Scandinavia has a strong tradition in quantum chemistry and electronic-structure theory, going back to the early days of quantum mechanics. After in discussion of the early contributions of Burrau, Hylleraas and Møltter in the 1920s and 1930s, I present the Swedish school of quantum chemistry, created in the 1950s and 1960s by Löwdin and Fischer-Hjalmars, and how their students diversified the field and established important research groups in Denmark and Norway in the 1970s. The account of the 1980s and 1990s is of a more personal character, emphasising those developments and contributions underlying the program system DALTON. Today, quantum chemistry and more generally theoretically chemistry is a lively and strong research field in all the Scandinavia countries, but the developments since 2000s are given little attention in the presentation.
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. Attempts to solve these issues within the current Kohn-Sham DFT framework are often limited and unreliable. Formally, the proper way to deal with strong correlation is with multiconfigurational methods, but their cost has simply been prohibitive for practical large-scale use.
Here, we present a way to generalize DFT to strong correlation problems by abandoning the spin-DFT formulation and instead turning to the on-top pair-density, giving rise to multiconfigurational pair-density functional theory (MC-PDFT). While this concept has been suggested for some years,[2] we introduced the first variational and highly efficient implementation, and demonstrated how the cost can be on-par or even sometimes below that of standard DFT.[3] We then showcase more recent work moving beyond pure PDFT functionals towards global and range-separated hybrids.
[1] 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)
I will describe our recent efforts towards an efficient implementation of the energies of variational many body perturbation theory and cluster perturbation theory series targeting the coupled cluster singles and doubles energy through fifth order utilizing the resolution of the identity approximation. I will illustrate the computational performance of the models relative to the coupled cluster singles and doubles model and show that the computational costs of the fourth and fifth order models are an order of magnitude lower than the CCSD target state calculation. For the fourth and fifth order perturbation models, we developed massively parallel implementations that utilize graphical processing units for accelerating the tensor contractions. Using the developed framework, coupled cluster singles and doubles quality results can be obtained for system sizes approaching 2000 basis functions which are far beyond the reach of conventional calculations and with small time to solution, arising from the massively parallel implementation.
Historically, electronic structure theory has revolved around closed quantum system (i.e., quantum systems completely isolated from the surrounding environment) wave function parameterizations. However, to accurately model charge and energy transport phenomena, the quantum system of interest must be able to interact with its environment. This calls for explicit electronic structure theories and response theory methodologies for electronically open quantum systems. Recently, Matveeva et al.[1] presented the particle-breaking Hartree-Fock (PBHF) model for electronically open quantum systems, and this marks the beginning of building an analogous framework (to that of closed quantum systems) of correlated wave function and response theory methodologies for electronically open quantum systems. In this work, we develop time-dependent particle-breaking Hartree-Fock (TDPBHF) theory, hereby allowing us to explore excited electronic manifolds and response properties of electronically open quantum systems.
[1] Matveeva et al., J. Phys. Chem. A, 2023, 127, 1329-1341
Quantum computing is an emerging technology with great promise for solving certain computational problems significantly faster than classical computer architectures. Currently, available quantum hardware is quite limited in terms of qubit counts and noise sensitivity, which prevents the execution of quantum algorithms that rely on deep quantum circuits. Nevertheless, one can hope that quantum computing hardware will eventually mature to the point of usefulness, motivating the development of quantum chemistry algorithms suitable for quantum computing architectures. Much attention has been paid to solving the ground-state electronic Schrödinger equation, in particular with the variational quantum eigensolver (VQE) algorithm. Considerably less attention has so far been paid to the treatment of general molecular properties and excited states. However, significant progress has recently been made with the quantum equation of motion (qEOM) and quantum linear response (qLR) frameworks. Here, we explore Davidson methods for obtaining excitation energies and other linear response properties within quantum self-consistent linear response (q-sc-LR) theory from a unitary coupled cluster (UCC) wave function. Davidson-type methods allow for obtaining only a few selected excitation energies without explicitly constructing the electronic Hessian since they only require the ability to perform Hessian-vector multiplications. We apply the Davidson method to calculate the excitation energies, linear response properties such as static polarizabilities, and damped (complex) linear response, with application to the K-edge X-ray absorption spectroscopy and the C6 coefficients.
