Clarke, D., Whitney, H., Sutton, G. & Robert, D. Detection and learning of floral electric fields by bumblebees. Science 340, 66–69 (2013).
Google Scholar
Futera, Z., Tse, J. S. & English, N. J. Possibility of realizing superionic ice vii in external electric fields of planetary bodies. Sci. Adv. 6, eaaz2915 (2020).
Google Scholar
Besalú-Sala, P., Solà, M., Luis, J. M. & Torrent-Sucarrat, M. Fast and simple evaluation of the catalysis and selectivity induced by external electric fields. ACS Catal. 11, 14467–14479 (2021).
Google Scholar
Shaik, S., Danovich, D., Joy, J., Wang, Z. & Stuyver, T. Electric-field mediated chemistry: Uncovering and exploiting the potential of (oriented) electric fields to exert chemical catalysis and reaction control. J. Am. Chem. Soc. 142, 12551–12562 (2020).
Google Scholar
Rycroft, M. J., Israelsson, S. & Price, C. The global atmospheric electric circuit, solar activity and climate change. J. Atmos. Sol. Terr. Phys. 62, 1563–1576 (2000).
Google Scholar
Toney, M. F. et al. Voltage-dependent ordering of water molecules at an electrode-electrolyte interface. Nature 368, 444–446 (1994).
Google Scholar
Hao, H., Leven, I. & Head-Gordon, T. Can electric fields drive chemistry for an aqueous microdroplet? Nat. Commun. 13, 280 (2022).
Google Scholar
Cassone, G., Sponer, J., Trusso, S. & Saija, F. Ab initio spectroscopy of water under electric fields. Phys. Chem. Chem. Phys. 21, 21205–21212 (2019).
Google Scholar
Cassone, G. & Martelli, F. Electrofreezing of liquid water at ambient conditions. Nat. Commun. 15, 1856 (2024).
Google Scholar
Schirmer, B. & Grimme, S. Electric field induced activation of h2-can dft do the job? Chem. Commun. 46, 7942–7944 (2010).
Google Scholar
Ashton, M., Mishra, A., Neugebauer, J. & Freysoldt, C. Ab initio description of bond breaking in large electric fields. Phys. Rev. Lett. 124, 176801 (2020).
Google Scholar
Stengel, M., Spaldin, N. A. & Vanderbilt, D. Electric displacement as the fundamental variable in electronic-structure calculations. Nat. Phys. 5, 304–308 (2009).
Google Scholar
Zhang, C. & Sprik, M. Computing the dielectric constant of liquid water at constant dielectric displacement. Phys. Rev. B 93, 144201 (2016).
Google Scholar
Sayer, T., Zhang, C. & Sprik, M. Charge compensation at the interface between the polar nacl(111) surface and a nacl aqueous solution. J. Chem. Phys. 147, 104702 (2017).
Google Scholar
Cox, S. J. & Sprik, M. Finite field formalism for bulk electrolyte solutions. J. Chem. Phys. 151, 064506 (2019).
Google Scholar
Marx, D. & Hutter, J.Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods (Cambridge University Press, Cambridge, 2009).
English, N. J. & Waldron, C. J. Perspectives on external electric fields in molecular simulation: progress, prospects and challenges. Phys. Chem. Chem. Phys. 17, 12407–12440 (2015).
Google Scholar
Elgabarty, H., Kaliannan, N. K. & Kühne, T. D. Enhancement of the local asymmetry in the hydrogen bond network of liquid water by an ultrafast electric field pulse. Sci. Rep. 9, 10002 (2019).
Google Scholar
Elgabarty, H. et al. Energy transfer within the hydrogen bonding network of water following resonant terahertz excitation. Sci. Adv. 6, eaay7074 (2020).
Google Scholar
Zhang, C., Sayer, T., Hutter, J. & Sprik, M. Modelling electrochemical systems with finite field molecular dynamics. J. Phys. Energy 2, 032005 (2020).
