- Editors' Suggestion
- Open Access
THz dynamics of hydrogen sulfide: Search for collective modes of a non-hydrogen-bonded analog of water
Phys. Rev. E 114, 015412 – Published 15 July, 2026
DOI: https://doi.org/10.1103/ccq9-618c
Abstract
Understanding the atomic-scale dynamics of liquids in the terahertz (THz) regime remains challenging because liquids sustain phonon-like collective excitations governed by complex interactions. To clarify the role of hydrogen bonding in such dynamics, we performed inelastic neutron scattering on hydrogen sulfide and its deuterated form , molecular analogues of water without a hydrogen-bonded network. By combining coherent and incoherent measurements, we show that liquid exhibits a clear fast-sound mode, with a propagation velocity about twice the adiabatic sound speed, as in water. In contrast to hydrogen-bonded liquids, which display a secondary, nearly momentum-independent mode at 6–7 meV, no corresponding feature is observed in liquid . This absence highlights the central role of hydrogen bonding in enabling additional low-energy excitations. Overall, while fast sound is not exclusive to hydrogen-bonded systems, the detailed vibrational spectrum is strongly shaped by the local bonding environment.
Physics Subject Headings (PhySH)
Article Text
References (89)
- W. Ke and Y. Yin, Does a quark-gluon plasma feature an extended hydrodynamic regime? Phys. Rev. Lett. 130, 212303 (2023).
- J. R. D. Copley and J. M. Rowe, Short-wavelength collective excitations in liquid rubidium observed by coherent neutron scattering, Phys. Rev. Lett. 32, 49 (1974).
- T. Bodensteiner, C. Morkel, W. Gläser, and B. Dorner, Collective dynamics in liquid cesium near the melting point, Phys. Rev. A 45, 5709 (1992).
- T. Scopigno, G. Ruocco, and F. Sette, Microscopic dynamics in liquid metals: The experimental point of view, Rev. Mod. Phys. 77, 881 (2005).
- L. E. Bove, F. Sacchetti, C. Petrillo, and B. Dorner, Neutron investigation of collective excitations in liquid K-Cs alloys: The role of the electron density, Phys. Rev. Lett. 85, 5352 (2000).
- L. Sani, C. Petrillo, and F. Sacchetti, Determination of the interstitial electron density in liquid metals, Phys. Rev. B 90, 024207 (2014).
- V. M. Giordano and G. Monaco, Universal acoustic dispersion in liquid alkali metals, Phys. Rev. B 79, 020201(R) (2009).
- E. Guarini, U. Bafile, F. Barocchi, A. De Francesco, E. Farhi, F. Formisano, A. Laloni, A. Orecchini, A. Polidori, M. Puglini, and F. Sacchetti, Dynamics of liquid Au from neutron Brillouin scattering and ab initio simulations, Phys. Rev. B 88, 104201 (2013).
- F. Demmel, D. Szubrin, W.-C. Pilgrim, A. De Francesco, and F. Formisano, Transition from hydrodynamic to viscoelastic propagation of sound in molten RbBr, Phys. Rev. E 92, 012307 (2015).
- E. Guarini, A. De Francesco, U. Bafile, A. Laloni, B. G. del Rio, D. J. González, L. E. González, F. Barocchi, and F. Formisano, Neutron Brillouin scattering and ab initio simulation study of the collective dynamics of liquid silver, Phys. Rev. B 102, 054210 (2020).
- U. Buchenau, N. Nücker, and A. J. Dianoux, Neutron scattering study of low-frequency vibrations in vitreous silica, Phys. Rev. Lett. 53, 2316 (1984).
- B. Rufflé, G. Guimbretière, E. Courtens, R. Vacher, and G. Monaco, Glass-specific behavior in the damping of acoustic-like vibrations, Phys. Rev. Lett. 96, 045502 (2006).
- G. Monaco and S. Mossa, Anomalous properties of the acoustic excitations in glasses on the mesoscopic length scale, Proc. Natl. Acad. Sci. USA 106, 16907 (2009).
- M. Zanatta, A. Fontana, A. Orecchini, C. Petrillo, and F. Sacchetti, Inelastic neutron scattering investigation in glassy : Complex dynamics at the atomic scale, J. Phys. Chem. Lett. 4, 1143 (2013).
- J. Teixeira, M. C. Bellissent-Funel, S. H. Chen, and B. Dorner, Observation of new short-wavelength collective excitations in heavy water, Phys. Rev. Lett. 54, 2681 (1985).
