arXiv subjects

Andreas Köhn

Publications and source records attributed to Andreas Köhn.

15 recordsLinked to original sources

arXiv2026

SeQuant Framework for Symbolic and Numerical Tensor Algebra. I. Core Capabilities

SeQuant is an open-source library for symbolic algebra of tensors over commutative (scalar) and non-commutative (operator) rings. The key innovation supporting most of its functionality is a graph-theoretic tensor network (TN) canonicalizer that can handle tensor networks with symmetries faster than their standard group-theoretic counterparts. The TN canonicalizer is used for routine simplification of conventional tensor expressions, for optimizing application of Wick's theorem (used to canonicalize products of tensors over operator fields), and for manipulation of the intermediate representation leading to the numerical evaluation. Notable features of SeQuant include support for noncovariant tensor networks (which often arise from tensor decompositions) and for tensors with modes that depend parametrically on indices of other tensor modes (such dependencies between degrees of freedom are naturally viewed as nesting of tensors, "tensors of tensors" arising in block-wise data compressions in data science and modern quantum simulation). SeQuant blurs the line between pure symbolic manipulation/code generation and numerical evaluation by including compiler-like components to optimize and directly interpret tensor expressions using external numerical tensor algebra frameworks. The SeQuant source code is available at https://github.com/ValeevGroup/SeQuant.

cs.MS↗

arXiv2026

Machine-learning interatomic potentials achieving CCSD(T) accuracy for systems with extended covalent networks and van der Waals interactions

Machine-learning interatomic potentials (MLIPs) enable large-scale atomistic simulations at moderate computational cost while retaining ab initio accuracy. MLIPs trained on coupled-cluster data, particularly CCSD(T), have emerged as a promising route to achieve chemical accuracy beyond the limits of density functional theory (DFT) and to incorporate non-empirical van der Waals (vdW) interactions. Most existing approaches are, however, still not straightforwardly applicable for systems with extended covalent networks such as covalent organic frameworks (COFs) due to the limited availability of CCSD(T) for periodic systems. Here we present a methodology to train MLIPs with CCSD(T) accuracy for these systems. The approach uses the Δ-learning method with a dispersion-corrected tight-binding baseline. This strategy enables training on compact molecular fragments while preserving transferability toward the periodic systems. Dispersion interactions are accounted for by adding vdW-bound multimers in the training set, and the combination with a vdW-aware tight-binding baseline allows the formally local MLIP to attain CCSD(T)-level accuracy even for systems dominated by long-range vdW forces. The resulting potential yields root-mean-square energy errors below 0.4 meV/atom on training and test sets and reproduces electronic total atomization energies, bond lengths, harmonic vibrational frequencies, and inter-molecular interaction energies for benchmark molecular systems. We apply the method to a prototypical quasi-two-dimensional COF composed of carbon and hydrogen. The COF structure, inter-layer binding energies, and hydrogen absorption are analyzed at CCSD(T) accuracy. The developed methodology opens a practical route to large-scale atomistic simulations for systems with extended covalent networks and vdW interactions with chemical accuracy.

cond-mat.mtrl-sci↗

arXiv2025

A Design Space for Visualization Transitions of 3D Spatial Data in Hybrid AR-Desktop Environments

We present a design space for animated transitions of the appearance of 3D spatial datasets in a hybrid Augmented Reality (AR)-desktop context. Such hybrid interfaces combine both traditional and immersive displays to facilitate the exploration of 2D and 3D data representations in the environment in which they are best displayed. One key aspect is to introduce transitional animations that change between the different dimensionalities to illustrate the connection between the different representations and to reduce the potential cognitive load on the user. The specific transitions to be used depend on the type of data, the needs of the application domain, and other factors. We summarize these as a transition design space to simplify the decision-making process and provide inspiration for future designs. First, we discuss 3D visualizations from a spatial perspective: a spatial encoding pipeline, where 3D data sampled from the physical world goes through various transformations, being mapped to visual representations, and then being integrated into a hybrid AR-desktop environment. The transition design then focuses on interpolating between two spatial encoding pipelines to provide a smooth experience. To illustrate the use of our design space, we apply it to three case studies that focus on applications in astronomy, radiology, and chemistry; we then discuss lessons learned from these applications.

