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Invited Review: Modern Methods for Accurately Simulating the Terahertz Spectra of Solids

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A Publisher Correction to this article was published on 22 September 2022

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Abstract

Terahertz spectroscopy has proven to be a powerful tool for the study of condensed phase materials, opening research directions in a number of fields ranging from the pharmaceutical to semiconducting industries. Recent developments in terahertz technology have made this technique more accessible than ever before, and an increasing number of researchers are turning to terahertz spectroscopy for analysis and characterization of advanced materials. However, unlike mid-IR techniques, there do not exist any functional group specific transitions at terahertz frequencies, making the interpretation and assignment of terahertz spectral data more complex than complementary techniques. Through the aid of computational tools, incredible insights into the atomic-level dynamics occurring at terahertz frequencies have been uncovered, yet such highly accurate simulations require more care than traditional simulation methods in order to obtain such results. This review aims to highlight the recent advances in the computational assignment of terahertz spectral data, as well as showcasing common pitfalls to avoid, in order to demonstrate the utility of simulation methods for terahertz spectral assignment. Finally, cutting edge techniques and applications will be discussed, opening the door for future work in this exciting area of terahertz science.

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References

  1. C.A. Schmuttenmaer, Exploring dynamics in the far-infrared with terahertz spectroscopy, Chem. Rev. 104 (2004), no. 4, 1759–1779.

  2. E. P. J. Parrott and J. A. Zeitler, Terahertz time-domain and low-frequency raman spectroscopy of organic materials, Appl Spectrosc. 69 (2014), no. 1, 1–25.

  3. J. A. Zeitler, P. F. Taday, D. A. Newnham, M. Pepper, K. C. Gordon, and T. Rades, Terahertz pulsed spectroscopy and imaging in the pharmaceutical setting–a review, J. Pharm Pharmacol. 59 (2007), no. 2, 209–223.

  4. P. U. Jepsen, D. G. Cooke, and M. Koch, Terahertz spectroscopy and imaging – Modern techniques and applications, Laser Photonics Rev. 5 (2011), no. 1, 124–166.

  5. D. F. Plusquellic, K. Siegrist, E. J. Heilweil, and O. Esenturk, Applications of terahertz spectroscopy in biosystems, ChemPhysChem 8 (2007), no. 17, 2412–2431.

  6. H.A. Harker, M.R. Viant, F.N. Keutsch, E. A. Michael, R.P. McLaughlin, and R.J. Saykally, Water Pentamer: Characterization of the torsional-puckering manifold by terahertz VRT spectroscopy, J. Phys. Chem. A 109 (2005), 6483–6497. ISSN 1089-5639.

  7. J.E. Boyd, A. Briskman, V.L. Colvin, and D.M. Mittleman, Direct observation of terahertz surface modes in nanometer-sized liquid water pools, Phys. Rev. Lett. 87 (2001), no. 14, 147401.

  8. M. T. Ruggiero, W. Zhang, A.D. Bond, D.M. Mittleman, and J.A. Zeitler, Uncovering the connection between low-frequency dynamics and phase transformation phenomena in molecular solids, Phys. Rev. Lett. 120 (2018), no. 19, 196002.

  9. N. Toyota, H. Matsumoto, T. Mori, M.A. Avila, T. Takabatake, M.A. Avila, S. Goshima, K. Iwamoto, S. Kushibiki, K. Suekuni, T. Takabatake, T. Hasegawa, N. Ogita, T. Hasegawa, M. Udagawa, N. Ogita, and M. Udagawa, Optical conductivity of rattling phonons in type-I clathrate Ba8Ga16Ge30, Phys. Rev. B 79 (2009), no. 21, 212301.

  10. S. P. Delaney, D. Pan, M. Galella, S. X. Yin, and T. M. Korter, Understanding the origins of conformational disorder in the crystalline polymorphs of irbesartan, Cryst. Growth Des. 12 (2012), no. 10, 5017.

  11. J. Sibik, S. R. Elliott, and J. A. Zeitler, Thermal decoupling of molecular-relaxation processes from the vibrational density of states at terahertz frequencies in supercooled hydrogen-bonded liquids, J. Phys. Chem. Lett. 5 (2014), no. 11, 1968–1972.

  12. M. Walther, P. Plochocka, B. Fischer, H. Helm, and P. U. Jepsen, Collective vibrational modes in biological molecules investigated by terahertz time-domain spectroscopy, Biopolymers 67 (2002), no. 4-5, 310–313.

  13. R. J. Falconer and A. G. Markelz, Terahertz spectroscopic analysis of peptides and proteins, J. Infrared Milli. Terahertz Waves 33 (2012), no. 10, 973–988.

  14. H.-B. Liu and X.-C. Zhang, Terahertz spectroscopy for explosive, pharmaceutical, and biological sensing applications. In Terahertz frequency detection and identification of materials and objects, pp. 251–323. Springer, Dordrecht, 2007.

  15. N. Y. Tan and J. A. Zeitler, Probing phase transitions in simvastatin with terahertz time-domain spectroscopy, Mol. Pharmaceutics 12 (2015), no. 3, 810–815.

  16. M. Otsuka, J. I. Nishizawa, N. Fukura, and T. Sasaki, Characterization of poly-amorphous indomethacin by terahertz spectroscopy, J. Infrared Milli. Terahertz Waves 33 (2012), no. 9, 953–962.

  17. C. J. Strachan, T. Rades, D. A. Newnham, K. C. Gordon, M. Pepper, and P. F. Taday, Using terahertz pulsed spectroscopy to study crystallinity of pharmaceutical materials, Chem. Phys. Lett. 390 (2004), no. 1-3, 20–24.

  18. G. Schweicher, G. Davino, M. T. Ruggiero, D. J. Harkin, K. Broch, D. Venkateshvaran, G. Liu, A. Richard, C. Ruzie, J. Armstrong, A.R. Kennedy, K. Shankland, K. Takimiya, Y.H. Geerts, J.A. Zeitler, S. Fratini, and H. Sirringhaus, Chasing the killer phonon mode for the rational design of low disorder, high mobility molecular semiconductors, Adv. Mater 31 (2019), 1902407.

  19. S. Illig, A. S. Eggeman, A. Troisi, L. Jiang, C. Warwick, M. Nikolka, G. Schweicher, S. G. Yeates, Y. H. Geerts, J. E. Anthony, and H. Sirringhaus, Reducing dynamic disorder in small-molecule organic semiconductors by suppressing large-amplitude thermal motions, Nat. Commun. 7 (2016), 10736.

  20. W. Zhang, J. Maul, D. Vulpe, P. Z. Moghadam, D. Fairen-Jimenez, D. M. Mittleman, J. A. Zeitler, A. Erba, and M. T. Ruggiero, Probing the mechanochemistry of metal-organic frameworks with low-frequency vibrational spectroscopy, J. Phys. Chem. C 122 (2018), no. 48, 27442–27450.

  21. B. Pattengale, J. Neu, S. Ostresh, G. Hu, J. A. Spies, R. Okabe, G. W. Brudvig, and C. A. Schmuttenmaer, Metal–organic framework photoconductivity via time-resolved terahertz spectroscopy, J. Am. Chem. Soc. 141 (2019), no. 25, 9793–9797.

