustrated by applications to an impulsive stimulated X-ray Raman scattering process in the Ne atom and to a transient pump–probe spectrum of the HF molecule.

• Schrader, Simon Elias; Kristiansen, Håkon Emil; Pedersen, Thomas Bondo & Kvaal, Simen (2025). Time-Dependent Gaussian Basis Sets for Many-Body Systems Using Rothe’s Method: A Mean-Field Study. Journal of Chemical Theory and Computation. ISSN 1549-9618. doi: 10.1021/acs.jctc.5c00970. Full text in Research Archive Show summary

  A challenge in modeling time-dependent strong-field processes such as high-harmonic generation for many-body systems is how to effectively represent the electronic continuum. We apply Rothe’s method to the time-dependent Hartree–Fock (TDHF) and density functional theory (TDDFT) equations of motion for the orbitals, which reformulate them as an optimization problem. We show that thawed, complex-valued Gaussian basis sets can be propagated efficiently for these orbital-based approaches, removing the need for grids. In particular, we illustrate that qualitatively correct results can often be obtained by using just a few fully flexible Gaussians that describe the unbound dynamics for both TDHF and TDDFT. Grid calculations can be reproduced quantitatively using 30–100 Gaussians for intensities up to 4 × 10^14 W/cm2 for the one-dimensional molecular systems considered in this work.

• Wang, Zhe; Kristiansen, Håkon Emil; Pedersen, Thomas Bondo & Crawford, Thomas Daniel (2025). Real-Time Coupled Cluster Theory with Approximate Triples. Journal of Physical Chemistry A. ISSN 1089-5639. 129(7), p. 1908–1927. doi: 10.1021/acs.jpca.4c08499. Full text in Research Archive Show summary

  In order to explore the effects of high levels of electron correlation on the real-time coupled cluster formalism and algorithmic behavior, we introduce a time-dependent implementation of the CC3 singles, doubles, and approximate triples method. We demonstrate the validity of our derivation and implementation using specific applications of frequency-dependent properties. Terms with triples are calculated and added to the existing CCSD equations, giving the method a nominal O(N7) scaling. We also use a graphics processing unit accelerated implementation to reduce the computational cost, which we find can speed up the calculation by up to a factor of 13 for test cases of water clusters. In addition, we compare the impact of using single-precision arithmetic compared to conventional double-precision arithmetic. We find no significant difference in polarizabilities and optical-rotation tensor results but a somewhat larger error for first hyperpolarizabilities. Compared to linear response CC3 results, the percentage errors of RT-CC3 polarizabilities and RT-CC3 first hyperpolarizabilities are under 0.1 and 1%, respectively, for a water-molecule test case in a double-ζ basis set. Furthermore, we compare the dynamic polarizabilities obtained using RT-CC3, RT-CCSD, and time-dependent nonorthogonal orbital-optimized coupled cluster doubles (TDNOCCDs) in order to examine the performance of RT-CC3 and the orbital-optimization effect using a set of ten-electron systems.

• Kristiansen, Håkon Emil; Kvernemoen, Håkon; Kvaal, Simen & Pedersen, Thomas Bondo (2025). Configuration Weights in Coupled-Cluster Theory. Journal of Physical Chemistry A. ISSN 1089-5639. 129(10), p. 2638–2654. doi: 10.1021/acs.jpca.4c07443. Full text in Research Archive Show summary

  We introduce a simple definition of the weight of any given Slater determinant in the coupled-cluster state, namely as the expectation value of the projection operator onto that determinant. The definition can be applied to any coupled-cluster formulation, including conventional coupled-cluster theory, perturbative coupled-cluster models, nonorthogonal orbital-optimized coupled-cluster theory, and extended coupled cluster theory, allowing for wave-function analyses on par with configuration-interaction-based wave functions. Numerical experiments show that for single-reference systems the coupled cluster weights are in excellent agreement with those obtained from the full configuration-interaction wave function. Moreover, the well-known insensitivity of the total energy obtained from truncated coupled-cluster models to the choice of orbital basis is clearly exposed by weights computed in the T1 transformed determinant basis. We demonstrate that the inseparability of the conventional linear parameterization of the bra (left state) for systems composed of noninteracting subsystems may lead to ill-behaved (negative or greater than unity) weights, an issue that can only be fully remedied by switching to extended coupled-cluster theory. The latter is corroborated by results obtained with quadratic coupled-cluster theory, which is shown numerically to yield a significant improvement.

• Aurbakken, Einar; Ofstad, Benedicte; Kristiansen, Håkon Emil; Schøyen, Øyvind Sigmundson; Kvaal, Simen & Sørensen, Lasse Kragh [Show all 8 contributors for this article] (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. Full text in Research Archive Show summary

  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.