Google Scholar
Jia, M., Zhang, C. & Cheng, J. Origin of asymmetric electric double layers at electrified oxide/electrolyte interfaces. J. Phys. Chem. Lett. 12, 4616–4622 (2021).
Google Scholar
Futera, Z. & English, N. J. Water breakup at fe2o3–hematite/water interfaces: Influence of external electric fields from nonequilibrium ab initio molecular dynamics. J. Phys. Chem. Lett. 12, 6818–6826 (2021).
Google Scholar
Huang, J., Zhang, Y., Li, M., Groß, A. & Sakong, S. Comparing ab initio molecular dynamics and a semiclassical grand canonical scheme for the electric double layer of the pt(111)/water interface. J. Phys. Chem. Lett. 14, 2354–2363 (2023).
Google Scholar
Behler, J. & Parrinello, M. Generalized neural-network representation of high-dimensional potential-energy surfaces. Phys. Rev. Lett. 98, 146401 (2007).
Google Scholar
Bartók, A. P., Payne, M. C., Kondor, R. & Csányi, G. Gaussian approximation potentials: The accuracy of quantum mechanics, without the electrons. Phys. Rev. Lett. 104, 136403 (2010).
Google Scholar
Behler, J. Four generations of high-dimensional neural network potentials. Chem. Rev. 121, 10037–10072 (2021).
Google Scholar
Bereau, T., DiStasio, J. R. A., Tkatchenko, A. & von Lilienfeld, O. A. Non-covalent interactions across organic and biological subsets of chemical space: Physics-based potentials parametrized from machine learning. J. Chem. Phys. 148, 241706 (2018).
Google Scholar
Zinovjev, K. Electrostatic embedding of machine learning potentials. J. Chem. Theory Comput. 19, 1888–1897 (2023).
Google Scholar
Zhang, Y. et al. Efficient and accurate simulations of vibrational and electronic spectra with symmetry-preserving neural network models for tensorial properties. J. Phys. Chem. B 124, 7284–7290 (2020).
Google Scholar
Zhang, L. et al. Deep neural network for the dielectric response of insulators. Phys. Rev. B 102, 041121 (2020).
Google Scholar
Sommers, G. M., Calegari Andrade, M. F., Zhang, L., Wang, H. & Car, R. Raman spectrum and polarizability of liquid water from deep neural networks. Phys. Chem. Chem. Phys. 22, 10592–10602 (2020).
Google Scholar
Schütt, K., Unke, O. & Gastegger, M. Equivariant message passing for the prediction of tensorial properties and molecular spectra. In Proceedings of the 38th International Conference on Machine Learning Research 9377–9388 (2021).
Wilkins, D. M. et al. Accurate molecular polarizabilities with coupled cluster theory and machine learning. Proc. Natl. Acad. Sci. USA 116, 3401–3406 (2019).
Google Scholar
Kapil, V., Wilkins, D. M., Lan, J. & Ceriotti, M. Inexpensive modeling of quantum dynamics using path integral generalized langevin equation thermostats. J. Chem. Phys. 152, 124104 (2020).
Google Scholar
Shepherd, S., Lan, J., Wilkins, D. M. & Kapil, V. Efficient quantum vibrational spectroscopy of water with high-order path integrals: From bulk to interfaces. J. Phys. Chem. Lett. 12, 9108–9114 (2021).
Google Scholar
Beckmann, R., Brieuc, F., Schran, C. & Marx, D. Infrared spectra at coupled cluster accuracy from neural network representations. J. Chem. Theory Comput. 18, 5492–5501 (2022).
Google Scholar
Schienbein, P. Spectroscopy from machine learning by accurately representing the atomic polar tensor. J. Chem. Theory Comput. 19, 705–712 (2023).
Google Scholar
Christensen, A. S., Faber, F. A. & von Lilienfeld, O. A. Operators in quantum machine learning: Response properties in chemical space. J. Chem. Phys. 150, 064105 (2019).
