Trygve Helgaker

Alle vitenskapelige publikasjoner (for nedlasting når tillatt)
 

• Penz, Markus; Herbst, Michael F.; Helgaker, Trygve & Laestadius, Andre (2026). Perspective on Moreau–Yosida regularization in density-functional theory. Electronic Structure. 8(2). doi: 10.1088/2516-1075/ae55eb. Fulltekst i vitenarkiv
• Hillers-Bendtsen, Andreas Erbs; Johansen, Magnus Bukhave; Buchwald, Theo Juncker von; Mikkelsen, Kurt V.; Olsen, Jeppe & Jørgensen, Poul [Vis alle 7 forfattere av denne artikkelen] (2025). Cluster perturbation theory. XI. Excitation-energy series using a variational excitation-energy function. Journal of Chemical Physics. ISSN 0021-9606. 162(2). doi: 10.1063/5.0236908. Fulltekst i vitenarkiv Vis sammendrag

  Traditionally, excitation energies in coupled-cluster (CC) theory have been calculated by solving the CC Jacobian eigenvalue equation. However, based on our recent work [Jørgensen et al., Sci. Adv. 10, eadn3454 (2024)], we propose a reformulation of the calculation of excitation energies where excitation energies are determined as a conventional molecular property. To this end, we introduce an excitation-energy function that depends on the CC Jacobian and the right and left eigenvectors for the Jacobian eigenvalue problem. This excitation-energy function is variational with respect to the right and left eigenvectors but not with respect to the cluster amplitudes. Instead, the cluster amplitudes satisfy the cluster-amplitude equations, and we set up an excitation-energy Lagrangian by adding to the excitation-energy function the cluster-amplitude equations with an undetermined multiplier for each cluster-amplitude constraint. The excitation-energy Lagrangian is variational in all its parameters. Based on the variational property of the Lagrangian, we have determined two quadratically convergent excitation-energy series: the total-order cluster-perturbation (tCP) and variational cluster-perturbation (vCP) excitation-energy series. Calculations of the excitation energies of three small molecules have shown that the vCP series is to be preferred over the tCP series. The test calculations have been carried out for CPS(D) expansions [targeting the CC singles-and-doubles (CCSD) wave function from the CC singles wave function] and the CPSD(T) expansion [targeting the CC singles-doubles-triples (CCSDT) wave function from the CCSD wave function]. For the S(D) and SD(T) orbital excitation space calculations, we obtain in the second vCP iteration excitation energies with a mean deviation from CCSD excitation energies of about 0.04 eV for the S(D) orbital spaces, and for the SD(T) orbital space calculation, we obtain a mean deviation from the CCSDT excitation energies of 0.001 eV.

• Jørgensen, Poul; Olsen, Jeppe; Johansen, Magnus Bukhave; Buchwald, Theo Juncker von; Hillers-Bendtsen, Andreas Erbs & Mikkelsen, Kurt V. [Vis alle 7 forfattere av denne artikkelen] (2024). A variational reformulation of molecular properties in electronic-structure theory. Science Advances. 10(17). doi: 10.1126/sciadv.adn3454. Fulltekst i vitenarkiv Vis sammendrag

  Conventional quantum-mechanical calculations of molecular properties, such as dipole moments and electronic excitation energies, give errors that depend linearly on the error in the wave function. An exception is the electronic energy, whose error depends quadratically on the error in wave function. We here describe how all properties may be calculated with a quadratic error, by setting up a variational Lagrangian for the property of interest. Because the construction of the Lagrangian is less expensive than the calculation of the wave function, this approach substantially improves the accuracy of quantum-chemical calculations without increasing cost. As illustrated for excitation energies, this approach enables the accurate calculation of molecular properties for larger systems, with a short time-to-solution and in a manner well suited for modern computer architectures.

• Culpitt, Tanner Phillip; Tellgren, Erik; Peters, Laurens & Helgaker, Trygve (2024). Non-adiabatic coupling matrix elements in a magnetic field: Geometric gauge dependence and Berry phase. Journal of Chemical Physics. ISSN 0021-9606. 161(18). doi: 10.1063/5.0229854. Fulltekst i vitenarkiv Vis sammendrag

  Non-adiabatic coupling matrix elements (NACMEs) are important in quantum chemistry, particularly for molecular dynamics methods such as surface hopping. However, NACMEs are gauge dependent. This presents a difficulty for their calculation in general, where there are no restrictions on the gauge function except that it be differentiable. These cases are relevant for complex-valued electronic wave functions, such as those that arise in the presence of a magnetic field or spin–orbit coupling. In addition, the Berry curvature and Berry force play an important role in molecular dynamics in a magnetic field and are also relevant in the context of spin–orbit coupling. For methods such as surface hopping, excited-state Berry curvatures will also be of interest. With this in mind, we have developed a scheme for the calculation of continuous, differentiable NACMEs as a function of the molecular geometry for complex-valued wave functions. We demonstrate the efficacy of the method using the H2 molecule at the full configuration–interaction (FCI) level of theory. In addition, ground- and excited-state Berry curvatures are computed for the first time using FCI theory. Finally, Berry phases are computed directly in terms of diagonal NACMEs.