• Schrader, Simon Elias; Kristiansen, Håkon Emil; Pedersen, Thomas Bondo & Kvaal, Simen (2024). Time evolution as an optimization problem: The hydrogen atom in strong laser fields in a basis of time-dependent Gaussian wave packets. Journal of Chemical Physics. ISSN 0021-9606. 161(4). doi: 10.1063/5.0213576. Full text in Research Archive Show summary

  Recent advances in attosecond science have made it increasingly important to develop stable, reliable, and accurate algorithms and methods to model the time evolution of atoms and molecules in intense laser fields. A key process in attosecond science is high-harmonic generation, which is challenging to model with fixed Gaussian basis sets, as it produces high-energy electrons, with a resulting rapidly varying and highly oscillatory wave function that extends over dozens of ångström. Recently, Rothe’s method, where time evolution is rephrased as an optimization problem, has been applied to the one-dimensional Schrödinger equation. Here, we apply Rothe’s method to the hydrogen wave function and demonstrate that thawed, complex-valued Gaussian wave packets with time-dependent width, center, and momentum parameters are able to reproduce spectra obtained from essentially exact grid calculations for high-harmonic generation with only 50–181 Gaussians for field strengths up to 5 × 10^14 W/cm2. This paves the way for

• Beysengulov, Niyaz R.; Schøyen, Øyvind Sigmundson; Bilek, Stian Dysthe; Flaten, Jonas Boym; Leinonen, Oskar & Hjorth-Jensen, Morten [Show all 11 contributors for this article] (2024). Coulomb Interaction-Driven Entanglement of Electrons on Helium. PRX Quantum. 5(3). doi: 10.1103/PRXQuantum.5.030324. Full text in Research Archive Show summary

  The generation and evolution of entanglement in many-body systems is an active area of research that spans multiple fields, from quantum information science to the simulation of quantum many-body systems encountered in condensed matter, subatomic physics, and quantum chemistry. Motivated by recent experiments exploring quantum information processing systems with electrons trapped above the surface of cryogenic noble gas substrates, we theoretically investigate the generation of motional entanglement between two electrons via their unscreened Coulomb interaction. The model system consists of two electrons confined in separate electrostatic traps that establish microwave-frequency quantized states of their motion. We compute the motional energy spectra of the electrons, as well as their entanglement, by diagonalizing the model Hamiltonian with respect to a single-particle Hartree product basis. We also compare our results with the predictions of an effective Hamiltonian. The computational procedure outlined here can be employed for device design and guidance of experimental implementations. In particular, the theoretical tools developed here can be used for fine-tuning and optimization of control parameters in future experiments with electrons trapped above the surface of superfluid helium or solid neon.

• Ofstad, Benedicte; Wibowo-Teale, Meilani; Kristiansen, Håkon Emil; Aurbakken, Einar; Kitsaras, Marios-Petros & Schøyen, Øyvind Sigmundson [Show all 12 contributors for this article] (2023). Magnetic optical rotation from real-time simulations in finite magnetic fields. Journal of Chemical Physics. ISSN 0021-9606. 159(20), p. 1–14. doi: 10.1063/5.0171927. Full text in Research Archive Show summary

  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.

• Hauge, Eirill Strand; Kristiansen, Håkon Emil; Konecny, Lukas; Kadek, Marius; Repisky, Michal & Pedersen, Thomas Bondo (2023). Cost-Efficient High-Resolution Linear Absorption Spectra Through Extrapolating the Dipole Moment from Real-Time Time-Dependent Electronic-Structure Theory. Journal of Chemical Theory and Computation. ISSN 1549-9618. 19(21), p. 7764–7775. doi: 10.1021/acs.jctc.3c00727. Full text in Research Archive Show summary

  We present a novel function fitting method for approximating the propagation of the time-dependent electric dipole moment from real-time electronic structure calculations. Real-time calculations of the electronic absorption spectrum require discrete Fourier transforms of the electric dipole moment. The spectral resolution is determined by the total propagation time, i.e. the trajectory length of the dipole moment, causing a high computational cost. Our developed method uses function fitting on shorter trajectories of the dipole moment, achieving arbitrary spectral resolution through extrapolation. Numerical testing shows that the fitting method can reproduce high-resolution spectra using short dipole trajectories. The method converges with as little as 100 a.u. dipole trajectories for some systems, though the difficulty converging increases with the spectral density. We also introduce an error estimate of the fit, reliably assessing its convergence and hence the quality of the approximated spectrum.

• 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), p. 9106–9120. doi: 10.1021/acs.jpca.3c01575. Full text in Research Archive Show summary

  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.

• 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. Full text in Research Archive Show summary

  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.

• 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. Full text in Research Archive Show summary

  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.

