Thomas Bondo Pedersen

• 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.

• Mikkelsen, Jonas E. S.; Reine, Simen; Pedersen, Thomas B. & Jensen, Frank (2026). Extending Atom–Atom Polarizabilities to Frequency-Dependent Coupled Cluster and MCSCF Response. Journal of Chemical Theory and Computation. ISSN 1549-9618. 22(14), p. 7217–7229. doi: 10.1021/acs.jctc.6c00903. Full text in Research Archive Show summary

  The methodology for calculating distributed atom–atom polarizabilities within the minimal basis iterative Stockholder partitioning framework is extended to coupled cluster (CC2, CCSD, CC3) and multiconfigurational self-consistent field (MCSCF) wave functions, as well as to frequency-dependent perturbations. The bond capacity, defined as the rank-0 atom–atom polarizability, is benchmarked on small molecules at equilibrium geometries, where various DFT functionals show good agreement with the CC3 reference. The same conclusion holds when probing geometry dependence through a change in the bond angle or dihedral angle, but a significant deviation is observed between the methods for reaction pathways such as SN2. The MCSCF implementation is used to study the values for bond breaking, where the rank-0 contribution to the molecular dipole polarizability is found to dominate for various systems. Non-nuclear sites for describing out-of-plane polarizability at the charge-only level are also explored but found to be ineffective with ab initio-derived parameters. Dynamic bond capacities at real and imaginary frequencies are presented and display method dependence consistent with that of the static values.

• 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.

• Schrader, Simon Elias; Pedersen, Thomas Bondo & Kvaal, Simen (2025). Multidimensional quantum dynamics with explicitly correlated Gaussian wave packets using Rothe’s method. Journal of Chemical Physics. ISSN 0021-9606. 162(2). doi: 10.1063/5.0247732. Full text in Research Archive Show summary

  In a previous publication [S. E. Schrader et al., J. Chem. Phys. 161, 044105 (2024)], it has been shown that Rothe’s method can be used to solve the time-dependent Schrödinger equation for the hydrogen atom in a strong laser field using time-dependent Gaussian wave packets. Here, we generalize these results, showing that Rothe’s method can propagate arbitrary numbers of thawed, complex-valued, Explicitly Correlated Gaussian (ECGs) functions with dense correlation matrices for systems with varying dimensionality. We consider the multidimensional Hénon–Heiles potential and show that the dynamics can be quantitatively reproduced using only 30 Gaussians in 2D and that accurate spectra can be obtained using 20 Gaussians in 2D and 30–40 Gaussians in 3D and 4D. Therefore, the relevant multidimensional dynamics can be described at high quality using only a small number of ECGs that give a very compact representation of the wave function. This efficient representation, along with the demonstrated ability of Rothe’s method to propagate Gaussian wave packets in strong fields and ECGs in complex potentials, paves the way for accurate molecular dynamics calculations beyond the Born–Oppenheimer approximation in strong fields.

• Kvaal, Simen; Fredheim, Håkon Richard; Højlund, Mads Greisen & Pedersen, Thomas Bondo (2025). Time-dependent Bivariational Principle: Theoretical Foundation for Real-Time Propagation Methods of Coupled-Cluster Type. Journal of Physical Chemistry A. ISSN 1089-5639. 129(15), p. 3508–3521. doi: 10.1021/acs.jpca.4c07417. Full text in Research Archive Show summary

  Real-time propagation methods for chemistry and physics are invariably formulated using variational techniques. The time-dependent bivariational principle (TD-BIVP) is known to be the proper framework for coupled-cluster type methods, and is here studied from a differential geometric point of view. It is demonstrated how two distinct classical Hamilton’s equations of motion arise from considering the real and imaginary parts of the action integral. This in turn leads to two distinct bivariational principles for real bivariational approximation submanifolds. Conservation laws and Poisson brackets are introduced, completing the analogy with classical mechanics. Furthermore, the time-dependent univariational principles (the time-dependent variational principle, the McLachlan principle, and the Dirac–Frenkel principle) are reconstructed using the TD-BIVP and a bivariational submanifold on product form. An overview of established real-time propagation methods is given in the context of our formulation of the TD-BIVP, namely time-dependent traditional coupled-cluster theory, orbital-adaptive coupled-cluster theory, time-dependent orthogonal optimized coupled-cluster theory, Brueckner coupled-cluster theory, and equation-of-motion coupled cluster theory.