cs.GR↗

arXiv2025

Traversing Dual Realities: Investigating Techniques for Transitioning 3D Objects between Desktop and Augmented Reality Environments

Desktop environments can integrate augmented reality (AR) head-worn devices to support 3D representations, visualizations, and interactions in a novel yet familiar setting. As users navigate across the dual realities -- desktop and AR -- a way to move 3D objects between them is needed. We devise three baseline transition techniques based on common approaches in the literature and evaluate their usability and practicality in an initial user study (N=18). After refining both our transition techniques and the surrounding technical setup, we validate the applicability of the overall concept for real-world activities in an expert user study (N=6). In it, computational chemists followed their usual desktop workflows to build, manipulate, and analyze 3D molecular structures, but now aided with the addition of AR and our transition techniques. Based on our findings from both user studies, we provide lessons learned and takeaways for the design of 3D object transition techniques in desktop + AR environments.

cs.HC↗

arXiv2024

The spin-phonon relaxation mechanism of single-molecule magnets in the presence of strong exchange coupling

Magnetic relaxation in coordination compounds is largely dominated by the interaction of the spin with phonons. Large zero-field splitting and exchange coupling values have been empirically found to strongly suppress spin relaxation and have been used as the main guideline for designing new molecular compounds. Although a comprehensive understanding of spin-phonon relaxation has been achieved for mononuclear complexes, only a qualitative picture is available for polynuclear compounds. Here we fill this critical knowledge gap by providing a full first-principle description of spin-phonon relaxation in an air-stable Co(II) dimer with both large single-ion anisotropy and exchange coupling. Simulations reproduce the experimental relaxation data with excellent accuracy and provide a microscopic understanding of Orbach and Raman relaxation pathways and their dependency on exchange coupling, zero-field splitting, and molecular vibrations. Theory and numerical simulations show that increasing cluster nuclearity to just four cobalt units would lead to a complete suppression of Raman relaxation. These results hold a general validity for single-molecule magnets, providing a deeper understanding of their relaxation and revised strategies for their improvement.

cond-mat.mtrl-sci↗

arXiv2023

Thermally Averaged Magnetic Anisotropy Tensors via Machine Learning Based on Gaussian Moments

We propose a machine learning method to model molecular tensorial quantities, namely the magnetic anisotropy tensor, based on the Gaussian-moment neural-network approach. We demonstrate that the proposed methodology can achieve an accuracy of 0.3--0.4 cm$^{-1}$ and has excellent generalization capability for out-of-sample configurations. Moreover, in combination with machine-learned interatomic potential energies based on Gaussian moments, our approach can be applied to study the dynamic behavior of magnetic anisotropy tensors and provide a unique insight into spin-phonon relaxation.

physics.comp-ph↗

arXiv2022

Capabilities and Limits of the Unitary Coupled-cluster Approach with Generalized Two-body Cluster Operators

Unitary cluster expansions of the electronic wavefunction have recently gained much interest because of their use in conjunction with quantum algorithms. In this contribution, we investigate some aspects of an ansatz using generalized two-body excitations operators, which has been considered in some recent works on quantum algorithms for quantum chemistry. Our numerical results show that in particular two-body operators with effective particle-hole excitation level of one in connection with the usual particle-hole double excitation operators lead to a very accurate yet compact representation of the wavefunction. Generalized two-body operators with effective excitation rank zero have a considerably less pronounced effect. We compare to standard and unitary coupled-cluster expansions and show that the above mentioned approach matches or even surpasses the accuracy of expansions with three-body particle-hole excitations, in particular at the onset of strong correlation. A downside of the approach is that it is rather difficult to rigorously converge it to its variational minimum.

physics.chem-ph↗

arXiv2022

High-accuracy Rb$_{2}^+$ interaction potentials based on coupled cluster calculations