• Kristiansen, Håkon Emil; Ofstad, Benedicte; Hauge, Eirill Strand; Aurbakken, Einar; Schøyen, Øyvind Sigmundson & Kvaal, Simen [Show all 7 contributors for this article] (2022). Linear and Nonlinear Optical Properties from TDOMP2 Theory. Journal of Chemical Theory and Computation. ISSN 1549-9618. 18(6), p. 3687–3702. doi: 10.1021/acs.jctc.1c01309. Full text in Research Archive Show summary

  We present a derivation of real-time (RT) time-dependent orbital-optimized Møller–Plesset (TDOMP2) theory and its biorthogonal companion, time-dependent non-orthogonal OMP2 theory, starting from the time-dependent bivariational principle and a parametrization based on the exponential orbital-rotation operator formulation commonly used in the time-independent molecular electronic structure theory. We apply the TDOMP2 method to extract absorption spectra and frequency-dependent polarizabilities and first hyperpolarizabilities from RT simulations, comparing the results with those obtained from conventional time-dependent coupled-cluster singles and doubles (TDCCSD) simulations and from its second-order approximation, TDCC2. We also compare our results with those from CCSD and CC2 linear and quadratic response theories. Our results indicate that while TDOMP2 absorption spectra are of the same quality as TDCC2 spectra, including core excitations where optimized orbitals might be particularly important, frequency-dependent polarizabilities and hyperpolarizabilities from TDOMP2 simulations are significantly closer to TDCCSD results than those from TDCC2 simulations.

• 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), p. 388–404. doi: 10.1021/acs.jctc.0c00977. Full text in Research Archive Show summary

  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.

• 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. Full text in Research Archive Show summary

  We investigate the numerical stability of time-dependent coupled-cluster theory for many-electron dynamics in intense laser pulses, comparing two coupled-cluster formulations with full configuration interaction theory. Our numerical experiments show that orbital-adaptive time-dependent coupled-cluster doubles (OATDCCD) theory offers significantly improved stability compared with the conventional Hartree-Fock-based time-dependent coupled-cluster singles-and-doubles (TDCCSD) formulation. The improved stability stems from greatly reduced oscillations in the doubles amplitudes, which, in turn, can be traced to the dynamic biorthonormal reference determinants of OATDCCD theory. As long as these are good approximations to the Brueckner determinant, OATDCCD theory is numerically stable. We propose the reference weight as a diagnostic quantity to identify situations where the TDCCSD and OATDCCD theories become unstable.

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• Pedersen, Thomas Bondo; Aurbakken, Einar; Kristiansen, Håkon Emil; Kvaal, Simen & Camper, Antoine Yves Marie Charles (2026). Mean-field theory of ultrafast laser-driven quantum dynamics in positronium chloride. Full text in Research Archive
• Pedersen, Thomas Bondo; Kvaal, Simen & Kristiansen, Håkon Emil (2026). Making Chemical Sense of Coupled-Cluster Dynamics. Full text in Research Archive
• Pedersen, Thomas Bondo; Adamowicz, Ludwik; Kristiansen, Håkon Emil; Kvaal, Simen & Schrader, Simon Elias (2025). Challenges and opportunities in attosecond quantum dynamics. Full text in Research Archive
• Schrader, Simon Elias; Kristiansen, Håkon Emil; Pedersen, Thomas Bondo & Kvaal, Simen (2025). Rothe’s method: Solving the time-dependent Schrödinger equation with flexible Gaussians. Full text in Research Archive
• Pedersen, Thomas Bondo; Kvaal, Simen; Schrader, Simon Elias & Kristiansen, Håkon Emil (2025). Quantum Dynamics without the Born-Oppenheimer Approximation. Full text in Research Archive
• Schrader, Simon Elias; Kristiansen, Håkon Emil; Pedersen, Thomas Bondo & Kvaal, Simen (2024). Time evolution as an optimization problem - solving the time-dependent Schrödinger equation with Explicitly Correlated Gaussians. Full text in Research Archive Show summary

  A linear combination of Explicitly Correlated Gaussians (ECGs) is a very compact parameterization of multidimensional wave functions. Gaussian wave packets can be propagated variationally in specific situations (see e.g. the variational multi-configurational Gaussian (vMCG) method), but in general, propagating ECGs using a time-dependent variational principle is challenging due to ill-conditioning of the Gramian matrix that needs to be inverted at every time step. This problem can be evaded by using Rothe's method, where time evolution is rephrased as an optimization problem. We show that Rothe's method can be used to propagate linear combinations of ECGs, illustrated by calculating the spectrum of a particle in the multi-dimensional Henon-Heiles potential using only 10-20 Gaussians, and by the HHG spectrum of the Hydrogen atom in strong fields, using only 50-181 Gaussians. This paves the way for the inclusion of continuum contributions into real-time, time-dependent electronic-structure theory with ECGs for strong fields, and eventually accurate simulations of the time evolution of molecules without the Born-Oppenheimer (BO) approximation.