• Teale, Andrew Michael; Huynh, Bang C.; Helgaker, Trygve & Tozer, David J. (2024). Classical Reaction Barriers in DFT: An Adiabatic-Connection Perspective. Journal of Chemical Theory and Computation. ISSN 1549-9618. s. 1–14. doi: 10.1021/acs.jctc.4c01038. Fulltekst i vitenarkiv Vis sammendrag

  Classical reaction barriers in density-functional theory are considered from the perspective of the density-fixed adiabatic connection. A ‘reaction adiabatic-connection integrand’, ℛ𝜆, is introduced, where λ is the electron–electron interaction strength, for which ∫10ℛ𝜆d𝜆 equals the barrier, meaning the barrier can be easily visualized as the area under a plot of ℛ𝜆 vs λ. For five chemical reactions, plots of reference ℛ𝜆, calculated from Lieb maximizations at the coupled-cluster level of theory, are compared with approximate ℛ𝜆, calculated from common exchange–correlation functionals using coordinate scaling, for coupled-cluster densities. The comparison provides a simple way to visualize and understand functional-driven errors and trends in barriers from approximate functionals, while allowing a clean separation of the role of exchange and correlation contributions to the barrier. Specifically, the accuracy of ℛ0 is determined entirely by the accuracy of the exchange functional, while the shape of ℛ𝜆 is determined entirely by the correlation functional. The results clearly illustrate why the optimal amount of exact (orbital) exchange in hybrid functionals differs between reactions, including forward and reverse directions in the same reaction, and hence why simply introducing larger amounts of exact exchange may not be a reliable approach for improving barriers. Instead, the shape of ℛ𝜆 must be captured more accurately through more accurate correlation functionals, and the numerical data presented may be useful for this purpose. Density-driven errors are then considered, and possible cancellation with functional-driven errors in barriers─noted in prior studies when Hartree–Fock densities are used─is illustrated from the perspective of ℛ𝜆.

• Laestadius, Andre; Csirik, Mihaly Andras; Penz, Markus; Tancogne-Dejean, Nicolas; Ruggenthaler, Michael & Rubio, Angel [Vis alle 7 forfattere av denne artikkelen] (2024). Exchange-only virial relation from the adiabatic connection. Journal of Chemical Physics. ISSN 0021-9606. 160(8). doi: 10.1063/5.0184934. Fulltekst i vitenarkiv Vis sammendrag

  The exchange-only virial relation due to Levy and Perdew is revisited. Invoking the adiabatic connection, we introduce the exchange energy in terms of the right-derivative of the universal density functional w.r.t. the coupling strength λ at λ = 0. This agrees with the Levy–Perdew definition of the exchange energy as a high-density limit of the full exchange–correlation energy. By relying on v-representability for a fixed density at varying coupling strength, we prove an exchange-only virial relation without an explicit local-exchange potential. Instead, the relation is in terms of a limit (λ ↘ 0) involving the exchange–correlation potential vλ xc, which exists by assumption of v-representability. On the other hand, a local-exchange potential vx is not warranted to exist as such a limit.

• Atsumi, Michiko; Zheng, Jia-Jia; Tellgren, Erik Ingemar; Sakaki, Shigeyoshi & Helgaker, Trygve (2023). Carbon dioxide adsorption to UiO-66: theoretical analysis of binding energy and NMR properties. Physical Chemistry, Chemical Physics - PCCP. ISSN 1463-9076. doi: 10.1039/d3cp04033j. Fulltekst i vitenarkiv
• Culpitt, Tanner Phillip; Peters, Laurens; Tellgren, Erik Ingemar & Helgaker, Trygve (2023). Time-dependent nuclear-electronic orbital Hartree-Fock theory in a strong uniform magnetic field. Journal of Chemical Physics. ISSN 0021-9606. 158(11). doi: 10.1063/5.0139675. Fulltekst i vitenarkiv
• Peters, Laurens; Culpitt, Tanner Phillip; Tellgren, Erik Ingemar & Helgaker, Trygve (2023). Berry population analysis: Atomic charges from the Berry curvature in a magnetic field. Journal of Chemical Theory and Computation. ISSN 1549-9618. s. 1–12. doi: 10.1021/acs.jctc.2c01138. Fulltekst i vitenarkiv Vis sammendrag

  The Berry curvature is essential in Born–Oppenheimer molecular dynamics, describing the screening of the nuclei by the electrons in a magnetic field. Parts of the Berry curvature can be understood as the external magnetic field multiplied by an effective charge so that the resulting Berry force behaves like a Lorentz force during the simulations. Here, we investigate whether these effective charges can provide insight into the electronic structure of a given molecule or, in other words, whether we can perform a population analysis based on the Berry curvature. To develop our approach, we first rewrite the Berry curvature in terms of charges that partially capture the effective charges and their dependencies on the nuclear velocities. With these Berry charges and charge fluctuations, we then construct our population analysis yielding atomic charges and overlap populations. Calculations at the Hartree–Fock level reveal that the atomic charges are similar to those obtained from atomic polar tensors. However, since we additionally obtain an estimate for the fluctuations of the charges and a partitioning of the atomic charges into contributions from all atoms, we conclude that the Berry population analysis is a useful alternative tool to analyze the electronic structures of molecules.

• Peters, Laurens; Tellgren, Erik Ingemar & Helgaker, Trygve (2023). Propagators for molecular dynamics in a magnetic field. Molecular Physics. ISSN 0026-8976. doi: 10.1080/00268976.2023.2259008. Fulltekst i vitenarkiv Vis sammendrag

  Ab initio molecular dynamics in a magnetic field requires solving equations of motion with velocity-dependent forces – namely, the Lorentz force arising from the nuclear charges moving in a magnetic field and the Berry force arising from the shielding of these charges from the magnetic field by the surrounding electrons. In this work, we revisit two existing propagators for these equations of motion, the auxiliary-coordinates-and-momenta (ACM) propagator and the Tajima propagator (TAJ), and compare them with a new exponential (EXP) propagator based on the Magnus expansion. Additionally, we explore limits (for example, the zero-shielding limit), the implementation of higher-order integration schemes, and series truncation to reduce computational cost by carrying out simulations of a HeH+ model system for a wide range of field strengths. While being as efficient as the TAJ propagator, the EXP propagator is the only propagator that converges to both the schemes of Spreiter and Walter (derived for systems without shielding of the Lorentz force) and to the exact cyclotronic motion of a charged particle. Since it also performs best in our model simulations, we conclude that the EXP propagator is the recommended propagator for molecules in magnetic fields.

