2023
Fabien Brieuc, Christoph Schran, Dominik Marx
Manifestations of local supersolidity of $^4$He around a charged molecular impurity Journal Article
In: Phys. Rev. Res., vol. 5, iss. 4, pp. 043083, 2023.
Links | BibTeX | Tags: Nuclear quantum effects, path integral molecular dynamics (PIMD), Superfluidity
@article{PhysRevResearch.5.043083,
title = {Manifestations of local supersolidity of $^4$He around a charged molecular impurity},
author = {Fabien Brieuc and Christoph Schran and Dominik Marx},
url = {https://link.aps.org/doi/10.1103/PhysRevResearch.5.043083},
doi = {10.1103/PhysRevResearch.5.043083},
year = {2023},
date = {2023-10-01},
urldate = {2023-10-01},
journal = {Phys. Rev. Res.},
volume = {5},
issue = {4},
pages = {043083},
publisher = {American Physical Society},
keywords = {Nuclear quantum effects, path integral molecular dynamics (PIMD), Superfluidity},
pubstate = {published},
tppubtype = {article}
}

Julia A. Davies, Christoph Schran, Fabien Brieuc, Dominik Marx, Andrew M. Ellis
Onset of Rotational Decoupling for a Molecular Ion Solvated in Helium: From Tags to Rings and Shells Journal Article
In: Phys. Rev. Lett., vol. 130, iss. 8, pp. 083001, 2023.
Links | BibTeX | Tags: Nuclear quantum effects, path integral molecular dynamics (PIMD), Superfluidity, Water
@article{Schran2023/10.1103/PhysRevLett.130.083001,
title = {Onset of Rotational Decoupling for a Molecular Ion Solvated in Helium: From Tags to Rings and Shells},
author = {Julia A. Davies and Christoph Schran and Fabien Brieuc and Dominik Marx and Andrew M. Ellis},
doi = {10.1103/PhysRevLett.130.083001},
year = {2023},
date = {2023-02-01},
urldate = {2023-02-01},
journal = {Phys. Rev. Lett.},
volume = {130},
issue = {8},
pages = {083001},
publisher = {American Physical Society},
keywords = {Nuclear quantum effects, path integral molecular dynamics (PIMD), Superfluidity, Water},
pubstate = {published},
tppubtype = {article}
}

Irén Simkó, Christoph Schran, Fabien Brieuc, Csaba Fábri, Oskar Asvany, Stephan Schlemmer, Dominik Marx, Attila G. Császár
Quantum Nuclear Delocalization and its Rovibrational Fingerprints Journal Article
In: Angewandte Chemie International Edition, vol. 62, no. 41, pp. e202306744, 2023.
Abstract | Links | BibTeX | Tags: Nuclear quantum effects, path integral molecular dynamics (PIMD), Quantum Dynamics
@article{Simko/10.1002/anie.202306744,
title = {Quantum Nuclear Delocalization and its Rovibrational Fingerprints},
author = {Irén Simkó and Christoph Schran and Fabien Brieuc and Csaba Fábri and Oskar Asvany and Stephan Schlemmer and Dominik Marx and Attila G. Császár},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/anie.202306744},
doi = {10.1002/anie.202306744},
year = {2023},
date = {2023-01-01},
urldate = {2023-01-01},
journal = {Angewandte Chemie International Edition},
volume = {62},
number = {41},
pages = {e202306744},
abstract = {Abstract Quantum mechanics dictates that nuclei must undergo some delocalization. In this work, emergence of quantum nuclear delocalization and its rovibrational fingerprints are discussed for the case of the van der Waals complex . The equilibrium structure of is planar and T-shaped, one He atom solvating the quasi-linear He−H+−He core. The dynamical structure of , in all of its bound states, is fundamentally different. As revealed by spatial distribution functions and nuclear densities, during the vibrations of the molecule the solvating He is not restricted to be in the plane defined by the instantaneously bent chomophore, but freely orbits the central proton, forming a three-dimensional torus around the chromophore. This quantum delocalization is observed for all vibrational states, the type of vibrational excitation being reflected in the topology of the nodal surfaces in the nuclear densities, showing, for example, that intramolecular bending involves excitation along the circumference of the torus.},
keywords = {Nuclear quantum effects, path integral molecular dynamics (PIMD), Quantum Dynamics},
pubstate = {published},
tppubtype = {article}
}
2022

