Skip to main content
Log in

Signature of the hydrogen-bonded environment of liquid water in X-ray emission spectra from first-principles calculations

  • Research Article
  • Published:
Frontiers of Physics Aims and scope Submit manuscript

Abstract

Based on ab initio molecular dynamics simulations and density functional theory, we performed a systematic theoretical study to elucidate the correlation between the H-bonded environment and Xray emission spectra of liquid water. The spectra generated from excited water molecules embedded in an intact H-bonded environment yield broader spectral peaks and a larger spectral range than the spectra generated from water molecules in a broken H-bonded environment. Such differences are caused by the local electronic structures on the excited water molecules within the core-hole lifetime that evolve differently through the rearrangement of neighboring water molecules in different H-bonded environments.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. P. Gallo, K. Amann-Winkel, C. A. Angell, M. A. Anisimov, F. Caupin, C. Chakravarty, E. Lascaris, T. Loerting, A. Z. Panagiotopoulos, J. Russo, J. A. Sellberg, H. E. Stanley, H. Tanaka, C. Vega, L. Xu, and L. G. M. Pettersson, Water: A tale of two liquids, Chem. Rev. 116(13), 7463 (2016)

    Article  Google Scholar 

  2. L. G. M. Pettersson, R. H. Henchman, and A. Nilsson, Water–The most anomalous liquid, Chem. Rev. 116(13), 7459 (2016)

    Article  Google Scholar 

  3. P. Ball, Water as an active constituent in cell biology, Chem. Rev. 108(1), 74 (2008)

    Article  Google Scholar 

  4. J. C. Palmer, F. Martelli, Y. Liu, R. Car, A. Z. Panagiotopoulos, and P. G. Debenedetti, Metastable liquidliquid transition in a molecular model of water, Nature 510(7505), 385 (2014)

    Article  ADS  Google Scholar 

  5. C. J. Fecko, J. D. Eaves, J. J. Loparo, A. Tokmakoff, and P. L. Geissler, Ultrafast hydrogen-bond dynamics in the infrared spectroscopy of water, Science 301(5640), 1698 (2003)

    Article  ADS  Google Scholar 

  6. T. Head-Gordon and G. Hura, Water structure from scattering experiments and simulation, Chem. Rev. 102(8), 2651 (2002)

    Article  Google Scholar 

  7. J. A. Sellberg, C. Huang, T. A. McQueen, N. D. Loh, H. Laksmono, et al., Ultrafast X-ray probing of water structure below the homogeneous ice nucleation temperature, Nature 510(7505), 381 (2014)

    Article  ADS  Google Scholar 

  8. T. Tokushima, Y. Harada, O. Takahashi, Y. Senba, H. Ohashi, L. G. M. Pettersson, A. Nilsson, and S. Shin, High resolution X-ray emission spectroscopy of liquid water: The observation of two structural motifs, Chem. Phys. Lett. 460(4–6), 387 (2008)

    Article  ADS  Google Scholar 

  9. F. H. Stillinger, Water revisited, Science 209(4455), 451 (1980)

    Article  ADS  Google Scholar 

  10. G. E. Walrafen, Effects of equilibrium H-bond distance and angle changes on Raman intensities from water, J. Chem. Phys. 120(10), 4868 (2004)

    Article  ADS  Google Scholar 

  11. M. Vedamuthu, S. Singh, and G. W. Robinson, Properties of liquid water: Origin of the density anomalies, J. Phys. Chem. 98(9), 2222 (1994)

    Article  Google Scholar 

  12. R. Bukowski, K. Szalewicz, G. C. Groenenboom, and A. van der Avoird, Prediction of the properties of water from first principles, Science 315(5816), 1249 (2007)

    Article  ADS  Google Scholar 

  13. B. Guillot, A reappraisal of what we have learnt during three decades of computer simulations on water, J. Mol. Liq. 101(1–3), 219 (2002)

    Article  Google Scholar 

  14. R. Car and M. Parrinello, Unified approach for molecular dynamics and density-functional theory, Phys. Rev. Lett. 55(22), 2471 (1985)