• Wozniak, Aleksander P.; Adamowicz, Ludwik; Pedersen, Thomas Bondo & Kvaal, Simen (2025). Rothe Time Propagation for Coupled Electronic and Rovibrational Quantum Dynamics. Journal of Physical Chemistry A. ISSN 1089-5639. 129(24), p. 5391–5404. doi: 10.1021/acs.jpca.5c01732. Full text in Research Archive Show summary

  When time-propagating a wave packet representing a molecular system interacting with strong attosecond laser pulses, one needs to use an approach that is capable of describing intricate coupled electronic-nuclear events that require departure from the conventional adiabatic Born–Oppenheimer (BO) approximation. Hence, the propagation should be carried out simultaneously for the electrons and nuclei, treating both particle types on an equal footing without invoking the BO approximation. In such calculations, in order to achieve high accuracy, the wave packet needs to be expanded in basis functions that explicitly depend on interparticle distances, such as all-particle explicitly correlated Gaussians (ECGs). In our previous work, we employed basis sets consisting of ECGs with optimizable complex exponential parameters to fit time-dependent wave functions obtained from grid-based propagations of two model systems: a nucleus in a Morse potential and an electron in a central-field Coulomb-like potential, subjected to intense laser pulses. In this work, we present a proof-of-principle study of the time propagation of linear combinations of ECGs for these two models using Rothe’s method. It is shown that the approach very closely reproduces the virtually exact results of grid-based propagation for both systems. This provides further evidence that ECGs constitute a viable alternative to purely grid-based simulations of coupled nuclear-electronic dynamics driven by intense laser pulses.

• Lang, Lucas; Cezar, Henrique Musseli; Adamowicz, Ludwik & Pedersen, Thomas Bondo (2024). Quantum Definition of Molecular Structure. Journal of the American Chemical Society. ISSN 0002-7863. 146(3), p. 1760–1764. doi: 10.1021/jacs.3c11467. Full text in Research Archive Show summary

  Molecular structure, a key concept of chemistry, has remained elusive from the perspective of all-particle quantum mechanics despite many efforts. Viewing molecular structure as a manifestation of strong statistical correlation between nuclear positions, we propose a practical method based on Markov chain Monte Carlo sampling and unsupervised machine learning. Application to the D3+ molecule unambiguously shows that it possesses an equilateral triangular structure. These results provide a major step forward in our understanding of molecular structure from fundamental quantum principles.

• 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.

• Pedersen, Thomas Bondo; Lehtola, Susi; Galván, Ignacio Fdez. & Lindh, Roland (2024). The versatility of the Cholesky decomposition in electronic structure theory. Wiley Interdisciplinary Reviews. Computational Molecular Science. ISSN 1759-0876. 14(1). doi: 10.1002/wcms.1692. Full text in Research Archive Show summary

  The resolution-of-the-identity (RI) or density fitting (DF) approximation for the electron repulsion integrals (ERIs) has become a standard component of accelerated and reduced-scaling implementations of first-principles Gaussian-type orbital electronic-structure methods. The Cholesky decomposition (CD) of the ERIs has also become increasingly deployed across quantum chemistry packages in the last decade, even though its early applications were mostly limited to high-accuracy methods such as coupled-cluster theory and multi-configurational approaches. Starting with a summary of the basic theory underpinning both the CD and RI/DF approximations, thus underlining the extremely close relation of the CD and RI/DF techniques, we provide a brief and largely chronological review of the evolution of the CD approach from its birth in 1977 to its current state. In addition to being a purely numerical procedure for handling ERIs, thus providing robust and computationally efficient approximations to the exact ERIs that have been found increasingly useful on modern computer platforms, CD also offers highly accurate approaches for generating auxiliary basis sets for the RI/DF approximation on the fly due to the deep mathematical connection between the two approaches. In this review, we aim to provide a concise reference of the main techniques employed in various CD approaches in electronic structure theory, to exemplify the connection between the CD and RI/DF approaches, and to clarify the state of the art to guide new implementations of CD approaches across electronic structure programs.