Laura Durán Caballero, Christoph Schran, Fabien Brieuc, Dominik Marx
Neural Network Interaction Potentials for para-Hydrogen with Flexible Molecules Journal Article
In: J. Chem. Phys., vol. 157, no. 7, pp. 074302, 2022, ISSN: 0021-9606.
Abstract | Links | BibTeX | Tags: Machine Learning Potentials, Nuclear quantum effects, Superfluidity, Water
@article{Duran2022/10.1063/5.0100953,
title = {Neural Network Interaction Potentials for para-Hydrogen with Flexible Molecules},
author = {Laura Durán Caballero and Christoph Schran and Fabien Brieuc and Dominik Marx},
doi = {10.1063/5.0100953},
issn = {0021-9606},
year = {2022},
date = {2022-08-01},
urldate = {2022-08-01},
journal = {J. Chem. Phys.},
volume = {157},
number = {7},
pages = {074302},
publisher = {AIP Publishing LLCAIP Publishing},
abstract = {The study of molecular impurities in para-hydrogen (pH2) clusters is key to push forward our understanding of intra- and intermolecular interactions including their impact on the superfluid response of this bosonic quantum solvent. This includes tagging with one or very few pH2, the microsolvation regime, and matrix isolation. However, the fundamental coupling between the bosonic pH2 environment and the (ro-)vibrational motion of molecular impurities remains poorly understood. Quantum simulations can in provide the necessary atomistic insight, but very accurate descriptions of the involved interactions are required. Here, we present a data-driven approach for the generation of impurity-pH2 interaction potentials based on machine learning techniques which retain the full flexibility of the impurity. We employ the well-established adiabatic hindered rotor (AHR) averaging technique to include the impact of the nuclear spin statistics on the symmetry-allowed rotational quantum numbers of pH2. Embedding this averaging procedure within the high-dimensional neural network potential (NNP) framework enables the generation of highly-accurate AHR-averaged NNPs at coupled cluster accuracy, namely CCSD(T*)-F12a/aVTZcp in an automated manner. We apply this methodology to the water and protonated water molecules, as representative cases for quasi-rigid and highly-flexible molecules respectively, and obtain AHR-averaged NNPs that reliably describe the H2O-pH2 and H3O+-pH2 interactions. Using path integral simulations we show for the hydronium cation that umbrella-like tunneling inversion has a strong impact on the first and second pH2 microsolvation shells. The data-driven nature of our protocol opens the door to the study of bosonic pH2 quantum solvation for a wide range of embedded impurities.},
keywords = {Machine Learning Potentials, Nuclear quantum effects, Superfluidity, Water},
pubstate = {published},
tppubtype = {article}
}
2020

