Prof. Dr. Christopher Stein
Academic Research Focus
- Theoretical description of physicochemical processes at interfaces
- Developing new models and algorithms
- Developing new models and algorithms
Fields of Application
Batteries, Data Science / Machine Learning, Photo-(electro)catalysis
Publications
8.
S Moradi, P Dabbaghi, C J Stein
Optimizing Extended Tight-Binding Methods for Metal-Surface Interactions Journal Article
In: Chemphyschem, 2025, ISSN: 1439-4235.
@article{nokey,
title = {Optimizing Extended Tight-Binding Methods for Metal-Surface Interactions},
author = {S Moradi and P Dabbaghi and C J Stein},
url = {\<Go to ISI\>://WOS:001613033100001},
doi = {10.1002/cphc.202500463},
issn = {1439-4235},
year = {2025},
date = {2025-11-12},
journal = {Chemphyschem},
abstract = {The accurate description of metal-water interfaces is essential for understanding processes in heterogeneous catalysis, electrochemistry, and surface science. Capturing the delicate balance between electrostatic and charge-transfer interactions in these systems, while efficiently sampling configurations to locate minima or approximate thermodynamic ensembles, requires electronic-structure methods that are both accurate and computationally efficient. Density functional tight-binding methods have the potential to strike the right balance, and here we demonstrate how systematic parameter optimization within the GFN1-xTB framework improves the description of water-metal interactions. Using previously published reference data for five metals (Cu, Ag, Au, Pd, Pt) and their (100) and (111) facets, we explore various adsorption sites, orientations, and distances. Sobol sensitivity analysis identifies the most influential parameters for each system, which are then optimized to minimize errors in adsorption energies. This targeted optimization yields substantial accuracy gains, reducing root-mean-square errors by approximately 20-60%. The modified method provides reliable predictions for catalytic studies where the default parameterization can fail qualitatively. However, such improvements come at the cost of reduced transferability across systems and properties, emphasizing that parameter optimization must be carefully tailored to the specific chemical context.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
The accurate description of metal-water interfaces is essential for understanding processes in heterogeneous catalysis, electrochemistry, and surface science. Capturing the delicate balance between electrostatic and charge-transfer interactions in these systems, while efficiently sampling configurations to locate minima or approximate thermodynamic ensembles, requires electronic-structure methods that are both accurate and computationally efficient. Density functional tight-binding methods have the potential to strike the right balance, and here we demonstrate how systematic parameter optimization within the GFN1-xTB framework improves the description of water-metal interactions. Using previously published reference data for five metals (Cu, Ag, Au, Pd, Pt) and their (100) and (111) facets, we explore various adsorption sites, orientations, and distances. Sobol sensitivity analysis identifies the most influential parameters for each system, which are then optimized to minimize errors in adsorption energies. This targeted optimization yields substantial accuracy gains, reducing root-mean-square errors by approximately 20-60%. The modified method provides reliable predictions for catalytic studies where the default parameterization can fail qualitatively. However, such improvements come at the cost of reduced transferability across systems and properties, emphasizing that parameter optimization must be carefully tailored to the specific chemical context.
7.
H Y Shen, N Bogo, C J Stein, M Head-Gordon
Understanding Electronic Excitations Between Single Determinants with Occupied-Virtual Orbitals for Chemical Valence Journal Article
In: Journal of Chemical Theory and Computation, vol. 21, no. 19, pp. 9525-9537, 2025, ISSN: 1549-9618.