• Tellgren, Erik Ingemar; Culpitt, Tanner Phillip; Peters, Laurens & Helgaker, Trygve (2023). Molecular vibrations in the presence of velocity-dependent forces. Journal of Chemical Physics. ISSN 0021-9606. 158(12), s. 124124–124124. doi: 10.1063/5.0139684. Fulltekst i vitenarkiv Vis sammendrag

  A semiclassical theory of small oscillations is developed for nuclei that are subject to velocity-dependent forces in addition to the usual interatomic forces. When the velocity-dependent forces are due to a strong magnetic field, novel effects arise—for example, the coupling of vibrational, rotational, and translational modes. The theory is first developed using Newtonian mechanics and we provide a simple quantification of the coupling between these types of modes. We also discuss the mathematical structure of the problem, which turns out to be a quadratic eigenvalue problem rather than a standard eigenvalue problem. The theory is then re-derived using the Hamiltonian formalism, which brings additional insight, including a close analogy to the quantum-mechanical treatment of the problem. Finally, we provide numerical examples for the H2, HT, and HCN molecules in a strong magnetic field.

• Helgaker, Trygve & Teale, Andrew M. (2022). Lieb variation principle in density-functional theory. I Frank, Rupert L.; Laptev, Ari; Lewin, Mathieu & Seiringer, Robert (Red.), The Physics and Mathematics of Elliot Lieb. European Mathematical Society (EMS) Press. ISSN 9783985470211. s. 527–559. doi: 10.4171/90-1/22. Fulltekst i vitenarkiv
• Dembiński, Stanisław; Karwowski, Jacek; Szudy, Józef & Helgaker, Trygve (2022). Lutosław Wolniewicz (1930–2020). Molecular Physics. ISSN 0026-8976. doi: 10.1080/00268976.2021.2024904. Fulltekst i vitenarkiv
• Pemberton, Miles J.; Irons, Tom J. P.; Helgaker, Trygve & Teale, Andrew Michael (2022). Revealing the exotic structure of molecules in strong magnetic fields. Journal of Chemical Physics. ISSN 0021-9606. 156(20). doi: 10.1063/5.0092520. Fulltekst i vitenarkiv Vis sammendrag

  A novel implementation for the calculation of molecular gradients under strong magnetic fields is employed at the current-density functional theory level to optimize the geometries of molecular structures, which change significantly under these conditions. An analog of the ab initio random structure search is utilized to determine the ground-state equilibrium geometries for He n and CH n systems at high magnetic field strengths, revealing the most stable structures to be those in high-spin states with a planar geometry aligned perpendicular to the field. The electron and current densities for these systems have also been investigated to develop an explanation of chemical bonding in the strong field regime, providing an insight into the exotic chemistry present in these extreme environments.

• Monzel, Laurenz; Pausch, Ansgar; Peters, Laurens; Tellgren, Erik Ingemar; Helgaker, Trygve & Klopper, Wim (2022). Molecular dynamics of linear molecules in strong magnetic fields. Journal of Chemical Physics. ISSN 0021-9606. 157(5). doi: 10.1063/5.0097800. Fulltekst i vitenarkiv Vis sammendrag

  Molecular rotations and vibrations have been extensively studied by chemists for decades, both experimentally using spectroscopic methods and theoretically with the help of quantum chemistry. However, the theoretical investigation of molecular rotations and vibrations in strong magnetic fields requires computationally more demanding tools. As such, proper calculations of rotational and vibrational spectra were not feasible up until very recently. In this work, we present rotational and vibrational spectra for two small linear molecules, H 2 and LiH, in strong magnetic fields. By treating the nuclei as classical particles, trajectories for rotations and vibrations are simulated from ab initio molecular dynamics. Born–Oppenheimer potential energy surfaces are calculated at the Hartree–Fock and MP2 levels of theory using London atomic orbitals to ensure gauge origin invariance. For the calculation of nuclear trajectories, a highly efficient Tajima propagator is introduced, incorporating the Berry curvature tensor accounting for the screening of nuclear charges.

• Culpitt, Tanner Phillip; Peters, Laurens; Tellgren, Erik Ingemar & Helgaker, Trygve (2022). Analytic calculation of the Berry curvature and diagonal Born-Oppenheimer correction for molecular systems in uniform magnetic fields. Journal of Chemical Physics. ISSN 0021-9606. 156(4). doi: 10.1063/5.0079304. Fulltekst i vitenarkiv Vis sammendrag

  The diagonal nonadiabatic term arising from the Born–Oppenheimer wave function ansatz contains contributions from a vector and scalar potential. The former is provably zero when the wave function can be taken to be real valued, and the latter, known as the diagonal Born–Oppenheimer correction (DBOC), is typically small in magnitude. Therefore, unless high accuracy is sought, the diagonal nonadiabatic term is usually neglected when calculating molecular properties. In the presence of a magnetic field, the wave function is generally complex, and the geometric vector potential gives rise to a screening force that is qualitatively important for molecular dynamics. This screening force is written in terms of the Berry curvature and is added to the bare Lorentz force acting on the nuclei in the presence of the field. In this work, we derive analytic expressions for the Berry curvature and DBOC using both first- and second-quantization formalisms for the case of generalized and restricted Hartree–Fock theories in a uniform magnetic field. The Berry curvature and DBOC are calculated as a function of the magnetic field strength and the bond distance for the ground-state singlets of H2, LiH, BH, and CH+. We also examine the stability and time-reversal symmetry of the underlying self-consistent field solutions. The character of the DBOC and Berry curvature is found to depend on the magnetic field and varies between molecules. We also identify instances of broken time-reversal symmetry for the dissociation curves of BH and CH+.