I will present recent work to develop a second-quantization formulation of frequency-domain response theory based on the Liouville-Von Neumann equation for non-eigenstates of the unperturbed molecular Hamiltonian, using an exponential parameterization for the time-dependent density operator.
Full quantum mechanical descriptions are not feasible for large molecular systems due to the high computational cost. Multiscale and multilevel/embedding methods divide the full system into two interacting subsystems: a target system of interest and an environment. These methods typically neglect interactions that allow electron flow between subsystems. This work incorporates charge-transfer interactions to achieve a more comprehensive description of the electronic environment's impact on the target system. Our approach employs the theory of open quantum systems, specifically utilizing the Redfield equation to focus on fractional charging phenomena and their implications for systems weakly coupled to their environments. The study includes a derivation of the Redfield equation accounting for charge transfer effects in electronically open molecular systems, alongside a discussion of the underlying assumptions.
The term "symmetry breaking" in electronic structure calculations is often considered as negative. Although the symmetry of electron density must be symmetric in respect to the symmetry of atomic nuclei, it is possible that such a symmetric solution is a linear combination of two either interactive or non-interactive states. The effect is highlighted for the systems with odd numbers of electrons, e.g. atoms, or atomic dimers with odd numbers of electrons. Multiconfigurational calculations of single center ions and molecules demonstrate the effect.
The eT program is a new open-source electronic structure program. The first version of eT— released in 2020—featured an efficient coupled cluster code (with CCS, CC2, CCSD, CC3, and CCSD(T)) built on Cholesky factorized electronic repulsion integrals. The program also included a multilevel and multiscale framework, targeting the calculation of intensive properties of large molecular systems at significantly reduced costs.
Cholesky factorization of the electron repulsion integrals has a long tradition within the Scandinavian quantum chemistry community. The factorization makes it possible to increase the molecular system size significantly, without the use of AO-integral-direct algorithms. In multilevel calculations, the Cholesky decomposition becomes even more useful, as it can be used to target the accuracy of the integrals in a reduced set of molecular orbitals. Previously, the Cholesky decomposition of the two-electron integrals has been a bottleneck, and density fitting (or resolution-of-identity) with a predefined set of auxiliary basis functions has been more popular. With the efficient two-step decomposition algorithm implemented in eT, this bottleneck is eliminated and the Cholesky decomposition typically costs less than determining the Hartree-Fock orbitals.
In 2024, eT v2.0 will be released. In its second major version, the program has developed beyond a coupled cluster program, with a wider variety of standard quantum chemistry models. The program also includes new models targeting new chemistries, such as the strong coupling with light inside optical cavities.
Quantum chemical modelling of atmospheric new particle formation, a process in which molecules form clusters growing into nanometer-sized particles, has attracted significant attention in last decades. Where classical nucleation theory fails, numerical solution of the cluster birth–death equations emerges as a promising alternative approach. Despite the successful prediction of trends in formation of strongly bound clusters aligning with experimental results, the absolute values are often off by several orders of magnitude and additional discrepancies particularly appear in weakly binding molecular systems.