Rafał Topolnicki, Fabien Brieuc, Christoph Schran, Dominik Marx
Deciphering High-Order Structural Correlations within Fluxional Molecules from Classical and Quantum Configurational Entropy Journal Article
In: J. Chem. Theory Comput., vol. 16, no. 11, pp. 6785–6794, 2020, ISSN: 15499626.
Abstract | Links | BibTeX | Tags: Nuclear quantum effects
@article{Topolnicki2020/10.1021/acs.jctc.0c00642,
title = {Deciphering High-Order Structural Correlations within Fluxional Molecules from Classical and Quantum Configurational Entropy},
author = {Rafał Topolnicki and Fabien Brieuc and Christoph Schran and Dominik Marx},
doi = {10.1021/acs.jctc.0c00642},
issn = {15499626},
year = {2020},
date = {2020-09-01},
urldate = {2020-09-01},
journal = {J. Chem. Theory Comput.},
volume = {16},
number = {11},
pages = {6785–6794},
abstract = {We employ the kth nearest-neighbor estimator of configurational entropy in order to decode within a parameter-free numerical approach the complex high-order structural correlations in fluxional molecules going much beyond the usual linear, bivariate correlations. This generic entropy-based scheme for determining many-body correlations is applied to the complex configurational ensemble of protonated acetylene, a prototype for fluxional molecules featuring large-Amplitude motion. After revealing the importance of high-order correlations beyond the simple two-coordinate picture for this molecule, we analyze in detail the evolution of the relevant correlations with temperature as well as the impact of nuclear quantum effects down to the ultralow temperature regime of 1 K. We find that quantum delocalization and zero-point vibrations significantly reduce all correlations in protonated acetylene in the deep quantum regime. Even at low temperatures up to about 100 K, most correlations are essentially absent in the quantum case and only gain importance at higher temperatures. In the high temperature regime, beyond roughly 800 K, the increasing thermal fluctuations are found to exert a destructive effect on the presence of correlations. At intermediate temperatures of approximately 100-800 K, a quantum-To-classical cross-over regime is found where classical mechanics starts to correctly describe trends in the correlations whereas it even qualitatively fails below 100 K. Finally, a classical description of the nuclei provides correlations that are in quantitative agreement with the quantum ones only at temperatures exceeding 1000 K. This data-intensive analysis has been made possible due to recent developments of machine learning techniques based on high-dimensional neural network potential energy surfaces in full dimensionality that allow us to exhaustively sample both the classical and quantum ensemble of protonated acetylene at essentially converged coupled cluster accuracy from 1 to more than 1000 K. The presented non-parametric analysis of correlations beyond usual linear two-coordinate terms is transferable to other system classes. The technique is also expected to complement and guide the analysis of experimental measurements, in particular multidimensional vibrational spectroscopy, by revealing the complex coupling between various degrees of freedom.},
keywords = {Nuclear quantum effects},
pubstate = {published},
tppubtype = {article}
}

Fabien Brieuc, Christoph Schran, Felix Uhl, Harald Forbert, Dominik Marx
Converged quantum simulations of reactive solutes in superfluid helium: The Bochum perspective Journal Article
In: J. Chem. Phys., vol. 152, no. 21, pp. 210901, 2020, ISSN: 10897690.
Abstract | Links | BibTeX | Tags: Nuclear quantum effects, path integral molecular dynamics (PIMD), Superfluidity
@article{Brieuc2020/10.1063/5.0008309,
title = {Converged quantum simulations of reactive solutes in superfluid helium: The Bochum perspective},
author = {Fabien Brieuc and Christoph Schran and Felix Uhl and Harald Forbert and Dominik Marx},
doi = {10.1063/5.0008309},
issn = {10897690},
year = {2020},
date = {2020-06-01},
urldate = {2020-06-01},
journal = {J. Chem. Phys.},
volume = {152},
number = {21},
pages = {210901},
abstract = {Superfluid helium has not only fascinated scientists for centuries but is also the ideal matrix for the investigation of chemical systems under ultra-cold conditions in helium nanodroplet isolation experiments. Together with related experimental techniques such as helium tagging photodissociation spectroscopy, these methods have provided unique insights into many interesting systems. Complemented by theoretical work, they were additionally able to greatly expand our general understanding of manifestations of superfluid behavior in finite sized clusters and their response to molecular impurities. However, most theoretical studies up to now have not included the reactivity and flexibility of molecular systems embedded in helium. In this perspective, the theoretical foundation of simulating fluxional molecules and reactive complexes in superfluid helium is presented in detail. Special emphasis is put on recent developments for the converged description of both the molecular interactions and the quantum nature of the nuclei at ultra-low temperatures. As a first step, our hybrid path integral molecular dynamics/bosonic path integral Monte Carlo method is reviewed. Subsequently, methods for efficient path integral sampling tailored for this hybrid coupling scheme are discussed while also introducing new developments to enhance the accurate incorporation of the solute⋯solvent coupling. Finally, highly accurate descriptions of the interactions in solute⋯helium systems using machine learning techniques are addressed. Our current automated and adaptive fitting procedures to parameterize high-dimensional neural network potentials for both the full-dimensional potential energy surface of solutes and the solute⋯solvent interaction potentials are concisely presented. They are demonstrated to faithfully represent many-body potential functions able to describe chemically complex and reactive solutes in helium environments seamlessly from one He atom up to bulk helium at the accuracy level of coupled cluster electronic structure calculations. Together, these advances allow for converged quantum simulations of fluxional and reactive solutes in superfluid helium under cryogenic conditions.},
keywords = {Nuclear quantum effects, path integral molecular dynamics (PIMD), Superfluidity},
pubstate = {published},
tppubtype = {article}
}
2019

