Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Primer
  • Published:

Computational molecular spectroscopy

Nature Reviews Methods Primers volume 1, Article number: 38 (2021) Cite this article

Subjects

Abstract

Spectroscopic techniques can probe molecular systems non-invasively and investigate their structure, properties and dynamics in different environments and physico-chemical conditions. Different spectroscopic techniques (spanning different ranges of the electromagnetic field) and their combination can lead to a more comprehensive picture of investigated systems. However, the growing sophistication of these experimental techniques makes it increasingly complex to interpret spectroscopic results without the help of computational chemistry. Computational molecular spectroscopy, born as a branch of quantum chemistry to provide predictions of spectroscopic properties and features, emerged as an independent and highly specialized field but has progressively evolved to become a general tool also employed by experimentally oriented researchers. In this Primer, we focus on the computational characterization of medium-sized molecular systems by means of different spectroscopic techniques. We first provide essential information about the characteristics, accuracy and limitations of the available computational approaches, and select examples to illustrate common trends and outcomes of general validity that can be used for modelling spectroscopic phenomena. We emphasize the need for estimating error bars and limitations, coupling accuracy with interpretability, touch upon data deposition and reproducibility issues, and discuss the results in terms of widely recognized chemical concepts.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Schematic representation of molecular energy levels and types of possible transitions.
Fig. 2: General theoretical framework for vibrational and vibronic spectroscopies and their chiral counterparts.
Fig. 3: Schematic interplay of experiment and theory in rotational spectroscopy to determine equilibrium structure.
Fig. 4: Computed113 and experimental157 matrix-isolation infrared spectra of glycine.
Fig. 5: Computed160 and experimental260 UV–Vis spectrum of chlorophyll a in methanol.
Fig. 6: Convergence properties of diffusion Monte Carlo.
Fig. 7: Computed and experimental VCD and ROA spectra for the determination of absolute configuration.
Fig. 8: Comparison of theory and experiment for the rotational spectrum of diazenylium cation.
Fig. 9: Comparison of theoretical and experimental near infrared spectra of crystalline DNA bases.
Fig. 10: Partially filled d and f shells lead to complex multiplet structures and rich spectroscopic phenomena.
Fig. 11: Computational chemistry in conjunction with ab initio ligand field theory can be used to understand subtle and complex spectroscopic phenomena.

Similar content being viewed by others

References

  1. Nafie, L. A. in Vibrational Optical Activity: Principles and Applications (Wiley, 2011). This book provides a comprehensive description of the underlying theory of the chiroptical spectroscopic methods VCD and ROA, and includes computational and experimental aspects as well as applications.

  2. Merkt, F. & Quack, M. Handbook of High-Resolution Spectroscopy (Wiley, 2011).

  3. Laane, J. Frontiers of Molecular Spectroscopy (Elsevier, 2008).

  4. Berova, N., Nakanishi, K. & Woody, R. W. Circular Dichroism: Principles and Applications 2nd edn (Wiley-VCH, 2000).

  5. Rijs, A. M. & Oomens, J. Gas-Phase IR Spectroscopy and Structure of Biological Molecules. Topics in Current Chemistry Vol. 364 (Springer International, 2015).

  6. Pulay, P., Meyer, W. & Boggs, J. E. Cubic force constants and equilibrium geometry of methane from Hartree–Fock and correlated wavefunctions. J. Chem. Phys. 68, 5077–5085 (1978).

    Article  ADS  Google Scholar 

  7. Obenchain, D. A. et al. Unveiling the sulfur–sulfur bridge: accurate structural and energetic characterization of a homochalcogen intermolecular bond. Angew. Chem. Int. Ed. 57, 15822–15826 (2018).

    Article  Google Scholar 

  8. Caminati, W. in Handbook of High-Resolution Spectroscopy (eds Merkt, F. & Quack, M.) (Wiley, 2011).

  9. Park, G. B. & Field, R. W. Perspective: the first ten years of broadband chirped pulse Fourier transform microwave spectroscopy. J. Chem. Phys. 144, 200901 (2016).

    Article  ADS  Google Scholar 

  10. Xie, F. et al. Discovering the elusive global minimum in a ternary chiral cluster: rotational spectra of propylene oxide trimer. Angew. Chem. Int. Ed. 59, 22427–22430 (2020).

    Article  Google Scholar 

  11. Wang, J. et al. The unexplored world of cycloalkene–water complexes: primary and assisting interactions unraveled by experimental and computational spectroscopy. Angew. Chem. Int. Ed. 58, 13935–13941 (2019).

    Article  Google Scholar 

  12. Alonso, J. L. & López, J. C. in Gas-Phase IR Spectroscopy and Structure of Biological Molecules (eds Rijs, A. M. & Oomens, J.) 335–401 (Springer International, 2015).

  13. Atanasov, M. et al. First principles approach to the electronic structure, magnetic anisotropy and spin relaxation in mononuclear 3d-transition metal single molecule magnets. Coord. Chem. Rev. 289-290, 177–214 (2015).

    Article  Google Scholar 

  14. Barone, V. in Computational Strategies for Spectroscopy: From Small Molecules to Nano Systems (Wiley, 2011).

  15. Grunenberg, J. in Computational Spectroscopy: Methods, Experiments and Applications (Wiley, 2011).

  16. Jensen, P., Bunker P. R. in Computational Molecular Spectroscopy (Wiley, 2000).

  17. Neese, F. Prediction of molecular properties and molecular spectroscopy with density functional theory: from fundamental theory to exchange-coupling. Coord. Chem. Rev. 253, 526–563 (2009).

    Article  Google Scholar 

  18. Neese, F., Petrenko, T., Ganyushin, D. & Olbrich, G. Advanced aspects of ab initio theoretical optical spectroscopy of transition metal complexes: multiplets, spin–orbit coupling and resonance Raman intensities. Coord. Chem. Rev. 251, 288–327 (2007). This review reports a careful analysis of quantum-chemical approaches for the study of transition metal complexes.

    Article  Google Scholar 

  19. Mata, R. A. & Suhm, M. A. Benchmarking quantum chemical methods: are we heading in the right direction? Angew. Chem. Int. Ed. 56, 11011–11018 (2017).

    Article  Google Scholar 

  20. Born, M. & Oppenheimer, R. Zur quantentheorie der molekeln. Ann. Phys. 389, 457–484 (1927).

    Article  MATH  Google Scholar 

  21. Eckart, C. Some studies concerning rotating axes and polyatomic molecules. Phys. Rev. 47, 552–558 (1935).

    Article  ADS  MATH  Google Scholar 

  22. Sayvetz, A. The kinetic energy of polyatomic molecules. J. Chem. Phys. 7, 383–389 (1939).

    Article  ADS  Google Scholar 

  23. Watson, J. K. G. Simplification of the molecular vibration–rotation Hamiltonian. Mol. Phys. 15, 479–490 (1968).

    Article  ADS  Google Scholar 

  24. Watson, J. K. G. The vibration–rotation Hamiltonian of linear molecules. Mol. Phys. 19, 465–487 (1970).

    Article  ADS  Google Scholar 

  25. Furtenbacher, T., Császár, A. G. & Tennyson, J. MARVEL: measured active rotational–vibrational energy levels. J. Mol. Spectrosc. 245, 115–125 (2007).