    Article  ADS  Google Scholar 

  15. J. D. Eaves, J. J. Loparo, C. J. Fecko, S. T. Roberts, A. Tokmakoff, and P. L. Geissler, Hydrogen bonds in liquid water are broken only fleetingly, Proc. Natl. Acad. Sci. USA 102(37), 13019 (2005)

    Article  ADS  Google Scholar 

  16. G. S. Fanourgakis, G. K. Schenter, and S. S. Xantheas, A quantitative account of quantum effects in liquid water, J. Chem. Phys. 125(14), 141102 (2006)

    Article  ADS  Google Scholar 

  17. R. Bukowski, K. Szalewicz, G. C. Groenenboom, and A. Van Der Avoird, Polarizable interaction potential for water from coupled cluster calculations (II): Applications to dimer spectra, virial coefficients, and simulations of liquid water, J. Chem. Phys. 128(9), 094314 (2008)

    Article  ADS  Google Scholar 

  18. F. Paesani, S. Iuchi, and G. A. Voth, Quantum effects in liquid water from an ab initio-based polarizable force field, J. Chem. Phys. 127(7), 074506 (2007)

    Article  ADS  Google Scholar 

  19. Y. A. Mantz, B. Chen, and G. J. Martyna, Structural correlations and motifs in liquid water at selected temperatures: ab initio and empirical model predictions, J. Phys. Chem. B 110(8), 3540 (2006)

    Article  Google Scholar 

  20. A. Nilsson and L. G. M. Pettersson, The structural origin of anomalous properties of liquid water, Nat. Commun. 6, 8998 (2015)

    Article  ADS  Google Scholar 

  21. J. D. Smith, C. D. Cappa, K. R. Wilson, R. C. Cohen, P. L. Geissler, and R. J. Saykally, Unified description of temperature-dependent hydrogen-bond rearrangements in liquid water, Proc. Natl. Acad. Sci. USA 102(40), 14171 (2005)

    Article  ADS  Google Scholar 

  22. J. D. Bernal and R. H. Fowler, A theory of water and ionic solution, with particular reference to hydrogen and hydroxyl ions, J. Chem. Phys. 1(8), 515 (1933)

    Article  ADS  Google Scholar 

  23. A. K. Soper, The quest for the structure of water and aqueous solutions, J. Phys.: Condens. Matter 9(13), 2717 (1997)

    ADS  Google Scholar 

  24. A. K. Soper, The radial distribution functions of water and ice from 220 to 673 K and at pressures up to 400 MPa, Chem. Phys. 258(2–3), 121 (2000)

    Article  ADS  Google Scholar 

  25. S. A. Corcelli and J. L. Skinner, Infrared and Ramute HOD in liquid H2O and D2O from 10 to 90 degrees celsius, J. Phys. Chem. A 109(28), 6154 (2005)

    Article  Google Scholar 

  26. T. S. Carlton, Using heat capacity and compressibility to choose among two-state models of liquid water, J. Phys. Chem. B 111(47), 13398 (2007)

    Article  Google Scholar 

  27. H. Tanaka, Simple physical model of liquid water, J. Chem. Phys. 112(2), 799 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  28. A. Zeidler, P. S. Salmon, H. E. Fischer, J. C. Neuefeind, J. Mike Simonson, and T. E. Markland, Isotope effects in water as investigated by neutron diffraction and path integral molecular dynamics, J. Phys.: Condens. Matter 24(28), 284126 (2012)

    Google Scholar 

  29. J. C. Dore, M. Garawi, and M. C. Bellissent-Funel, Neutron diffraction studies of the structure of water at ambient temperatures, revisited [a review of past developments and current problems], Mol. Phys. 102(19–20), 2015 (2004)

    Article  ADS  Google Scholar 

  30. M. C. Bellissent-Funel, and L. Bosio, A neutron scattering study of liquid D2O under pressure and at various temperatures, J. Chem. Phys. 102(9), 3727 (1995)

    Article  ADS  Google Scholar 

  31. J. C. Dore, M. A. M. Sufi, and M. C. Bellissent-Funel, Structural change in D2O water as a function of temperature: The isochoric temperature derivative function for neutron diffraction, Phys. Chem. Chem. Phys. 2(8), 1599 (2000)