@article{nokey,
title = {Understanding Electronic Excitations Between Single Determinants with Occupied-Virtual Orbitals for Chemical Valence},
author = {H Y Shen and N Bogo and C J Stein and M Head-Gordon},
url = {\<Go to ISI\>://WOS:001571614800001},
doi = {10.1021/acs.jctc.5c01029},
issn = {1549-9618},
year = {2025},
date = {2025-10-14},
journal = {Journal of Chemical Theory and Computation},
volume = {21},
number = {19},
pages = {9525-9537},
abstract = {One approach to calculating electronic excited states treats both ground and excited states as single determinants, either by direct optimization or with the aid of constraints. In this work, we extend the theory of occupied-virtual orbitals for chemical valence (OVOCV) to analyze the orbital character of excitations computed in this way. An intermediate frozen state that is polarization-free is introduced to cleanly separate the primary excitation from the accompanying orbital relaxation of spectator orbitals. A variety of chemical examples are reported using the OVOCV excitation analysis on orbital-optimized density functional theory (OO-DFT) calculations, including charge-transfer excitations, core excitations and singly and doubly excited valence states. Orbital relaxation effects are typically collective, and can be as large as 4-5 eV (with roughly 0.1 e - promoted) in charge transfer states, and even larger in core excited states. OVOCV analysis differs from natural transition orbital (NTO) analysis; we show that direct use of NTOs can largely obscure the role of orbital relaxation in favor of the primary excitation.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
One approach to calculating electronic excited states treats both ground and excited states as single determinants, either by direct optimization or with the aid of constraints. In this work, we extend the theory of occupied-virtual orbitals for chemical valence (OVOCV) to analyze the orbital character of excitations computed in this way. An intermediate frozen state that is polarization-free is introduced to cleanly separate the primary excitation from the accompanying orbital relaxation of spectator orbitals. A variety of chemical examples are reported using the OVOCV excitation analysis on orbital-optimized density functional theory (OO-DFT) calculations, including charge-transfer excitations, core excitations and singly and doubly excited valence states. Orbital relaxation effects are typically collective, and can be as large as 4-5 eV (with roughly 0.1 e - promoted) in charge transfer states, and even larger in core excited states. OVOCV analysis differs from natural transition orbital (NTO) analysis; we show that direct use of NTOs can largely obscure the role of orbital relaxation in favor of the primary excitation.
6.
E Kolodzeiski, C J Stein
Efficient Electronic-Structure Methods Toward Catalyst Screening: Projection-Based Embedding Theory for CO2 Reduction Reaction Intermediates Journal Article
In: Angewandte Chemie-International Edition, 2025.
@article{nokey,
title = {Efficient Electronic-Structure Methods Toward Catalyst Screening: Projection-Based Embedding Theory for CO2 Reduction Reaction Intermediates},
author = {E Kolodzeiski and C J Stein},
url = {\<Go to ISI\>://WOS:001547141000001},
doi = {10.1002/anie.202503418},
year = {2025},
date = {2025-08-07},
journal = {Angewandte Chemie-International Edition},
abstract = {Catalyst screening is a demanding task for computational chemistry since the profound diversity of surface structures under operando conditions is accompanied by high demands on the accuracy to predict the relevant kinetics. Embedding approaches that allow researchers to focus the computational effort on the chemically active regions of interest are promising tools in the pursuit of balancing accuracy and efficiency. However, for metallic catalysts, the required separation of the system into an active part treated with highly accurate methods and an environment is technically hard to achieve due to the delocalization of electrons in the conducting surface. Therefore, studies analyzing the potential of embedding methods for heterogeneous (electro-)catalyst screening are scarce. In this contribution, we demonstrate that simple embedding approaches are indeed achievable for studying metallic catalysts if i) the active orbital space is held consistent over a reaction coordinate and ii) the nonadditive exchange-correlation functional used to calculate the embedding potential includes a fraction of exact exchange to mitigate delocalization errors. We verify the approach for a set of open- and closed-shell CO2 reduction reaction intermediates on different adsorption sites of a Cu(111) surface represented by cluster models to demonstrate that catalyst screening with embedding approaches is achievable.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Catalyst screening is a demanding task for computational chemistry since the profound diversity of surface structures under operando conditions is accompanied by high demands on the accuracy to predict the relevant kinetics. Embedding approaches that allow researchers to focus the computational effort on the chemically active regions of interest are promising tools in the pursuit of balancing accuracy and efficiency. However, for metallic catalysts, the required separation of the system into an active part treated with highly accurate methods and an environment is technically hard to achieve due to the delocalization of electrons in the conducting surface. Therefore, studies analyzing the potential of embedding methods for heterogeneous (electro-)catalyst screening are scarce. In this contribution, we demonstrate that simple embedding approaches are indeed achievable for studying metallic catalysts if i) the active orbital space is held consistent over a reaction coordinate and ii) the nonadditive exchange-correlation functional used to calculate the embedding potential includes a fraction of exact exchange to mitigate delocalization errors. We verify the approach for a set of open- and closed-shell CO2 reduction reaction intermediates on different adsorption sites of a Cu(111) surface represented by cluster models to demonstrate that catalyst screening with embedding approaches is achievable.