    Article  ADS  Google Scholar 

  26. Furtenbacher, T. & Császár, A. G. On employing H216O, H217O, H218O, and D216O lines as frequency standards in the 15–170 cm−1 window. J. Quant. Spectrosc. Radiat. Transfer 109, 1234–1251 (2008).

    Article  ADS  Google Scholar 

  27. Aliev, M. R. & Watson, J. K. G. in Molecular Spectroscopy: Modern Research (ed. Narahari Rao, K.) 1–67 (Academic, 1985). This book presents the higher-order effects in the vibration–rotation spectra of semi-rigid molecules.

  28. Gordy, W. & Cook, R. L. in Microwave Molecular Spectra (ed. Weissberger, A.) (Wiley, 1984).

  29. Watson, J. K. G. in Vibrational Spectra and Structure: A Series of Advances (ed. Durig, J. R.) (Elsevier, 1977).

  30. Kaupp, M., Buhl, M. & Malkin, V. G. in Calculation of NMR and EPR Parameters. Theory and Applications (eds Kaupp, M., Buhl, M. & Malkin, V. G.) (Wiley, 2004).

  31. Barone, V. & Polimeno, A. in Electron Paramagnetic Resonance: A Practitioner’s Toolkit Ch. 7 (eds Brustolon, M. & Giamello, E.) 251–284 (Wiley, 2008).

  32. Jose, K. V. & Raghavachari, K. Fragment-based approach for the evaluation of NMR chemical shifts for large biomolecules incorporating the effects of the solvent environment. J. Chem. Theory Comput. 13, 1147–1158 (2017).

    Article  Google Scholar 

  33. Neese, F. Quantum chemistry and EPR parameters. eMagRes 6, 1–22 (2017). This article presents a recent and exhaustive review on the quantum-chemical computation of the parameters involved in the electron paramagnetic resonance spectroscopy.

    Google Scholar 

  34. Puzzarini, C., Bloino, J., Tasinato, N. & Barone, V. Accuracy and interpretability: the Devil and the Holy Grail. New routes across old boundaries in computational spectroscopy. Chem. Rev. 119, 8131–8191 (2019). This recent review on computational (rotational and vibrational) spectroscopy also addresses accuracy and interpretability challenges.

    Article  Google Scholar 

  35. Bloino, J., Biczysko, M. & Barone, V. Anharmonic effects on vibrational spectra intensities: infrared, Raman, vibrational circular dichroism, and raman optical activity. J. Phys. Chem. A 119, 11862–11874 (2015).

    Article  Google Scholar 

  36. Nielsen, H. H. The vibration–rotation energies of molecules. Rev. Mod. Phys. 23, 90–136 (1951).

    Article  ADS  MATH  Google Scholar 

  37. Mills, I. A. in Molecular Spectroscopy: Modern Research (eds Rao, K. N. & Mathews, C. N.) (Academic, 1972).

  38. Barone, V. Anharmonic vibrational properties by a fully automated second-order perturbative approach. J. Chem. Phys. 122, 14108 (2005).

    Article  Google Scholar 

  39. Bloino, J. & Barone, V. A second-order perturbation theory route to vibrational averages and transition properties of molecules: general formulation and application to infrared and vibrational circular dichroism spectroscopies. J. Chem. Phys. 136, 124108 (2012).

    Article  ADS  Google Scholar 

  40. Vázquez, J. & Stanton, J. F. Simple(r) algebraic equation for transition moments of fundamental transitions in vibrational second-order perturbation theory. Mol. Phys. 104, 377–388 (2006).

    Article  ADS  Google Scholar 

  41. Willetts, A., Handy, N. C., Green, W. H. & Jayatilaka, D. Anharmonic corrections to vibrational transition intensities. J. Phys. Chem. 94, 5608–5616 (1990).

    Article  Google Scholar 

  42. Császár, A. G. Anharmonic molecular force fields. WIREs Comput. Mol. Sci. 2, 273–289 (2012).

    Article  Google Scholar 

  43. Franke, P. R., Stanton, J. F. & Douberly, G. E. How to VPT2: accurate and intuitive simulations of CH stretching infrared spectra using VPT2 + K with large effective Hamiltonian resonance treatments. J. Phys. Chem. A 125, 1301–1324 (2021). This recent and instructive review on vibrational perturbation theory also discusses in detail the treatment of resonances.

    Article  Google Scholar 

  44. Cornaton, Y., Ringholm, M., Louant, O. & Ruud, K. Analytic calculations of anharmonic infrared and Raman vibrational spectra. Phys. Chem. Chem. Phys. 18, 4201–4215 (2016).

    Article  Google Scholar 

  45. Maslen, P. E., Jayatilaka, D., Colwell, S. M., Amos, R. D. & Handy, N. C. Higher analytic derivatives. II. The fourth derivative of self-consistent-field energy. J. Chem. Phys. 95, 7409–7417 (1991).

    Article  ADS  Google Scholar 

  46. Piccardo, M., Bloino, J. & Barone, V. Generalized vibrational perturbation theory for rotovibrational energies of linear, symmetric and asymmetric tops: theory, approximations, and automated approaches to deal with medium-to-large molecular systems. Int. J. Quantum Chem. 115, 948–982 (2015).

    Article  Google Scholar 

  47. Roy, T. K. & Gerber, R. B. Vibrational self-consistent field calculations for spectroscopy of biological molecules: new algorithmic developments and applications. Phys. Chem. Chem. Phys. 15, 9468–9492 (2013).

    Article  Google Scholar 

  48. Neff, M. & Rauhut, G. Toward large scale vibrational configuration interaction calculations. J. Chem. Phys. 131, 124129 (2009).

    Article  ADS  Google Scholar 

  49. Christiansen, O. Vibrational coupled cluster theory. J. Chem. Phys. 120, 2149–2159 (2004).

    Article  ADS  Google Scholar 

  50. Erfort, S., Tschöpe, M. & Rauhut, G. Toward a fully automated calculation of rovibrational infrared intensities for semi-rigid polyatomic molecules. J. Chem. Phys. 152, 244104 (2020).

    Article  Google Scholar 

  51. Biczysko, M., Bloino, J., Santoro, F. & Barone, V. in Computational Strategies for Spectroscopy: From Small Molecules to Nano Systems Ch. 8 (ed. Barone, V.) 361–443 (Wiley, 2011).

  52. Bloino, J., Biczysko, M., Santoro, F. & Barone, V. General approach to compute vibrationally resolved one-photon electronic spectra. J. Chem. Theory Comput. 6, 1256–1274 (2010).

    Article  Google Scholar 

  53. Baiardi, A., Bloino, J. & Barone, V. General time dependent approach to vibronic spectroscopy including Franck–Condon, Herzberg–Teller, and Duschinsky effects. J. Chem. Theory Comput. 9, 4097–4115 (2013).