This work discusses a protocol for constructing highly accurate potential energy curves (PECs) for the lowest two states of Rb$_{2}^+$, i.e. $X\,{}^2Σ{_g^+}$ and $(1) {}^2Σ{_u^+}$, using an additivity scheme based on coupled-cluster theory. The approach exploits the findings of our previous work [J. Schnabel, L. Cheng and A. Köhn, J. Chem. Phys. 155, 124101 (2021)] to avoid the unphysical repulsive long-range barrier occurring for symmetric molecular ions when perturbative estimates of higher-order cluster operators are employed. Furthermore, care was taken to reproduce the physically correct exchange splitting of the $X {}^2Σ{_g^+}$ and $(1) {}^2Σ{_u^+}$ PECs. The accuracy of our computational approach is benchmarked for ionization energies of Rb and for spectroscopic constants as well as vibrational levels of the $a {}^3Σ{_u^+}$ triplet state of Rb\textsubscript{2}. We study high-level correlation contributions, high-level relativistic effects and inner-shell correlation contributions and find very good agreement with experimental reference values for the atomic ionization potential and the binding energy of Rb$_{2}$ in the $a\,{}^3Σ{_u^+}$ triplet state. Our final best estimate for the binding energy of the Rb$_{2}^+$ $X {}^2Σ{_g^+}$ state including zero-point vibrational contributions is $D_0 = 6179\,\mathrm{cm}^{-1}$ with an estimated error bound of $\mathcal{O}(\pm 30\,\mathrm{cm}^{-1})$. This value is smaller than the experimentally inferred lower bond of $D_0\ge 6307.5\,\mathrm{cm}^{-1}$ [Bellos et al., Phys. Rev. A 87, 012508 (2013)] and will require further investigation. For the $(1) {}^2Σ{_u^+}$ state a shallow potential with $D_0 = 78.4\,\mathrm{cm}^{-1}$ and an error bound of $\pm 9\,\mathrm{cm}^{-1}$ is computed.

physics.atom-ph↗

arXiv2022

MolecuSense: Using Force-Feedback Gloves for Creating and Interacting with Ball-and-Stick Molecules in VR

We contribute MolecuSense, a virtual version of a physical molecule construction kit, based on visualization in Virtual Reality (VR) and interaction with force-feedback gloves. Targeting at chemistry education, our goal is to make virtual molecule structures more tangible. Results of an initial user study indicate that the VR molecular construction kit was positively received. Compared to a physical construction kit, the VR molecular construction kit is on the same level in terms of natural interaction. Besides, it fosters the typical digital advantages though, such as saving, exporting, and sharing of molecules. Feedback from the study participants has also revealed potential future avenues for tangible molecule visualizations.

cs.HC↗

arXiv2021

Limitations of coupled cluster approximations for highlyaccurate investigations of Rb$_2^+$

We reveal limitations of several standard coupled-cluster (CC) methods with perturbation-theorybased noniterative or approximate iterative treatments of triple excitations when applied to thedetermination of highly accurate potential energy curves (PECs) of ionic dimers, such as the X $^2Σ^+_g$ electronic ground state of Rb$_2^+$. Such computations are of current interest for the understanding ofion-atom interactions in the ultracold regime. We demonstrate that these coupled-cluster methodslead to an unphysical long-range barrier for the Rb$_2^+$ system. The barrier is small but clearly spoilsthe entire long-range behavior of the PEC. The effect is also found for other X$_2^+$ systems, like X = Li, Na, and K. Calculations using a new flexible framework for obtaining leading perturbativetriples corrections derived using an analytic CC singles and doubles (CCSD) energy derivativeformulation demonstrate that the origin of this problem lies in the use of $T_3$ amplitudes obtained from approximate CC singles, doubles and triples (CCSDT) amplitude equations. It is shown thatthe unphysical barrier is related to a symmetry instability of the underlying Hartree-Fock mean-fieldsolution. Physically meaningful perturbative corrections in the long-range tail of the PEC mayinstead be obtained using symmetry-broken reference determinants.

physics.chem-ph↗

arXiv2021

Towards photoassociation processes of ultracold rubidium trimers

We theoretically investigate the prospects for photoassociation (PA) of Rb$_3$, in particular at close range. We provide an overview of accessible states and possible transitions. The major focus is placed on the calculation of equilibrium structures, the survey of spin-orbit effects and the investigation of transition dipole moments. Furthermore we discuss Franck-Condon overlaps and special aspects of trimers including the (pseudo) Jahn-Teller effect and the resulting topology of adiabatic potential-energy surfaces. With this we identify concrete and suitable PA transitions to potentially produce long-lived trimer bound states. Calculations are performed using the multireference configuration-interaction method together with a large-core effective core potential and a core-polarization potential with a large uncontracted even-tempered basis set.