We have automated tools for communication with 3rd party quantum chemistry program (Gaussian, ORCA, XTB, Turbomole, etc.) and programs for exploring configurational space of molecules/clusters (ABCluster or CREST). An enhanced massive data file manipulation as well as the communication with SLURM job scheduler allows as to automate the configuration sampling workflow for obtaining thermochemical data of molecular clusters, significantly augmenting the scale of systems that can be investigated from tens to hundreds/thousands compared to prior studies. However, the data quality is as important as their quantity. Therefore, in this particular work, we focused on benchmarking our computational methods for wide range of molecular clusters systems. We refrain from conventional benchmark between electronic energy methods, instead prioritizing the acquisition of more precise binding free energies and reaction free energies, which dictate evaporation rates and cluster stabilities. Particularly, we are after capturing vibrational anharmonic frequencies, population of low-energy minima, and the dynamics of transition between these minima.
As an illustrative example, we studied the hydration process of the bisulfate ion, where theoretical predictions struggle to reconcile with experimental data. While our rapid and automated workflow yield qualitative results similar to other theoretical calculations at another level of theory, the deviations between these calculations are not always negligible. Furthermore, none of these calculations fully align with experimental findings. While acknowledging the experimental challenges inherent in measuring systems containing sulfuric acid/bisulfate, it is plausible that the commonly used theoretical methodology is ill-suited for weakly bound systems with dynamic structural fluctuation. Hence, an alternative verification strategy becomes imperative to compare theoretical results with experiments.
To this end, we employ umbrella sampling to obtain free energy profiles for the evaporation of molecules from clusters. Given the computational complexity of performing molecular dynamics simulations at the quantum chemistry level, we train a machine learning models, specifically neural networks, using a dataset comprising molecular cluster energies and gradients obtained through high-level quantum-chemistry methods. This approach enables us to capture the dynamic behaviour exhibited by weakly bound clusters and opens up for accurate free energy calculations, which has previously been out of reach.
The status quo in electronic structure software is that programs are developed in isolation, as in the so-called silo model. When new methods and algorithms are published, they have to be reimplemented separately in every software package to become usable. As most development efforts come from graduate students, who start out with little to no programming knowledge and who stop maintaining and developing the code after their PhDs, this model has lead to the present situation in which many of the core algorithms of various program packages are (i) outdated, in the sense that better algorithms are available in the literature, as well as (ii) hard to maintain, meaning that adding new features is difficult.
However, there are better alternatives. Literature shows that free and open source software (FOSS) carries economic benefits in software development and product quality, which facilitates building up mature FOSS components of the highest quality. An excellent example is afforded by our open source Libxc library of density functional approximations (DFAs), which is currently used by >40 FOSS and commercial electronic structure programs for various types of systems (atoms, molecules, crystals) with various numerical approaches (atomic basis sets, plane waves, finite differences, finite elements). The standard implementations in Libxc have removed the need to maintain >40 separate implementations of DFAs, and facilitate access to novel DFAs as new functionals only have to be implemented in Libxc to make them usable in any of the programs supporting Libxc.
I argue that the example of Libxc shows that any embarrasingly parallel operations that are required in electronic structure calculations can and should be standardized, as this will enable unforeseen efficiencies in implementation and algorithm development similarly to what happened to basic linear algebra subprograms (BLAS) upon their standardization in the 1970s. The main stopping stone is the issue of reusability, which has traditionally not been a core consideration by electronic structure software developers: hand-in-hand with the silo model, most developers only operate within one code and are not aware of the requirements and rewards of software reusability. This aim of talk is to raise awareness on these issues and call other developers to arms: to answer the demands of big data, we need more reusable standard libraries to deprecate outdated hard-to-maintain code.
I will focus on methods for implementing coupled-cluster methods on GPUs using CUDA math libraries like CUBLAS and CUTENSOR, in conjunction with asynchronous data movement, but also describe the relative merits of OpenMP, OpenACC and standard language parallelism (Fortran DO CONCURRENT) for implementing tensor expressions found in quantum chemistry codes. This is motivated by my work on NWChem but is applicable to codes like Dalton and CFOUR, among others.