    Article  Google Scholar 

  54. Franck, J. & Dymond, E. G. Elementary processes of photochemical reactions. Trans. Faraday Society 21, 536–542 (1926).

    Article  Google Scholar 

  55. Condon, E. U. Nuclear motions associated with electron transitions in diatomic molecules. Phys. Rev. 32, 858–872 (1928).

    Article  ADS  MATH  Google Scholar 

  56. Herzberg, G. & Teller, E. Schwingungsstruktur der Elektronenübergänge bei mehratomigen Molekülen. Z. Phys. Chem. 21B, 410–446 (1933).

    Article  MATH  Google Scholar 

  57. Duschinsky, F. Acta Physicochim. 7, 551–566 (URSS, 1937) .

  58. Baiardi, A., Bloino, J. & Barone, V. General formulation of vibronic spectroscopy in internal coordinates. J. Chem. Phys. 144, 084114 (2016).

    Article  ADS  Google Scholar 

  59. Reimers, J. R. A practical method for the use of curvilinear coordinates in calculations of normal-mode-projected displacements and Duschinsky rotation matrices for large molecules. J. Chem. Phys. 115, 9103–9109 (2001).

    Article  ADS  Google Scholar 

  60. Baiardi, A., Bloino, J. & Barone, V. Simulation of vibronic spectra of flexible systems: hybrid DVR-harmonic approaches. J. Chem. Theory Comput. 13, 2804–2822 (2017).

    Article  Google Scholar 

  61. Barone, V. The virtual multifrequency spectrometer: a new paradigm for spectroscopy. Wiley Interdiscip. Rev. Comput. Mol. Sci. 6, 86–110 (2016). This review introduces a new and more intuitive approach of computational spectroscopy based on the vis-à-vis comparison of calculated and experimental spectra instead of the mere computation of spectroscopic parameters.

    Article  Google Scholar 

  62. Bloino, J., Baiardi, A. & Biczysko, M. Aiming at an accurate prediction of vibrational and electronic spectra for medium-to-large molecules: an overview. Int. J. Quantum Chem. 116, 1543–1574 (2016). This tutorial review presents a detailed computational protocol and guidelines for the simulation of vibrational and vibrationally resolved electronic spectra for medium to large molecular systems of increasing flexibility.

    Article  Google Scholar 

  63. Autschbach, J. in Comprehensive Chiroptical Spectroscopy: Instrumentation, Methodologies, and Theoretical Simulations Vol. 1 Ch. 21 (eds Berova, N., Polavarapu, P. L., Nakanishi, K. & Woody, R. W) 593–642 (Wiley, 2011).

  64. Crawford, T. D. in Comprehensive Chiroptical Spectroscopy: Instrumentation, Methodologies, and Theoretical Simulations Vol. 1 Ch. 23 (eds Berova, N., Polavarapu, P. L., Nakanishi, K. & Woody, R. W.) 675–697 (Wiley, 2011).

  65. Srebro-Hooper, M. & Autschbach, J. Calculating natural optical activity of molecules from first principles. Annu. Rev. Phys. Chem. 68, 399–420 (2017). This recent review outlines computational models and methodological developments for chiroptical spectroscopic methods that include optical rotation, ECD, VCD and ROA.

    Article  ADS  Google Scholar 

  66. Stephens, P. J., Devlin, F. J. & Cheeseman, J. R. in VCD Spectroscopy for Organic Chemists (CRC, 2012).

  67. Ruud, K. in Comprehensive Chiroptical Spectroscopy: Instrumentation, Methodologies, and Theoretical Simulations Vol. 1 Ch. 24 (eds Berova, N., Polavarapu, P. L., Nakanishi, K. & Woody, R. W.) 699–727 (Wiley, 2011).

  68. Beer, A. Bestimmung der absorption des rothen lichts in farbigen flüssigkeiten. Ann. Phys. 162, 78–88 (1852).

    Article  Google Scholar 

  69. Polavarapu, P. L. in Chiroptical Spectroscopy: Fundamentals and Applications (CRC, 2016).

  70. Stephens, P. J. & Harada, N. ECD cotton effect approximated by the Gaussian curve and other methods. Chirality 22, 229–233 (2010).

    Google Scholar 

  71. Cheeseman, J. R. & Frisch, M. J. Basis set dependence of vibrational Raman and Raman optical activity intensities. J. Chem. Theory Comput. 7, 3323–3334 (2011).

    Article  Google Scholar 

  72. Liégeois, V., Ruud, K. & Champagne, B. An analytical derivative procedure for the calculation of vibrational Raman optical activity spectra. J. Chem. Phys. 127, 204105 (2007).

    Article  ADS  Google Scholar 

  73. Nafie, L. A. Theory of Raman scattering and Raman optical activity: near resonance theory and levels of approximation. Theor. Chem. Acc. 119, 39–55 (2008).

    Article  Google Scholar 

  74. Barron, L. D. in Molecular Light Scattering and Optical Activity (Cambridge Univ. Press, Cambridge, 2004).

  75. Long, D. A. in The Raman Effect: A Unified Treatment of the Theory of Raman Scattering by Molecules (Wiley, 2002).

  76. Neugebauer, J., Reiher, M., Kind, C. & Hess, B. A. Quantum chemical calculation of vibrational spectra of large molecules—Raman and IR spectra for Buckminsterfullerene. J. Comput. Chem. 23, 895–910 (2002).

    Article  Google Scholar 

  77. Dzugan, L. C., DiRisio, R. J., Madison, L. R. & McCoy, A. B. Spectral signatures of proton delocalization in H+(H2O)n=1−4 ions. Faraday Discuss 212, 443–466 (2018).

    Article  ADS  Google Scholar 

  78. Tanaka, S., Roy, P.-N. & Mitas, L. in Recent progress in Quantum Monte Carlo Vol. 1234 (ACS, 2016).

  79. Tanaka, S., Rothstein, S. M. & Lester Jr, W. A. in Advances in Quantum Monte Carlo Vol. 1094 (ACS, 2012).

  80. Anderson, J. B. & Rothstein, S. M. in Advances in Quantum Monte Carlo Vol. 953 (ACS, 2007).

  81. Lester, W. A., Rothstein, S. M. & Tanaka, S. in Recent Advances in Quantum Monte Carlo Methods: Part II Recent Advances in Computational Chemistry Vol. 2 (World Scientific, 2002).

  82. Lester, W. A., Rothstein, S. M. & Tanaka, S. in Recent Advances in Quantum Monte Carlo Methods Recent Advances in Computational Chemistry (World Scientific, 1997).

  83. McCoy, A. B. Diffusion Monte Carlo approaches for investigating the structure and vibrational spectra of fluxional systems. Int. Rev. Phys. Chem. 25, 77–107 (2006).

    Article  ADS  Google Scholar 

  84. Suhm, M. A. & Watts, R. O. Quantum Monte Carlo studies of vibrational states in molecules and clusters. Phys, Rep. 204, 293–329 (1991). This article presents an extensive review of the DMC approach and its application to the studies of nuclear quantum effects in molecules and clusters.