Google Scholar
Gastegger, M., Schütt, K. T. & Müller, K.-R. Machine learning of solvent effects on molecular spectra and reactions. Chem. Sci. 12, 11473–11483 (2021).
Google Scholar
Gao, A. & Remsing, R. C. Self-consistent determination of long-range electrostatics in neural network potentials. Nat. Commun. 13, 1572 (2022).
Google Scholar
Shao, Y., Andersson, L., Knijff, L. & Zhang, C. Finite-field coupling via learning the charge response kernel. Electron. Struct. 4, 014012 (2022).
Google Scholar
Zhang, Y. & Jiang, B. Universal machine learning for the response of atomistic systems to external fields. Nat. Commun. 14, 6424 (2023).
Google Scholar
Person, W. B. & Newton, J. H. Dipole moment derivatives and infrared intensities. i. polar tensors. J. Chem. Phys. 61, 1040–1049 (1974).
Google Scholar
Schran, C., Brezina, K. & Marsalek, O. Committee neural network potentials control generalization errors and enable active learning. J. Chem. Phys. 153, 104105 (2020).
Google Scholar
Szabo, A. & Ostlund, N. S. Modern Quantum Chemistry (Dover Publications, Inc., 1996).
Resta, R. Theory of the electric polarization in crystals. Ferroelectrics 136, 51–55 (1992).
Google Scholar
Resta, R. & Vanderbilt, D. Theory of polarization: a modern approach. In Physics of Ferroelectrics: a Modern Perspective, 31–68 (Springer, 2007).
Natarajan, S. K. & Behler, J. Neural network molecular dynamics simulations of solid-liquid interfaces: water at low-index copper surfaces. Phys. Chem. Chem. Phys. 18, 28704–28725 (2016).
Google Scholar
Schienbein, P. & Blumberger, J. Nanosecond solvation dynamics of the hematite/liquid water interface at hybrid dft accuracy using committee neural network potentials. Phys. Chem. Chem. Phys. 24, 15365–15375 (2022).
Google Scholar
Schran, C. et al. Machine learning potentials for complex aqueous systems made simple. Proc. Natl. Acad. Sci. USA 118, e2110077118 (2021).
Google Scholar
Montenegro, A. et al. Asymmetric response of interfacial water to applied electric fields. Nature 594, 62–65 (2021).
Google Scholar
Ceriotti, M. et al. Nuclear quantum effects in water and aqueous systems: Experiment, theory, and current challenges. Chem. Rev. 116, 7529–7550 (2016).
Google Scholar
Cassone, G. Nuclear quantum effects largely influence molecular dissociation and proton transfer in liquid water under an electric field. J. Phys. Chem. Lett. 11, 8983–8988 (2020).
Google Scholar
Fernández, D. P., Goodwin, A. R. H., Lemmon, E. W., Levelt Sengers, J. M. H. & Williams, R. C. A formulation for the static permittivity of water and steam at temperatures from 238 k to 873 k at pressures up to 1200 mpa, including derivatives and debye-hückel coefficients. J. Phys. Chem. Ref. Data 26, 1125–1166 (1997).
Google Scholar
Kirkwood, J. G. The dielectric polarization of polar liquids. J. Chem. Phys. 7, 911–919 (1939).
Google Scholar
Neumann, M. & Steinhauser, O. On the calculation of the frequency-dependent dielectric constant in computer simulations. Chem. Phys. Lett. 102, 508–513 (1983).
Google Scholar
de Leeuw, S. W., Perram, J. W., Smith, E. R. & Rowlinson, J. S. Simulation of electrostatic systems in periodic boundary conditions. i. lattice sums and dielectric constants. Proc. R. Soc. Lond. A 373, 27–56 (1980).
Google Scholar
Lu, D., Gygi, Fmc & Galli, G. Dielectric properties of ice and liquid water from first-principles calculations. Phys. Rev. Lett. 100, 147601 (2008).