  22. Q. Li, A. J. Zaczek, T. M. Korter, J. A. Zeitler, and M. T. Ruggiero, Methyl-rotation dynamics in metal-organic frameworks probed with terahertz spectroscopy, Chem. Commun. 54 (2018), no. 45, 5776–5779.

  23. M. R. Ryder, B. Civalleri, G. Cinque, and J. -C. Tan, Discovering connections between terahertz vibrations and elasticity underpinning the collective dynamics of the HKUST-1 metal–organic framework, CrystEngComm 18 (2016), no. 23, 4303–4312.

  24. M.R. Ryder, B. Civalleri, T.D. Bennett, S. Henke, S. Rudić, G. Cinque, F. Fernandez-Alonso, and J.-C. Tan, Identifying the role of terahertz vibrations in metal-organic frameworks: From gate-opening phenomenon to shear-driven structural destabilization, Phys. Rev. Lett. 113 (2014), no. 21, 215502.

  25. S. Ray, J. Dash, N. Devi, S. Sasmal, and B. Pesala, Comparative study of hydration kinetics of cement and tricalcium silicate using terahertz spectroscopy and density functional theory simulations, J. Infrared Milli. Terahertz Waves 39 (2018), no. 7, 651–666.

  26. S. P. Delaney, D. Pan, S. X. Yin, and T.M. Smith, Evaluating the roles of conformational strain and cohesive binding in crystalline polymorphs of aripiprazole, Crys. Growth Des. 13 (2013), no. 7, 2943–2952.

  27. M. T. Ruggiero, J. Sibik, J. A. Zeitler, and T.M. Korter, Examination of L-glutamic acid polymorphs by solid-state density functional theory and terahertz spectroscopy, J. Phys. Chem. A 120 (2016), no. 38, 7490.

  28. K. Ajito, Y. Ueno, H. -J. Song, E. Tamechika, and N. Kukutsu, Terahertz spectroscopic imaging of polymorphic forms in pharmaceutical crystals, Mol. Cryst. Liq. Cryst. 538 (2011), no. 1, 33–38.

  29. T. R. Juliano, M. D. King, and T. M. Korter, Evaluating London dispersion force corrections in crystalline nitroguanidine by terahertz spectroscopy, IEEE Trans. THz Sci. Technol. 3 (2013), no. 3, 281–287.

  30. H. Zhang, K. Siegrist, D. F. Plusquellic, and S. K. Gregurick, Terahertz spectra and normal mode analysis of the crystalline VA class dipeptide nanotubes, J. Am. Chem Soc. 130 (2008), no. 52, 17846–17857.

  31. T.R. Juliano Jr and T.M. Korter, London force correction disparity in the modeling of crystalline asparagine and glutamine, J. Phys. Chem. A 118 (2014), no. 51, 12221–12228.

  32. F. Zhang, H. -W. Wang, K. Tominaga, and M. Hayashi, Mixing of intermolecular and intramolecular vibrations in optical phonon modes: terahertz spectroscopy and solid-state density functional theory, WIREs Comput. Mol. Sci. 6 (2016), no. 4, 386–409.

  33. M.T. Ruggiero, J. Gooch, J. Zubieta, and T.M. Korter, Evaluation of range-corrected density functionals for the simulation of pyridinium-containing molecular crystals, J. Phys. Chem. A 120 (2016), no. 6, 939–947.

  34. M. R. C. Williams, D. J. Aschaffenburg, B. K. Ofori-Okai, and C. A. Schmuttenmaer, Intermolecular vibrations in hydrophobic amino acid crystals: Experiments and calculations, J. Phys. Chem. B 117 (2013), no. 36, 10444–10461.

  35. M. D. King, T. N. Blanton, S. T. Misture, and T. M. Korter, Prediction of the unknown crystal structure of creatine using fully quantum mechanical methods, Cryst. Growth Des. 11 (2011), no. 12, 5733–5740.

  36. M. T. Ruggiero, J. Kölbel, Q. Li, and J. A. Zeitler, Predicting the structures and associated phase transition mechanisms in disordered crystals via a combination of experimental and theoretical methods, Faraday Discuss. 107 (2018), 926.

  37. M.T. Ruggiero, J. Sibik, R. Orlando, J.A. Zeitler, and T.M. Korter, Measuring the elasticity of poly-L-proline helices with terahertz spectroscopy, Angew. Chem. Int. Ed. 55 (2016), no. 24, 6877–6881.

  38. H. Hoshina, H. Suzuki, C. Otani, M. Nagai, K. Kawase, A. Irizawa, and G. Isoyama, Polymer morphological change induced by terahertz irradiation, Sci. Rep. 6 (2016), 27180.

  39. MT Ruggiero, M Krynski, EO Kissi, J Sibik, D Markl, NY Tan, D Arslanov, W Van Der Zande, B Redlich, TM Korter, H Grohganz, K Lobmann, T Rades, SR Elliott, and JA Zeitler, The significance of the amorphous potential energy landscape for dictating glassy dynamics and driving solid-state crystallisation, Phys. Chem. Chem. Phys. 19 (2017), no. 44, 30039–47. https://doi.org/10.1039/C7CP06664C.

  40. M. T. Ruggiero, T. Bardon, M. Strlič, P. F. Taday, and T. M. Korter, The role of terahertz polariton absorption in the characterization of crystalline iron sulfate hydrates, Phys. Chem. Chem. Phys. 17 (2015), no. 14, 9326–9334.

  41. E. P. J. Parrott, N. Y. Tan, R. Hu, J. A. Zeitler, B. Z. Tang, and E. Pickwell-MacPherson, Direct evidence to support the restriction of intramolecular rotation hypothesis for the mechanism of aggregation-induced emission: temperature resolved terahertz spectra of tetraphenylethene, Mater. Horiz. 1 (2014), no. 2, 251–258.

  42. K. L. Nguyen, T. Friščić, G. M. Day, L. F. Gladden, and W. Jones, Terahertz time-domain spectroscopy and the quantitative monitoring of mechanochemical cocrystal formation, Nat Mater. 6 (2007), no. 3, 206–209.

  43. P. C. Upadhya, K. L. Nguyen, Y. C. Shen, J. Obradovic, K. Fukushige, R. Griffiths, L. F. Gladden, A. G. Davies, and E. H. Linfield, Characterization of crystalline phase-transformations in theophylline by time-domain terahertz spectroscopy, Spectrosc. Lett. 39 (2006), no. 3, 215–224.

  44. L. Ho, M. Pepper, and P. Taday, Signatures and fingerprints, Nat. Photonics 2 (2008), no. 9, 541–543.

  45. J. A. Zeitler, D. A. Newnham, P. F. Taday, T. L. Threlfall, R. W. Lancaster, R. W. Berg, C. J. Strachan, M. Pepper, K. C. Gordon, and T. Rades, Characterization of temperature-induced phase transitions in five polymorphic forms of sulfathiazole by terahertz pulsed spectroscopy and differential scanning calorimetry, J. Pharm. Sci. 95 (2006), no. 11, 2486–2498.

  46. G. M. Day, J. A. Zeitler, W. Jones, T. Rades, and P. F. Taday, Understanding the influence of polymorphism on phonon spectra: Lattice dynamics calculations and terahertz spectroscopy of carbamazepine, J. Phys. Chem. B 110 (2006), no. 1, 447–456.