    Article  ADS  Google Scholar 

  85. Anderson, J. B. A random-walk simulation of the Schrödinger equation: H+3. J. Chem. Phys. 63, 1499–1503 (1975). This key publication introduces the DMC approaches described in this Primer to the chemistry community.

    Article  ADS  Google Scholar 

  86. Anderson, J. B. Quantum chemistry by random walk. H 2P, H+3 D3h 1A′1, H2 3Σ+u, H4 1Σ+g, Be 1S. J. Chem. Phys. 65, 4121–4127 (1976).

    Article  ADS  Google Scholar 

  87. Barnett, R. N., Reynolds, P. J. & Lester, W. A. Monte Carlo algorithms for expectation values of coordinate operators. J. Comput. Phys. 96, 258–276 (1991).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  88. Petit, A. S., Wellen, B. A. & Mccoy, A. B. Using fixed-node diffusion Monte Carlo to investigate the effects of rotation-vibration coupling in highly fluxional asymmetric top molecules: application to H2D+. J. Chem. Phys. 138, 034105 (2013).

    Article  ADS  Google Scholar 

  89. Lee, H.-S., Herbert, J. M. & McCoy, A. B. Adiabatic diffusion Monte Carlo approaches for studies of ground and excited state properties of van der Waals complexes. J. Chem. Phys. 110, 5481–5484 (1999).

    Article  ADS  Google Scholar 

  90. Császár, A. G., Allen, W. D. & Schaefer III, H. F. In pursuit of the ab initio limit for conformational energy prototypes. J. Chem. Phys. 108, 9751–9764 (1998).

    Article  ADS  Google Scholar 

  91. Montgomery, J. A., Frisch, M. J., Ochterski, J. W. & Petersson, G. A. A complete basis set model chemistry. VI. Use of density functional geometries and frequencies. J. Chem. Phys. 110, 2822–2827 (1999).

    Article  ADS  Google Scholar 

  92. Demaison, J., Margules, L. & Boggs, J. E. The equilibrium C–Cl, C–Br, and C–I bond lengths from ab initio calculations, microwave and infrared spectroscopies, and empirical correlations. Struct. Chem. 14, 159–174 (2003).

    Article  Google Scholar 

  93. Puzzarini, C. Extrapolation to the complete basis set limit of structural parameters: comparison of different approaches. J. Phys. Chem. A 113, 14530–14535 (2009).

    Article  Google Scholar 

  94. Puzzarini, C. & Barone, V. Extending the molecular size in accurate quantum-chemical calculations: the equilibrium structure and spectroscopic properties of uracil. Phys. Chem. Chem. Phys. 13, 7189–7197 (2011).

    Article  Google Scholar 

  95. Alessandrini, S., Barone, V. & Puzzarini, C. Extension of the “cheap” composite approach to noncovalent interactions: the jun–ChS scheme. J. Chem. Theory Comput. 16, 988–1006 (2020).

    Article  Google Scholar 

  96. Tajti, A. et al. HEAT: high accuracy extrapolated ab initio thermochemistry. J. Chem. Phys. 121, 11599–11613 (2004).

    Article  ADS  Google Scholar 

  97. Heckert, M., Kállay, M., Tew, D. P., Klopper, W. & Gauss, J. Basis-set extrapolation techniques for the accurate calculation of molecular equilibrium geometries using coupled-cluster theory. J. Chem. Phys. 125, 044108 (2006).

    Article  ADS  Google Scholar 

  98. Puzzarini, C., Heckert, M. & Gauss, J. The accuracy of rotational constants predicted by high-level quantum-chemical calculations. I. Molecules containing first-row atoms. J. Chem. Phys. 128, 194108 (2008).

    Article  ADS  Google Scholar 

  99. Yu, Q. et al. Structure, anharmonic vibrational frequencies, and intensities of NNHNN+. J. Phys. Chem. A 119, 11623–11631 (2015).

    Article  Google Scholar 

  100. Boese, A. D. et al. W3 theory: robust computational thermochemistry in the kJ/mol accuracy range. J. Chem. Phys. 120, 4129–4141 (2004).

    Article  ADS  Google Scholar 

  101. Karton, A., Rabinovich, E., Martin, J. M. L. & Ruscic, B. W4 theory for computational thermochemistry: in pursuit of confident sub-kJ/mol predictions. J. Chem. Phys. 125, 144108 (2006).

    Article  ADS  Google Scholar 

  102. Peterson, K. A., Feller, D. & Dixon, D. A. Chemical accuracy in ab initio thermochemistry and spectroscopy: current strategies and future challenges. Theor. Chem. Acc. 131, 1079 (2012).

    Article  Google Scholar 

  103. Shavitt, I. & Bartlett, R. J. in Many-Body Methods in Chemistry and Physics: MBPT and Coupled-Cluster Theory Cambridge Molecular Science (Cambridge Univ. Press, 2009).

  104. Raghavachari, K., Trucks, G. W., Pople, J. A. & Head-Gordon, M. A fifth-order perturbation comparison of electron correlation theories. Chem. Phys. Lett. 589, 37–40 (2013).

    Article  ADS  Google Scholar 

  105. Kong, L., Bischoff, F. A. & Valeev, E. F. Explicitly correlated R12/F12 methods for electronic structure. Chem. Rev. 112, 75–107 (2012).

    Article  Google Scholar 

  106. Neese, F., Hansen, A. & Liakos, D. G. Efficient and accurate approximations to the local coupled cluster singles doubles method using a truncated pair natural orbital basis. J. Chem. Phys. 131, 064103 (2009).

    Article  ADS  Google Scholar 

  107. Neese, F., Wennmohs, F. & Hansen, A. Efficient and accurate local approximations to coupled-electron pair approaches: an attempt to revive the pair natural orbital method. J. Chem. Phys. 130, 114108 (2009). This key publication reports the development and validation of an approach to extend the application of accurate quantum-chemical methods to large molecular systems.

    Article  ADS  Google Scholar 

  108. Becke, A. D. Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 98, 5648–5652 (1993).

    Article  ADS  Google Scholar 

  109. Lee, C., Yang, W. & Parr, R. G. Development of the Colle–Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 37, 785–789 (1988).

    Article  ADS  Google Scholar 

  110. Grimme, S. Semiempirical hybrid density functional with perturbative second-order correlation. J. Chem. Phys. 124, 034108 (2006). This key publication reports the introduction of double-hybrid functionals allowing quantitative spectroscopic studies by DFT.

    Article  ADS  Google Scholar 

  111. Møller, C. & Plesset, M. S. Note on an approximation treatment for many-electron systems. Phys. Rev. 46, 618–622 (1934).

    Article  ADS  MATH  Google Scholar 

  112. Barone, V., Biczysko, M., Bloino, J. & Puzzarini, C. Accurate molecular structures and infrared spectra of trans-2,3-dideuterooxirane, methyloxirane, and trans-2,3-dimethyloxirane. J. Chem. Phys. 141, 034107 (2014).