    Article  Google Scholar 

  32. A. K. Soper, The radial distribution functions of water as derived from radiation total scattering experiments: Is there anything we can say for sure? ISRN Phys. Chem. 2013, 1 (2013)

    Article  ADS  Google Scholar 

  33. P. Postorino, M. A. Ricci, and A. K. Soper, Water above its boiling point: Study of the temperature and density dependence of the partial pair correlation functions (I): Neutron diffraction experiment, J. Chem. Phys. 101(5), 4123 (1994)

    Article  ADS  Google Scholar 

  34. 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(13), 7570 (2016)

    Article  Google Scholar 

  35. L. B. Skinner, C. Huang, D. Schlesinger, L. G. M. Pettersson, A. Nilsson, and C. J. Benmore, Benchmark oxygen-oxygen pair-distribution function of ambient water from X-ray diffraction measurements with a wide Q-range, J. Chem. Phys. 138(7), 074506 (2013)

    Article  ADS  Google Scholar 

  36. J. Morgan and B. E. Warren, X-ray analysis of the structure of water, J. Chem. Phys. 6(11), 666 (1938)

    Article  ADS  Google Scholar 

  37. H. Ohtaki, T. Radnai, and T. Yamaguchi, Structure of water under subcritical and supercritical conditions studied by solution X-ray diffraction, Chem. Soc. Rev. 26(1), 41 (1997)

    Article  Google Scholar 

  38. J. M. Sorenson, G. Hura, R. M. Glaeser, and T. Head-Gordon, What can X-ray scattering tell us about the radial distribution functions of water? J. Chem. Phys. 113(20), 9149 (2000)

    Article  ADS  Google Scholar 

  39. C. Huang, T. M. Weiss, D. Nordlund, K. T. Wikfeldt, L. G. M. Pettersson, and A. Nilsson, Increasing correlation length in bulk supercooled H2O, D2O, and NaCl solution determined from small angle X-ray scattering, J. Chem. Phys. 133(13), 134504 (2010)

    Article  ADS  Google Scholar 

  40. F. N. Keutsch and R. J. Saykally, Water clusters: Untangling the mysteries of the liquid, one molecule at a time, Proc. Natl. Acad. Sci. USA 98(19), 10533 (2001)

    Article  ADS  Google Scholar 

  41. K. A. Tay and F. Bresme, Kinetics of hydrogen-bond rearrangements in bulk water, Phys. Chem. Chem. Phys. 11(2), 409 (2009)

    Article  Google Scholar 

  42. R. Laenen, C. Rauscher, and A. Laubereau, Dynamics of local substructures in water observed by ultrafast infrared hole burning, Phys. Rev. Lett. 80(12), 2622 (1998)

    Article  ADS  Google Scholar 

  43. R. H. Henchman and S. J. Irudayam, Topological hydrogen-bond definition to characterize the structure and dynamics of liquid water, J. Phys. Chem. B 114(50), 16792 (2010)

    Article  Google Scholar 

  44. H. J. Bakker and J. L. Skinner, Vibrational spectroscopy as a probe of structure and dynamics in liquid water, Chem. Rev. 110(3), 1498 (2010)

    Article  Google Scholar 

  45. K. Ramasesha, S. T. Roberts, R. A. Nicodemus, A. Mandal, and A. Tokmakoff, Ultrafast 2D IR anisotropy of water reveals reorientation during hydrogen-bond switching, J. Chem. Phys. 135(5), 054509 (2011)

    Article  ADS  Google Scholar 

  46. R. Kumar, J. R. Schmidt, and J. L. Skinner, Hydrogen bonding definitions and dynamics in liquid water, J. Chem. Phys. 126(20), 204107 (2007)

    Article  ADS  Google Scholar 

  47. F. Perakis, L. D. Marco, A. Shalit, F. Tang, Z. R. Kann, T. D. Kühne, R. Torre, M. Bonn, and Y. Nagata, Vibrational spectroscopy and dynamics of water, Chem. Rev. 116(13), 7590 (2016)