Christoph Schran, Dominik Marx
Quantum nature of the hydrogen bond from ambient conditions down to ultra-low temperatures Journal Article
In: Phys. Chem. Chem. Phys., vol. 21, no. 45, pp. 24967–24975, 2019, ISSN: 14639076.
Abstract | Links | BibTeX | Tags: Hydrogen bonding, Nuclear quantum effects, path integral molecular dynamics (PIMD), Water
@article{Schran2019/10.1039/C9CP04795F,
title = {Quantum nature of the hydrogen bond from ambient conditions down to ultra-low temperatures},
author = {Christoph Schran and Dominik Marx},
doi = {10.1039/c9cp04795f},
issn = {14639076},
year = {2019},
date = {2019-10-01},
urldate = {2019-10-01},
journal = {Phys. Chem. Chem. Phys.},
volume = {21},
number = {45},
pages = {24967–24975},
abstract = {Many experimental techniques such as tagging photodissociation and helium nanodroplet isolation spectroscopy operate at very low temperatures in order to investigate hydrogen bonding. To elucidate the differences between such ultra-cold and usual ambient conditions, different hydrogen bonded systems are studied systematically from 300 K down to about 1 K using path integral simulations that explicitly consider both the quantum nature of the nuclei and thermal fluctuations. For this purpose, finite sized water clusters, specifically the water dimer and hexamer, protonated water clusters including the Zundel and Eigen complexes, as well as hexagonal ice as a condensed phase representative are compared directly as a function of temperature. While weaker hydrogen bonds, as present in the neutral systems, show distinct structural differences between ambient conditions and the ultra-cold regime, the stronger hydrogen bonds of the protonated water clusters are less perturbed by temperature compared to their quantum ground state. In all the studied systems, the quantum delocalization of the nuclei is found to vary drastically with temperature. Interestingly, upon reaching temperatures of about 1 K, the spatial quantum delocalization of the heavy oxygens approaches that of the protons for relatively weak spatial constraints, and even significantly exceeds the latter in the case of the centered hydrogen bond in the Zundel complex. These findings are relevant for comparisons between experiments on hydrogen bonding carried out under ultra-cold versus ambient conditions as well as to understand quantum delocalization phenomena of nuclei by seamlessly extending our insights into noncovalent interactions down to ultra-low temperatures.},
keywords = {Hydrogen bonding, Nuclear quantum effects, path integral molecular dynamics (PIMD), Water},
pubstate = {published},
tppubtype = {article}
}
2018

Christoph Schran, Fabien Brieuc, Dominik Marx
Converged Colored Noise Path Integral Molecular Dynamics Study of the Zundel Cation Down to Ultralow Temperatures at Coupled Cluster Accuracy Journal Article
In: J. Chem. Theory Comput., vol. 14, no. 10, pp. 5068–5078, 2018, ISSN: 15499626.
Abstract | Links | BibTeX | Tags: Nuclear quantum effects, path integral molecular dynamics (PIMD), Water
@article{Schran2018/10.1021/acs.jctc.8b00705,
title = {Converged Colored Noise Path Integral Molecular Dynamics Study of the Zundel Cation Down to Ultralow Temperatures at Coupled Cluster Accuracy},
author = {Christoph Schran and Fabien Brieuc and Dominik Marx},
doi = {10.1021/acs.jctc.8b00705},
issn = {15499626},
year = {2018},
date = {2018-09-01},
urldate = {2018-09-01},
journal = {J. Chem. Theory Comput.},
volume = {14},
number = {10},
pages = {5068–5078},
abstract = {For a long time, performing converged path integral simulations at ultra-low, but finite temperatures of a few Kelvin has been a nearly impossible task. However, recent developments in advanced colored noise thermostatting schemes for path integral simulations, namely the Path Integral Generalized Langevin Equation Thermostat (PIGLET) and the Path Integral Quantum Thermal Bath (PIQTB), have been able to greatly reduce the computational cost of these simulations, thus making the ultra-low temperature regime accessible in practice. In this work, we investigate the influence of these two thermostatting schemes on the description of hydrogen-bonded systems at temperatures down to a few Kelvin as encountered, for example, in helium nanodroplet isolation or tagging photodissociation spectroscopy experiments. For this purpose, we analyze the prototypical hydrogen bond in the Zundel cation (H5O2+) as a function of both, oxygen-oxygen distance and temperature in order to elucidate how the anisotropic quantum deloc...},
keywords = {Nuclear quantum effects, path integral molecular dynamics (PIMD), Water},
pubstate = {published},
tppubtype = {article}
}