    Article  ADS  Google Scholar 

  113. Barone, V., Biczysko, M., Bloino, J. & Puzzarini, C. Accurate structure, thermodynamic and spectroscopic parameters from CC and CC/DFT schemes: the challenge of the conformational equilibrium in glycine. Phys. Chem. Chem. Phys. 15, 10094–10111 (2013).

    Article  Google Scholar 

  114. Jurec˘ka, P., Šponer, J., Cˇerný, J. & Hobza, P. Benchmark database of accurate (MP2 and CCSD(T) complete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs. Phys. Chem. Chem. Phys. 8, 1985–1993 (2006).

    Article  Google Scholar 

  115. Řezáč, J., Riley, K. E. & Hobza, P. S66: a well-balanced database of benchmark interaction energies relevant to biomolecular structures. J. Chem. Theory Comput. 7, 2427–2438 (2011).

    Article  Google Scholar 

  116. Řezáč, J., Bím, D., Gutten, O. & Rulíšek, L. Toward accurate conformational energies of smaller peptides and medium-sized macrocycles: MPCONF196 benchmark energy data set. J. Chem. Theory Comput. 14, 1254–1266 (2018).

    Article  Google Scholar 

  117. Goerigk, L. et al. A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry, kinetics and noncovalent interactions. Phys. Chem. Chem. Phys. 19, 32184–32215 (2017).

    Article  Google Scholar 

  118. Biczysko, M., Panek, P., Scalmani, G., Bloino, J. & Barone, V. Harmonic and anharmonic vibrational frequency calculations with the double-hybrid B2PLYP method: analytic second derivatives and benchmark studies. J. Chem. Theory Comput. 6, 2115–2125 (2010).

    Article  Google Scholar 

  119. Barone, V., Biczysko, M. & Bloino, J. Fully anharmonic IR and Raman spectra of medium-size molecular systems: accuracy and interpretation. Phys. Chem. Chem. Phys. 16, 1759–1787 (2014).

    Article  Google Scholar 

  120. Shu, C., Jiang, Z. & Biczysko, M. Toward accurate prediction of amino acid derivatives structure and energetics from DFT: glycine conformers and their interconversions. J. Mol. Model. 26, 129 (2020).

    Article  Google Scholar 

  121. Brémond, É. et al. Benchmarking density functionals on structural parameters of small-/medium-sized organic molecules. J. Chem. Theory Comput. 12, 459–465 (2016).

    Article  Google Scholar 

  122. Risthaus, T., Steinmetz, M. & Grimme, S. Implementation of nuclear gradients of range-separated hybrid density functionals and benchmarking on rotational constants for organic molecules. J. Comput. Chem. 35, 1509–1516 (2014).

    Article  Google Scholar 

  123. Su, N. Q. & Xu, X. Beyond energies: geometry predictions with the XYG3 type of doubly hybrid density functionals. Chem. Commun. 52, 13840–13860 (2016).

    Article  Google Scholar 

  124. Witte, J., Goldey, M., Neaton, J. B. & Head-Gordon, M. Beyond energies: geometries of nonbonded molecular complexes as metrics for assessing electronic structure approaches. J. Chem. Theory Comput. 11, 1481–1492 (2015).

    Article  Google Scholar 

  125. Yu, H. S., He, X., Li, S. L. & Truhlar, D. G. MN15: a Kohn–Sham global-hybrid exchange–correlation density functional with broad accuracy for multi-reference and single-reference systems and noncovalent interactions. Chem. Sci. 7, 5032–5051 (2016).

    Article  Google Scholar 

  126. Boussessi, R., Ceselin, G., Tasinato, N. & Barone, V. DFT meets the segmented polarization consistent basis sets: performances in the computation of molecular structures, rotational and vibrational spectroscopic properties. J. Mol. Struct. 1208, 127886 (2020).

    Article  Google Scholar 

  127. Hanson-Heine, M. W. D. Benchmarking DFT-D dispersion corrections for anharmonic vibrational frequencies and harmonic scaling factors. J. Phys. Chem. A 123, 9800–9808 (2019).

    Article  Google Scholar 

  128. Loos, P.-F., Lipparini, F., Boggio-Pasqua, M., Scemama, A. & Jacquemin, D. A mountaineering strategy to excited states: highly accurate energies and benchmarks for medium sized molecules. J. Chem. Theory Comput. 16, 1711–1741 (2020).

    Article  Google Scholar 

  129. Brémond, E., Savarese, M., Adamo, C. & Jacquemin, D. Accuracy of TD-DFT geometries: a fresh look. J. Chem. Theory Comput. 14, 3715–3727 (2018).

    Article  Google Scholar 

  130. Egidi, F. et al. Effective inclusion of mechanical and electrical anharmonicity in excited electronic states: VPT2–TDDFT route. J. Chem. Theory Comput. 13, 2789–2803 (2017).

    Article  Google Scholar 

  131. Bomble, Y. J. et al. Equation-of-motion coupled-cluster methods for ionized states with an approximate treatment of triple excitations. J. Chem. Phys. 122, 154107 (2005).

    Article  ADS  Google Scholar 

  132. Roos, B. O., Lindh, R., Malmqvist, P. Å., Veryazov, V. & Widmark, P.-O. in Multiconfigurational Quantum Chemistry (Wiley, 2016).

  133. Auer, A. A. et al. A case study of density functional theory and domain-based local pair natural orbital coupled cluster for vibrational effects on EPR hyperfine coupling constants: vibrational perturbation theory versus ab initio molecular dynamics. Mol. Phys. 118, e1797916 (2020).

    Article  ADS  Google Scholar 

  134. Datta, D., Saitow, M., Sandhöfer, B. & Neese, F. 57Fe Mössbauer parameters from domain based local pair-natural orbital coupled-cluster theory. J. Chem. Phys. 153, 204101 (2020).

    Article  ADS  Google Scholar 

  135. Sirohiwal, A., Berraud-Pache, R., Neese, F., Izsák, R. & Pantazis, D. A. Accurate computation of the absorption spectrum of chlorophyll a with pair natural orbital coupled cluster methods. J. Phys. Chem. B 124, 8761–8771 (2020).

    Article  Google Scholar 

  136. Baiardi, A. & Reiher, M. The density matrix renormalization group in chemistry and molecular physics: recent developments and new challenges. J. Chem. Phys. 152, 040903 (2020). This review is the most recent on the use of methods rooted in the density matrix renormalization group for vibrational and electronic spectroscopy.

    Article  Google Scholar 

  137. Andersson, K., Malmqvist, P. Å. & Roos, B. O. Second-order perturbation theory with a complete active space self-consistent field reference function. J. Chem. Phys. 96, 1218–1226 (1992).

    Article  ADS  Google Scholar 

  138. Andersson, K., Malmqvist, P. A., Roos, B. O., Sadlej, A. J. & Wolinski, K. Second-order perturbation theory with a CASSCF reference function. J. Phys. Chem. 94, 5483–5488 (1990).

    Article  Google Scholar 

  139. Angeli, C., Cimiraglia, R., Evangelisti, S., Leininger, T. & Malrieu, J.-P. Introduction of n-electron valence states for multireference perturbation theory. J. Chem. Phys. 114, 10252–10264 (2001).