• Kristiansen, Håkon Emil & Aurbakken, Einar (2024). Pseudospectral discretization of the time-dependent Schrödinger equation. arXiv.org. ISSN 2331-8422. doi: 10.48550/arXiv.2404.04109. Full text in Research Archive
• Pedersen, Thomas Bondo; Schrader, Simon Elias; Kristiansen, Håkon Emil & Kvaal, Simen (2024). Attosecond quantum dynamics as an optimization problem. Full text in Research Archive Show summary

  The 2023 Nobel Prize for Physics was awarded to Agostini, Krausz, and L'Huillier for their seminal contributions to the development of attosecond laser pulses by means of high-harmonic generation. Attosecond laser pulses allow us to monitor electronic motion in atoms, molecules, and materials, providing insights into and potentially control the quantum dynamics that govern chemical processes. Moreover, attosecond spectroscopy gives new opportunities to study the structure and dynamics of short-lived matter-antimatter complexes, which may provide clues to fundamental research questions such as the nature of dark matter. Needless to say, simulations are crucial for understanding, interpreting, and predicting the quantum dynamics. However, accurate simulations are highly challenging since - ionization processes are almost unavoidable due to the inherently broad intensity distribution in the frequency domain - the population of numerous electronic states of neutral and potentially multiple ionized species necessitates computational models beyond the Born-Oppenheimer approximation - the ensuing coupled electronic-nuclear dynamics likely leads to bond breaking Highly adaptive computational models that do not rely on assumptions about the possible dynamics are needed to tackle these challenges. In this talk, I will present a novel approach developed at the Hylleraas Centre over the past $2$--$3$ years. It is based on recasting the time-dependent Schrödinger equation as an optimization problem with built-in wave-function error control and, thus, full adaptivity [1,2]. Using wave-function models expressed as linear combinations of Gaussians [3], it is demonstrated that high-harmonic generation processes and rovibrational dynamics can be simulated with high accuracy. [1] S. Kvaal, C. Lasser, T. B. Pedersen, and L. Adamowicz, No need for a grid: Adaptive fully-flexible gaussians for the time-dependent Schrödinger equation, arXiv:2207.00271 [2] S. E. Schrader, H. E. Kristiansen, T. B. Pedersen, and S. Kvaal, Time evolution as an optimization problem: The hydrogen atom in strong laser fields in a basis of time-dependent Gaussian wave packets, arXiv:2404.07699 \newline [3] A. P. Wozniak, L. Adamowicz, T. B. Pedersen, and S. Kvaal, Gaussians for Electronic and Rovibrational Quantum Dynamics, J. Phys. Chem. A 128, 3659-3671 (2024)

• Schrader, Simon Elias; Kristiansen, Håkon Emil; Pedersen, Thomas Bondo & Kvaal, Simen (2024). Time evolution of the Hydrogen atom in a strong laser field using Rothe's method. Full text in Research Archive
• Schrader, Simon Elias; Kristiansen, Håkon Emil; Pedersen, Thomas Bondo & Kvaal, Simen (2024). Rothe’s method for time evolution in strong laser fields with Explicitly Correlated Gaussians. Full text in Research Archive
• Schrader, Simon Elias; Kristiansen, Håkon Emil; Pedersen, Thomas Bondo & Kvaal, Simen (2024). Rothe’s method for time evolution in strong laser fields with Explicitly Correlated Gaussians. Full text in Research Archive
• Schrader, Simon Elias; Kristiansen, Håkon Emil; Pedersen, Thomas Bondo & Kvaal, Simen (2024). Rothe's method for quantum dynamics with Explicitly Correlated Gaussians. Full text in Research Archive
• Schrader, Simon Elias; Kristiansen, Håkon Emil; Pedersen, Thomas Bondo & Kvaal, Simen (2024). Time evolution as an optimization problem - solving the time-dependent Schrödinger equation with Explicitly Correlated Gaussians. Full text in Research Archive
• 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. Full text in Research Archive
• 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. Full text in Research Archive
• 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 1549-9618. 18(9), p. 5755–5757. doi: 10.1021/acs.jctc.2c00830. Full text in Research Archive
• Kristiansen, Håkon Emil (2019). Time-dependent coupled-cluster theory for atoms and molecules in intense laser fields. Full text in Research Archive
• Kristiansen, Håkon Emil (2019). Numerical stability of time-dependent coupled-cluster methods for many-electron dynamics in intense laser pulses. Full text in Research Archive
• Kristiansen, Håkon Emil (2019). Time-dependent coupled-cluster theory for atoms & molecules in intense laser fields. Full text in Research Archive
• Kristiansen, Håkon Emil; Pedersen, Thomas Bondo; Kvaal, Simen & Ruud, Kenneth (2022). Coupled cluster theory for electron dynamics. Universitetet i Oslo. Full text in Research Archive 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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