• 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

• 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), p. 3659–3671. doi: 10.1021/acs.jpca.4c00364. Full text in Research Archive Show summary

  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.

• Kneiding, Hannes; Lukin, Ruslan; Lang, Lucas; Reine, Simen; Pedersen, Thomas Bondo & Bin, Riccardo De [Show all 7 contributors for this article] (2023). Deep learning metal complex properties with natural quantum graphs. Digital Discovery. 2(3), p. 618–633. doi: 10.1039/d2dd00129b. Full text in Research Archive Show summary

  Machine learning can make a strong contribution to accelerating the discovery of transition metal complexes (TMC). These compounds will play a key role in the development of new technologies for which there is an urgent need, including the production of green hydrogen from renewable sources. Despite the recent developments in machine learning for drug discovery and organic chemistry in general, the application of these methods to TMCs remains challenged by their higher complexity and the limited availability of large datasets. In this work, we report a representation for deep graph learning on TMCs – the natural quantum graph (NatQG), which leverages the electronic structure data available from natural bond orbital (NBO) analysis. This data was used to define both the topology and the information expressed by the NatQG graphs. At the topology level, two different NatQG flavors were developed: u-NatQG, with undirected edges, and d-NatQG, with edges directed along donor → acceptor orbital interactions. At the information level, the node and edge attribute vectors of both graphs contain NBO data, including natural charges and bond orders. The NatQG graphs were used to develop graph neural networks (GNNs) for the prediction of the quantum properties underlying the structure and reactivity of TMCs (e.g. HOMO–LUMO gap and polarizability). These models surpassed baselines based on traditional descriptors and performed at a level similar to, or higher than, state-of-the-art GNNs based on radial cutoffs. The results showed that the electronic structure information encoded by the models has a stronger impact on its accuracy than the geometric information. With the aim of benchmarking the GNNs, we also developed the transition metal quantum mechanics graph dataset (tmQMg), which provides the geometries, properties, and NatQG graphs of 60k TMCs.

• 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.

• Adamowicz, Ludwik; Kvaal, Simen; Lasser, Caroline & Pedersen, Thomas Bondo (2022). No need for a grid: Adaptive fully-flexible gaussians for the time-dependent Schrödinger equation. arXiv.org. ISSN 2331-8422. doi: 10.48550/arXiv.2207.0027. Full text in Research Archive Show summary

  Linear combinations of complex gaussian functions, where the linear and nonlinear parameters are allowed to vary, are shown to provide an extremely flexible and effective approach for solving the time-dependent Schrödinger equation in one spatial dimension. The use of flexible basis sets has been proven notoriously hard within the systematics of the Dirac--Frenkel variational principle. In this work we present an alternative time-propagation scheme that de-emphasizes optimal parameter evolution but directly targets residual minimization via the method of Rothe's method, also called the method of vertical time layers. We test the scheme using a simple model system mimicking an atom subjected to an extreme laser pulse. Such a pulse produces complicated ionization dynamics of the system. The scheme is shown to perform very well on this model and notably does not rely on a computational grid. Only a handful of gaussian functions are needed to achieve an accuracy on par with a high-resolution, grid-based solver. This paves the way for accurate and affordable solution of the time-dependent Schrödinger equation for atoms and molecules within and beyond the Born--Oppenheimer approximation.

• 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. Full text in Research Archive Show summary

  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 [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.

• Hansen, Audun Skau; Aurbakken, Einar & Pedersen, Thomas Bondo (2021). Smooth potential-energy surfaces in fragmentation-based local correlation methods for periodic systems. Molecular Physics. ISSN 0026-8976. 119(9). doi: 10.1080/00268976.2021.1896046. Full text in Research Archive Show summary

  Local approximations facilitate the application of post-Hartree–Fock methods in the condensed phase, but simultaneously introduce errors leading to discontinuous potential-energy surfaces. In this work, we explore how these discontinuities arise in periodic systems, their implications, and possible ways of controlling them. In addition, we present a fully periodic Divide-Expand-Consolidate second-order Møller–Plesset approach using an attenuated resolution-of-the-identity approximation for the electron repulsion integrals and a convenient class to handle translation-symmetric tensors in block-Toeplitz format.