    Article  ADS  Google Scholar 

  140. Puzzarini, C., Stanton, J. F. & Gauss, J. Quantum-chemical calculation of spectroscopic parameters for rotational spectroscopy. Int. Rev. Phys. Chem. 29, 273–367 (2010). This article presents an authoritative review on computational rotational spectroscopy.

    Article  Google Scholar 

  141. Licari, D., Tasinato, N., Spada, L., Puzzarini, C. & Barone, V. VMS-ROT: a new module of the virtual multifrequency spectrometer for simulation, interpretation, and fitting of rotational spectra. J. Chem. Theory Comput. 13, 4382–4396 (2017).

    Article  Google Scholar 

  142. Lesarri, A., Mata, S., López, J. C. & Alonso, J. L. A laser-ablation molecular-beam Fourier-transform microwave spectrometer: the rotational spectrum of organic solids. Rev. Sci. Instrum. 74, 4799–4804 (2003).

    Article  ADS  Google Scholar 

  143. Mancini, G., Fusè, M., Lazzari, F., Chandramouli, B. & Barone, V. Unsupervised search of low-lying conformers with spectroscopic accuracy: a two-step algorithm rooted into the island model evolutionary algorithm. J. Chem. Phys. 153, 124110 (2020).

    Article  ADS  Google Scholar 

  144. Császár, A. G. et al. The fourth age of quantum chemistry: molecules in motion. Phys. Chem. Chem. Phys. 14, 1085–1106 (2012).

    Article  Google Scholar 

  145. Baiardi, A., Stein, C. J., Barone, V. & Reiher, M. Vibrational density matrix renormalization group. J. Chem. Theory Comput. 13, 3764–3777 (2017).

    Article  Google Scholar 

  146. Carter, S., Sharma, A. R., Bowman, J. M., Rosmus, P. & Tarroni, R. Calculations of rovibrational energies and dipole transition intensities for polyatomic molecules using MULTIMODE. J. Chem. Phys. 131, 224106 (2009).

    Article  ADS  Google Scholar 

  147. Begušic´, T. & Vanícˇek, J. On-the-fly ab initio semiclassical evaluation of vibronic spectra at finite temperature. J. Chem. Phys. 153, 024105 (2020).

    Article  Google Scholar 

  148. Hirshberg, B., Sagiv, L. & Gerber, R. B. Approximate quantum dynamics using ab initio classical separable potentials: spectroscopic applications. J. Chem. Theory Comput. 13, 982–991 (2017).

    Article  Google Scholar 

  149. Gaigeot, M.-P. Theoretical spectroscopy of floppy peptides at room temperature. A DFTMD perspective: gas and aqueous phase. Phys. Chem. Chem. Phys. 12, 3336–3359 (2010).

    Article  Google Scholar 

  150. Pracht, P., Bohle, F. & Grimme, S. Automated exploration of the low-energy chemical space with fast quantum chemical methods. Phys. Chem. Chem. Phys. 22, 7169–7192 (2020).

    Article  Google Scholar 

  151. Del Galdo, S., Fusè, M. & Barone, V. The ONIOM/PMM model for effective yet accurate simulation of optical and chiroptical spectra in solution: camphorquinone in methanol as a case study. J. Chem. Theory Comput. 16, 3294–3306 (2020).

    Article  Google Scholar 

  152. Panek, P. T. & Jacob, C. R. Anharmonic theoretical vibrational spectroscopy of polypeptides. J. Phys. Chem. Lett. 7, 3084–3090 (2016).

    Article  Google Scholar 

  153. Roy, T. K., Sharma, R. & Gerber, R. B. First-principles anharmonic quantum calculations for peptide spectroscopy: VSCF calculations and comparison with experiments. Phys. Chem. Chem. Phys. 18, 1607–1614 (2016).

    Article  Google Scholar 

  154. Barone, V., Improta, R. & Rega, N. Quantum mechanical computations and spectroscopy: from small rigid molecules in the gas phase to large flexible molecules in solution. Acc. Chem. Res. 41, 605–616 (2008).

    Article  Google Scholar 

  155. Balabin, R. M. Conformational equilibrium in glycine: focal-point analysis and ab initio limit. Chem. Phys. Lett. 479, 195–200 (2009).

    Article  ADS  Google Scholar 

  156. Bazsó, G., Magyarfalvi, G. & Tarczay, G. Tunneling lifetime of the ttc/VIp conformer of glycine in low-temperature matrices. J. Phys. Chem. A 116, 10539–10547 (2012).

    Article  Google Scholar 

  157. Stepanian, S. G. et al. Matrix-isolation infrared and theoretical studies of the glycine conformers. J. Phys. Chem. A 102, 1041–1054 (1998).

    Article  Google Scholar 

  158. Balabin, R. M. Conformational equilibrium in glycine: experimental jet-cooled Raman spectrum. J. Phys. Chem. Lett. 1, 20–23 (2010).

    Article  Google Scholar 

  159. Lockyear, J. F. et al. Isomer specific product detection in the reaction of CH with acrolein. J. Phys. Chem. A 117, 11013–11026 (2013).

    Article  Google Scholar 

  160. Barone, V., Biczysko, M., Borkowska-Panek, M. & Bloino, J. A multifrequency virtual spectrometer for complex bio-organic systems: vibronic and environmental effects on the UV/Vis spectrum of chlorophyll-a. ChemPhysChem 15, 3355–3364 (2014).

    Article  Google Scholar 

  161. Gouterman, M. Spectra of porphyrins. J. Mol. Spectrosc. 6, 138–163 (1961).

    Article  ADS  Google Scholar 

  162. Rätsep, M. et al. Absorption-emission symmetry breaking and the different origins of vibrational structures of the 1Qy and 1Qx electronic transitions of pheophytin a. J. Chem. Phys. 151, 165102 (2019).

    Article  ADS  Google Scholar 

  163. Huang, X., Braams, B. J. & Bowman, J. M. Ab initio potential energy and dipole moment surfaces for H5O2+. J. Chem. Phys. 122, 044308 (2005).

    Article  ADS  Google Scholar 

  164. Petit, A. S., Ford, J. E. & McCoy, A. B. Simultaneous evaluation of multiple rotationally excited states of H3 + , H3O+, and CH5+ using diffusion Monte Carlo. J. Phys. Chem. A 118, 7206–7220 (2014).

    Article  Google Scholar 

  165. Petit, A. S. & McCoy, A. B. Diffusion Monte Carlo approaches for evaluating rotationally excited states of symmetric top molecules: application to H3O+ and D3O+. J. Phys. Chem. A 113, 12706–12714 (2009).

    Article  Google Scholar 

  166. Sandler, P., Buch, V. & Clary, D. C. Calculation of expectation values of molecular systems using diffusion Monte Carlo in conjunction with the finite field method. J. Chem. Phys. 101, 6353–6355 (1994).