Google Scholar
Morawietz, T., Singraber, A., Dellago, C. & Behler, J. How van der waals interactions determine the unique properties of water. Proc. Natl. Acad. Sci. USA 113, 8368–8373 (2016).
Google Scholar
Neumann, M. & Steinhauser, O. Computer simulation and the dielectric constant of polarizable polar systems. Chem. Phys. Lett. 106, 563–569 (1984).
Google Scholar
Bertie, J. E. & Lan, Z. Infrared intensities of liquids xx: The intensity of the oh stretching band of liquid water revisited, and the best current values of the optical constants of h2o(l) at 25∘c between 15000 and 1 cm−1. Appl. Spectrosc. 50, 1047–1057 (1996).
Google Scholar
Rey, R., Møller, K. B. & Hynes, J. T. Hydrogen bond dynamics in water and ultrafast infrared spectroscopy. J. Phys. Chem. A 106, 11993–11996 (2002).
Google Scholar
Lawrence, C. P. & Skinner, J. L. Vibrational spectroscopy of HOD in liquid D2O. iii. spectral diffusion, and hydrogen-bonding and rotational dynamics. J. Chem. Phys. 118, 264–272 (2003).
Google Scholar
Fecko, C. J., Eaves, J. D., Loparo, J. J., Tokmakoff, A. & Geissler, P. L. Ultrafast hydrogen-bond dynamics in the infrared spectroscopy of water. Science 301, 1698–1702 (2003).
Google Scholar
Schienbein, P. & Marx, D. Supercritical water is not hydrogen bonded. Angew. Chem. Int. Ed. 59, 18578–18585 (2020).
Google Scholar
Schienbein, P. & Marx, D. Liquid-vapor phase diagram of rpbe-d3 water: Electronic properties along the coexistence curve and in the supercritical phase. J. Phys. Chem. B 122, 3318–3329 (2018).
Google Scholar
Schienbein, P. & Marx, D. Assessing the properties of supercritical water in terms of structural dynamics and electronic polarization effects. Phys. Chem. Chem. Phys. 22, 10462–10479 (2020).
Google Scholar
Imoto, S., Forbert, H. & Marx, D. Water structure and solvation of osmolytes at high hydrostatic pressure: pure water and tmao solutions at 10 kbar versus 1 bar. Phys. Chem. Chem. Phys. 17, 24224–24237 (2015).
Google Scholar
Forster-Tonigold, K. & Groß, A. Dispersion corrected RPBE studies of liquid water. J. Chem. Phys. 141, 064501 (2014).
Google Scholar
Groß, A. & Sakong, S. Ab initio simulations of water/metal interfaces. Chem. Rev. 122, 10746–10776 (2022).
Google Scholar
Ko, T. W., Finkler, J. A., Goedecker, S. & Behler, J. A fourth-generation high-dimensional neural network potential with accurate electrostatics including non-local charge transfer. Nat. Commun.12, 398 (2021).
Ko, T. W., Finkler, J. A., Goedecker, S. & Behler, J. Accurate fourth-generation machine learning potentials by electrostatic embedding. J. Chem. Theory Comput. 19, 3567–3579 (2023).
Google Scholar
Geiger, M. et al. Euclidean neural networks: e3nn. Preprint at (2022).
Paszke, A. et al. Pytorch: An imperative style, high-performance deep learning library. Adv. Neural Inf. Process. Syst. 32 (2019).
Kapil, V. et al. i-pi 2.0: A universal force engine for advanced molecular simulations. Comput. Phys. Commun. 236, 214–223 (2019).
Google Scholar
Singraber, A., Morawietz, T., Behler, J. & Dellago, C. Parallel multistream training of high-dimensional neural network potentials. J. Chem. Theory Comput. 15, 3075–3092 (2019).
Google Scholar
Ditler, E., Kumar, C. & Luber, S. Analytic calculation and analysis of atomic polar tensors for molecules and materials using the Gaussian and plane waves approach. J. Chem. Phys. 154, 104121 (2021).