- F. Sette, G. Ruocco, M. Krisch, U. Bergmann, C. Masciovecchio, V. Mazzacurati, G. Signorelli, and R. Verbeni, Collective dynamics in water by high-energy resolution inelastic x-ray scattering, Phys. Rev. Lett. 75, 850 (1995).
- F. Sacchetti, J.-B. Suck, C. Petrillo, and B. Dorner, Brillouin neutron scattering in heavy water: Evidence for two-mode collective dynamics, Phys. Rev. E 69, 061203 (2004).
- E. Pontecorvo, M. Krisch, A. Cunsolo, G. Monaco, A. Mermet, R. Verbeni, F. Sette, and G. Ruocco, High-frequency longitudinal and transverse dynamics in water, Phys. Rev. E 71, 011501 (2005).
- A. Cunsolo, C. N. Kodituwakku, F. Bencivenga, M. Frontzek, B. M. Leu, and A. H. Said, Transverse dynamics of water across the melting point: A parallel neutron and x-ray inelastic scattering study, Phys. Rev. B 85, 174305 (2012).
- K. Amann-Winkel, M. C. Bellissent-Funel, L. E. Bove, T. Loerting, A. Nilsson, A. Paciaroni, D. Schlesinger, and L. Skinner, X-ray and neutron scattering of water, Chem. Rev. 116, 7570 (2016).
- A. De Francesco, L. Scaccia, F. Formisano, E. Guarini, U. Bafile, A. Alatas, S. T. Lynch, and A. Cunsolo, Ice phonon spectra and Bayes inference. A gateway to a new understanding of terahertz sound propagation in water, J. Chem. Phys. 158, 134509 (2023).
- M. C. Bellissent-Funel, J. Teixeira, S. H. Chen, B. Dorner, H. D. Middendorf, and H. L. Crespi, Low-frequency collective modes in dry and hydrated proteins, Biophys. J. 56, 713 (1989).
- M. Tarek and D. J. Tobias, Single-particle and collective dynamics of protein hydration water: A molecular dynamics study, Phys. Rev. Lett. 89, 275501 (2002).
- A. Orecchini, A. Paciaroni, A. De Francesco, C. Petrillo, and F. Sacchetti, Collective dynamics of protein hydration water by Brillouin neutron spectroscopy, J. Am. Chem. Soc. 131, 4664 (2009).
- Z. Wang, C. E. Bertrand, W. S. Chiang, E. Fratini, P. Baglioni, A. Alatas, E. E. Alp, and S. H. Chen, Short-time collective vibrational motions in hydrated lysozyme powders and their relation to enzymatic function, J. Phys. Chem. B 117, 1186 (2013).
- F. Sebastiani, A. Orecchini, A. Paciaroni, M. Jasnin, G. Zaccai, M. Moulin, M. Haertlein, A. De Francesco, C. Petrillo, and F. Sacchetti, Collective THz dynamics in living Escherichia coli cells, Chem. Phys. 424, 84 (2013).
- U. R. Shrestha, E. Mamontov, H. M. O'Neill, Q. Zhang, A. I. Kolesnikov, and X. Chu, Experimental mapping of short-wavelength phonons in proteins, The Innovation 3, 100199 (2022).
- V. Libera, F. Bianchi, B. Rossi, F. D'Amico, C. Masciovecchio, C. Petrillo, F. Sacchetti, A. Paciaroni, and L. Comez, Solvent vibrations as a proxy of telomere g-quadruplex rearrangements across thermal unfolding, Int. J. Mol. Sci. 23, 5123 (2022).
- M. C. Bellissent-Funel, A. Hassanali, M. Havenith, R. Henchman, P. Pohl, F. Sterpone, D. van der Spoel, Y. Xu, and A. E. Garcia, Water determines the structure and dynamics of proteins, Chem. Rev. 116, 7673 (2016).
- D. Russo, A. Orecchini, A. De Francesco, F. Formisano, A. Laloni, C. Petrillo, and F. Sacchetti, Brillouin neutron spectroscopy as a probe to investigate collective density fluctuations in biomolecules hydration water, J. Spectrosc. 27, 293 (2012).
- D. Russo, A. Laloni, A. Filabozzi, and M. Heyden, Pressure effects on collective density fluctuations in water and protein solutions, Proc. Natl. Acad. Sci. USA 114, 11410 (2017).
- E. Mamontov, A. De Francesco, F. Formisano, A. Laloni, L. Sani, B. M. Leu, A. H. Said, and A. I. Kolesnikov, Water dynamics in a lithium chloride aqueous solution probed by neutron and x-ray scattering, J. Phys.: Condens. Matter 24, 064102 (2012).