    Article  Google Scholar 

  48. T. Fransson, Y. Harada, N. Kosugi, N. A. Besley, B. Winter, J. J. Rehr, L. G. M. Pettersson, and A. Nilsson, X-ray and electron spectroscopy of water, Chem. Rev. 116(13), 7551 (2016)

    Article  Google Scholar 

  49. Ph. Wernet, D. Nordlund, U. Bergmann, M. Cavalleri, M. Odelius, H. Ogasawara, L. Å. Näslund, T. K. Hirsch, L. Ojamäe, P. Glatzel, L. G. M. Pettersson, and A. Nilsson, The structure of the first coordination shell in liquid water, Science 304(5673), 995 (2004)

    Article  ADS  Google Scholar 

  50. J. A. Sellberg, S. Kaya, V. H. Segtnan, C. Chen, T. Tyliszczak, H. Ogasawara, D. Nordlund, L. G. M. Pettersson, and A. Nilsson, Comparison of X-ray absorption spectra between water and ice: New ice data with low pre-edge absorption cross-section, J. Chem. Phys. 141(3), 034507 (2014)

    Article  ADS  Google Scholar 

  51. B. Hetényi, F. De Angelis, P. Giannozzi, and R. Car, Calculation of near-edge X-ray-absorption fine structure at finite temperatures: Spectral signatures of hydrogen bond breaking in liquid water, J. Chem. Phys. 120(18), 8632 (2004)

    Article  ADS  Google Scholar 

  52. T. Head-Gordon and M. E. Johnson, Tetrahedral structure or chains for liquid water, Proc. Natl. Acad. Sci. USA 103(21), 7973 (2006)

    Article  ADS  Google Scholar 

  53. L. Kong, X. Wu, and R. Car, Roles of quantum nuclei and inhomogeneous screening in the X-ray absorption spectra of water and ice, Phys. Rev. B 86(13), 134203 (2012)

    Article  ADS  Google Scholar 

  54. J. D. Smith, C. D. Cappa, B. M. Messer, W. S. Drisdell, R. C. Cohen, and R. J. Saykally, Probing the local structure of liquid water by X-ray absorption spectroscopy, J. Phys. Chem. B 110(40), 20038 (2006)

    Article  Google Scholar 

  55. W. Chen, X. Wu, and R. Car, X-ray absorption signatures of the molecular environment in water and ice, Phys. Rev. Lett. 105(1), 017802 (2010)

    Article  ADS  Google Scholar 

  56. D. Prendergast and G. Galli, X-ray absorption spectra of water from first principles calculations, Phys. Rev. Lett. 96(21), 215502 (2006)

    Article  ADS  Google Scholar 

  57. T. Fransson, I. Zhovtobriukh, S. Coriani, K. T. Wikfeldt, P. Norman, and L. G. M. Pettersson, Requirements of first-principles calculations of X-ray absorption spectra of liquid water, Phys. Chem. Chem. Phys. 18(1), 566 (2016)

    Article  Google Scholar 

  58. A. Nilsson, D. Nordlund, I. Waluyo, N. Huang, H. Ogasawara, S. Kaya, U. Bergmann, L. Å. Näslund, H. Öström, P. Wernet, K. J. Andersson, T. Schiros, and L. G. M. Pettersson, X-ray absorption spectroscopy and Xray Raman scattering of water and ice–An experimental view, J. Electron Spectrosc. Relat. Phenom. 177(2–3), 99 (2010)

    Article  Google Scholar 

  59. M. Leetmaa, M. P. Ljungberg, A. Lyubartsev, A. Nilsson, and L. G. M. Pettersson, Theoretical approximations to X-ray absorption spectroscopy of liquid water and ice, J. Electron Spectrosc. Relat. Phenom. 177(2–3), 135 (2010)

    Article  Google Scholar 

  60. J. Vinson, J. J. Kas, F. D. Vila, J. J. Rehr, and E. L. Shirley, Theoretical optical and X-ray spectra of liquid and solid H2O, Phys. Rev. B 85(4), 045101 (2012)