VeloxChem is a science- and educational-enabling software platform for quantum molecular modeling at the levels of DFT and TDDFT. It is strictly object-oriented and written in a hybrid of the Python and C++/CUDA/HIP programming languages and it implements extremely efficient parallelism through MPI and OpenMP. Noteworthy functionalities include real and complex response functions up to cubic order and built-in interoperability with classical molecular dynamics simulations by means of an automatized force-field generation. It installs with conda on Windows/macOS/Linux personal computers as well as it can harness the power of modern supercomputers with GPU hardware acceleration.
Largely based on VeloxChem is the eChem Jupyter book initiative that allows for interactive deep learning of the theory and methods in theoretical chemistry. The Jupyter notebooks upon which this electronic book is built present theory and numerical methods with intertwined illustrative Python code cells. In addition to this educational aspect, we find notebooks to be useful for code prototyping as a means to accelerate the process of software development.
The VIAMD graphical user interface enables visual interactive analysis of the complex molecular systems that VeloxChem can address, including the electronic structures of ground and excited states together with the associated transition densities.
Neurodegenerative conditions like Parkinson's and Alzheimer’s are the most common forms of dementia. Optogenetics combines optics and genetics to gain insight into brain function by genetically inserting light-sensitive transmembrane proteins into neurons. Channelrhodopsin-2 (ChR2) is an ion channel protein that enables precise temporal control turning neurons on or off in response to light.
In vivo optogenetic experiments have a number of complications. One such complication is related to the wavelength of the visible light needed to activate ChR2. This results in high scattering by biological tissue as well as competition with hemoglobin which absorbs at a similar wavelength. Activation by multi-photon absorption processes (i.e., simultaneous absorption of multiple photons of longer wavelength) has the potential to mitigate both effects. Another complication is that ChR2 becomes inactive after prolonged illumination. This is related to its intricate photocycle. Gaining a detailed understanding of the molecular mechanism of the complete photocycle is crucial for solving these complications.
In this work, we have used molecular mechanics, molecular dynamics simulations, multiscale quantum-classical molecular dynamics (QM/MM MD), statistical analysis and fragment-based polarizable embedding methods to obtain the multiphoton absorption spectra. ChR2 contains two equivalent chromophores (i.e., two Retinal Schiff Base moieties). We show the QM/MM MD sampling is crucial for obtaining accurate spectra.
This work gives an atomistic insight into the first step of the photoactivation of the ChR2, and sets the basis for understanding the complete intricate photocycle, which is not completely understood and a matter of ongoing debate.
Organic molecules where the first excited singlet state is lower in energy than the first excited triplet state hold great potential as emitters in the next generation of light emitting diodes. These molecules that violate Hund’s rule of maximum spin multiplicity roughly fall into two classes: azaphenalenes and polycyclic non-alternant hydrocarbons. We have recently uncovered several molecular design rules for the latter class. Here we examine the fate of the singlet-triplet splitting in low-lying singlet and triplet excited states by using the nuclear ensemble method at the equation-of-motion coupled cluster singles and doubles (EOM-CCSD) and second-order approximated CC (CC2) levels. This way we study the resilience of the inverted gaps in the excited state when we probe vibrational dynamics, and we compute the related rates of intersystem-crossing and fluorescence. This improved understanding is important as we seek to retain singlet-triplet inversion in molecules that can be applied as molecular emitters.
At Algorithmiq we develop methods to utilize current and future quantum computers to overcome current computational limitations in the field of drug design. In addition to our novel methods for quantum circuit transpilation, measuring strategies and error mitigation, we investigate new pathways to turn computational chemistry problems into efficient quantum circuits which can lead to successful hardware experiments. In this talk I will present our recent efforts in this direction including the use of orbital-optimized CCD frozen natural orbitals to improve the description of strongly correlated systems as well as the exploration of semi-automated active space selection methods based on entanglement information from DMRG for a selection of BODIPY systems.