Google Scholar
Kühne, T. D. et al. CP2K: An electronic structure and molecular dynamics software package – Quickstep: Efficient and accurate electronic structure calculations. J. Chem. Phys. 152, 194103 (2020).
Google Scholar
VandeVondele, J. et al. Quickstep: Fast and accurate density functional calculations using a mixed gaussian and plane waves approach. Comput. Phys. Commun. 167, 103–128 (2005).
Google Scholar
Marques, M. A., Oliveira, M. J. & Burnus, T. Libxc: A library of exchange and correlation functionals for density functional theory. Comput. Phys. Commun. 183, 2272–2281 (2012).
Google Scholar
Grimme, S., Antony, J., Ehrlich, S. & Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 132, 154104 (2010).
Google Scholar
Lippert, G., Hutter, J. & Parrinello, M. A hybrid gaussian and plane wave density functional scheme. Mol. Phys. 92, 477–488 (1997).
Google Scholar
VandeVondele, J. & Hutter, J. Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases. J. Chem. Phys. 127, 114105 (2007).
Google Scholar
Goedecker, S., Teter, M. & Hutter, J. Separable dual-space gaussian pseudopotentials. Phys. Rev. B 54, 1703–1710 (1996).
Google Scholar
Hartwigsen, C., Goedecker, S. & Hutter, J. Relativistic separable dual-space gaussian pseudopotentials from h to rn. Phys. Rev. B 58, 3641–3662 (1998).
Google Scholar
Umari, P. & Pasquarello, A. Ab initio molecular dynamics in a finite homogeneous electric field. Phys. Rev. Lett. 89, 157602 (2002).
Google Scholar
Pick, R. M., Cohen, M. H. & Martin, R. M. Microscopic theory of force constants in the adiabatic approximation. Phys. Rev. B 1, 910–920 (1970).
Google Scholar
Nicu, V. P., Neugebauer, J., Wolff, S. K. & Baerends, E. J. A vibrational circular dichroism implementation within a slater-type-orbital based density functional framework and its application to hexa-and hepta-helicenes. Theor. Chem. Acc. 119, 245–263 (2008).
Google Scholar
Unke, O. T. & Meuwly, M. Physnet: A neural network for predicting energies, forces, dipole moments, and partial charges. J. Chem. Theor. Comput. 15, 3678–3693 (2019).
Google Scholar
Unke, O. T. et al. Spookynet: Learning force fields with electronic degrees of freedom and nonlocal effects. Nat. Commun. 12, 7273 (2021).
Google Scholar
Song, Z., Han, J., Henkelman, G. & Li, L. Charge-optimized electrostatic interaction atom-centered neural network algorithm. J. Chem. Theor. Comput. 20, 2088–2097 (2024).
Bussi, G., Donadio, D. & Parrinello, M. Canonical sampling through velocity rescaling. J. Chem. Phys. 126, (2007).
Nosé, S. A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys. 81, 511–519 (1984).
Google Scholar
Nosé, S. A molecular dynamics method for simulations in the canonical ensemble. Mol. Phys. 52, 255–268 (1984).
Google Scholar
Joll, K., Schienbein, P., Rosso, K. & Blumberger, J. Machine learning the electric field response of condensed phase systems using perturbed neural network potentials. Source data 1, (2024).
Joll, K., Schienbein, P., Rosso, K. & Blumberger, J. Machine learning the electric field response of condensed phase systems using perturbed neural network potentials. Supplementary data 1, (2024).
Joll, K., Schienbein, P., Rosso, K. & Blumberger, J. Machine learning the electric field response of condensed phase systems using perturbed neural network potentials. custom APT CP2K, (2024).
Joll, K., Schienbein, P., Rosso, K. & Blumberger, J. Machine learning the electric field response of condensed phase systems using perturbed neural network potentials. AtomicPolarTensor, (2024).
Zhang, C. & Galli, G. Dipolar correlations in liquid water. J. Chem. Phys. 141, (2014).
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