- A. De Francesco, L. Scaccia, M. Maccarini, F. Formisano, Y. Zhang, O. Gang, D. Nykypanchuk, A. H. Said, B. M. Leu, and A. Alatas, Damping of terahertz sound modes of a liquid upon immersion of nanoparticles, ACS Nano 12, 8867 (2018).
- A. De Francesco, L. Scaccia, F. Formisano, E. Guarini, U. Bafile, M. Maccarini, A. Alatas, Y. Q. Cai, D. Nykypanchuk, and A. Cunsolo, Onset of interfacial waves in the terahertz spectrum of a nanoparticle suspension, Phys. Rev. E 102, 022601 (2020).
- A. De Francesco, L. Scaccia, F. Formisano, E. Guarini, U. Bafile, M. Maccarini, A. Alatas, Y. Q. Cai, and A. Cunsolo, The terahertz dynamics of an aqueous nanoparticle suspension: An inelastic x-ray scattering study, Nanomaterials 10, 860 (2020).
- A. De Francesco, L. Scaccia, F. Formisano, E. Guarini, U. Bafile, M. Maccarini, Y. Zhang, D. Nykypanchuk, A. Alatas, and A. Cunsolo, The damping of terahertz acoustic modes in aqueous nanoparticle suspensions, Sci. Rep. 11, 20110 (2021).
- A. De Francesco, F. Formisano, L. Scaccia, E. Guarini, U. Bafile, M. Maccarini, D. Nykypanchuk, A. Suvorov, Y. Q. Cai, S. T. Lynch, and A. Cunsolo, Altering terahertz sound propagation in a liquid upon nanoparticle immersion, Nanomaterials 12, 2401 (2022).
- A. De Francesco, L. Scaccia, F. Formisano, E. Guarini, U. Bafile, D. Nykypanchuk, A. Alatas, M. Li, S. T. Lynch, and A. Cunsolo, The effect of embedded nanoparticles on the phonon spectrum of ice: An inelastic x-ray scattering study, Nanomaterials 13, 918 (2023).
- A. De Francesco, L. Scaccia, F. Formisano, M. Maccarini, F. De Luca, A. Parmentier, A. Alatas, A. Suvorov, Y. Q. Cai, and R. Li, Shaping the terahertz sound propagation in water under highly directional confinement, Phys. Rev. B 101, 054306 (2020).
- A. Rahman and F. H. Stillinger, Propagation of sound in water: A molecular-dynamics study, Phys. Rev. A 10, 368 (1974).
- J. Bosse, G. Jacucci, M. Ronchetti, and W. Schirmacher, Fast sound in two-component liquids, Phys. Rev. Lett. 57, 3277 (1986).
- U. Balucani, G. Ruocco, A. Torcini, and R. Vallauri, Fast sound in liquid water, Phys. Rev. E 47, 1677 (1993).
- F. Sette, G. Ruocco, A. Cunsolo, C. Masciovecchio, G. Monaco, and R. Verbeni, Determination of the short-wavelength propagation threshold in the collective excitations of liquid ammonia, Phys. Rev. Lett. 84, 4136 (2000).
- R. Angelini, P. Giura, G. Monaco, G. Ruocco, F. Sette, and R. Verbeni, Structural and microscopic relaxation processes in liquid hydrogen fluoride, Phys. Rev. Lett. 88, 255503 (2002).
- E. Cornicchi, F. Sebastiani, A. De Francesco, A. Orecchini, A. Paciaroni, C. Petrillo, and F. Sacchetti, Collective density fluctuations of DNA hydration water in the time-window below 1 ps, J. Chem. Phys. 135, 025101 (2011).
- S. Hosokawa, T. Kamiyama, K. Yoshida, T. Yamaguchi, S. Tsutsui, and A. Q. R. Baron, Collective dynamics of liquid acetone investigated by inelastic x-ray scattering, J. Mol. Liq. 332, 115825 (2021).
- S. Hosokawa and K. Yoshida, A possible origin of very fast sound in the terahertz region in liquid benzene, J. Mol. Liq. 390, 123063 (2023).
- I. M. de Schepper, P. Verkerk, A. A. van Well, and L. A. de Graaf, Short-wavelength sound modes in liquid argon, Phys. Rev. Lett. 50, 974 (1983).
- S. Hosokawa, M. Inui, Y. Kajihara, S. Tsutsui, and A. Q. R. Baron, Transverse excitations in liquid Fe, Cu and Zn, J. Phys.: Condens. Matter 27, 194104 (2015).