    Article  ADS  Google Scholar 

  61. O. Fuchs, M. Zharnikov, L. Weinhardt, M. Blum, M. Weigand, Y. Zubavichus, M. Bär, F. Maier, J. D. Denlinger, C. Heske, M. Grunze, and E. Umbach, Isotope and temperature effects in liquid water probed by X-ray absorption and resonant X-ray emission spectroscopy, Phys. Rev. Lett. 100(2), 027801 (2008)

    Article  ADS  Google Scholar 

  62. D. Nordlund, H. Ogasawara, K. J. Andersson, M. Tatarkhanov, M. Salmerón, L. G. M. Pettersson, and A. Nilsson, Sensitivity of X-ray absorption spectroscopy to hydrogen bond topology, Phys. Rev. B 80(23), 233404 (2009)

    Article  ADS  Google Scholar 

  63. S. Kashtanov, A. Augustsson, Y. Luo, J. H. Guo, C. Såthe, J. E. Rubensson, H. Siegbahn, J. Nordgren, and H. Ågren, Local structures of liquid water studied by Xray emission spectroscopy, Phys. Rev. B 69(2), 024201 (2004)

    Article  ADS  Google Scholar 

  64. J. A. Sellberg, T. A. McQueen, H. Laksmono, S. Schreck, M. Beye, et al., X-ray emission spectroscopy of bulk liquid water in “no-man’s land”, J. Chem. Phys. 142(4), 044505 (2015)

    Article  ADS  Google Scholar 

  65. M. Odelius, H. Ogasawara, D. Nordlund, O. Fuchs, L. Weinhardt, F. Maier, E. Umbach, C. Heske, Y. Zubavichus, M. Grunze, J. D. Denlinger, L. G. M. Pettersson, and A. Nilsson, Ultrafast core-hole-induced dynamics in water probed by X-ray emission spectroscopy, Phys. Rev. Lett. 94(22), 227401 (2005)

    Article  ADS  Google Scholar 

  66. J. H. Guo, Y. Luo, A. Augustsson, J. E. Rubensson, C. Såthe, H. Ågren, H. Siegbahn, and J. Nordgren, Xray emission spectroscopy of hydrogen bonding and electronic structure of liquid water, Phys. Rev. Lett. 89(13), 137402 (2002)

    Article  ADS  Google Scholar 

  67. M. Odelius, Molecular dynamics simulations of fine structure in oxygen K-edge X-ray emission spectra of liquid water and ice, Phys. Rev. B 79(14), 144204 (2009)

    Article  ADS  Google Scholar 

  68. L. Weinhardt, O. Fuchs, M. Blum, M. Bär, M. Weigand, J. D. Denlinger, Y. Zubavichus, M. Zharnikov, M. Grunze, C. Heske, and E. Umbach, Resonant X-ray emission spectroscopy of liquid water: Novel instrumentation, high resolution, and the “map” approach, J. Electron Spectrosc. Relat. Phenom. 177(2–3), 206 (2010)

    Article  Google Scholar 

  69. T. Tokushima, Y. Harada, Y. Horikawa, O. Takahashi, Y. Senba, H. Ohashi, L. G. M. Pettersson, A. Nilsson, and S. Shin, High resolution X-ray emission spectroscopy of water and its assignment based on two structural motifs, J. Electron Spectrosc. Relat. Phenom. 177(2–3), 192 (2010)

    Article  Google Scholar 

  70. K. M. Lange, M. Soldatov, R. Golnak, M. Gotz, N. Engel, R. Könnecke, J. E. Rubensson, and E. F. Aziz, X-ray emission from pure and dilute H2O and D2O in a liquid microjet: Hydrogen bonds and nuclear dynamics, Phys. Rev. B 85(15), 155104 (2012)

    Article  ADS  Google Scholar 

  71. Z. Sun, M. Chen, J. Wang, S. Biswajit, H. Shen, L. Xu, W. Kang, and X. Wu, X-ray absorption of liquid water studied by advanced ab initio methods, Phys. Rev. B (Submitted)