5.
N Bogo, Z Y Zhang, M Head-Gordon, C J Stein
An improved guess for the variational calculation of charge-transfer excitations in large systems Journal Article
In: Physical Chemistry Chemical Physics, 2025, ISSN: 1463-9076.
@article{nokey,
title = {An improved guess for the variational calculation of charge-transfer excitations in large systems},
author = {N Bogo and Z Y Zhang and M Head-Gordon and C J Stein},
url = {\<Go to ISI\>://WOS:001544470300001},
doi = {10.1039/d5cp01867f},
issn = {1463-9076},
year = {2025},
date = {2025-07-25},
journal = {Physical Chemistry Chemical Physics},
abstract = {Ab initio quantum-chemical methods that perform well for computing the electronic ground state are not straightforwardly transferable to electronically excited states, particularly in large molecular systems. Wave function theory offers high accuracy, but is often prohibitively expensive. Methods based on time-dependent density functional theory (TD-DFT) are crucially sensitive to the chosen exchange-correlation functional (XCF) parameterization, and system-specific tuning protocols were therefore proposed to address the method's robustness. Methods based on the variational relaxation of the excited-state electron density showcased promising results for the calculation of charge-transfer excitations, but the complex shape of the electronic hypersurface makes convergence to a specific excited state much more difficult than for the ground state when standard variational techniques are applied. We address the latter aspect by providing suitable initial guesses, which we obtain by two separate constrained algorithms. Combined with the squared-gradient minimization algorithm for all-electrons relaxation in a freeze-and-release scheme (FRZ-SGM), we demonstrate that orbital-optimized density functional theory (OO-DFT) calculations can reliably converge to the charge-transfer states of interest even for large molecular systems. We test the FRZ-SGM method on a phenothiazine-anthraquinone CT excitation in a supramolecular Pd(ii) coordination cage complex as a function of the cage conformation. This compound has been studied experimentally prior to our work. We compare this freeze-and-release scheme to two XCF reparameterizations, which were recently proposed as low-cost TD-DFT-based alternatives to variational methods. Two dye-semiconductor complexes, which were previously investigated in the context of photovoltaic applications, serve as a second example to investigate the convergence and stability of the FRZ-SGM approach. Our results demonstrate that FRZ-SGM provides reliable convergence for charge-transfer excited states and avoids variational collapse to lower-lying electronic states, whereas time-dependent DFT calculations with an adequate tuning procedure for the range-separation parameter provide a computationally efficient initial estimate of the corresponding energies, with a computational cost comparable to that of configuration-interaction singles (CIS) calculations.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Ab initio quantum-chemical methods that perform well for computing the electronic ground state are not straightforwardly transferable to electronically excited states, particularly in large molecular systems. Wave function theory offers high accuracy, but is often prohibitively expensive. Methods based on time-dependent density functional theory (TD-DFT) are crucially sensitive to the chosen exchange-correlation functional (XCF) parameterization, and system-specific tuning protocols were therefore proposed to address the method's robustness. Methods based on the variational relaxation of the excited-state electron density showcased promising results for the calculation of charge-transfer excitations, but the complex shape of the electronic hypersurface makes convergence to a specific excited state much more difficult than for the ground state when standard variational techniques are applied. We address the latter aspect by providing suitable initial guesses, which we obtain by two separate constrained algorithms. Combined with the squared-gradient minimization algorithm for all-electrons relaxation in a freeze-and-release scheme (FRZ-SGM), we demonstrate that orbital-optimized density functional theory (OO-DFT) calculations can reliably converge to the charge-transfer states of interest even for large molecular systems. We test the FRZ-SGM method on a phenothiazine-anthraquinone CT excitation in a supramolecular Pd(ii) coordination cage complex as a function of the cage conformation. This compound has been studied experimentally prior to our work. We compare this freeze-and-release scheme to two XCF reparameterizations, which were recently proposed as low-cost TD-DFT-based alternatives to variational methods. Two dye-semiconductor complexes, which were previously investigated in the context of photovoltaic applications, serve as a second example to investigate the convergence and stability of the FRZ-SGM approach. Our results demonstrate that FRZ-SGM provides reliable convergence for charge-transfer excited states and avoids variational collapse to lower-lying electronic states, whereas time-dependent DFT calculations with an adequate tuning procedure for the range-separation parameter provide a computationally efficient initial estimate of the corresponding energies, with a computational cost comparable to that of configuration-interaction singles (CIS) calculations.