• 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.

• Hansen, Audun Skau; Baardsen, Gustav; Rebolini, Elisa; Maschio, Lorenzo & Pedersen, Thomas Bondo (2020). Representation of the virtual space in extended systems – a correlation energy convergence study. Molecular Physics. ISSN 0026-8976. doi: 10.1080/00268976.2020.1733118. Full text in Research Archive Show summary

  We present an investigation of the convergence behaviour of the local second-order Møller-Plesset perturbation theory (MP2) correlation energy toward the canonical result for three insulating crystals with either projected atomic orbitals (PAOs) or various orthonormal representations of the virtual orbital space. Echoing recent results for finite molecular systems, we find that significantly fewer PAOs than localised orthonormal virtual orbitals are required to reproduce the canonical correlation energy. We find no clear-cut correlation between conventional measures of orbital locality and the ability of the representation to span the excitation space of local domains. We show that the PAOs of the reference unit cell span parts of the excitation space that can only be reached with distant local orthonormal virtual orbitals.

• Aquilante, Francesco; Autschbach, Jochen; Baiardi, Alberto; Battaglia, Stefano; Borin, Veniamin A. & Chibotaru, Liviu F. [Show all 39 contributors for this article] (2020). Modern quantum chemistry with [Open]Molcas. Journal of Chemical Physics. ISSN 0021-9606. 152(21). doi: 10.1063/5.0004835. Full text in Research Archive Show summary

  MOLCAS/OpenMolcas is an ab initio electronic structure program providing a large set of computational methods from Hartree–Fock and density functional theory to various implementations of multiconfigurational theory. This article provides a comprehensive overview of the main features of the code, specifically reviewing the use of the code in previously reported chemical applications as well as more recent applications including the calculation of magnetic properties from optimized density matrix renormalization group wave functions.

• Olsen, Jógvan Magnus Haugaard; Reine, Simen Sommerfelt; Vahtras, Olav; Kjellgren, Erik; Reinholdt, Peter & Dundas, Karen O.H [Show all 25 contributors for this article] (2020). Dalton Project: A Python platform for molecular- and electronic-structure simulations of complex systems. Journal of Chemical Physics. ISSN 0021-9606. 152(21). doi: 10.1063/1.5144298. Full text in Research Archive Show summary

  The <i>Dalton Project</i> provides a uniform platform access to the underlying full-fledged quantum chemistry codes Dalton and LSDalton as well as the PyFraME package for automatized fragmentation and parameterization of complex molecular environments. The platform is written in Python and defines a means for library communication and interaction. Intermediate data such as integrals are exposed to the platform and made accessible to the user in the form of NumPy arrays, and the resulting data are extracted, analyzed, and visualized. Complex computational protocols that may, for instance, arise due to a need for environment fragmentation and configuration-space sampling of biochemical systems are readily assisted by the platform. The platform is designed to host additional software libraries and will serve as a hub for future modular software development efforts in the distributed Dalton community.

• 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. Full text in Research Archive Show summary

  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.

• Rebolini, Elisa; Baardsen, Gustav; Hansen, Audun Skau; Leikanger, Karl Roald & Pedersen, Thomas Bondo (2018). Divide-Expand-Consolidate Second-Order Møller-Plesset Theory with Periodic Boundary Conditions. Journal of Chemical Theory and Computation. ISSN 1549-9618. 14(5), p. 2427–2438. doi: 10.1021/acs.jctc.8b00021. Full text in Research Archive Show summary

  We present a generalization of the divide–expand–consolidate (DEC) framework for local coupled-cluster calculations to periodic systems and test it at the second-order Møller–Plesset (MP2) level of theory. For simple model systems with periodicity in one, two, and three dimensions, comparisons with extrapolated molecular calculations and the local MP2 implementation in the Cryscor program show that the correlation energy errors of the extended DEC (X-DEC) algorithm can be controlled through a single parameter, the fragment optimization threshold. Two computational bottlenecks are identified: the size of the virtual orbital spaces and the number of pair fragments required to achieve a given accuracy of the correlation energy. For the latter, we propose an affordable algorithm based on cubic splines interpolation of a limited number of pair-fragment interaction energies to determine a pair cutoff distance in accordance with the specified fragment optimization threshold.