  72. B. Brena, D. Nordlund, M. Odelius, H. Ogasawara, A. Nilsson, and L. G. M. Pettersson, Ultrafast molecular dissociation of water in ice, Phys. Rev. Lett. 93(14), 148302 (2004)

    Article  ADS  Google Scholar 

  73. M. Neeb, J. E. Rubensson, M. Biermann, and W. Eberhardt, Coherent excitation of vibrational wave functions observed in core hole decay spectra of O2, N2 and CO, J. Electron Spectrosc. Relat. Phenom. 67(2), 261 (1994)

    Article  Google Scholar 

  74. F. Gel’mukhanov, H. Ågren, M. Neeb, J. E. Rubensson, and A. Bringer, Integral properties of channel interference in resonant X-ray scattering, Phys. Lett. A 211(2), 101 (1996)

    Article  ADS  Google Scholar 

  75. M. Odelius, Information content in O[1s] K-edge X-ray emission spectroscopy of liquid water, J. Phys. Chem. A 113(29), 8176 (2009)

    Article  Google Scholar 

  76. N. A. Besley, Equation of motion coupled cluster theory calculations of the X-ray emission spectroscopy of water, Chem. Phys. Lett. 542, 42 (2012)

    Article  ADS  Google Scholar 

  77. L. Weinhardt, A. Benkert, F. Meyer, M. Blum, R. G. Wilks, W. Yang, M. Bär, F. Reinert, and C. Heske, Nuclear dynamics and spectator effects in resonant inelastic soft X-ray scattering of gas-phase water molecules, J. Chem. Phys. 136(14), 144311 (2012)

    Article  ADS  Google Scholar 

  78. W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140(4A), A1133 (1965)

    Article  ADS  MathSciNet  Google Scholar 

  79. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. 77, 3865 (1996)

    ADS  Google Scholar 

  80. P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, et al., QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials, J. Phys.: Condens. Matter 21(39), 395502 (2009)

    Google Scholar 

  81. N. Troullier and J. L. Martins, Efficient pseudopotentials for plane-wave calculations, Phys. Rev. B 43(3), 1993 (1991)

    Article  ADS  Google Scholar 

  82. D. R. Hamann, M. Schlüter, and C. Chiang, Normconserving pseudopotentials, Phys. Rev. Lett. 43(20), 1494 (1979)

    Article  ADS  Google Scholar 

  83. D. R. Hamann, Generalized norm-conserving pseudopotentials, Phys. Rev. B 40(5), 2980 (1989)

    Article  ADS  Google Scholar 

  84. J. A. Morrone and R. Car, Nuclear quantum effects in water, Phys. Rev. Lett. 101(1), 017801 (2008)

    Article  ADS  Google Scholar 

  85. G. J. Martyna, M. L. Klein, and M. Tuckerman, Nose–Hoover chains: The canonical ensemble via continuous dynamics, J. Chem. Phys. 97(4), 2635 (1992)

    Article  ADS  Google Scholar 

  86. W. G. Hoover, Canonical dynamics: Equilibrium phasespace distributions, Phys. Rev. A 31(3), 1695 (1985)

    Article  ADS  Google Scholar 

  87. S. Nosé, A unified formulation of the constant temperature molecular dynamics methods, J. Chem. Phys. 81(1), 511 (1984)

    Article  ADS  Google Scholar 

  88. A. Luzar and D. Chandler, Hydrogen-bond kinetics in liquid water, Nature 379(6560), 55 (1996)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

We acknowledge the National Science Foundation (NSF), DMR under Award DMR-1552287. We also acknowledge the financial support by the National Key Research and Development Program of China (Grant No. 2016YFA0300901) and the National Natural Science Foundation of China (Grant Nos. 11525520 and 11290162). This research used computational resources of the National Energy Research Scientific Computing Center (NERSC), a Department of Energy (DOE) Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Enge Wang or Xifan Wu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shen, H., Chen, M., Sun, Z. et al. Signature of the hydrogen-bonded environment of liquid water in X-ray emission spectra from first-principles calculations. Front. Phys. 13, 138204 (2018). https://doi.org/10.1007/s11467-017-0700-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11467-017-0700-z

Keywords

Navigation