  47. J. Dash, S. Ray, K. Nallappan, V. Kaware, N. Basutkar, R. G. Gonnade, A. V. Ambade, K. Joshi, and B. Pesala, Terahertz spectroscopy and solid-state density functional theory calculations of cyanobenzaldehyde isomers, J. Phys. Chem. A 119 (2015), no. 29, 7991–7999.

  48. J. Dash, S. Ray, N. Devi, N. Basutkar, R. G. Gonnade, A. V. Ambade, and B. Pesala, Tuning of terahertz resonances of pyridyl benzamide derivatives by electronegative atom substitution, J. Infrared Milli Terahertz Waves 39 (2018), no. 7, 636–650.

  49. D. G. Allis and T. M. Korter, Theoretical analysis of the terahertz spectrum of the high explosive PETN, ChemPhysChem 7 (2006), no. 11, 2398–2408.

  50. Y. Hu, P. Huang, L. Guo, X. Wang, and C. Zhang, Terahertz spectroscopic investigations of explosives, Phys. Lett. A 359 (2006), no. 6, 728–732.

  51. T. M. Korter, R. Balu, M. B. Campbell, M. C. Beard, S. K. Gregurick, and E.J. Heilweil, Terahertz spectroscopy of solid serine and cysteine, Chem. Phys. Lett. 418 (2006), no. 1-3, 65–70.

  52. O. Esenturk, A. Evans, and E. J. Heilweil, Terahertz spectroscopy of dicyanobenzenes: Anomalous absorption intensities and spectral calculations, Chem. Phys. Lett. 442 (2007), no. 1-3, 71–77.

  53. L. Jiang, M. Li, C. Li, H. Sun, L. Xu, B. Jin, and Y. Liu, Terahertz spectra of L-ascorbic acid and thiamine hydrochloride studied by terahertz spectroscopy and density functional theory, J. Infrared Milli Terahertz Waves 35 (2014), no. 10, 871–880.

  54. F. Qu, Y. Pan, L. Lin, C. Cai, T. Dong, Y. He, and P. Nie, Experimental and theoretical study on terahertz absorption characteristics and spectral de-noising of three plant growth regulators, J. Infrared Milli Terahertz Waves 39 (2018), no. 10, 1015–1027.

  55. F. Qu, L. Lin, Y. He, P. Nie, C. Cai, T. Dong, Y. Pan, Y. Tang, and S. Luo, Terahertz multivariate spectral analysis and molecular dynamics simulations of three pyrethroid pesticides, J. Infrared Milli Terahertz Waves 39 (2018), no. 11, 1148–1161.

  56. G.J.O. Beran, Modeling polymorphic molecular crystals with electronic structure theory, Chem Rev. 116 (2016), no. 9, 5567–5613.

  57. P. U. Jepsen and S. J. Clark, Precise ab-initio prediction of terahertz vibrational modes in crystalline systems, Chem. Phys. Lett. 442 (2007), no. 4-6, 275–280.

  58. R. E. Stratmann, J. C. Burant, G. E. Scuseria, and M. J. Frisch, Improving harmonic vibrational frequencies calculations in density functional theory, J. Chem. Phys. 106 (1998), no. 24, 10175–10183.

  59. A.F. Izmaylov and G.E. Scuseria, Efficient evaluation of analytic vibrational frequencies in Hartree-Fock and density functional theory for periodic nonconducting systems, J. Chem. Phys. 127 (2007), no. 14, 144106.

  60. F. Pascale, C. M. Zicovich-Wilson, F. L. Gejo, B. Civalleri, R. Orlando, and R. Dovesi, The calculation of the vibrational frequencies of crystalline compounds and its implementation in the CRYSTAL code, J. Comput. Chem. 25 (2004), no. 6, 888–897.

  61. S. Toxvaerd, Algorithms for canonical molecular dynamics simulations, Mol. Phys. 72 (2006), no. 1, 159–168.

  62. Y. -G. Hu, K. M. Liew, and Q. Wang, Modeling of vibrations of carbon nanotubes, Procedia Eng. 31 (2012), 343–347.

  63. R. Dovesi, A. Erba, R. Orlando, C. M. Zicovich-Wilson, B. Civalleri, L. Maschio, M. Rérat, S. Casassa, J. Baima, S. Salustro, and B. Kirtman, Quantum-mechanical condensed matter simulations with CRYSTAL, WIREs Comput. Mol. Sci. 110 (2018), no. 39, e1360.

  64. C. M. Zicovich-Wilson, F. Pascale, C. Roetti, V. R. Saunders, R. Orlando, and R. Dovesi, Calculation of the vibration frequencies of alpha-quartz: the effect of Hamiltonian and basis set, J. Comput. Chem. 25 (2004), no. 15, 1873–1881.

  65. G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47 (1993), no. 1, 558–561.

  66. G. Kresse and J. Hafner, Ab initio molecular-dynamics simulation of the liquid-metal amorphous-semiconductor transition in germanium, Phys. Rev. B 49 (1994), no. 20, 14251–14269.

  67. G. Kresse and J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mat. Sci. 6 (1996), no. 1, 15–50.

  68. G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54 (1996), no. 16, 11169–11186.

  69. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59 (1999), no. 3, 1758–1775.

  70. P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G.L. Chiarotti, M. Cococcioni, I. Dabo, A.D. Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A.P. Seitsonen, A. Smogunov, P. Umari, and R.M. Wentzcovitch, Quantum ESPRESSO: A modular and open-source software project for quantum simulations of materials, J. Phys.: Condens. Matter. 21 (2009), no. 39, 395502.

  71. P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M.B. Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni, N. Colonna, I. Carnimeo, A.D. Corso, S. de Gironcoli, P. Delugas, R.A. Jr DiStasio, A. Ferretti, A. Floris, G. Fratesi, G. Fugallo, R. Gebauer, U. Gerstmann, F. Giustino, T. Gorni, J. Jia, M. Kawamura, H.-Y. Ko, A. Kokalj, E. Küçükbenli, M. Lazzeri, M. Marsili, N. Marzari, F. Mauri, N.L. Nguyen, H.-V. Nguyen, A. Otero-de-la Roza, L. Paulatto, S. Poncé, D. Rocca, R. Sabatini, B. Santra, M. Schlipf, A.P. Seitsonen, A. Smogunov, I. Timrov, T. Thonhauser, P. Umari, N. Vast, X. Wu, and S. Baroni, Advanced capabilities for materials modelling with Quantum ESPRESSO, J. Phys.: Condens. Matter 29 (2017), no. 46, 465901.

  72. S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. J. Probert, K. Refson, and M. C. Payne, First principles methods using CASTEP, Z. Kristallogr. 220 (2005), no. 5-6, 567–570.

  73. K. Refson, P.R. Tulip, and S.J. Clark, Variational density-functional perturbation theory for dielectrics and lattice dynamics, Phys. Rev. B 73 (2006), no. 15, 155114.

  74. T. Lin, X. -Y. Liu, and C. He, Calculation of infrared/raman spectra and dielectric properties of various crystalline poly(lactic acid)s by density functional perturbation theory (DFPT) method, J. Phys. Chem. B 116 (2012), no. 5, 1524–1535.