4.
T Kühl, L Hetzel, C J Stein, K Koszinowski
Competition Between One- and Two-Electron Unimolecular Reactions of Late 3d-Metal Complexes [(Me3SiCH2)nM]– (M = Fe, Co, Ni, Cu; n = 2 – 4) Journal Article
In: Angewandte Chemie International Edition, vol. n/a, no. n/a, pp. e202500524, 2025, ISSN: 1433-7851.
@article{nokey,
title = {Competition Between One- and Two-Electron Unimolecular Reactions of Late 3d-Metal Complexes [(Me3SiCH2)nM]\textendash (M = Fe, Co, Ni, Cu; n = 2 \textendash 4)},
author = {T K\"{u}hl and L Hetzel and C J Stein and K Koszinowski},
url = {https://doi.org/10.1002/anie.202500524},
doi = {https://doi.org/10.1002/anie.202500524},
issn = {1433-7851},
year = {2025},
date = {2025-03-15},
journal = {Angewandte Chemie International Edition},
volume = {n/a},
number = {n/a},
pages = {e202500524},
abstract = {Although organometallic complexes of the late 3d elements are known to undergo both one- and two-electron reactions, their relative propensities to do so remain poorly understood. To gain direct insight into the competition between these different pathways, we have analyzed the unimolecular gas-phase reactivity of a series of well-defined model complexes [(Me3SiCH2)nM]? (M = Fe, Co, Ni, Cu; n = 2 ? 4). Applying a combination of tandem-mass spectrometry, quantum-chemical computations, and statistical rate theory calculations, we find several different fragmentation reactions, among which the homolytic cleavage of metal-carbon bonds and radical dissociations are particularly prominent. In all cases, these one-electron reactions are entropically favored. For the ferrate and cobaltate complexes, they are also energetically preferred, which explains their predominance in the corresponding fragmentation experiments. For [(Me3SiCH2)4Ni]? and, even more so, for [(Me3SiCH2)4Cu]?, a concerted reductive elimination as a prototypical two-electron reaction is energetically more favorable and gains in importance. [(Me3SiCH2)3Ni]? is special in that it has two nearly degenerate spin states, both of which react in different ways. A simple thermochemical analysis shows that the relative order of the first and second bond-dissociation energies is of key importance in controlling the competition between radical dissociations and concerted reductive eliminations.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Although organometallic complexes of the late 3d elements are known to undergo both one- and two-electron reactions, their relative propensities to do so remain poorly understood. To gain direct insight into the competition between these different pathways, we have analyzed the unimolecular gas-phase reactivity of a series of well-defined model complexes [(Me3SiCH2)nM]? (M = Fe, Co, Ni, Cu; n = 2 ? 4). Applying a combination of tandem-mass spectrometry, quantum-chemical computations, and statistical rate theory calculations, we find several different fragmentation reactions, among which the homolytic cleavage of metal-carbon bonds and radical dissociations are particularly prominent. In all cases, these one-electron reactions are entropically favored. For the ferrate and cobaltate complexes, they are also energetically preferred, which explains their predominance in the corresponding fragmentation experiments. For [(Me3SiCH2)4Ni]? and, even more so, for [(Me3SiCH2)4Cu]?, a concerted reductive elimination as a prototypical two-electron reaction is energetically more favorable and gains in importance. [(Me3SiCH2)3Ni]? is special in that it has two nearly degenerate spin states, both of which react in different ways. A simple thermochemical analysis shows that the relative order of the first and second bond-dissociation energies is of key importance in controlling the competition between radical dissociations and concerted reductive eliminations.