physics.chem-ph↗

arXiv2019

On the distinguishable cluster approximation for triple excitations

The distinguishable cluster approximation applied to coupled cluster doubles equations greatly improves absolute and relative energies. We apply the same approximation to the triples equations and demonstrate that it can also improve results of the coupled cluster with singles, doubles and triples. The resulting method has a nominal computational scaling of ${\cal O}(N^7)$ in the real-space representation, is orbital invariant, size extensive, and exact for three electrons.

physics.chem-ph↗

arXiv2019

Surface Hopping Dynamics Including Intersystem Crossing using the Algebraic Diagrammatic Construction Method

We report an implementation for employing the algebraic diagrammatic construction to second order [ADC(2)] ab initio electronic structure level of theory in nonadiabatic dynamics simulations in the framework of the SHARC (surface hopping including arbitrary couplings) dynamics method. The implementation is intended to enable computationally efficient, reliable, and easy-to-use nonadiabatic dynamics simulations of intersystem crossing in organic molecules. The methodology is evaluated for the 2-thiouracil molecule. It is shown that ADC(2) yields reliable excited-state energies, wave functions, and spin-orbit coupling terms for this molecule. Dynamics simulations are compared to previously reported results using high-level multi-state complete active space perturbation theory, showing favorable agreement.

physics.chem-ph↗

arXiv2018

Do CCSD and approximate CCSD-F12 variants converge to the same basis set limits? The case of atomization energies

While the title question is a clear 'yes' from purely theoretical arguments, the case is less clear for practical calculations with finite (one-particle) basis sets. To shed further light on this issue, the basis set limits of CCSD (coupled cluster theory with all single and double excitations) and of different approximate implementations of CCSD-F12 (explicitly correlated CCSD) have been investigated on detail for the W4-17 thermochemical benchmark. Near the CBS ([1-particle] complete basis set) limit, CCSD and CCSD(F12*) agree to within their respective uncertainties (about \pm0.04 kcal/mol) due to residual basis set incompleteness error, but a nontrivial difference remains between CCSD-F12b and CCSD(F12*), which is roughly proportional to the degree of static correlation. The observed basis set convergence behavior results from the superposition of a rapidly converging, attractive, CCSD[F12]--CCSD-F12b difference (consisting mostly of third-order terms), and a more slowly converging, repulsive, fourth-order difference between CCSD(F12*) and CCSD[F12]. For accurate thermochemistry, we recommend CCSD(F12*) over CCSD-F12b if at all possible. There are some indications that the nZaPa family of basis sets exhibits somewhat smoother convergence than the correlation consistent family.

physics.chem-ph↗

arXiv2016

Quantum tunneling during interstellar surface-catalyzed formation of water: the reaction H + H$_2$O$_2$ $\rightarrow$ H$_2$O + OH

The final step of the water formation network on interstellar grain surfaces starting from the H + O$_2$ route is the reaction between H and H$_2$O$_2$. This reaction is known to have a high activation energy and therefore at low temperatures it can only proceed via tunneling. To date, however, no rate constants are available at temperatures below 200 K. In this work, we use instanton theory to compute rate constants for the title reaction with and without isotopic substitutions down to temperatures of 50 K. The calculations are based on density functional theory, with additional benchmarks for the activation energy using unrestricted single-reference and multireference coupled-cluster single-point energies. Gas-phase bimolecular rate constants are calculated and compared with available experimental data not only for H + H$_2$O$_2$ $\rightarrow$ H$_2$O + OH, but also for H + H$_2$O$_2$ $\rightarrow$ H$_2$ + HO$_2$. We find a branching ratio where the title reaction is favored by at least two orders of magnitude at 114 K. In the interstellar medium this reaction predominantly occurs on water surfaces, which increases the probability that the two reactants meet. To mimic this one, two, or three spectator H2O molecules are added to the system. Eley-Rideal bimolecular and Langmuir-Hinshelwood unimolecular rate constants are presented here. The kinetic isotope effects for the various cases are compared to experimental data as well as to expressions commonly used in astrochemical models. Both the rectangular barrier and the Eckart approximations lead to errors of about an order of magnitude. Finally, fits of the rate constants are provided as input for astrochemical models.

physics.chem-ph↗