  75. B. Cromp, Jr Carrington T., D. R. Salahub, O. L. Malkina, and V.G. Malkin, Effect of rotation and vibration on nuclear magnetic resonance chemical shifts: Density functional theory calculations, J. Chem. Phys. 110 (1999), no. 15, 7153–7159.

  76. S. Y. Savrasov, A linearized direct approach for calculating the static response in solids, Solid State Commun. 74 (1990), no. 2, 69–72.

  77. E. Moreira, C. A. Barboza, E. L. Albuquerque, U. L. Fulco, J. M. Henriques, and A. I. Araújo, Vibrational and thermodynamic properties of orthorhombic CaSnO3 from DFT and DFPT calculations, J. Phys. Chem. Solids 77 (2015), 85–91.

  78. B. Mennucci, G. Scalmani, and D. Jacquemin, Excited-state vibrations of solvated molecules: Going beyond the linear-response polarizable continuum model, J. Chem. Theory Comput. 11 (2015), no. 3, 847–850.

  79. Y. C. Shen, P. C. Upadhya, E. H. Linfield, and A.G. Davies, Temperature-dependent low-frequency vibrational spectra of purine and adenine, Appl. Phys. Lett. 82 (2350), no. 14, 2003.

  80. T. M. Korter and D. F. Plusquellic, Continuous-wave terahertz spectroscopy of biotin: vibrational anharmonicity in the far-infrared, Chem. Phys. Lett. 385 (2004), no. 1-2, 45–51.

  81. A. Xie, Q. He, L. Miller, B. Sclavi, M. R. Chance, L. Miller, and B. Sclavi, Low frequency vibrations of amino acid homopolymers observed by synchrotron far-IR absorption spectroscopy: Excited state effects dominate the temperature dependence of the spectra, Biopolymers 49 (1999), no. 7, 591–603.

  82. M. T. Ruggiero and J. A. Zeitler, Resolving the origins of crystalline anharmonicity using terahertz time-domain spectroscopy and ab initio simulations, J. Phys. Chem. B 120 (2016), no. 45, 11733–11739.

  83. M. T. Ruggiero, J. A. Zeitler, and A. Erba, Intermolecular anharmonicity in molecular crystals: interplay between experimental low-frequency dynamics and quantum quasi-harmonic simulations of solid purine, Chem. Commun. 53 (2017), no. 26, 3781–3784.

  84. A. Erba, J. Maul, M. Ferrabone, P. Carbonniere, M. Rérat, and R. Dovesi, Anharmonic vibrational states of solids from DFT calculations. Part I: Description of the potential energy surface, J. Chem. Theory Comput. 15 (2019), no. 6, 3755–3765.

  85. A. Erba, J. Maul, M. Ferrabone, R. Dovesi, M. Rérat, and P. Carbonniere, Anharmonic vibrational States of solids from DFT calculations. Part II: Implementation of the VSCF and VCI Methods, J. Chem. Theory Comput. 15 (2019), no. 6, 3766–3777.

  86. A. Erba, On combining temperature and pressure effects on structural properties of crystals with standard ab initio techniques, J. Chem. Phys. 141 (2014), 124115.

  87. A. Erba, J. Maul, and B. Civalleri, Thermal properties of molecular crystals through dispersion-corrected quasi-harmonic ab initio calculations: the case of urea, Chem. Commun. 52 (2016), no. 9, 1820–1823.

  88. R. D. King-Smith and D. Vanderbilt, Theory of polarization of crystalline solids, Phys. Rev. B 47 (1993), no. 3, 1651–1654.

  89. R. Resta, Macroscopic polarization in crystalline dielectrics: the geometric phase approach, Rev. Mod. Phys. 66 (1994), no. 3, 899–915.

  90. Y. Noël, C.M. Zicovich-Wilson, B. Civalleri, P. D’Arco, and R. Dovesi, Polarization properties of ZnO and BeO: An ab initio study through the Berry phase and Wannier functions approaches. Phys. Rev. B, 65 (1).

  91. R. Iftimie and M.E. Tuckerman, Decomposing total IR spectra of aqueous systems into solute and solvent contributions: A computational approach using maximally localized Wannier orbitals, J. Chem. Phys. 122 (2005), no. 21, 214508.

  92. I. Souza, R. M. Martin, N. Marzari, X. Zhao, and D. Vanderbilt, Wannier-function description of the electronic polarization and infrared absorption of high-pressure hydrogen, Phys. Rev. B 62 (2000), no. 23, 15505–15520.

  93. L. Maschio, B. Kirtman, M. Rérat, R. Orlando, and R. Dovesi, Ab initio analytical Raman intensities for periodic systems through a coupled perturbed Hartree-Fock/Kohn-Sham method in an atomic orbital basis I Theory, J. Chem. Phys. 139 (2013), no. 16, 164101.

  94. L. Maschio, B. Kirtman, M. Rérat, R. Orlando, and R. Dovesi, Ab initio analytical Raman intensities for periodic systems through a coupled perturbed Hartree-Fock/Kohn-Sham method in an atomic orbital basis. II. Validation and comparison with experiments, J. Chem. Phys. 139 (2013), no. 16, 164102.

  95. L. Maschio, B. Kirtman, M. Rérat, R. Orlando, and R. Dovesi, Comment on Ab initioanalytical infrared intensities for periodic systems through a coupled perturbed Hartree-Fock/Kohn-Sham method [J. Chem. Phys. 137, 204113 (2012)], J. Chem. Phys. 139 (2013), no. 16, 167101.

  96. R. Dovesi, B. Kirtman, L. Maschio, J. Maul, F. Pascale, and M. Rérat, Calculation of the Infrared Intensity of Crystalline Systems. A Comparison of Three Strategies Based on Berry Phase, Wannier Function, and Coupled-Perturbed Kohn–Sham Methods, J. Phys. Chem. C 123 (2019), no. 13, 8336–8346.

  97. C.J. Cramer, Essentials of computational chemistry: Theories and models, 2nd ed., Wiley, New York, 2004.

  98. P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136 (1964), no. 3B, B864–B871.

  99. W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140 (1965), no. 4A, A1133–A1138.

  100. R. O. Jones, Density functional theory: Its origins, rise to prominence, and future, Rev. Mod. Phys. 87 (2015), no. 3, 897–923.

  101. A. D. Boese and J. M. L. Martin, Development of density functionals for thermochemical kinetics, J. Chem. Phys. 121 (2004), no. 8, 3405–3416.

  102. J. Gräfenstein and D. Cremer, Development of a CAS-DFT method covering non-dynamical and dynamical electron correlation in a balanced way, Mol. Phys. 103 (2005), no. 2-3, 279–308.

  103. Y. Zhao, B. J. Lynch, and D. G. Truhlar, Assessment of a new hybrid density functional model for thermochemical kinetics, J. Phys. Chem Development A 108 (2004), no. 14, 2715–2719.

  104. L.A. Burns, Á. Vázquez-Mayagoitia, B.G. Sumpter, and C.D. Sherrill, Density-functional approaches to noncovalent interactions: A comparison of dispersion corrections (DFT-D), exchange-hole dipole moment (XDM) theory, and specialized functionals, J. Chem. Phys. 134 (2011), no. 8, 084107.