• Skjelstad, Bastian; Helgaker, Trygve; Maeda, Satoshi & Badia, David Balcells (2022). Oxyl Character and Methane Hydroxylation Mechanism in Heterometallic M(O)Co3O4Cubanes (M = Cr, Mn, Fe, Mo, Tc, Ru, and Rh). ACS Catalysis. 12(19), s. 12326–12335. doi: 10.1021/acscatal.2c03748. Fulltekst i vitenarkiv Vis sammendrag

  C–H activation in alkanes poses a major challenge in chemistry due to the inert character of this bond, manifesting the necessity of improved catalysts. Although various metal–oxo complexes are known to facilitate alkane hydroxylation, probing the mechanistic nature of the reaction is difficult due to the extremely fast rebound of the radical intermediate in the postulated oxygen-rebound pathway. Automated reaction mechanism discovery methods, such as the artificial force induced reaction (AFIR) method, enable the efficient exploration of both expected and unexpected reaction pathways, revealing the reaction mechanism. Here, we employed this approach combined with density-functional theory (DFT) to investigate the structure and reactivity of heterometallic cubane complexes similar to the oxygen-evolving complex of photosystem II. For a series of M(O)Co3O4 cubanes, where M(O) is a terminal oxo with M = Cr, Mn, Fe, Mo, Tc, Ru, and Rh, we computed the stability of the possible spin states and the radical (i.e., oxyl) character of the M(O) moiety as a measure of their potential activity in the catalytic hydroxylation of alkanes. DFT calculations on these reactions promoted by Ru(O)Co3O4 and Fe(O)Co3O4 suggest that the latter promotes the hydroxylation of methane with a rate-determining H-abstraction barrier of 24.6 kcal/mol. The moderate height of this barrier, together with the low cost and low toxicity of iron and cobalt, suggests that the Fe(O)Co3O4 cubane is a promising candidate for the catalytic oxidation of methane to methanol. AFIR calculations showed that the oxygen-rebound pathway yields the lowest-energy profile, thus validating this mechanism for the hydroxylation of alkanes by heterometallic cubanes. Furthermore, unexpected intermediates in which the methyl radical couples with either the metal center or the bridging oxo ligands were also observed.

• Teale, Andrew Michael; Helgaker, Trygve; Savin, Andreas; Adamo, Carlo; Aradi, Balint & Arbuznikov, Alexei V. [Vis alle 70 forfattere av denne artikkelen] (2022). DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science. Physical Chemistry, Chemical Physics - PCCP. ISSN 1463-9076. doi: 10.1039/d2cp02827a. Fulltekst i vitenarkiv Vis sammendrag

  In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

• Peters, Laurens; Culpitt, Tanner Phillip; Tellgren, Erik Ingemar & Helgaker, Trygve (2022). Magnetic-translational sum rule and approximate models of the molecular Berry curvature. Journal of Chemical Physics. ISSN 0021-9606. 157(13). doi: 10.1063/5.0112943. Fulltekst i vitenarkiv Vis sammendrag

  The Berry connection and curvature are key components of electronic structure calculations for atoms and molecules in magnetic fields. They ensure the correct translational behavior of the effective nuclear Hamiltonian and the correct center-of-mass motion during molecular dynamics in these environments. In this work, we demonstrate how these properties of the Berry connection and curvature arise from the translational symmetry of the electronic wave function and how they are fully captured by a finite basis set of London orbitals but not by standard Gaussian basis sets. This is illustrated by a series of Hartree–Fock calculations on small molecules in different basis sets. Based on the resulting physical interpretation of the Berry curvature as the shielding of the nuclei by the electrons, we introduce and test a series of approximations using the Mulliken fragmentation scheme of the electron density. These approximations will be particularly useful in ab initio molecular dynamics calculations in a magnetic field since they reduce the computational cost, while recovering the correct physics and up to 95% of the exact Berry curvature.

• Ryley, Matthew S.; Withnall, Michael; Irons, Tom J. P.; Helgaker, Trygve & Teale, Andrew Michael (2021). Robust All-Electron Optimization in Orbital-Free Density-Functional Theory Using the Trust-Region Image Method. Journal of Physical Chemistry A. ISSN 1089-5639. 125(1), s. 459–475. doi: 10.1021/acs.jpca.0c09502. Fulltekst i vitenarkiv
• Kvaal, Simen; Laestadius, Andre; Tellgren, Erik Ingemar & Helgaker, Trygve (2021). Lower Semicontinuity of the Universal Functional in Paramagnetic Current-Density Functional Theory. The Journal of Physical Chemistry Letters. 12(5), s. 1421–1425. doi: 10.1021/acs.jpclett.0c03422. Fulltekst i vitenarkiv Vis sammendrag

  A cornerstone of current–density functional theory (CDFT) in its paramagnetic formulation is proven. After a brief outline of the mathematical structure of CDFT, the lower semicontinuity and expectation-valuedness of the CDFT constrained-search functional is proven, meaning that there is always a minimizing density matrix in the CDFT constrained-search universal density functional. These results place the mathematical framework of CDFT on the same footing as that of standard DFT.

• Peters, Laurens; Culpitt, Tanner Phillip; Monzel, Laurenz; Tellgren, Erik Ingemar & Helgaker, Trygve (2021). Ab Initio molecular dynamics with screened Lorentz forces. II. Efficient propagators and rovibrational spectra in strong magnetic fields. Journal of Chemical Physics. ISSN 0021-9606. 155. doi: 10.1063/5.0056235. Fulltekst i vitenarkiv
• Culpitt, Tanner Phillip; Peters, Laurens; Tellgren, Erik Ingemar & Helgaker, Trygve (2021). Ab initio molecular dynamics with screened Lorentz forces. I. Calculation and atomic charge interpretation of Berry curvature. Journal of Chemical Physics. ISSN 0021-9606. 155(2). doi: 10.1063/5.0055388. Fulltekst i vitenarkiv Vis sammendrag

  The dynamics of a molecule in a magnetic field is significantly different from its zero-field counterpart. One important difference in the presence of a field is the Lorentz force acting on the nuclei, which can be decomposed as the sum of the bare nuclear Lorentz force and a screening force due to the electrons. This screening force is calculated from the Berry curvature and can change the dynamics qualitatively. It is therefore important to include the contributions from the Berry curvature in molecular dynamics simulations in a magnetic field. In this work, we present a scheme for calculating the Berry curvature numerically using a finite-difference technique, addressing challenges related to the arbitrary global phase of the wave function. The Berry curvature is calculated as a function of bond distance for H2 at the restricted and unrestricted Hartree–Fock levels of theory and for CH+ as a function of the magnetic field strength at the restricted Hartree–Fock level of theory. The calculations are carried out using basis sets of contracted Gaussian functions equipped with London phase factors (London orbitals) to ensure gauge-origin invariance. In this paper, we also interpret the Berry curvature in terms of atomic charges and discuss its convergence in basis sets with and without London phase factors. The calculation of the Berry curvature allows for its inclusion in ab initio molecular dynamics simulations in a magnetic field.