• Wirz, Lukas Nico; Reine, Simen Sommerfelt & Pedersen, Thomas Bondo (2017). On Resolution-of-the-Identity Electron Repulsion Integral Approximations and Variational Stability. Journal of Chemical Theory and Computation. ISSN 1549-9618. 13(10), p. 4897–4906. doi: 10.1021/acs.jctc.7b00801. Full text in Research Archive Show summary

  The definiteness of the Mulliken and Dirac electron repulsion integral (ERI) matrices is examined for different classes of resolution-of-the-identity (RI) ERI approximations with particular focus on local fitting techniques. For global RI, robust local RI, and nonrobust local RI we discuss the definiteness of the approximated ERI matrices as well as the resulting bounds of Hartree, exchange, and total energies. Lower bounds of Hartree and exchange energy contributions are crucial as their absence may lead to variational instabilities, causing severe convergence problems or even convergence to a spurious state in self-consistent-field optimizations. While the global RI approximation guarantees lower bounds of Hartree and exchange energies, local RI approximations are generally unbounded. The robust local RI approximation guarantees a lower bound of the exchange energy but not of the Hartree energy. The nonrobust local RI approximation guarantees a lower bound of the Hartree energy but not of the exchange energy. These issues are demonstrated by sample calculations on carbon dioxide and benzene using the pair atomic RI approximation. © 2017 American Chemical Society

• Aquilante, Francesco; Delcey, Mickaël G.; Pedersen, Thomas Bondo; Galvan, Ignacio Fdez & Lindh, Roland (2017). Inner projection techniques for the low-cost handling of two-electron integrals in quantum chemistry. Molecular Physics. ISSN 0026-8976. 115(17-18), p. 2052–2064. doi: 10.1080/00268976.2017.1284354. Full text in Research Archive Show summary

  The density-fitting technique for approximating electron-repulsion integrals relies on the quality of auxiliary basis sets. These are commonly obtained through data fitting, an approach that presents some shortcomings. On the other hand, it is possible to derive auxiliary basis sets by removing elements from the product space of both contracted and primitive orbitals by means of a particular form of inner projection technique that has come to be known as Cholesky decomposition (CD). This procedure allows for on-the-fly construction of auxiliary basis sets that may be used in conjunction with any quantum chemical method, i.e. unbiased auxiliary basis sets. One key feature of these sets is that they represent the electron-repulsion integral matrix in atomic orbital basis with an accuracy that can be systematically improved. Another key feature is represented by the fact that locality of fitting coefficients is obtained even with the long-ranged Coulomb metric, as result of integral accuracy. Here we report on recent advances in the development of the CD-based density fitting technology. In particular, the implementation of analytical gradients algorithms is reviewed and the present status of local formulations – potentially linear scaling – is analysed in detail. © 2017 Taylor & Francis

• Sinha, Shashi Bhushan; Shopov, Dimitar Y; Sharninghausen, Liam S.; Stein, Christopher J.; Mercado, Brandon Q. & Balcells, David [Show all 10 contributors for this article] (2017). Redox Activity of Oxo-Bridged Iridium Dimers in an N,O-Donor Environment: Characterization of Remarkably Stable Ir(IV,V) Complexes. Journal of the American Chemical Society. ISSN 0002-7863. 139(28), p. 9672–9683. doi: 10.1021/jacs.7b04874. Full text in Research Archive
• Aquilante, Francesco; Autschbach, Jochen; Carlson, Rebecca K.; Chibotaru, Liviu F.; Delcey, Mickaël G. & Vico, Luca de [Show all 38 contributors for this article] (2016). Molcas 8: New capabilities for multiconfigurational quantum chemical calculations across the periodic table. Journal of Computational Chemistry. ISSN 0192-8651. 37(5), p. 506–541. doi: 10.1002/jcc.24221. Full text in Research Archive
• Galván, Ignacio Fdez.; Delcey, Mickaël G.; Pedersen, Thomas Bondo; Aquilante, Francesco & Lindh, Roland (2016). Analytical State-Average Complete-Active-Space Self-Consistent Field Nonadiabatic Coupling Vectors: Implementation with Density-Fitted Two-Electron Integrals and Application to Conical Intersections. Journal of Chemical Theory and Computation. ISSN 1549-9618. 12(8), p. 3636–3653. doi: 10.1021/acs.jctc.6b00384. Full text in Research Archive