  105. E. J. Bylaska, K. Tsemekhman, and F. Gao, New development of self-interaction corrected DFT for extended systems applied to the calculation of native defects in 3C–SiC, Phys. Scr. 2006 (2006), no. T124, 86–90.

  106. A.J. Cohen, P. Mori-Sánchez, and W. Yang, Development of exchange-correlation functionals with minimal many-electron self-interaction error, J. Chem. Phys. 126 (2007), no. 19, 191109.

  107. A. J. Cohen, P. Mori-Sánchez, and W. Yang, Insights into current limitations of density functional theory, Science 321 (2008), no. 5890, 792–794.

  108. Z. -L. Cai, M. J. Crossley, J. R. Reimers, R. Kobayashi, and R. D. Amos, Density functional theory for charge transfer: The nature of the N-bands of porphyrins and chlorophylls revealed through CAM-B3LYP, CASPT2, and SAC-CI calculations, J. Phys. Chem. B 110 (2006), no. 31, 15624–15632.

  109. E. Engel, S. Keller, and R. M. Dreizler, Generalized gradient approximation for the relativistic exchange-only energy functional, Phys. Rev. A 53 (1996), no. 3, 1367–1374.

  110. M. Lazzeri, C. Attaccalite, L. Wirtz, and F. Mauri, Impact of the electron-electron correlation on phonon dispersion: Failure of LDA and GGA DFT functionals in graphene and graphite, Phys. Rev. B 78 (2008), no. 8, 081406.

  111. A. Marini, G. Onida, and R. Del Sole, Plane-wave DFT-LDA calculation of the electronic structure and absorption spectrum of copper, Phys. Rev. B 64 (2001), no. 19, 195125.

  112. J. A. Snyder, D. R. Alfonso, J. E. Jaffe, Z. Lin, A. C. Hess, and M. Gutowski, Periodic density functional LDA and GGA study of CO adsorption at the (001) surface of MgO, J. Phys. Chem. B 104 (2000), no. 19, 4717–4722.

  113. P. Hao, J. Sun, B. Xiao, A. Ruzsinszky, G.I. Csonka, J. Tao, S. Glindmeyer, and J. P. Perdew, Performance of meta-GGA functionals on general main group thermochemistry, kinetics, and noncovalent interactions, J. Chem. Theory Comput. 9 (2012), no. 1, 355–363.

  114. Y. Zhao and D.G. Truhlar, Density functionals with broad applicability in chemistry, Acc. Chem. Res. 41 (2008), no. 2, 157–167.

  115. S. Kossmann, B. Kirchner, and F. Neese, Performance of modern density functional theory for the prediction of hyperfine structure: meta-GGA and double hybrid functionals, Mol. Phys. 105 (2010), no. 15-16, 2049–2071.

  116. L. Goerigk and S. Grimme, A general database for main group thermochemistry, kinetics, and noncovalent interactions - assessment of common and reparameterized (meta-)GGA density functionals, J. Chem. Theory Comput. 6 (2009), no. 1, 107–126.

  117. A.D. Becke, A new mixing of Hartree–Fock and local density-functional theories, J. Chem. Phys. 98 (1998), no. 2, 1372–1377.

  118. A.D. Becke, Density-functional thermochemistry. III. The role of exact exchange, J. Chem. Phys. 98 (1998), no. 7, 5648–5652.

  119. J. P. Perdew, M. Ernzerhof, and K. Burke, Rationale for mixing exact exchange with density functional approximations, J. Chem. Phys. 105 (1998), no. 22, 9982–9985.

  120. C. Adamo and V. Barone, Toward reliable density functional methods without adjustable parameters: The PBE0 model, J. Chem. Phys. 110 (1999), no. 13, 6158–6170.

  121. R. Peverati and D. G. Truhlar, Improving the accuracy of hybrid meta-GGA density functionals by range separation, J. Phys. Chem. Lett. 2 (2011), no. 21, 2810–2817.

  122. J. Heyd and G. E. Scuseria, Efficient hybrid density functional calculations in solids: Assessment of the Heyd–Scuseria–Ernzerhof screened Coulomb hybrid functional, J. Chem. Phys. 121 (2004), no. 3, 1187–1192.

  123. J. M. del Campo, J.L. Gázquez, S. B. Trickey, and A. Vela, Non-empirical improvement of PBE and its hybrid PBE0 for general description of molecular properties, J. Chem. Phys. 136 (2012), no. 10, 104108.

  124. C. Adamo and V. Barone, Physically motivated density functionals with improved performances: The modified Perdew–Burke–Ernzerhof model, J. Chem. Phys. 116 (2002), no. 14, 5933–5940.

  125. P. M. Hakey, D. G. Allis, M. R. Hudson, and T. M. Korter, Density functional dependence in the theoretical analysis of the terahertz spectrum of the illicit drug MDMA (ecstasy), IEEE Sens. J 10 (2010), no. 3, 478–484.

  126. Y. Zhao and D. G. Truhlar, The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals, Theor. Chem. Acc. 120 (2007), no. 1-3, 215–241.

  127. N. Y. Tan, M. T. Ruggiero, C. Orellana-Tavra, T. Tian, A. D. Bond, T. M. Korter, D. Fairen-Jimenez, and J.A. Zeitler, Investigation of the terahertz vibrational modes of ZIF-8 and ZIF-90 with terahertz time-domain spectroscopy, Chem. Commun. 51 (2015), no. 89, 16037–16040.

  128. J. Maul, M.R. Ryder, M.T. Ruggiero, and A. Erba, Pressure-driven mechanical anisotropy and destabilization in zeolitic imidazolate frameworks, Phys. Rev. B 99 (2019), no. 1, 014102.

  129. A. Erba, Self-consistent hybrid functionals for solids: a fully-automated implementation, J. Phys.: Condens. Matter 29 (2017), no. 31, 314001.

  130. K. Kaufmann, W. Baumeister, and M. Jungen, Universal Gaussian basis sets for an optimum representation of Rydberg and continuum wavefunctions, J. Phys. B: At., Mol. Opt. Phys. 22 (1989), no. 14, 2223–2240.

  131. P. J. C. Aerts and W. C. Nieuwpoort, On the use of Gaussian basis sets to solve the Hartree—Fock—Dirac equation. I. Application to one-electron atomic systems., Chem. Phys. Lett. 113 (1985), no. 2, 165–172.

  132. D. W. Schwenke, K. Haug, D. G. Truhlar, Y. Sun, J. Z. H. Zhang, and D. J. Kouri, Variational basis-set calculations of accurate quantum mechanical reaction probabilities, J. Phys. Chem. 91 (1987), no. 24, 6080–6082.

  133. M. T. Ruggiero, A. Erba, R. Orlando, and T. M. Korter, Origins of contrasting copper coordination geometries in crystalline copper sulfate pentahydrate, Phys. Chem. Chem. Phys. 17 (2015), 30123–30129.

  134. S. Maintz, V. L. Deringer, A. L. Tchougréeff, and R. Dronskowski, Analytic projection from plane-wave and PAW wavefunctions and application to chemical-bonding analysis in solids, J. Comput. Chem. 34 (2013), no. 29, 2557–2567.