3.
P Yan, S Stegbauer, Q Wu, E Kolodzeiski, C J Stein, P Lu, T Bach
Enantioselective Intramolecular ortho Photocycloaddition Reactions of 2-Acetonaphthones Journal Article
In: Angewandte Chemie International Edition, vol. 63, no. 13, pp. e202318126, 2024, ISSN: 1433-7851.
@article{nokey,
title = {Enantioselective Intramolecular ortho Photocycloaddition Reactions of 2-Acetonaphthones},
author = {P Yan and S Stegbauer and Q Wu and E Kolodzeiski and C J Stein and P Lu and T Bach},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/anie.202318126},
doi = {https://doi.org/10.1002/anie.202318126},
issn = {1433-7851},
year = {2024},
date = {2024-01-26},
journal = {Angewandte Chemie International Edition},
volume = {63},
number = {13},
pages = {e202318126},
abstract = {Abstract 2-Acetonaphthones, which bear an alkenyl group tethered to its C1 carbon atom via an oxygen atom, were found to undergo an enantioselective intramolecular ortho photocycloaddition reaction. A chiral oxazaborolidine Lewis acid leads to a bathochromic absorption shift of the substrate and enables an efficient enantioface differentiation. Visible light irradiation (λ=450 nm) triggers the reaction which is tolerant of various groups at almost any position except carbon atom C8 (16 examples, 53\textendash99 % yield, 80\textendash97 % ee). Consecutive reactions were explored including a sensitized rearrangement to tetrahydrobiphenylenes, which occurred with full retention of configuration. Evidence was collected that the catalytic photocycloaddition occurs via triplet intermediates, and the binding mode of the acetonaphthone to the chiral Lewis acid was elucidated by DFT calculations.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Abstract 2-Acetonaphthones, which bear an alkenyl group tethered to its C1 carbon atom via an oxygen atom, were found to undergo an enantioselective intramolecular ortho photocycloaddition reaction. A chiral oxazaborolidine Lewis acid leads to a bathochromic absorption shift of the substrate and enables an efficient enantioface differentiation. Visible light irradiation (λ=450 nm) triggers the reaction which is tolerant of various groups at almost any position except carbon atom C8 (16 examples, 53–99 % yield, 80–97 % ee). Consecutive reactions were explored including a sensitized rearrangement to tetrahydrobiphenylenes, which occurred with full retention of configuration. Evidence was collected that the catalytic photocycloaddition occurs via triplet intermediates, and the binding mode of the acetonaphthone to the chiral Lewis acid was elucidated by DFT calculations.
2.
P Yan, S Stegbauer, Q Wu, E Kolodzeiski, C J Stein, P Lu, T Bach
Enantioselective Intramolecular ortho Photocycloaddition Reactions of 2-Acetonaphthones Journal Article
In: Angewandte Chemie International Edition, vol. 63, no. 13, pp. e202318126, 2024, ISSN: 1433-7851.