Christoph Schran, Felix Uhl, Jörg Behler, Dominik Marx
High-dimensional neural network potentials for solvation: The case of protonated water clusters in helium Journal Article
In: J. Chem. Phys., vol. 148, no. 10, pp. 102310, 2018, ISSN: 00219606.
Abstract | Links | BibTeX | Tags: Machine Learning Potentials, Nuclear quantum effects, Superfluidity, Water
@article{Schran2018/10.1063/1.4996819,
title = {High-dimensional neural network potentials for solvation: The case of protonated water clusters in helium},
author = {Christoph Schran and Felix Uhl and Jörg Behler and Dominik Marx},
doi = {10.1063/1.4996819},
issn = {00219606},
year = {2018},
date = {2018-03-01},
urldate = {2018-03-01},
journal = {J. Chem. Phys.},
volume = {148},
number = {10},
pages = {102310},
abstract = {The design of accurate helium-solute interaction potentials for the simulation of chemically complex molecules solvated in superfluid helium has long been a cumbersome task due to the rather weak but strongly anisotropic nature of the interactions. We show that this challenge can be met by using a combination of an effective pair potential for the He–He interactions and a flexible high-dimensional neural network potential (NNP) for describing the complex interaction between helium and the solute in a pairwise additive manner. This approach yields an excellent agreement with a mean absolute deviation as small as 0.04 kJ mol−1 for the interaction energy between helium and both hydronium and Zundel cations compared with coupled cluster reference calculations with an energetically converged basis set. The construction and improvement of the potential can be performed in a highly automated way, which opens the door for applications to a variety of reactive molecules to study the effect of solvation on the solu...},
keywords = {Machine Learning Potentials, Nuclear quantum effects, Superfluidity, Water},
pubstate = {published},
tppubtype = {article}
}
2017

Christoph Schran, Ondrej Marsalek, Thomas E. Markland
Unravelling the influence of quantum proton delocalization on electronic charge transfer through the hydrogen bond Journal Article
In: Chem. Phys. Lett., vol. 678, pp. 289–295, 2017, ISSN: 00092614.
Abstract | Links | BibTeX | Tags: Charge transfer, Hydrogen bonding, Ions in Water, Nuclear quantum effects, Water
@article{Schran2017/10.1016/j.cplett.2017.04.034,
title = {Unravelling the influence of quantum proton delocalization on electronic charge transfer through the hydrogen bond},
author = {Christoph Schran and Ondrej Marsalek and Thomas E. Markland},
doi = {10.1016/j.cplett.2017.04.034},
issn = {00092614},
year = {2017},
date = {2017-06-01},
urldate = {2017-06-01},
journal = {Chem. Phys. Lett.},
volume = {678},
pages = {289–295},
abstract = {Upon hydrogen bond formation, electronic charge density is transferred between the donor and acceptor, impacting processes ranging from hydration to spectroscopy. Here we use ab initio path integral simulations to elucidate the role of nuclear quantum effects in determining the charge transfer in a range of hydrogen bonded species in the gas and liquid phase. We show that the quantization of the nuclei gives rise to large changes in the magnitude of the charge transfer as well as its temperature dependence. We then explain how a single geometric parameter determines the charge transfer through the hydrogen bond. These results thus demonstrate that nuclear quantum effects are vital for the accurate description of charge transfer and offer a physically transparent way to understand how hydrogen bonding gives rise to it.},
keywords = {Charge transfer, Hydrogen bonding, Ions in Water, Nuclear quantum effects, Water},
pubstate = {published},
tppubtype = {article}
}