  135. M. T. Ruggiero, T. Bardon, M. Strlič, P. F. Taday, and T.M. Korter, Assignment of the terahertz spectra of crystalline copper sulfate and its hydrates via solid-state density functional theory, J. Phys. Chem. A 118 (2014), no. 43, 10101–10108.

  136. M. Gutowski, J. H. Van Lenthe, J. Verbeek, F. B. Van Duijneveldt, and G. Chałasinski, The basis set superposition error in correlated electronic structure calculations, Chem. Phys. Lett. 124 (1986), no. 4, 370–375.

  137. S. Simon, M. Duran, and J. J. Dannenberg, How does basis set superposition error change the potential surfaces for hydrogen-bonded dimers, J. Chem. Phys. 105 (1998), no. 24, 11024–11031.

  138. J. G. Brandenburg, M. Alessio, B. Civalleri, M. F. Peintinger, T. Bredow, and S. Grimme, Geometrical correction for the inter- and intramolecular basis set superposition error in periodic density functional theory calculations, J. Phys. Chem. A 117 (2013), no. 38, 9282–9292.

  139. K. Drużbicki, E. Mikuli, N. Pałka, S. Zalewski, and M.D. Ossowska-Chruściel, Polymorphism of resorcinol explored by complementary vibrational spectroscopy (FT-RS, THz-TDS, INS) and first-principles solid-state computations (plane-wave DFT), J. Phys. Chem. B 119 (2015), no. 4, 1681–1695.

  140. P. Hermet, J.-L. Bantignies, A. Rahmani, J.-L. Sauvajol, M. R. Johnson, and F. Serein, Far- and mid-infrared of crystalline 2,2’-bithiophene: Ab initio analysis and comparison with infrared response, J. Phys. Chem. A 109 (2005), no. 8, 1684–1691.

  141. S. Grimme, Density functional theory with London dispersion corrections, WIREs Comput. Mol. Sci. 1 (2011), no. 2, 211–228.

  142. J. Moellmann and S. Grimme, DFT-D3 study of some molecular crystals, J. Phys. Chem. C. 118 (2014), no. 14, 7615–7621.

  143. J. Moellmann and S. Grimme, Importance of London dispersion effects for the packing of molecular crystals: a case study for intramolecular stacking in a bis-thiophene derivative, Phys. Chem. Chem. Phys. 12 (2010), no. 30, 8500–8504.

  144. J.G. Brandenburg and S. Grimme, Dispersion corrected hartree-fock and density functional theory for organic crystal structure prediction., volume 345 of Prediction and Calculation of Crystal Structures. Topics in Current Chemistry. Springer International Publishing, Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie der Universität Bonn, Beringstraße 4, 53115, Bonn, Germany, gerit.brandenburg@thch.unibonn.de., 2014.

  145. N. Marom, R.A. DiStasio, V. Atalla, S. Levchenko, A.M. Reilly, J.R. Chelikowsky, L. Leiserowitz, and A. Tkatchenko, Many-body dispersion interactions in molecular crystal polymorphism, Angew. Chem. Int. Ed. 52 (2013), no. 26, 6629–6632.

  146. J. Kim, O. -P. Kwon, M. Jazbinsek, Y. C. Park, and Y. S. Lee, First-principles calculation of Terahertz absorption with dispersion correction of 2,2-Bithiophene as model compound, The Journal of Physical Chemistry C 119 (2015), no. 22, 12598–12607.

  147. M. D. King, W. D. Buchanan, and T. M. Korter, Application of London-type dispersion corrections to the solid-state density functional theory simulation of the terahertz spectra of crystalline pharmaceuticals, Phys. Chem. Chem. Phys. 13 (2011), no. 10, 4250.

  148. E. M. Witko, W. D. Buchanan, and T. M. Korter, The importance of London dispersion forces in crystalline magnesium nitrate hexahydrate, Inorg. Chim. Acta 389 (2012), 176–182.

  149. M. D. King and T.M. Korter, Modified corrections for London forces in solid-state density functional theory calculations of structure and lattice dynamics of molecular crystals, J. Phys. Chem. A 116 (2012), no. 25, 6927–6934.

  150. P. M. Hakey, D. G. Allis, M. R. Hudson, W. Ouellette, and T. M. Korter, Investigation of (1R,2S)–ephedrine by cryogenic terahertz spectroscopy and solid-state density functional theory, ChemPhysChem 10 (2009), no. 14, 2434–2444.

  151. D. J. Tozer, N. C. Handy, R. D. Amos, J. A. Pople, R. H. Nobes, Y. Xie, and H. F. Schaefer, Theory and applications of spin-restricted open-shell Møller-Plesset theory, Mol Theory Phys. 79 (2006), no. 4, 777–793.

  152. T. Helgaker, P. Jørgensen, and N. C. Handy, A numerically stable procedure for calculating Møller-Plesset energy derivatives, derived using the theory of Lagrangians, Theor. Chim. Acta 76 (1989), no. 4, 227–245.

  153. L.W. Bertels, J. Lee, and M. Head-Gordon, Third-order Møller-Plesset perturbation theory made useful? Choice of orbitals and scaling greatly improves accuracy for thermochemistry, kinetics, and intermolecular interactions, J. Phys. Chem. Lett. 10 (2019), no. 15, 4170–4176.

  154. H. Su, H. Wang, H. Wang, Y. Lu, and Z. Zhu, Description of noncovalent interactions involving π-system with high precision: An assessment of RPA, MP2, and DFT-D methods, J. Comput. Chem. 40 (2019), no. 17, 1643–1651.

  155. S. Grimme, Improved second-order Møller–Plesset perturbation theory by separate scaling of parallel- and antiparallel-spin pair correlation energies, J. Chem. Phys. 118 (2003), no. 20, 9095–9102.

  156. C. Pisani, M. Schütz, S. Casassa, D. Usvyat, L. Maschio, M. Lorenz, and A. Erba, CRYSCOR: A program for the post-Hartree-Fock treatment of periodic systems, Phys. Chem. Chem. Phys. 14 (2012), no. 21, 7615–7628.

  157. D. Usvyat, L. Maschio, C. Pisani, and M. Schütz, Second order local Møller-Plesset perturbation theory for periodic systems: the CRYSCOR code, Z. Phys. Chem. 224 (2010), no. 3-4, 441–454.

  158. C. Pisani, M. Busso, G. Capecchi, S. Casassa, R. Dovesi, L. Maschio, C. Zicovich-Wilson, and M. Schütz, Local-MP2 electron correlation method for nonconducting crystals, J. Chem. Phys. 122 (2005), no. 9, 094113.

  159. L. Maschio, D. Usvyat, M. Schütz, and B. Civalleri, Periodic local Møller-Plesset second order perturbation theory method applied to molecular crystals: study of solid NH3 and CO2 using extended basis sets, J. Phys. Chem. 132 (2010), no. 13, 134706.

  160. A. Erba, S. Casassa, L. Maschio, and C. Pisani, DFT and local-MP2 periodic study of the structure and stability of two proton-ordered polymorphs of ice, J. Phys. Chem. B 113 (2009), no. 8, 2347–2354.

  161. C. Pisani, L. Maschio, S. Casassa, M. Halo, M. Schütz, and D. Usvyat, Periodic local MP2 method for the study of electronic correlation in crystals: Theory and preliminary applications, J. Comput. Chem. 29 (2008), no. 13, 2113–2124.