    Article  ADS  Google Scholar 

  167. Paesani, F. & Whaley, K. B. Rotational excitations of N2O in small helium clusters and the role of Bose permutation symmetry. J. Chem. Phys. 121, 5293–5311 (2004).

    Article  ADS  Google Scholar 

  168. Cho, H. M. & Singer, S. J. Correlation function quantum Monte Carlo study of the excited vibrational states of H5O2+. J. Phys. Chem. A 108, 8691–8702 (2004).

    Article  Google Scholar 

  169. McCoy, A. B., Diken, E. G. & Johnson, M. A. Generating spectra from ground-state wave functions: unraveling anharmonic effects in the OH−·H2O vibrational predissociation spectrum. J. Phys. Chem. A 113, 7346–7352 (2009).

    Article  Google Scholar 

  170. Polavarapu, P. L. et al. A single chiroptical spectroscopic method may not be able to establish the absolute configurations of diastereomers: dimethylesters of hibiscus and garcinia acids. J. Phys. Chem. A 115, 5665–5673 (2011).

    Article  Google Scholar 

  171. Debie, E. et al. A confidence level algorithm for the determination of absolute configuration using vibrational circular dichroism or Raman optical activity. ChemPhysChem 12, 1542–1549 (2011).

    Article  Google Scholar 

  172. Fusè, M. et al. Unbiased determination of absolute configurations by vis-à-vis comparison of experimental and simulated spectra: the challenging case of diplopyrone. J. Phys. Chem. B 123, 9230–9237 (2019).

    Article  Google Scholar 

  173. Bogaerts, J. et al. A combined Raman optical activity and vibrational circular dichroism study on artemisinin-type products. Phys. Chem. Chem. Phys. 22, 18014–18024 (2020). This very recent study demonstrates the combined use of two chiroptical spectroscopic methods, VCD and ROA, in determining the absolute configuration of a molecule with seven chiral centres.

    Article  Google Scholar 

  174. Johnson, J. L. et al. Dissymmetry factor spectral analysis can provide useful diastereomer discrimination: chiral molecular structure of an analogue of (–)-crispine A. ACS Omega 4, 6154–6164 (2019).

    Article  Google Scholar 

  175. Hopmann, K. H. et al. Determining the absolute configuration of two marine compounds using vibrational chiroptical spectroscopy. J. Org. Chem 77, 858–869 (2012).

    Article  Google Scholar 

  176. Covington, C. L. & Polavarapu, P. L. Similarity in dissymmetry factor spectra: a quantitative measure of comparison between experimental and predicted vibrational circular dichroism. J. Phys. Chem. A 117, 3377–3386 (2013).

    Article  Google Scholar 

  177. Nicu, V. P. & Baerends, E. J. Robust normal modes in vibrational circular dichroism spectra. Phys. Chem. Chem. Phys. 11, 6107–6118 (2009).

    Article  Google Scholar 

  178. Tommasini, M. et al. Mode robustness in Raman optical activity. J. Chem. Theory Comput. 10, 5520–5527 (2014).

    Article  Google Scholar 

  179. Freedman, T. B., Shih, M.-L., Lee, E. & Nafie, L. A. Electron transition current density in molecules. 3. Ab initio calculations for vibrational transitions in ethylene and formaldehyde. J. Am. Chem. Soc. 119, 10620–10626 (1997).

    Article  Google Scholar 

  180. Fusè, M., Egidi, F. & Bloino, J. Vibrational circular dichroism under the quantum magnifying glass: from the electronic flow to the spectroscopic observable. Phys. Chem. Chem. Phys. 21, 4224–4239 (2019).

    Article  Google Scholar 

  181. Hug, W. Visualizing Raman and Raman optical activity generation in polyatomic molecules. Chem. Phys. 264, 53–69 (2001).

    Article  Google Scholar 

  182. Yamamoto, S. in Introduction to Astrochemistry: Chemical Evolution from Interstellar Clouds to Star and Planet Formation (Springer, 2017).

  183. Jørgensen, J. K., Belloche, A. & Garrod, R. T. Astrochemistry during the formation of stars. Annu. Rev. Astron. Astrophys. 58, 727–778 (2020).

    Article  ADS  Google Scholar 

  184. McGuire, B. A. 2018 census of interstellar, circumstellar, extragalactic, protoplanetary disk, and exoplanetary molecules. Astrophys. J., Suppl. Ser. 239, 17 (2018).

    Article  ADS  Google Scholar 

  185. Herbst, E. & van Dishoeck, E. F. Complex organic interstellar molecules. Annu. Rev. Astron. Astrophys. 47, 427–480 (2009).

    Article  ADS  Google Scholar 

  186. Lattelais, M., Pauzat, F., Ellinger, Y. & Ceccarelli, C. Interstellar complex organic molecules and the minimum energy principle. Astrophys. J. 696, L133–L136 (2009).

    Article  ADS  Google Scholar 

  187. Puzzarini, C. & Barone, V. A never-ending story in the sky: the secrets of chemical evolution. Phys. Life Rev. 32, 59–94 (2020). This recent review addresses the role of spectroscopic investigation for the characterization of molecules of astrochemical interest and their detection in space.

    Article  ADS  Google Scholar 

  188. Cernicharo, J., Guélin, M., Agúndez, M., McCarthy, M. C. & Thaddeus, P. Detection of C5N– and vibrationally excited C6H in IRC+ 10216. Astrophys. J. 688, L83–L86 (2008).

    Article  ADS  Google Scholar 

  189. Botschwina, P. & Oswald, R. Carbon chains of type C2n+1N− (n = 2–6): a theoretical study of potential interstellar anions. J. Chem. Phys. 129, 044305 (2008).

    Article  ADS  Google Scholar 

  190. Cazzoli, G., Cludi, L., Buffa, G. & Puzzarini, C. Precise THz measurements of HCO+, N2H+ and CF+ for astrophysical observations. Astrophys. J. Suppl. Ser. 203, 11 (2012).

    Article  ADS  Google Scholar 

  191. Guzmán, V. et al. The hyperfine structure in the rotational spectrum of CF+. Astron. Astrophys. 548, A94 (2012).

    Article  Google Scholar 

  192. Kłos, J. & Lique, F. in Cold Chemistry: Molecular Scattering and Reactivity Near Absolute Zero Ch. 2 (eds Dulieu, O. & Osterwalder, A.) 46–91 (RSC, 2018).

  193. Borrego-Varillas, R. et al. Two-dimensional UV spectroscopy: a new insight into the structure and dynamics of biomolecules. Chem. Sci. 10, 9907–9921 (2019).

    Article  Google Scholar 

  194. East, K. W. et al. NMR and computational methods for molecular resolution of allosteric pathways in enzyme complexes. Biophys. Rev. 12, 155–174 (2020).

    Article  Google Scholar 

  195. Huang, J., Zhou, Y. & Xie, D. Predicted infrared spectra in the HF stretching band of the H2–HF complex. J. Chem. Phys. 149, 094307 (2018).

    Article  ADS  Google Scholar 

  196. Clary, D. C. & Nesbitt, D. J. Calculation of vibration–rotation spectra for rare gas–HCl complexes. J. Chem. Phys. 90, 7000–7013 (1989).