• Pasteka, Lukáš Félix; Helgaker, Trygve; Saue, Trond; Sundholm, Dage; Werner, Hans-Joachim & Hasanbulli, Mustafa [Vis alle 8 forfattere av denne artikkelen] (2020). Atoms and molecules in soft confinement potentials. Molecular Physics. ISSN 0026-8976. s. 1–23. doi: 10.1080/00268976.2020.1730989. Fulltekst i vitenarkiv
• Castro, Abril C; Balcells, David; Repisky, Michal; Helgaker, Trygve & Cascella, Michele (2020). First-principles calculation of 1H NMR chemical shifts of complex metal polyhydrides: The essential inclusion of relativity and dynamics. Inorganic Chemistry. ISSN 0020-1669. 59(23), s. 17509–17518. doi: 10.1021/acs.inorgchem.0c02753. Fulltekst i vitenarkiv Vis sammendrag

  ¹H NMR spectroscopy has become an important technique for the characterization of transition-metal hydride complexes, whose metal-bound hydrides are often difficult to locate by X-ray diffraction. In this regard, the accurate prediction of ¹H NMR chemical shifts provides a useful, but challenging, strategy to help in the interpretation of the experimental spectra. In this work, we establish a density-functional-theory protocol that includes relativistic, solvent, and dynamic effects at a high level of theory, allowing us to report an accurate and reliable interpretation of ¹H NMR hydride chemical shifts of iridium polyhydride complexes. In particular, we have studied in detail the hydride chemical shifts of the [Ir₆(IMe)₈(CO)₂H₁₄]²⁺ complex in order to validate previous assignments. The computed ¹H NMR chemical shifts are strongly dependent on the relativistic treatment, the choice of the DFT exchange–correlation functional, and the conformational dynamics. By combining a fully relativistic four-component electronic-structure treatment with ab initio molecular dynamics, we were able to reliably model both the terminal and bridging hydride chemical shifts and to show that two NMR hydride signals were inversely assigned in the experiment.

• Irons, Tom J P; Spence, Lucy; Speake, Gregoire David; Speake, Benjamin T.; Helgaker, Trygve & Teale, Andrew Michael (2020). Analyzing Magnetically Induced Currents in Molecular Systems Using Current-Density-Functional Theory. Journal of Physical Chemistry A. ISSN 1089-5639. 124, s. 1321–1333. doi: 10.1021/acs.jpca.9b10833. Fulltekst i vitenarkiv
• Brandenburg, Jan Gerit; Burke, Kieron; Fromager, Emmanuel; Gatti, Matteo; Giarrusso, Sara & Gidopoulos, Nikitas I. [Vis alle 29 forfattere av denne artikkelen] (2020). New approaches to study excited states in density functional theory: general discussion. Faraday discussions. ISSN 1359-6640. 224, s. 483–508. doi: 10.1039/D0FD90026E. Fulltekst i vitenarkiv
• Fromager, Emmanuel; Gidopoulos, Nikitas I.; Gori-Giorgi, Paola; Helgaker, Trygve; Loos, Pierre-François & Malcomson, Thomas [Vis alle 11 forfattere av denne artikkelen] (2020). Strong correlation in density functional theory: general discussion. Faraday discussions. ISSN 1359-6640. 224, s. 373–381. doi: 10.1039/D0FD90025G. Fulltekst i vitenarkiv
• Brandenburg, Jan Gerit; Burke, Kieron; Civalleri, Bartolomeo; Cole, Daniel J.; Csanyi, Gabor & Gregoire, David [Vis alle 27 forfattere av denne artikkelen] (2020). Challenges for large scale simulation: general discussion. Faraday discussions. ISSN 1359-6640. 224, s. 309–332. doi: 10.1039/D0FD90024A. Fulltekst i vitenarkiv
• Brandenburg, Jan Gerit; Burke, Kieron; Cancio, Antonio; Erhard, Jannis; Fromager, Emmanuel & Ghosal, Abhisek [Vis alle 25 forfattere av denne artikkelen] (2020). New density-functional approximations and beyond: general discussion. Faraday discussions. ISSN 1359-6640. 224, s. 166–200. doi: 10.1039/D0FD90023K. Fulltekst i vitenarkiv
• Austad, Jon; Borgoo, Alex; Tellgren, Erik & Helgaker, Trygve (2020). Bonding in the helium dimer in strong magnetic fields: The role of spin and angular momentum. Physical Chemistry, Chemical Physics - PCCP. ISSN 1463-9076. 22(41), s. 23502–23521. doi: 10.1039/d0cp03259j. Fulltekst i vitenarkiv
• Olsen, Jógvan Magnus Haugaard; Reine, Simen Sommerfelt; Vahtras, Olav; Kjellgren, Erik; Reinholdt, Peter & Dundas, Karen O.H [Vis alle 25 forfattere av denne artikkelen] (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. Fulltekst i vitenarkiv Vis sammendrag

  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.