  162. S. Grimme, Accurate description of van der Waals complexes by density functional theory including empirical corrections, J. Comput. Chem. 25 (2004), no. 12, 1463–1473.

  163. P. Jurečka, J. Černý, P. Hobza, and D. R. Salahub, Density functional theory augmented with an empirical dispersion term. Interaction energies and geometries of 80 noncovalent complexes compared with ab initio quantum mechanics calculations, J. Comput. Chem. 28 (2007), no. 2, 555–569.

  164. W. Reckien, F. Janetzko, M. F. Peintinger, and T. Bredow, Implementation of empirical dispersion corrections to density functional theory for periodic systems, J. Comput. Chem. 33 (2012), no. 25, 2023–2031.

  165. S. Feng and T. Li, Predicting lattice energy of organic crystals by density functional theory with empirically corrected dispersion energy, J. Chem. Theory Comput. 2 (2006), no. 1, 149–156.

  166. B. Civalleri, C. M. Zicovich-Wilson, L. Valenzano, and P. Ugliengo, B3LYP augmented with an empirical dispersion term (B3LYP-D*) as applied to molecular crystals, CrystEngComm 10 (2008), no. 4, 405–410.

  167. S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu, J. Chem. Phys. 132 (2010), no. 15, 154104.

  168. S. Grimme, S. Ehrlich, and L. Goerigk, Effect of the damping function in dispersion corrected density functional theory, J. Comput. Chem. 32 (2011), no. 7, 1456–1465.

  169. A. Tkatchenko and M. Scheffler, Accurate molecular van der Waals interactions from ground-state electron density and free-atom reference data, Phys. Rev. Lett. 102 (2009), no. 7, 073005.

  170. O.A. von Lilienfeld, I. Tavernelli, U. Rothlisberger, and D. Sebastiani, Optimization of effective atom centered potentials for London dispersion forces in density functional theory, Phys. Rev. Lett. 93 (2004), no. 15, 153004.

  171. T. Sato, T. Tsuneda, and K. Hirao, Van der Waals interactions studied by density functional theory, Mol. Phys. 103 (2005), no. 6-8, 1151–1164.

  172. Y. Andersson, D. C. Langreth, and B. I. Lundqvist, Van der Waals interactions in density-functional theory, Phys. Rev. Lett. 76 (1996), no. 1, 102–105.

  173. O.A. Vydrov and T. Van Voorhis, Nonlocal van der Waals density functional: The simpler the better, J. Chem. Phys. 133 (2010), no. 24, 244103.

  174. T.R. Juliano Jr. and T.M. Korter, Terahertz vibrations of crystalline acyclic and cyclic diglycine: Benchmarks for London force correction models, J. Phys. Chem. A 117 (2013), no. 40, 10504–10512.

  175. G. Folpini, K. Reimann, M. Woerner, T. Elsaesser, J. Hoja, and A. Tkatchenko, Strong local-field enhancement of the nonlinear soft-mode response in a molecular crystal, Phys. Rev. Lett. 119 (2017), no. 9, 097404.

  176. M. C. Payne, J. D. Joannopoulos, D. C. Allan, M. P. Teter, and D. H. Vanderbilt, Molecular dynamics and ab initio total energy calculations, Phys. Rev. Lett. 56 (1986), no. 24, 2656–2656.

  177. H. J. C. Berendsen, D. van der Spoel, and R. van Drunen, GROMACS: A message-passing parallel molecular dynamics implementation, Comput. Phys. Commun. 91 (1995), no. 1-3, 43–56.

  178. D. Van Der Spoel, E. Lindahl, B. Hess, G. Groenhof, A. E. Mark, and H. J. C. Berendsen, GROMACS: Fast, flexible, and free, J. Comput. Chem. 26 (2005), no. 16, 1701–1718.

  179. S. Páll, M.J. Abraham, C. Kutzner, B. Hess, and E. Lindahl, Tackling exascale software challenges in molecular dynamics simulations with GROMACS, Springer, Cham, 2014.

  180. M. J. Abraham, T. Murtola, R. Schulz, S. Páll, J. C. Smith, B. Hess, and E. Lindahl, GROMACS High performance molecular simulations through multi-level parallelism from laptops to supercomputers, SoftwareX 1-2 (2015), 19–25.

  181. R. S. Ferrer, D. A. Case, and R. C. Walker, An overview of the AMBER biomolecular simulation package, WIREs Comput. Mol. Sci. 3 (2013), no. 2, 198–210.

  182. R. W. Williams and E. J. Heilweil, Measuring molecular force fields: Terahertz, inelastic neutron scattering, Raman, FTIR, DFT, and BOMD molecular dynamics of solid L-serine, Chem. Phys. 373 (2010), no. 3, 251–260.

  183. R. Car and M. Parrinello, Unified approach for molecular dynamics and density-functional theory, Phys. Rev. Lett. 55 (1985), no. 22, 2471–2474.

  184. J. S. Tse, Ab initio molecular dynamics with density functional theory, Annu. Rev. Phys Chem. 53 (2002), no. 1, 249–290.

  185. K. Laasonen, R. Car, C. Lee, and D. Vanderbilt, Implementation of ultrasoft pseudopotentials in ab initio molecular dynamics, Phys. Rev. B 43 (1991), no. 8, 6796–6799.

  186. J. VandeVondele, M. Krack, F. Mohamed, M. Parrinello, T. Chassaing, and J. Hutter, Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach, Comput. Phys. Commun. 167 (2005), no. 2, 103–128.

  187. M. Thomas, B. Kirchner, M. Brehm, M. Brehm, B. Kirchner, M. Thomas, O. Hollóczki, Z. Kelemen, L. Nyulászi, T. Pasinszki, L. Nyulászi, and T. Pasinszki, Simulating the vibrational spectra of ionic liquid systems: 1-ethyl-3-methylimidazolium acetate and its mixtures, J. Chem. Phys. 141 (2014), no. 2, 024510.

  188. M. Thomas, M. Brehm, and B. Kirchner, Voronoi dipole moments for the simulation of bulk phase vibrational spectra, Phys. Chem. Chem. Phys. 17 (2015), no. 5, 3207–3213.

  189. M. Thomas, M. Brehm, R. Fligg, P. Vöhringer, and B. Kirchner, Computing vibrational spectra from ab initio molecular dynamics, Phys. Chem. Chem. Phys. 15 (2013), no. 18, 6608–6622.

  190. P. H. Berens and K. R. Wilson, Molecular dynamics and spectra. I. Diatomic rotation and vibration, J. Chem. Phys. 74 (1998), no. 9, 4872–4882.

  191. M. Praprotnik and D. Janežič, Molecular dynamics integration and molecular vibrational theory. III. The infrared spectrum of water, J. Chem. Phys. 122 (2005), no. 17, 174103.

  192. M. Brehm and B. Kirchner, TRAVIS - a free analyzer and visualizer for Monte Carlo and molecular dynamics trajectories, J. Chem. Inf. Model. 51 (2011), no. 8, 2007–2023.

  193. M. Martinez, M.-P. Gaigeot, D. Borgis, and R. Vuilleumier, Extracting effective normal modes from equilibrium dynamics at finite temperature, J. Chem. Phys. 125 (2006), no. 14, 144106.