View all works in NVA

• 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; Tellgren, Erik; Cascella, Michele & Coriani, Sonia (2025). Tribute to Trygve Helgaker. Journal of Physical Chemistry A. ISSN 1089-5639. 129(50), p. 11469–11470. doi: 10.1021/acs.jpca.5c07794. Full text in Research Archive
• Pedersen, Thomas Bondo (2025). Kvantekjemi og Elektronstruktursimuleringer. 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
• Pedersen, Thomas Bondo (2024). Fully Coupled Electronic-Nuclear Quantum Dynamcis. Full text in Research Archive
• Pedersen, Thomas Bondo (2024). Time-dependent coupled-cluster theory. Full text in Research Archive
• Pedersen, Thomas Bondo (2024). Attosecond Quantum Dynamics with Coupled-Cluster Theory. 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.

• Pedersen, Thomas Bondo; Kvaal, Simen; Adamowicz, Ludwik; Cezar, Henrique Musseli; Lang, Lucas & Lasser, Caroline [Show all 7 contributors for this article] (2024). Molecular Structure and Quantum Dynamics Without the Born-Oppenheimer Approximation. Full text in Research Archive
• Pedersen, Thomas Bondo (2024). Molecular Structure and Quantum Dynamics Without the Born-Oppenheimer Approximation. Full text in Research Archive
• Pedersen, Thomas Bondo (2024). Avslør naturens hemmeligheter med en laptop. Full text in Research Archive
• Pedersen, Thomas Bondo (2024). Research at the Hylleraas Centre. 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
• Pedersen, Thomas Bondo (2024). Electron Dynamics with Coupled-Cluster Theory. Full text in Research Archive
• Pedersen, Thomas Bondo (2024). Time-Dependent Coupled-Cluster Theory. Full text in Research Archive Show summary

  Providing benchmark-quality results for static and frequency-dependent properties as well as ground- and excited-state energetics, coupled-cluster theory is the most successful wavefunction-based method in quantum chemistry. Recent years have witnessed an increasing interest in time-dependent coupled-cluster theory [1], both as an alternative to perturbation-based response theory and as a computational tool for studying ultrafast correlated electron dynamics. In this talk, I will give an overview of these developments with emphasis on work carried out at the Hylleraas Centre and focusing on two major challenges one encounters in the nonvariational formulation of coupled-cluster theory: * Interpretation of the coupled-cluster quantum state * Description of the electronic continuum to enable ionization dynamics For the latter, emphasis will be on our recent studies of Gaussian wave packets as basis functions and Rothe's method for time propagation [2]. [1] Ofstad et al., WIREs Comput. Mol. Sci. 13, e1666 (2023) [2] Schrader et al., J. Chem. Phys. 161, 044105 (2024)

• Pedersen, Thomas Bondo (2024). Time-dependent coupled-cluster theory. Full text in Research Archive
• Pedersen, Thomas Bondo (2023). Recent Developments in Time-Dependent Coupled-Cluster Theory. 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
• Pedersen, Thomas Bondo (2023). Grunnforskning for fremtiden. Full text in Research Archive
• Pedersen, Thomas Bondo (2023). Ny viten og utvikling fra virtuelle eksperimenter. Full text in Research Archive
• Pedersen, Thomas Bondo (2023). Coupled-cluster theory of electron dynamics. Full text in Research Archive Show summary

  Highly accurate simulation of laser-driven electron dynamics is important for the prediction and interpretation of advanced spectroscopic experiments, including electronic response to sub-femtosecond laser pulses, which allow investigation and control of matter at the time scale of the electron. While multi-configurational methods have dominated the field for decades, recent years have witnessed increased interest in single-reference coupled-cluster methods for the simulation of electron dynamics [1]. Time-dependent coupled-cluster methods will be reviewed with emphasis on the major challenges for future developments. [1] B. S. Ofstad, E. Aurbakken, O. S. Schoyen, H. E. Kristiansen, S. Kvaal, and T. B. Pedersen, "Time-Dependent Coupled-Cluster Theory", WIREs Comput. Mol. Sci. 2023, e1666 (in press; DOI: 10.1002/wcms.1666)