- M. Zanatta, F. Sacchetti, E. Guarini, A. Orecchini, A. Paciaroni, L. Sani, and C. Petrillo, Collective ion dynamics in liquid zinc: Evidence for complex dynamics in a non-free-electron liquid metal, Phys. Rev. Lett. 114, 187801 (2015).
- S. Hosokawa, Y. Katayama, S. Tsutsui, and A. Q. R. Baron, Collective dynamics of liquid sulfur across the polymerisation transition temperature probed by inelastic x-ray scattering, J. Phys.: Condens. Matter 36, 425102 (2024).
- F. Formisano and S. De Panfilis, Comment on “Boson peak in deeply cooled confined water,” Phys. Rev. Lett. 115, 149801 (2015).
- G. E. Walrafen, Raman spectrum of water: Transverse and longitudinal acoustic modes below and optic modes above , J. Phys. Chem. 94, 2237 (1990).
- E. Guarini, M. Neumann, A. De Francesco, F. Formisano, A. Cunsolo, W. Montfrooij, D. Colognesi, and U. Bafile, Onset of collective excitations in the transverse dynamics of simple fluids, Phys. Rev. E 107, 014139 (2023).
- E. Guarini, U. Bafile, D. Colognesi, A. Cunsolo, A. De Francesco, and F. Formisano, Progress in the understanding of liquids dynamics via a general theory of correlation functions, Liquids 5, 9 (2025).
- S. Bellissima, S. De Panfilis, U. Bafile, A. Cunsolo, M. A. González, E. Guarini, and F. Formisano, The hydrogen-bond collective dynamics in liquid methanol, Sci. Rep. 6, 39533 (2016).
- S. Bellissima, M. A. González, U. Bafile, A. Cunsolo, F. Formisano, S. De Panfilis, and E. Guarini, Switching off hydrogen-bond-driven excitation modes in liquid methanol, Sci. Rep. 7, 10057 (2017).
- A. De Francesco, F. Formisano, L. Scaccia, E. Guarini, U. Bafile, M. A. González, A. Alatas, S. T. Lynch, and A. Cunsolo, Fingerprints of hydrogen bonding in the terahertz dynamics of ethanol and water, J. Chem. Phys. 159, 244501 (2023).
- M. C. Bellissent-Funel, S. H. Chen, and J.-M. Zanotti, Single-particle dynamics of water molecules in confined space, Phys. Rev. E 51, 4558 (1995).
- A. Paciaroni, A. Orecchini, E. Cornicchi, M. Marconi, C. Petrillo, M. Haertlein, M. Moulin, H. Schober, M. Tarek, and F. Sacchetti, Fingerprints of amorphous-ice-like behavior in the vibrational density of states of protein hydration water, Phys. Rev. Lett. 101, 148104 (2008).
- M. Zanatta, A. Orecchini, F. Sacchetti, and C. Petrillo, Disclosing the nature of the collective THz dynamics in hydrogen-bonded liquids, J. Mol. Liq. 393, 123550 (2024).
- A. Arbe, G. J. Nilsen, J. R. Stewart, F. Alvarez, V. G. Sakai, and J. Colmenero, Coherent structural relaxation of water from meso- to intermolecular scales measured with neutron polarization analysis, Phys. Rev. Res. 2, 022015(R) (2020).
- NIST Center for Neutron Research, Neutron scattering lengths, https://www.ncnr.nist.gov/resources/n-lengths/.
- Cambridge Crystallographic Data Centre, CCDC database, https://www.ccdc.cam.ac.uk/structures/.
- L. M. Ziurys, The chemistry in circumstellar envelopes of evolved stars: Following the origin of the elements to the origin of life, Proc. Natl. Acad. Sci. USA 103, 12274 (2006).
- A. P. Drozdov, M. I. Eremets, I. A. Troyan, V. Ksenofontov, and S. I. Shylin, Conventional superconductivity at 203 K at high pressures in the sulfur hydride system, Nature (London) 525, 73 (2015).
- Y. Li, J. Hao, H. Liu, Y. Li, and Y. Ma, The metallization and superconductivity of dense hydrogen sulfide, J. Chem. Phys. 140, 174712 (2014).
- M. Einaga, M. Sakata, T. Ishikawa, K. Shimizu, M. I. Eremets, A. P. Drozdov, I. A. Troyan, N. Hirao, and Y. Ohishi, Crystal structure of the superconducting phase of sulfur hydride, Nat. Phys. 12, 835 (2016).
- E. S. Sandor and S. O. Ogunade, Structure and phase transition in solid hydrogen and deuterium sulphides, Nature (London) 224, 905 (1969).