  194. A. Bastida, M. A. Soler, J. Zúñiga, A. Requena, A. Kalstein, and S. Fernández-Alberti, Molecular dynamics simulations and instantaneous normal-mode analysis of the vibrational relaxation of the C-H stretching modes of N-methylacetamide-d in liquid deuterated water, J. Phys. Chem A 114 (2010), no. 43, 11450–11461.

  195. V. N. Kabadi and B. M. Rice, Molecular dynamics simulations of normal mode vibrational energy transfer in liquid nitromethane, J. Phys. Chem. A 108 (2004), no. 4, 532–540.

  196. G. Katz, S. Zybin, W.A. III Goddard, Y. Zeiri, and R. Kosloff, Direct MD simulations of terahertz absorption and 2D spectroscopy applied to explosive crystals, J. Phys. Chem. Lett. 5 (2014), no. 5, 772–776.

  197. M. R. Leahy-Hoppa, M. J. Fitch, and R. Osiander, Terahertz spectroscopy techniques for explosives detection, Anal Bioanal. Chem. 395 (2009), no. 2, 247–257.

  198. J. Wilkinson, C. T. Konek, J. S. Moran, E. M. Witko, and T. M. Korter, Terahertz absorption spectrum of triacetone triperoxide (TATP), Chem. Phys. Lett. 478 (2009), no. 4-6, 172–174.

  199. M. A. González, Force fields and molecular dynamics simulations, École thématique de la Société Française de la Neutronique 12 (2011), 169–200.

  200. F. Martín-García, E. Papaleo, P. Gomez-Puertas, W. Boomsma, and K. Lindorff-Larsen, Comparing molecular dynamics force fields in the essential subspace, PLoS One 10 (2015), no. 3, e0121114.

  201. T. E. Cheatham and D. A. Case, Twenty-five years of nucleic acid simulations, Biopolymers 99 (2013), no. 12, 969–977.

  202. P. Bhadra and S. W. I. Siu, Refined empirical force field to model protein-self-assembled monolayer interactions based on AMBER14 and GAFF, Langmuir 35 (2019), no. 29, 9622–9633.

  203. J. W. Ponder and D. A. Case, Force fields for protein simulations, Adv. Protein Chem. 66 (2003), 27–85.

  204. J. A. Maier, C. Martinez, K. Kasavajhala, L. Wickstrom, K. E. Hauser, and C. Simmerling, ff14SB: Improving the accuracy of protein side chain and backbone parameters from ff99SB, J. Chem. Theory Comput. 11 (2015), no. 8, 3696–3713.

  205. A. D. MacKerell, D. Bashford, M. Bellott, R. L. Dunbrack, J. D. Evanseck, M. J. Field, S. Fischer, J. Gao, H. Guo, S. Ha, D. Joseph-McCarthy, L. Kuchnir, K. Kuczera, F. T. Lau, C. Mattos, S. Michnick, T. Ngo, D. T. Nguyen, B. Prodhom, W. E. Reiher, B. Roux, M. Schlenkrich, J. C. Smith, R. Stote, J. Straub, M. Watanabe, J. Wiórkiewicz-Kuczera, D. Yin, and M. Karplus, All-atom empirical potential for molecular modeling and dynamics studies of proteins, J. Phys. Chem. B 102 (1998), no. 18, 3586–3616.

  206. A. D. Mackerell, M. Feig, and C. L. Brooks, Extending the treatment of backbone energetics in protein force fields: limitations of gas-phase quantum mechanics in reproducing protein conformational distributions in molecular dynamics simulations, J. Comput. Chem. 25 (2004), no. 11, 1400–1415.

  207. A. D. MacKerell, N. Banavali, and N. Foloppe, Development and current status of the CHARMM force field for nucleic acids, Biopolymers 56 (2000), no. 4, 257–265.

  208. K. Vanommeslaeghe, E. Hatcher, C. Acharya, S. Kundu, S. Zhong, J. Shim, E. Darian, O. Guvench, P. Lopes, I. Vorobyov, and A. D. MacKerell, CHARMM general force field: A force field for drug-like molecules compatible with the CHARMM all-atom additive biological force fields, J. Comput. Chem. 31 (2010), no. 4, 671–690.

  209. T.P. Senftle, S. Hong, M.M. Islam, S.B. Kylasa, Y. Zheng, Y.K. Shin, C. Junkermeier, R. Engel-Herbert, M.J. Janik, H.M. Aktulga, T. Verstraelen, A. Grama, and A.C.T. van Duin, The ReaxFF reactive force-field: development, applications and future directions. npj Comput. Mater., 2. ISSN 2057–3960.

  210. M. Heyden and M. Havenith, Combining THz spectroscopy and MD simulations to study protein-hydration coupling, Methods 52 (2010), no. 1, 74–83.

  211. K. A. Niessen, M. Xu, A. Paciaroni, A. Orecchini, E. H. Snell, and A. G. Markelz, Moving in the right direction: Protein vibrations steering function, Biophys. J. 112 (2017), no. 5, 933–942.

  212. J. Hutter, M. Iannuzzi, F. Schiffmann, and J. VandeVondele, CP2K: atomistic simulations of condensed matter systems, WIREs Comput. Mol. Sci. 4 (2013), no. 1, 15–25.

  213. J. VandeVondele and J. Hutter, An efficient orbital transformation method for electronic structure calculations, J. Chem. Phys. 118 (2003), no. 10, 4365.

  214. J. VandeVondele and J. Hutter, Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases, J. Chem. Phys. 127 (2007), no. 11, 114105.

  215. J. Mahé, D. J. Bakker, S. Jaeqx, A. M. Rijs, and M.-P. Gaigeot, Mapping gas phase dipeptide motions in the far-infrared and terahertz domain, Phys. Chem. Chem. Phys. 19 (2017), no. 21, 13778–13787.

  216. R. B. Sessions, P. Dauber-Osguthorpe, and D. J. Osguthorpe, Filtering molecular dynamics trajectories to reveal low-frequency collective motions: Phospholipase A2, J. Mol. Biol. 210 (1989), no. 3, 617–633.

  217. D.A. Turton, H.M. Senn, T. Harwood, A.J. Lapthorn, E.M. Ellis, and K. Wynne, Terahertz underdamped vibrational motion governs protein-ligand binding in solution, Nature Commun. 5 (2014), 028103.

  218. A. Pereverzev and T.D. Sewell, Terahertz normal mode relaxation in pentaerythritol tetranitrate, J. Chem. Phys. 134 (2011), no. 1, 014513.

  219. A. Pereverzev and T.D. Sewell, Terahertz spectrum and normal-mode relaxation in pentaerythritol tetranitrate: Effect of changes in bond-stretching force-field terms, J. Chem. Phys. 134 (2011), no. 24, 244502.

  220. A. Pereverzev, T.D. Sewell, and D.L. Thompson, Calculation of anharmonic couplings and THz linewidths in crystalline PETN, J. Chem. Phys. 140 (2014), no. 10, 104508.

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Ruggiero, M.T. Invited Review: Modern Methods for Accurately Simulating the Terahertz Spectra of Solids. J Infrared Milli Terahz Waves 41, 491–528 (2020). https://doi.org/10.1007/s10762-019-00648-3

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