• Pedersen, Thomas Bondo (2022). From Electronic Dynamics to Fully Coupled Electronic-Nuclear Dynamics. Full text in Research Archive Show summary

  Molecular control at the time and length scale of the electron is a grand challenge for science, which may be achieved using ultrashort laser pulses down to the attosecond time scale In order to understand and predict phenomena arising from the interaction between laser pulses and matter, we are forced t solve the time-dependent Schr{\"o}dinger equation for both electronic and nuclear degrees of freedom. I will give a brief overview of our recent work on explicitly time-dependent quantum-mechanical methods, both laser-induced electronic dynamics within the Born-Oppenheimer approximation [1-4] and coupled electronic-nuclear dynamics without the Born-Oppenheimer approximation [5]. For the electronic dynamics part, emphasis will be put on the interpretation of time dependent coupled-cluster theory in terms of autocorrelation functions and stationary-state populations, whereas the non-Born-Oppenheimer part will focus on the important phenomenon of laser-induced molecular alignment.

• Pedersen, Thomas Bondo (2022). From Electronic Dynamics to Fully Coupled Electronic-Nuclear Dynamics. 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
• Kvaal, Simen; Pedersen, Thomas Bondo; Lasser, Caroline & Adamowicz, Ludwik (2022). No need for a grid: Gaussians for the time-dependent Schrödinger equation. Full text in Research Archive
• Kvaal, Simen; Pedersen, Thomas Bondo; Lasser, Caroline & Adamowicz, Ludwik (2022). Time evolution using linear combinations of gaussians. Full text in Research Archive
• Hauge, Eirill Strand & Pedersen, Thomas Bondo (2021). Extrapolating the electric dipole moment of real-time electronic structure calculations. Full text in Research Archive
• Pedersen, Thomas Bondo (2021). Interpretation of Coupled-Cluster Quantum Dynamics. Full text in Research Archive
• Pedersen, Thomas Bondo (2020). Laser-Driven Many-Electron Dynamics with Coupled-Cluster Theory. Full text in Research Archive
• Pedersen, Thomas Bondo (2019). Can Coupled-Cluster Theory Describe Ultrashort, High-Intensity Laser-Driven Electron Dynamics? Full text in Research Archive
• Pedersen, Thomas Bondo (2019). Electron Dynamics in Extreme Laser Pulses: A Challenge to Coupled-Cluster Theory. Full text in Research Archive
• Rebolini, Elisa; Baardsen, Gustav; Hansen, Audun Skau; Leikanger, Karl Roald & Pedersen, Thomas Bondo (2018). Error-controlled MP2 for periodic molecular systems. Full text in Research Archive
• Pedersen, Thomas Bondo (2018). New Directions in Coupled-Cluster Theory. Full text in Research Archive
• Pedersen, Thomas Bondo & Kvaal, Simen (2018). Time-Dependent Coupled-Cluster Theory. Full text in Research Archive
• Pedersen, Thomas Bondo & Kvaal, Simen (2018). Electron Dynamics with Coupled-Cluster Theory. Full text in Research Archive
• Hansen, Audun Skau; Baardsen, Gustav; Maschio, Lorenzo & Pedersen, Thomas Bondo (2018). Locality and sparsity in local correlation calculations. Full text in Research Archive
• Baardsen, Gustav; Rebolini, Elisa; Hansen, Audun Skau; Maschio, Lorenzo; Leikanger, Karl Roald & Pedersen, Thomas Bondo (2018). The divide-expand-consolidate method for extended systems. Full text in Research Archive
• Pedersen, Thomas Bondo (2017). Divide-Expand-Consolidate Coupled-Cluster Theory for Extended Systems. Full text in Research Archive
• Pedersen, Thomas Bondo (2017). Local Coupled-Cluster Theory with Periodic Boundary Conditions. Full text in Research Archive
• Pedersen, Thomas Bondo (2017). Coupled-cluster theory: Quo Vadis? Full text in Research Archive
• Rebolini, Elisa; Baardsen, Gustav; Hansen, Audun Skau; Leikanger, Karl Roald & Pedersen, Thomas Bondo (2017). Local coupled cluster methods for periodic systems. Full text in Research Archive
• Pedersen, Thomas Bondo (2017). Esoteric or Exoteric? Gauge Invariance, Time Propagation, and Coupled-Cluster Theory. Full text in Research Archive
• Pedersen, Thomas Bondo (2016). Local coupled-cluster methods for periodic systems. Full text in Research Archive
• Galván, Ignacio Fdez.; Delcey, Mickaël G.; Pedersen, Thomas Bondo; Aquilante, Francesco & Lindh, Roland (2016). Conical intersection optimization and characterization with density-fitted two-electron integrals. Full text in Research Archive
• Rebolini, Elisa; Izsak, Robert; Reine, Simen Sommerfelt; Helgaker, Trygve & Pedersen, Thomas Bondo (2016). Comparison of three efficient approximate exact-exchange algorithms: chain-of-spheres, pair-atomic resolution of the identity, and the auxiliary density matrix method. Full text in Research Archive
• Wirz, Lukas Nico; Reine, Simen Sommerfelt; Pedersen, Thomas Bondo & Helgaker, Trygve (2016). Efficient auxiliary bases for the non-robust pair atomic resolution of the identity (PARI) method. Full text in Research Archive
• Pedersen, Thomas Bondo (2016). Coupled cluster methods for periodic systems. Full text in Research Archive
• Leikanger, Karl R.; Rebolini, Elisa; Hansen, Audun Skau; Baardsen, Gustav & Pedersen, Thomas Bondo (2016). Hartree-Fock calculations using a priori Wannier orbitals for solids. Full text in Research Archive
• Pedersen, Thomas Bondo (2016). A quantum chemistry approach to condensed phases using periodic boundary conditions. Full text in Research Archive
• Schrader, Simon Elias; Kvaal, Simen; Pedersen, Thomas Bondo & Hjorth-Jensen, Morten (2026). Rothe’s method with Gaussians for quantum dynamics: Solving the time-dependent Schrödinger equation as an optimization problem. Universitetet i Oslo. Full text in Research Archive Show summary