@article{nokey,
title = {Enantioselective Intramolecular ortho Photocycloaddition Reactions of 2-Acetonaphthones},
author = {P Yan and S Stegbauer and Q Wu and E Kolodzeiski and C J Stein and P Lu and T Bach},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/anie.202318126},
doi = {https://doi.org/10.1002/anie.202318126},
issn = {1433-7851},
year = {2024},
date = {2024-01-26},
journal = {Angewandte Chemie International Edition},
volume = {63},
number = {13},
pages = {e202318126},
abstract = {Abstract 2-Acetonaphthones, which bear an alkenyl group tethered to its C1 carbon atom via an oxygen atom, were found to undergo an enantioselective intramolecular ortho photocycloaddition reaction. A chiral oxazaborolidine Lewis acid leads to a bathochromic absorption shift of the substrate and enables an efficient enantioface differentiation. Visible light irradiation (λ=450 nm) triggers the reaction which is tolerant of various groups at almost any position except carbon atom C8 (16 examples, 53\textendash99 % yield, 80\textendash97 % ee). Consecutive reactions were explored including a sensitized rearrangement to tetrahydrobiphenylenes, which occurred with full retention of configuration. Evidence was collected that the catalytic photocycloaddition occurs via triplet intermediates, and the binding mode of the acetonaphthone to the chiral Lewis acid was elucidated by DFT calculations.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Abstract 2-Acetonaphthones, which bear an alkenyl group tethered to its C1 carbon atom via an oxygen atom, were found to undergo an enantioselective intramolecular ortho photocycloaddition reaction. A chiral oxazaborolidine Lewis acid leads to a bathochromic absorption shift of the substrate and enables an efficient enantioface differentiation. Visible light irradiation (λ=450 nm) triggers the reaction which is tolerant of various groups at almost any position except carbon atom C8 (16 examples, 53–99 % yield, 80–97 % ee). Consecutive reactions were explored including a sensitized rearrangement to tetrahydrobiphenylenes, which occurred with full retention of configuration. Evidence was collected that the catalytic photocycloaddition occurs via triplet intermediates, and the binding mode of the acetonaphthone to the chiral Lewis acid was elucidated by DFT calculations.
1.
E Kolodzeiski, C J Stein
Automated, Consistent, and Even-handed Selection of Active Orbital Spaces for Quantum Embedding Journal Article
In: arXiv preprint arXiv:2306.09488, 2023.
@article{nokey,
title = {Automated, Consistent, and Even-handed Selection of Active Orbital Spaces for Quantum Embedding},
author = {E Kolodzeiski and C J Stein},
url = {https://arxiv.org/abs/2306.09488},
doi = {https://doi.org/10.48550/arXiv.2306.09488},
year = {2023},
date = {2023-06-15},
urldate = {2023-06-15},
journal = {arXiv preprint arXiv:2306.09488},
abstract = {A widely used strategy to reduce the computational cost in quantum-chemical calculations is to partition the system into an active subsystem, which is the focus of the computational efforts and an environment that is treated at a lower computational level. The system partitioning is mostly based on localized molecular orbitals. When reaction paths or energy differences are to be calculated, it is crucial to keep the orbital space consistent for all structures. Inconsistencies in the orbital space can lead to unpredictable errors in the potential energy surface. While successful strategies to ensure this consistency have been established for organic and even metal-organic systems, these methods often fail for metal clusters or nanoparticles with a high density of near-degenerate and delocalized molecular orbitals. However, such systems are highly relevant for catalysis. Accurate yet feasible quantum-mechanical ab initio calculations are therefore highly desired. In this work, we present an approach based on the SPADE algorithm that allows us to ensure an automated and consistent partitioning even for systems with delocalized and near-degenerate molecular orbitals and demonstrate the validity of this method for the binding energies of small molecules on transition-metal clusters.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
A widely used strategy to reduce the computational cost in quantum-chemical calculations is to partition the system into an active subsystem, which is the focus of the computational efforts and an environment that is treated at a lower computational level. The system partitioning is mostly based on localized molecular orbitals. When reaction paths or energy differences are to be calculated, it is crucial to keep the orbital space consistent for all structures. Inconsistencies in the orbital space can lead to unpredictable errors in the potential energy surface. While successful strategies to ensure this consistency have been established for organic and even metal-organic systems, these methods often fail for metal clusters or nanoparticles with a high density of near-degenerate and delocalized molecular orbitals. However, such systems are highly relevant for catalysis. Accurate yet feasible quantum-mechanical ab initio calculations are therefore highly desired. In this work, we present an approach based on the SPADE algorithm that allows us to ensure an automated and consistent partitioning even for systems with delocalized and near-degenerate molecular orbitals and demonstrate the validity of this method for the binding energies of small molecules on transition-metal clusters.