• Adamowicz, Ludwik; Stanke, Monika; Tellgren, Erik & Helgaker, Trygve (2020). A quantum-mechanical non-Born–Oppenheimer model of a molecule in a strong magnetic field. Chemical Physics Letters. ISSN 0009-2614. 761, s. 1–7. doi: 10.1016/j.cplett.2020.138041. Fulltekst i vitenarkiv Vis sammendrag

  Interactions of a stationary external magnetic field with the spin and orbital magnetic momenta of a molecule are included in the quantum mechanical model where the Born–Oppenheimer approximation is not assumed. The model is used to calculate some of the lowest-lying internal bound states of the molecule for various strengths of the magnetic field. All-particle explicitly correlated Gaussian functions are used in the calculations.

• Holzer, Christof; Teale, Andrew Michael; Hampe, Florian; Stopkowicz, Stella; Helgaker, Trygve & Klopper, Wim (2019). GW quasiparticle energies of atoms in strong magnetic fields. Journal of Chemical Physics. ISSN 0021-9606. 150(21), s. 214112-1–214112-9. doi: 10.1063/1.5093396. Fulltekst i vitenarkiv
• Laestadius, Andre; Tellgren, Erik; Penz, Markus; Ruggenthaler, Michael; Kvaal, Simen & Helgaker, Trygve (2019). Kohn–Sham Theory with Paramagnetic Currents: Compatibility and Functional Differentiability. Journal of Chemical Theory and Computation. ISSN 1549-9618. 15(7), s. 4003–4020. doi: 10.1021/acs.jctc.9b00141. Fulltekst i vitenarkiv
• Castro, Abril C.; Fliegl, Heike; Cascella, Michele; Helgaker, Trygve; Repisky, Michal & Komorovsky, Stanislav [Vis alle 9 forfattere av denne artikkelen] (2019). Four-component relativistic 31P NMR calculations for: Trans -platinum(ii) complexes: Importance of the solvent and dynamics in spectral simulations. Dalton Transactions. ISSN 1477-9226. 48(23), s. 8076–8083. doi: 10.1039/c9dt00570f. Fulltekst i vitenarkiv Vis sammendrag

  We report a combined experimental-theoretical study on the 31P NMR chemical shift for a number of trans-platinum(II) complexes. Validity and reliability of the 31P NMR chemical shift calculations are examined by comparing with the experimental data. A successful computational protocol for the accurate prediction of the 31P NMR chemical shifts was established for trans-[PtCl2(dma)PPh3] (dma = dimethylamine) complex. The reliability of the computed values is shown to be critically dependent on the level of relativistic effects (two-component vs. four component), choice of density functional, dynamical averaging, and solvation effects. Snapshots from ab initio molecular dynamics simulations were used to identify those solvent molecules which show the largest interactions with the platinum complex, through inspection by the non-covalent interaction program. We observe satisfactory accuracy from the full four-component matrix Dirac-Kohn-Sham method (mDKS) based on the Dirac-Coulomb Hamiltonian, in conjunction with the KT2 density functional, and dynamical averaging with explicit solvent molecules

• Reimann, Sarah; Borgoo, Alex; Austad, Jon; Tellgren, Erik; Teale, Andrew Michael & Helgaker, Trygve [Vis alle 7 forfattere av denne artikkelen] (2019). Kohn–Sham energy decomposition for molecules in a magnetic field. Molecular Physics. ISSN 0026-8976. 117(1), s. 97–109. doi: 10.1080/00268976.2018.1495849. Fulltekst i vitenarkiv

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• Nordholm, Sture; Baerends, Evert Jan; Burke, Kieron; Gill, Peter; Gori-Giorgi, Paola & Grimme, Stefan [Vis alle 18 forfattere av denne artikkelen] (2026). The rocky path of DFT into chemistry—Discussions at a symposium and reflections on a circular journey in honor of Axel Becke 1953–2025. Journal of Chemical Physics. ISSN 0021-9606. 165(5). doi: 10.1063/5.0337560. Fulltekst i vitenarkiv Vis sammendrag

  We summarize a recent symposium on density functional theory for electronic structure in chemical applications and honor a key contributor, Axel Becke. The theory of electronic structure is entirely quantum mechanical and, in its original wave function form, runs into mathematical and numerical problems due to high spatial dimensionality, as each electron adds three new coordinates. The approximate reduction of dimensionality in the form of density functional theory (DFT) was first proposed in the mid-1920s but took 40 years to be verified as possible in principle. The development of increasingly accurate functionals, expressing the electronic energy in terms of the density of the electrons, was initially driven by the physics community, but after a series of innovations, including (i) going from local to non-local exchange–correlation energy functionals and (ii) partial retention of exact exchange in terms of wave functions, there was a breakthrough in the early 1990s, and leading quantum chemists accepted DFT. The resulting improved ability to solve chemical problems by computation was rewarded with a Nobel Prize to Walter Kohn and John Pople in 1998. Given the many controversies surrounding the introduction of DFT into chemistry, a symposium was held at the Royal Swedish Academy of Sciences on November 7 and 8, 2024, to look back at the barriers and breakthroughs and identify the key contributors and their advancements. Axel Becke played a major role in bringing DFT into chemistry. We record the unique breadth and depth of the discussions at the symposium and the role of Becke, whose life ended a year thereafter.

• Helgaker, Trygve (2025). A variational reformulation of molecular properties in electronic-structure theory. Fulltekst i vitenarkiv
• Helgaker, Trygve (2025). The Exotic Chemistry of Ultrastrong Magnetic Fields. Fulltekst i vitenarkiv
• Helgaker, Trygve (2025). Egil Hylleraas — Norges første kvantefysiker. Fulltekst i vitenarkiv
• Helgaker, Trygve (2025). A variational reformulation of molecular properties in electronic-structure theory. Fulltekst i vitenarkiv
• Helgaker, Trygve (2025). A variational reformulation of molecular properties in electronic-structure theory. Fulltekst i vitenarkiv
• Helgaker, Trygve (2025). A variational reformulation of molecular properties in electronic-structure theory. Fulltekst i vitenarkiv
• Helgaker, Trygve (2025). Autobiography of Trygve Helgaker. Journal of Physical Chemistry A. ISSN 1089-5639. 129(50), s. 11471–11479. doi: 10.1021/acs.jpca.5c07793. Fulltekst i vitenarkiv
• Helgaker, Trygve (2024). My Journey in Theoretical Chemistry — Experiences and Tips. Fulltekst i vitenarkiv
• Helgaker, Trygve (2024). Minnetale over Arne Haaland. Fulltekst i vitenarkiv
• Helgaker, Trygve (2024). My Journey in Theoretical Chemisty—Experiences and Tips. Fulltekst i vitenarkiv
• Helgaker, Trygve (2024). Molecular Dynamics and Rovibrational Spectra in a Magnetic Field. Fulltekst i vitenarkiv
• Helgaker, Trygve (2024). Hundred Years of Quantum Chemistry in Scandinavia. Fulltekst i vitenarkiv
• Helgaker, Trygve (2024). High-accuracy quantum chemistry. Fulltekst i vitenarkiv
• Helgaker, Trygve (2024). Kvantekjemi — på liv og død. Fulltekst i vitenarkiv
• Helgaker, Trygve (2024). Molecular Bonding, Structure, and Dynamics in a Strong Magnetic Field. Fulltekst i vitenarkiv
• Helgaker, Trygve (2024). Kvantekjemi. Fulltekst i vitenarkiv
• Helgaker, Trygve (2023). Kvantekjemi — på liv og død. Fulltekst i vitenarkiv
• Helgaker, Trygve (2023). Kvantekjemi — på liv og død. Fulltekst i vitenarkiv
• Helgaker, Trygve (2023). Kvantemekanikk og kjemi. Fulltekst i vitenarkiv
• Helgaker, Trygve (2023). Kvantekjemi. Fulltekst i vitenarkiv
• Helgaker, Trygve (2023). Molecular dynamics and rovibrational spectra in a magnetic field. Fulltekst i vitenarkiv
• Helgaker, Trygve (2023). Kvantekjemi. Fulltekst i vitenarkiv
• Helgaker, Trygve (2023). Molecular dynamics and rovibrational spectra in a magnetic field. Fulltekst i vitenarkiv
• Helgaker, Trygve (2022). Kvantemekanikk og kjemi. Fulltekst i vitenarkiv
• Hansen, Audun Skau; Helgaker, Trygve & Laestadius, Andre (2022). En introduksjon til kvantekjemi / Samarbeid med Talentsenter i realfag. Fulltekst i vitenarkiv
• Helgaker, Trygve (2022). The Exotic Chemistry in an Ultrastrong Magnetic Field. Fulltekst i vitenarkiv
• Dembinski, S.; Karwowski, J.; Szudy, J. & Helgaker, Trygve (2022). Foreword. Molecular Physics. ISSN 0026-8976. 120(19-20). doi: 10.1080/00268976.2022.2144060. Fulltekst i vitenarkiv
• Helgaker, Trygve (2022). Current-Density-Functional Theory in a Convex Treatment. Fulltekst i vitenarkiv
• Helgaker, Trygve (2022). Molecular Bonding, Structure, and Dynamics in a Strong Magnetic Field. Fulltekst i vitenarkiv
• Helgaker, Trygve (2022). Molecular Bonding, Structure, and Dynamics in a Strong Magnetic Field. Fulltekst i vitenarkiv
• Stenseth, Nils Christian; Andreassen, Karin Marie; Danielsen, Anne; Helgaker, Trygve; Jansen, Eystein & Moser, Edvard Ingjald [Vis alle 11 forfattere av denne artikkelen] (2022). Grunnforskningen er truet. Fulltekst i vitenarkiv
• Helgaker, Trygve (2022). Kvantekjemi—på liv og død. Fulltekst i vitenarkiv
• Helgaker, Trygve (2022). Diversity at the Hylleraas Centre. Fulltekst i vitenarkiv
• Helgaker, Trygve (2021). The Exotic Chemistry in a Strong Magnetic Field. Fulltekst i vitenarkiv
• Helgaker, Trygve (2021). Molecular Dynamics and Rovibrational Spectra in a Strong Magnetic Field. Fulltekst i vitenarkiv
• Helgaker, Trygve (2021). The Exotic Chemistry in a Strong Magnetic Field. Fulltekst i vitenarkiv
• Helgaker, Trygve (2021). The Exotic Chemistry in an Ultrastrong Magnetic Field. Fulltekst i vitenarkiv
• Helgaker, Trygve (2021). Hylleraas-senteret. Fulltekst i vitenarkiv
• Helgaker, Trygve (2021). Forskere på sporet av gammelt mysterium: Slik «ser» trekkfugler magnetfelt. [Internet]. NRK. Fulltekst i vitenarkiv
• Tellgren, Erik & Helgaker, Trygve (2020). Strong Magnetic Field-Induced Chemical Bonding. Fulltekst i vitenarkiv
• Helgaker, Trygve (2020). Chemistry in a Strong Magnetic Field. Fulltekst i vitenarkiv
• Eriksen, Janus J.; Stopkowicz, Stella; Jagau, Thomas-C. & Helgaker, Trygve (2020). Foreword: Prof. Gauss Festschrift. Molecular Physics. ISSN 0026-8976. 118. doi: 10.1080/00268976.2020.1817247. Fulltekst i vitenarkiv
• Helgaker, Trygve (2020). Quantum Chemistry – A Matter of Life and Death. Fulltekst i vitenarkiv
• Helgaker, Trygve (2020). Hylleraas Centre for Quantum Molecular Sciences – Applying For and Setting Up a Centre of Excellence. Fulltekst i vitenarkiv
• Helgaker, Trygve (2020). SFF V: Assessment Criteria — Applying For and Setting Up a Centre of Excellence. Fulltekst i vitenarkiv
• Laestadius, Andre; Penz, Markus; Tellgren, Erik; Ruggenthaler, Michael; Kvaal, Simen & Helgaker, Trygve (2019). Guaranteed convergence of a regularized Kohn-Sham iteration in finite dimensions. Fulltekst i vitenarkiv Vis sammendrag

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

• Tellgren, Erik; Helgaker, Trygve & Sen, Sangita (2019). Unifying kinetic energy density and current density in density-functional theory. Fulltekst i vitenarkiv
• Tellgren, Erik; Helgaker, Trygve & Sen, Sangita (2019). Unifying kinetic energy density and current density in density-functional theory. Fulltekst i vitenarkiv
• Tellgren, Erik; Helgaker, Trygve & Sen, Sangita (2019). Unifying kinetic energy density and current density in density-functional theory. Fulltekst i vitenarkiv
• Helgaker, Trygve (2019). Molecular Magnetic Properties. Fulltekst i vitenarkiv
• Helgaker, Trygve (2019). Geometry optimization. Fulltekst i vitenarkiv
• Helgaker, Trygve (2019). Kvantekjemi — på liv og død. Fulltekst i vitenarkiv
• Helgaker, Trygve (2019). Utenomjordisk kjemi. Fulltekst i vitenarkiv
• Helgaker, Trygve (2019). Kvantemekanikk og kjemi. Fulltekst i vitenarkiv
• Helgaker, Trygve (2019). Egil A. Hylleraas – en norsk pioner innen kvantemekanikk. Fulltekst i vitenarkiv
• Holzer, Christof; Teale, Andrew Michael; Hampe, Florian; Stopkowicz, Stella; Helgaker, Trygve & Klopper, Wim (2019). Erratum: GW quasiparticle energies of atoms in strong magnetic fields (Journal of Chemical Physics (2019) 150 (214112) DOI: 10.1063/1.5093396). Journal of Chemical Physics. ISSN 0021-9606. 151(6). doi: 10.1063/1.5120100. Fulltekst i vitenarkiv
• Helgaker, Trygve (2019). Robust All-Electron Optimization of Orbital-Free Density-Functional Theory. Fulltekst i vitenarkiv
• Hauge, Eirill Strand; Pedersen, Thomas Bondo & Helgaker, Trygve (2021). Extrapolating the Electric Dipole Moment. Universitetet i Oslo. Fulltekst i vitenarkiv
• Jestilä, Joakim Samuel; Uggerud, Einar & Helgaker, Trygve (2021). Reductive gas-phase ion chemistry of simple oxocarbons in the presence of alkali and alkaline earth metals. Universitetet i Oslo. Fulltekst i vitenarkiv Vis sammendrag

  In a circular carbon economy, carbon dioxide (CO2) is recycled and used as a molecular building block to make fuels, chemicals and materials, driven by renewable energy sources. Hence, the molecule represents a potential replacement for oil, natural gas and coal as one of the primary sources of carbon. A major bottleneck stems from the fact that CO2 requires activation before it can be converted. This work explores the activation and reduction of CO2 by the alkali metal and alkaline earth metal chloride anions on a fundamental level. It sheds light on relevant factors in the conversion of CO2 to valuable products such as oxalate (C2O42−) and carbon monoxide (CO), as well as further conversion of the latter. The aforementioned processes proceed via metal-CO2 intermediates—chemical species formed during conversion of reactants to products—and this thesis links their properties to the extent of CO2 activation. Specifically, more complete electron transfer from the metal to CO2 and larger structural changes in the intermediates are associated with lower energetic demands for further reaction and conversion. These results could prove useful for the development of efficient CO2-recycling processes.

• Hansen, Audun Skau; Pedersen, Thomas Bondo; Helgaker, Trygve & Kvaal, Simen (2021). Local correlation methods for infinite systems. Universitetet i Oslo. Fulltekst i vitenarkiv Vis sammendrag

  Quantum Chemistry constitutes an extensive framework for accurately simulating the electronic wavefunction of atoms and molecules. The same framework may in principle be applied to the domain of periodic structures such as crystals, but is in practice severely limited by the infinite nature of these structures in conjunction with the computational complexity of quantum chemical methods. In his thesis, the candidate utilizes a mathematical structure known as bi-infinite block-Toeplitz matrices in order to smoothly transition between the molecular and periodic realm. Furthermore, he extends the divide-expand-consolidate methods originally devised for molecules to the periodic case, and demonstrates that this procedure can reduce the computational scaling of the simulation while retaining systematic control over the error.

• Skjelstad, Bastian; Balcells, David & Helgaker, Trygve (2020). A Computational Perspective on the Interplay Between Metal Dopant and Support in the Structure and Reactivity of Oxidized Cubanes. Universitetet i Oslo. Fulltekst i vitenarkiv
• Austad, Jon; Helgaker, Trygve & Tellgren, Erik (2020). Theoretical Investigations of Molecular Electronic Structure in a Magnetic Field. Universitetet i Oslo. Fulltekst i vitenarkiv Vis sammendrag

  Most available literature on molecular systems in magnetic fields are limited to special cases: Either small or highly symmetric species of specific orientation to the field, or fields of low intensity - or combinations of the above. This dissertation is devoted to the development, implementation, calibration, analysis and usage of computational quantum chemistry methods that are freed from such restrictions. Three research papers are presented. One deals with the inner workings of a generalized variant of Density Functional Theory which allows the magnetic field to be directly included (BDFT), and explores in depth how various functionals handle diamagnetic, paramagnetic and aromatic molecules. The second paper investigates the rich chemistry of the helium dimer in a strong magnetic field, thoroughly maps out the electronic structure of the molecule, and presents the many different magnetic bonding mechanisms and interactions that exist in this regime. The final paper revolves around application of highly accurate wave-function methods to determine the influence of terrestrially available magnetic fields on water. The work of this thesis presents important contributions to theoretical chemistry in the pres- ence of magnetic fields.

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