    Article  ADS  Google Scholar 

  197. Felker, P. M. & Bacˇic´, Z. H2O–CO and D2O–CO complexes: intra- and intermolecular rovibrational states from full-dimensional and fully coupled quantum calculations. J. Chem. Phys. 153, 074107 (2020).

    Article  Google Scholar 

  198. Keutsch, F. N. & Saykally, R. J. Water clusters: untangling the mysteries of the liquid, one molecule at a time. Proc. Natl Acad. Sci. USA. 98, 10533–10540 (2001). This comprehensive review discusses how theory is used to predict and interpret experimental measurements of spectra for water clusters.

    Article  ADS  Google Scholar 

  199. Mukhopadhyay, A., Xantheas, S. S. & Saykally, R. J. The water dimer II: theoretical investigations. Chem. Phys. Lett. 700, 163–175 (2018).

    Article  ADS  Google Scholar 

  200. Schwan, R. et al. Observation of the low-frequency spectrum of the water dimer as a sensitive test of the water dimer potential and dipole moment surfaces. Angew. Chem. Int. Ed. 58, 13119–13126 (2019).

    Article  Google Scholar 

  201. Cisneros, G. A. et al. Modeling molecular interactions in water: from pairwise to many-body potential energy functions. Chem. Rev. 116, 7501–7528 (2016).

    Article  Google Scholar 

  202. Mallory, J. D. & Mandelshtam, V. A. Diffusion Monte Carlo studies of MB-pol (H2O)2−6 and (D2O)2−6 clusters: structures and binding energies. J. Chem. Phys. 145, 064308 (2016).

    Article  ADS  Google Scholar 

  203. Liu, K. et al. Characterization of a cage form of the water hexamer. Nature 381, 501–503 (1996).

    Article  ADS  Google Scholar 

  204. Lee, V. G. M., Vetterli, N. J., Boyer, M. A. & McCoy, A. B. Diffusion Monte Carlo studies on the detection of structural changes in the water hexamer upon isotopic substitution. J. Phys. Chem. A 124, 6903–6912 (2020).

    Article  Google Scholar 

  205. Richardson, J. O. et al. Concerted hydrogen-bond breaking by quantum tunneling in the water hexamer prism. Science 351, 1310–1313 (2016).

    Article  ADS  Google Scholar 

  206. Vaillant, C. L., Wales, D. J. & Althorpe, S. C. Tunneling splittings in water clusters from path integral molecular dynamics. J. Phys. Chem. Lett. 10, 7300–7304 (2019).

    Article  Google Scholar 

  207. Gaigeot, M. P. Unravelling the conformational dynamics of the aqueous alanine dipeptide with first-principle molecular dynamics. J. Phys. Chem. B 113, 10059–10062 (2009).

    Article  Google Scholar 

  208. Clary, D. C., Benoit, D. M. & van Mourik, T. H-Densities:  a new concept for hydrated molecules. Acc. Chem. Res. 33, 441–447 (2000).

    Article  Google Scholar 

  209. Fornaro, T., Burini, D., Biczysko, M. & Barone, V. Hydrogen-bonding effects on infrared spectra from anharmonic computations: uracil–water complexes and uracil dimers. J. Phys. Chem. A 119, 4224–4236 (2015).

    Article  Google Scholar 

  210. Bec´, K. B. & Huck, C. W. Breakthrough potential in near-infrared spectroscopy: spectra simulation. a review of recent developments. Front. Chem. 7, 48 (2019). This article presents a detailed review on the computational methods used for calculating the near infrared spectra of larger polyatomic molecules.

    Article  ADS  Google Scholar 

  211. Benoit, D. M. Rationalising the vibrational spectra of biomolecules using atomistic simulations. Front. Biosci. 14, 4229–4241 (2009).

    Article  Google Scholar 

  212. Bec´, K. B., Grabska, J., Ozaki, Y., Czarnecki, M. A. & Huck, C. W. Simulated NIR spectra as sensitive markers of the structure and interactions in nucleobases. Sci. Rep. 9, 17398 (2019).

    Article  ADS  Google Scholar 

  213. Atanasov, M., Ganyushin, D., Sivalingam, K. & Neese, F. in Molecular Electronic Structures of Transition Metal Complexes II Ch. 6 (eds Mingos, D. M. P., Day, P. & Dahl, J. P.) 149–220 (Springer, 2012).

  214. Singh, S. K., Atanasov, M. & Neese, F. Challenges in multireference perturbation theory for the calculations of the g-tensor of first-row transition-metal complexes. J. Chem. Theory Comput. 14, 4662–4677 (2018).

    Article  Google Scholar 

  215. Maganas, D. et al. First principles calculations of the structure and V L-edge X-ray absorption spectra of V2O5 using local pair natural orbital coupled cluster theory and spin–orbit coupled configuration interaction approaches. Phys. Chem. Chem. Phys. 15, 7260–7276 (2013).

    Article  Google Scholar 

  216. Roemelt, M., Maganas, D., DeBeer, S. & Neese, F. A combined DFT and restricted open-shell configuration interaction method including spin-orbit coupling: spplication to transition metal L-edge X-ray absorption spectroscopy. J. Chem. Phys. 138, 204101 (2013).

    Article  ADS  Google Scholar 

  217. Neese, F. A critical evaluation of DFT, including time-dependent DFT, applied to bioinorganic chemistry. J. Biol. Inorg. Chem. 11, 702–711 (2006).

    Article  Google Scholar 

  218. Neese, F. High-level spectroscopy, quantum chemistry, and catalysis: not just a passing fad. Angew. Chem. Int. Ed. 56, 11003–11010 (2017).

    Article  Google Scholar 

  219. Neese, F., Atanasov, M., Bistoni, G., Maganas, D. & Ye, S. Chemistry and quantum mechanics in 2019: give us insight and numbers. J. Am. Chem. Soc. 141, 2814–2824 (2019).

    Article  Google Scholar 

  220. Zadrozny, J. M. & Long, J. R. Slow magnetic relaxation at zero field in the tetrahedral complex [Co(SPh)4]2–. J. Am. Chem. Soc. 133, 20732–20734 (2011).

    Article  Google Scholar 

  221. Neese, F. & Pantazis, D. A. What is not required to make a single molecule magnet. Faraday Discuss. 148, 229–238 (2011).

    Article  ADS  Google Scholar 

  222. Suturina, E. A. et al. Magneto-structural correlations in pseudotetrahedral forms of the [Co(SPh)4]2– complex probed by magnetometry, MCD spectroscopy, advanced EPR techniques, and ab initio electronic structure calculations. Inorg. Chem. 56, 3102–3118 (2017).

    Article  Google Scholar 

  223. Suturina, E. A., Maganas, D., Bill, E., Atanasov, M. & Neese, F. Magneto-structural correlations in a series of pseudotetrahedral [CoII(XR)4]2– single molecule magnets: an ab initio ligand field study. Inorg. Chem. 54, 9948–9961 (2015).

    Article  Google Scholar 

  224. