This years biannual Löwdin Symposium is dedicated to show case the research of the Löwdin Lecturers and at the same time high light the work of six young promising scientists in the field from the Nordic countries. This is inline with the deed of the donation, which is to honor Per-Olov Löwdin for his contributions to the field, and to support the realization of quantum chemical lectures for the enlightenment  of students and scientists with respect to the field. Thus, it is our pleasure this year to invite the Löwdin Lecturers of  2022, 2023, and 2024 together with 6 selected lecturers to give us a flavor of the current status of theoretical chemistry research in the world and the Nordic Countries.Below you will find the schedule to the symposium and the abstracts for each of the presentations.

You are very welcome!

On behalf of the Committee for Quantum Chemical Löwdin Lectures,
Prof. Roland Lindh, chairman
 The venue is at the Biomedical Center at Uppsala University, the Svedberg lecture hall (B8). Click here to find your way at BMC. BMC is conveniently reached from Uppsala Central train station with buses, 3, 4 and 11.  

Schedule

          Session I
  • 10:00-10:15  Deputy Vice Chancellor Prof. Charlotte Platzer Björkman/Prof. Roland Lindh: Opening statement
  • 10:15-11:00 Prof. Clemence Corminboeuf, "Solving computational/quantum chemical problems with a “digital” touch (or vice versa)"
  • 11:00-11:30 Prof. David Balcells, "Data-Driven Transition Metal Chemistry with Evolutionary and Deep Learning Approaches"
  • 11:30-12:00 Prof.  Susi Lehtola, "Recent developments in fully numerical electronic structure calculations"
 
  • 12:00-13:15 Lunch

          Session II
  • 13:15-14:00 Prof. Heather Kulik, "Machine learning accelerated design from molecules to materials"
  • 14:00-14:30 Prof. Janus J. Eriksen, "Exploiting Non-Abelian Point-Group Symmetry to Estimate the Exact Ground-State Correlation                                                                        Energy of Benzene in a Polarized Split-Valence Triple-Zeta Basis Set"
  • 14:30-15:00 Prof. Ida-Marie Høyvik, "Wave function-based density operators for electronic structure theory"
 
  • 15:00-15:15 Coffee break

           Session III
  • 15:15-16:00 Prof. Joseph Subotnik, "Phase Space Approaches to Electronic Structure: A New Paradigm For Chiral Induced Spin                                                                              Selectivity"
  • 16:00-16:30 Prof. Nanna List, "Ultrafast multimodal probing of excited-state dynamics from first principles"
  • 16:30-17:00 Prof. Mickaël Delcey, "A universal framework for multiconfigurational DFT"
  • 17:00-17:15 Prof. Roland Lindh: Closing Statement 

Session Chairs

Prof. Eszter Borbas, Uppsala University
Chair Session I, 10:15-12:00

Prof. Philippe Wernet, Uppsala University
Chair Session II, 13:15-15:00

Prof. Henrik Ottosson, Uppsala University
Chair Session III, 15:15-17:00

List of abstracts

Solving computational/quantum chemical problems with a “digital” touch (or vice versa)
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Prof. Clemence Corminboeuf
Laboratory for Computational Molecular Design, Lausanne, Switzerland
​Löwdin Lecturer 2022

Abstract
A source of inspiration for quantum chemists involves overcoming the complexity of the electronic structure problem by leveraging physics-based statistical models.[1] Likewise, the field of computational chemistry has increasingly relied on data-driven pipelines aimed at facilitating or accelerating the discovery of molecules and materials. This talk will specifically illustrate the valuable interplay between computational, quantum, and digital chemistry.
The talk will thus focus on the distinct ingredients that are essential to achieve efficient computational molecular discovery (e.g., accurate statistical models, objective function, top-down/bottom-up database).[2] We will highlight the benefits and challenges that result from the use of statistical models to predict properties associated with chemical reactions[3] and illustrate how we improve the accuracy of physics-based representations and broaden their field of applicability. We will demonstrate how the above developments are naturally integrated in inverse design workflows and present assortment of computational and digital tools developed to accelerate the exploration[4] and optimization of homogeneous catalysts. The interoperability of these tools, assembled into the NaviCat (Navigating Catalysis) platform, will be illustrated through proof-of-principle examples and experimental
validations.[5] This overview illuminates our determination to adopt an interdisciplinary approach to the field of theoretical/computational chemistry.

References:
[1] O. A. von Lilienfeld, Angew. Chem. Int. Ed.; 2018, 57, 4164.
[2] S. Gallarati, P. van Gerwen, A. A. Schoepfer, R. Laplaza, C. Corminboeuf Chimia, 2023, 77, 39.
[3] S. Gallarati, F. Fabregat, R. Laplaza, S. Bhattacharjee, M. D. Wodrich, C. Corminboeuf Chem. Sci. 2021, 12,
6879.
[4] R. Laplaza, S. Das, M. D. Wodrich, C. Corminboeuf Nat. Protoc. 2022, 17, 2550.
[5] S. Das, R. Laplaza, J. T. Blaskovits, C. Corminboeuf J. Am. Chem. Soc. 2024, 146, 15806.
Data-Driven Transition Metal Chemistry with Evolutionary and Deep Learning Approaches
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Res. Prof. David Balcells
Hylleraas Centre of Excellence for Quantum Molecular Sciences, Oslo, Norway
​Abstract
In this talk, I will present a brief overview on the research done in my group in the fields of evolutionary and deep machine learning, and how we are trying to combine these two approaches[1] in the discovery of transition metal complexes. In particular, I will focus on multiobjective optimization problems[2], moving from 2D Pareto fronts to 3D Pareto surfaces using genetic algorithms. Further, I will discuss our efforts to implement a  variational autoencoder based on the junction-tree formalism for the unconditional and conditional generation of metal ligands[3]. More recent work on the combination of these two approaches will also be presented.

References:
[1] Kneiding, H.; Balcells, D. Chem. Sci., 2024, 15, 15522;
[2] Kneiding, H.; Nova, A.; Balcells, D. Nat. Comput. Sci., 2024, 4, 263;
​[3] Strandgaard, M.; Linjordet, T.; Kneiding, H.; Burnage, A.; Nova, A.; Jensen, J. H.; Balcells, D. ChemRxiv, 2024, DOI: 10.26434/chemrxiv-2024-mzs7b.


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Recent developments in fully numerical electronic structure calculations
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Prof. Susi Lehtola
Univ. of Helsinki, Helsinki, Finland
​Abstract
I will discuss our recent avenues into fully numerical [1] electronic structure calculations, with the ultimate goal of developing new reusable [2] software infrastructure for electronic structure calculations with numerical atomic orbital (NAO) basis sets, which we expect to replace Gaussian basis technology in the near future. Although NAO methods have been used for a long time in the solid state physics community, the shortcoming of the traditional implementations is the use of non-variational solution methods for the atomic problems combined with the use of low-order numerical methods.
​We have recently demonstrated that the use of high-order polynomial approximations affords considerably faster convergence to the complete basis set (CBS) limit [3, 4], resulting in orders of magnitude reductions in the necessary number of degrees of freedom in the discretization (see attached figure). The new implementations have also proven to be invaluable for the study of numerical ill-behavior in recent density functionals [5]: for example, self-consistent fully numerical calculations on atoms demonstrate that most members of the Minnesota family do not converge to the CBS limit due to unphysical kinks they produce in the wave functions [4, 6], which can tentatively be addressed to overfitting. NAO basis sets can be constructed for well-behaved density functionals by studying atoms in confinement, the simplest model being the spherical hard-wall cavity. Although such models have been previously examined in the literature, the studies have been non-systematic and usually considered only small parts of the periodic table. Our recent systematic study [7] has shown that many interesting aspects of various elements' chemistry can already be observed in density functional calculations of atoms in hard-wall confinement: for example, the well known chemical d-orbital character of Ca is obvious in our calculations, the valence electrons hopping from the 4s orbital to the 3d orbital already in mild confinement.

References:
[1] S. Lehtola, Int. J. Quantum Chem. 119, e25968 (2019). doi:10.1002/qua.25968
[2] S. Lehtola, J. Chem. Phys. 159, 180901 (2023). doi:10.1063/5.0175165
​[3] S. Lehtola, Int. J. Quantum Chem. 119, e25945 (2019). doi:10.1002/qua.25945
[4] S. Lehtola, J. Phys. Chem. A 127, 4180 (2023). doi:10.1021/acs.jpca.3c00729
[5] S. Lehtola and M. A. L. Marques, J. Chem. Phys. 157, 174114 (2022). doi:10.1063/5.0121187
[6] S. Lehtola, J. Chem. Theory Comput. 19, 2502 (2023). doi:10.1021/acs.jctc.3c00183
​[7] H. Åström and S. Lehtola, arXiv:2408.11595.


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Machine learning accelerated design from molecules to materials
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Prof. Heather Kulik
MIT, Cambridge, MA, USA
​Löwdin Lecturer 2023
​Abstract
Machine learning (ML)-accelerated discovery of materials, i.e., via surrogate models paired with efficient optimization algorithms, holds immense promise to overcome the conventional limitations of computational cost of first-principles electronic structure calculations. Nevertheless, surrogate models inherit the bias of the underlying electronic structure method. In most cases, the electronic structure method of choice is Kohn-Sham density functional theory (DFT), which suffers simultaneously from both self-interaction error or density delocalization error and static correlation error, to varying degrees depending on the density functional approximation. When novel and challenging materials, such as open shell transition metal complexes, is the target of a discovery campaign, few benchmarks are liable to be available for selecting the optimal electronic structure method or DFT functional. Furthermore, investigation of large regions of chemical space (e.g., by varying metal, coordination environment, or oxidation state in a transition metal complex) will likely lead to the conclusion that different electronic structure methods are more suitable for some compounds than others. I will describe our development of ML-informed density functional models, including a recommender that can identify which DFT functional or parameterization is most predictive to obtain accurate properties of transition metal complexes. As an alternative strategy, I will discuss our efforts to use machine learning (ML) to accelerate the computational tailoring and design of complex materials by leveraging experimental datasets. I will discuss ways we have leveraged experimental data to build models on smaller data sets of molecular properties. Natural language processing has enabled us to train ML models to predict experimentally reported measures of metal-organic framework (MOF) stability ranging from thermal stability to stability in water. I will describe how we have leveraged this to design de novo materials. Finally, I will describe how we have gone from machine learning accelerated discovery of novel mechanically reactive (i.e., mechanophore) substituents to network level polymer properties. This example demonstrates how it is now possible to go from computational prediction to experimentally realized materials with novel properties visible to the human eye.


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Exploiting Non-Abelian Point-Group Symmetry to Estimate the Exact Ground-State Correlation Energy of Benzene in a Polarized Split-Valence Triple-Zeta Basis Set
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Prof. Janus J. Eriksen
DTU Chemistry, Denmark
​Abstract
Local electronic-structure methods in quantum chemistry operate on the ability to compress electron correlations more efficiently in a basis of spatially localized molecular orbitals than in a parent set of canonical orbitals. However, many typical choices of localized orbitals tend to be related by selected, near-exact symmetry operations whenever a molecule belongs to a point group, a feature which remains largely unexploited in most local correlation methods. In this talk, I will demonstrate how to leverage a recent unitary protocol for enforcing symmetry properties among localized orbitals [1] to yield a high-accuracy estimate of the exact ground-state correlation energy of benzene (D6h) in correlation-consistent polarized basis sets of both double- and triple-ζ quality [2]. Through an initial application to many-body expanded full configuration interaction (MBE-FCI) theory [3-5], we show how molecular point-group symmetry can lead to computational savings that are inversely proportional to the order of the point group in a manner generally applicable to the acceleration of modern local correlation methods [6]. In combination with an efficient clustering of orbitals [7], the developments reported here considerably improve upon the computational efficacy of MBE-FCI.
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References:
[1]: Greiner, J.; Eriksen, J. J.: Symmetrization of Localized Molecular Orbitals. J. Phys. Chem. A 127, 3535 (2023)
[2]: Greiner, J.; Gauss, J.; Eriksen, J. J.: Exploiting Non-Abelian Point-Group Symmetry to Estimate the Exact Ground-State Correlation Energy of Benzene in a Polarized Split-Valence Triple-Zeta Basis Set. J. Phys. Chem. Lett. 15, 9881 (2024)
[3]: Eriksen, J. J.; Lipparini, F.; Gauss, J.: Virtual Orbital Many-Body Expansions: A Possible Route towards the Full Configuration Interaction Limit. J. Phys. Chem. Lett. 8, 4633 (2017)
[4]: Eriksen, J. J.; Gauss, J.: Generalized Many-Body Expanded Full Configuration Interaction Theory. J. Phys. Chem. Lett. 10, 7910 (2019)
[5]: Eriksen, J. J.; Gauss, J.: Incremental Treatments of the Full Configuration Interaction Problem. WIREs Comput. Mol. Sci. 11, e1525 (2021)
[6]: Eriksen, J. J.: The Shape of Full Configuration Interaction to Come. J. Phys. Chem. Lett. 12, 418 (2021)
​[7]: Greiner, J.; Gauss, J.; Eriksen, J. J.: Error Control and Automatic Detection of Reference Active Spaces in Many-Body Expanded Full Configuration Interaction. J. Phys. Chem. A 128, 6806 (2024)



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Wave function-based density operators for electronic structure theory
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Prof. Ida-Marie Høyvik
NTNU, Trondheim, Norway 
​Abstract
In molecular electronic-structure theory we have a wide variety of electronic wave function models, ranging from the simple Hartree-Fock model to the exact (for a given one-electron basis) full configuration interaction model. The wave function models have been extensively tested and benchmarked with respect to capabilities and limitations, so we often know which wave function model provides a descent description for the molecule at hand. However, if a molecule interacts with a large environment such as a surface or solvent, information will irreversibly be lost over time and this introduces uncertainty about the state of the molecule. This uncertainty cannot be described by a wave function, but a density operator provides the natural framework for representing such statistical mixtures. In this talk I will present our work on establishing density operators from standard wave function parametrizations with emphasis on exact state theory (full configuration interaction) and coupled cluster theory. Constructing density operators from known wave functions makes it possible to describe processes not covered by wave functions while still being in control of the electronic-structure description of the molecule. Furthermore, such an approach allows us to use existing highly efficient coupled cluster implementations for the density operator framework. ​


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Phase Space Approaches to Electronic Structure: A New Paradigm For Chiral Induced Spin Selectivity
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Prof. Joseph Subotnik
Princeton Univ. NJ, USA
Löwdin Lecturer 2024
Abstract
 The Born-Oppenheimer approximation is the cornerstone of chemistry, the idea that electronic structure and molecular orbitals are defined relative to a stationary set of coordinates for the nuclei.  This premise is based on the important differences in mass between electrons and nuclei, and the all important fact that nuclei move much slower than electrons and appear effectively frozen on the time scale of electronic fluctuations. Nevertheless, it is known that the Born-Oppenheimer approximation breaks down quite often, quite famously in the context of photochemistry and/or electron transfer. Slightly less well known is the fact that a classical BO theory does not conserve momentum (linear or angular) even when there is no obvious breakdown.  In this talk, I will discuss this failure of the BO approximation, offer up a phase space electronic Hamiltonian as an improvement to restore conservation, and then suggest a new paradigm for understanding how nuclear entanglement with electronic degrees of freedom may well lead to chiral induced spin selectivity (an exciting phenomenon discovered in recent years).​
Ultrafast multimodal probing of excited-state dynamics from first principles
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Prof. Nanna List
KTH, Stockholm, Sweden
Abstract
Ultrafast excited-state dynamics in molecules are ubiquitous across various disciplines ranging from biology through chemistry to physics. The additional energy introduced by photoexcitation can drive processes significantly different from those available under thermal conditions, underpinning an ever-expanding range of technological applications. Time-resolved experiments provide windows into the evolving dynamics, however, the complexity of the measured data often complicates interpretation. In this talk, I will discuss the role of theory and simulations both as an exploratory (predating experiment) and interpretative (postdating experiment) tool in deciphering ultrafast excited-state dynamics. I will present recent joint theory-experiment work on probing ultrafast electronic structure changes and hydrogen dynamics using time-resolved spectroscopic and diffraction probes. Our results highlight the interplay between theory and experiment, and the importance of a multimodal approach in revealing mechanistic pictures of ultrafast excited-state dynamics.​
A universal framework for multiconfigurational DFT
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Prof. Mickaël Delcey
Lund University, Sweden

Abstract
 Strong correlation has been argued to be the last remaining weakness of DFT.[1] It shows up in several situations of high relevance to modern chemistry, such as transition metal complexes, especially antiferromagnetically coupled multi-metallic complexes, as well as in photochemistry, especially around conical intersections. Decades of development have provided us with a zoo of methods trying to solve this issue by combining DFT with multiconfigurational wavefunctions. This plethora of methods has dispersed the efforts of the community and prevented the emergence of a standard.
Here, I show how most of these methods can be united under a single framework. Indeed, most of these approaches which are not already a form of multiconfigurational pair-density functional theory (MC-PDFT)[2] can benefit from being re-cast as one, simply becoming different MC-PDFT functionals. By implementing all these approaches into our recently introduced and highly efficient variational MC-PDFT implementation[3], we can for the first time compare them on a number of strong correlation cases. From these results and formal arguments, we provide useful insights for future functional developments.
References:
[1] A. D. Becke, J. Chem. Phys. 140, 18A301 (2014); N. Mardirossian and M. Head-Gordon, Mol. Phys., 115, 2315–2372 (2017)
[2] F. Moscardó and E. San-Fabián, Phys. Rev. A, 44, 1549−1553 (1991); G. Li Manni, R. K. Carlson, S. Luo, D. Ma. J. Olsen, D. G. Truhlar and L. Gagliardi, J. Chem. Theory Comput., 10, 3669–3680. (2014)
​[3] M. Scott, G. L. S. Rodrigues, X. Li and M. G. Delcey, J. Chem. Theory Comput., 20, 2423–2432 (2024)