The conductance properties of single molecules connected to macroscopic electrodes can be studied using quantum transport calculations based on non-equilibrium Green’s functions (NEGFs) in combination with density functional theory (DFT). Advanced computational implementations [1] allow for the inclusion of various external stimuli of the molecules like bias voltages, electric fields and chemical environments. This contribution discusses a number of model systems where the transport properties of the atomistic components are externally modulated. Via the bias-voltage, tautomerization processes of a molecule can be induced, which significantly alters its transport properties [2]. Furthermore, a molecule can exhibit considerably different conductance properties when it is in its neutral or in its oxidized state [3]. We also discuss how electron transport through 2D graphene nanoribbons at high bias voltages and electric fields can drive metal adatoms, and investigate how the bias-induced forces on the atoms are related to the redistribution of electron density, the chemical bonds and the molecular orbital structure [4]. We show how a simple molecular model of a metal atom on benzene can explain the forces in the extended system in an inorganic chemistry picture. Our findings demonstrate how the combination of DFT-NEGF calculations with mechanical break-junction and scanning probe experiments enables closely matching molecular junctions in theory and experiment.
[1] N. Papior et al, Improvements on non-equilibrium and transport Green function techniques: The next-generation transiesta, Com. Phys.Com. 212 , 8–24 (2017)
[2] D. Weckbecker et al, Controlling the Conductance of a Graphene−Molecule Nanojunction by Proton Transfer, Nano Lett. 17, 3341−3346 (2017)
[3] Li. L, et al, Highly conducting single-molecule topological insulators based on mono- and di-radical cations. Nat Chem. 14(9):1061-1067 (2022)
[4] S. Leitherer et al, Electromigration Forces on Atoms on Graphene Nanoribbons: The Role of Adsorbate-Surface Bonding, JACS Au 4 (1), 189–196 (2024)
Nitrogenase is the only enzyme that can cleave the strong triple N–N bond in N2, making nitrogen available for biological life. It contains a complicated MoFe7S9C(homocitrate) FeMo cofactor in the active site. Previous studies have shown that different DFT method give widely different predictions of energetics of the FeMo cofactor, e.g. differing by 600 kJ/mol for relative energies of different protonation states [1]. We have designed several model systems for which high-level calculations are possible, but which still show large differences in the prediction of different DFT methods. We have studied these with several methods, including coupled-cluster calculations up to CCSDT and LR-CCSD(TQ) with Padé extrapolation, semistochastic heat-bath configuration-interaction (SHCI) calculations, multiconfigurational approaches (e.g. CASPT2 and DMRG-CASCI) and phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) calculations [2–4]. I will discuss the results and implications of these calculations.
1. L. Cao & U. Ryde (2019) "Extremely large differences in DFT energies for nitrogenase models", Phys. Chem. Chem. Phys., 21, 2480-2488; DOI 10.1039/C8CP06930A.
2. V. Vysotskiy, M. Torbjörnsson, H. Jiang, E. D. Larsson, L. Cao, U. Ryde, H. Zhai, S. Lee, G. K.-L. Chan (2023) "Assessment of DFT functionals for a minimal nitrogenase [Fe(SH)4H]– model employing state-of-the-art ab initio methods", J. Chem. Phys, 159, 044106; DOI: 10.1063/5.0152611.
3. H. Zhai, S. Lee, Z.-H. Cui, L. Cao, U. Ryde, G. K.-L. Chan (2023) "Multireference protonation energetics of a dimeric model of nitrogenase iron-sulfur clusters", J. Phys. Chem. A, 127, 9974-9984; DOI: 10.1021/acs.jpca.3c06142.
4. V. Vysotskiy, C. Filippi, U. Ryde (2024) "Scalar relativistic all-electron and pseudopotential ab initio study of a minimal nitrogenase [Fe(SH)4H]– model employing coupled-cluster and auxiliary-field quantum Monte Carlo many-body methods", J. Phys. Chem. A, 128, 1358–1374; DOI: 10.1021/acs.jpca.3c05808.