- J. K. Cockcroft and A. N. Fitch, The solid phases of deuterium sulphide by powder neutron diffraction, Z. Kristallogr. 193, 1 (1990).
- I. Errea, M. Calandra, C. J. Pickard, J. Nelson, R. J. Needs, Y. Li, H. Liu, Y. Zhang, Y. Ma, and F. Mauri, High-pressure hydrogen sulfide from first principles: A strongly anharmonic phonon-mediated superconductor, Phys. Rev. Lett. 114, 157004 (2015).
- C. Andreani, E. Degiorgi, R. Senesi, F. Cilloco, D. Colognesi, J. Mayers, M. Nardone, and E. Pace, Single-particle dynamics in fluid and solid hydrogen sulfide: An inelastic neutron scattering study, J. Chem. Phys. 114, 387 (2001).
- A. G. Cubitt, C. Henderson, L. A. K. Staveley, I. M. A. Fonseca, A. G. Ferreira, and L. Q. Lobo, Thermodynamic properties of liquid hydrogen sulphide and deuterium sulphide, J. Chem. Thermodyn. 19, 703 (1987).
- NIST Chemistry WebBook, https://webbook.nist.gov/chemistry/.
- D. Aisa, E. Babucci, F. Barocchi, A. Cunsolo, F. D'Anca, A. De Francesco, F. Formisano, T. Gahl, E. Guarini, S. Jahn, A. Laloni, H. Mutka, A. Orecchini, C. Petrillo, F. Sacchetti, J.-B. Suck, and G. Venturi, The development of the BRISP spectrometer at the Institut Laue-Langevin, Nucl. Instrum. Methods Phys. Res. Sect. A 544, 620 (2005).
- D. Aisa, S. Aisa, E. Babucci, F. Barocchi, A. Cunsolo, A. De Francesco, F. Formisano, T. Gahl, E. Guarini, A. Laloni, H. Mutka, A. Orecchini, C. Petrillo, W.-C. Pilgrim, A. Piluso, F. Sacchetti, J.-B. Suck, and G. Venturi, BRISP: A new thermal-neutron spectrometer for small-angle studies of disordered matter, J. Non-Cryst. Solids 352, 5130 (2006).
- D. I. Garber and R. R. Kinsey, Neutron Cross Sections, Vol. II: Curves (Brookhaven National Laboratory, Upton, NY, 1976).
- C. Andreani, C. Petrillo, and F. Sacchetti, Diffraction studies of liquid deuterium sulphide, Mol. Phys. 58, 299 (1986).
- F. Dupré, D. Piaggesi, and F. P. Ricci, Self-diffusion coefficient in along the coexistence curve, Phys. Lett. A 80, 178 (1980).
- V. M. Giordano and G. Monaco, Fingerprints of order and disorder on the high-frequency dynamics of liquids, Proc. Natl. Acad. Sci. USA 107, 21985 (2010).
- S. Hosokawa, M. Inui, Y. Kajihara, K. Matsuda, T. Ichitsubo, W.-C. Pilgrim, H. Sinn, L. E. González, D. J. González, S. Tsutsui, and A. Q. R. Baron, Transverse acoustic excitations in liquid gallium, Phys. Rev. Lett. 102, 105502 (2009).
- S. W. Lovesey, Theory of Neutron Scattering from Condensed Matter (Oxford Univ. Press, Oxford, 1986), Vol. 1.
- J. P. Boon and S. Yip, Molecular Hydrodynamics (Dover, New York, 1980).
- A. Rahman, K. S. Singwi, and A. Sjölander, Theory of slow neutron scattering by liquids, Phys. Rev. 126, 986 (1962).
- A. Zaccone and M. Baggioli, Universal law for the vibrational density of states of liquids, Proc. Natl. Acad. Sci. USA 118, e2022303118 (2021).
- C. Stamper, D. Cortie, Z. Yue, X. Wang, and D. Yu, Experimental confirmation of the universal law for the vibrational density of states of liquids, J. Phys. Chem. Lett. 13, 3105 (2022).
- S. Jin, X. Fan, C. Stamper, R. A. Mole, Y. Yu, L. Hong, D. Yu, and M. Baggioli, On the temperature dependence of the density of states of liquids at low energies, Sci. Rep. 14, 18805 (2024).
- A. A. van Well and L. A. de Graaf, Density fluctuations in liquid neon studied by neutron scattering, Phys. Rev. A 32, 2396 (1985).
- M. Sampoli, U. Bafile, E. Guarini, and F. Barocchi, Collective dynamics and molecular interactions in liquid by inelastic neutron scattering and computer simulations, Phys. Rev. B 79, 214203 (2009).