  To understand how molecules and atoms interact with intense laser fields, one needs to solve the time-dependent Schrödinger equation on a computer. This equation describes how quantum systems evolve over time. However, solving it is a computationally demanding task, often requiring the use of supercomputers. This thesis develops and demonstrates a new computational approach that aims to reduce this computational cost. The main result of this thesis is the demonstration that Rothe’s method can be successfully applied to quantum dynamics using Gaussian functions. Rothe’s method is a mathematical approach for solving time-dependent equations, and Gaussian functions provide a very compact way of representing quantum states. This work develops the necessary computational protocols and theoretical considerations to apply Rothe’s method to both single-electron and many-electron systems, including approaches such as density functional theory. In addition, the method can be used to propagate nuclear quantum states represented using explicitly correlated Gaussians, a highly flexible type of Gaussian function.

• 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.

• Hauge, Eirill Strand; Pedersen, Thomas Bondo & Helgaker, Trygve (2021). Extrapolating the Electric Dipole Moment. Universitetet i Oslo. Full text in Research Archive
• Hansen, Audun Skau; Pedersen, Thomas Bondo; Helgaker, Trygve & Kvaal, Simen (2021). Local correlation methods for infinite systems. Universitetet i Oslo. 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.

• Aurbakken, Einar; Pedersen, Thomas Bondo; Fredianini, Luca & Hjorth-Jensen, Morten (2020). Local Møller-Plesset perturbation theory for periodic systems - a study of long-range interactions and convergence. Universitetet i Oslo. Full text in Research Archive
• Peltzer, Raphael Mathias; Cascella, Michele; Pedersen, Thomas Bondo & Helgaker, Trygve (2018). Multi-scale computational modelling of bio-chemical systems in the condensed phase. Universitetet i Oslo. Full text in Research Archive

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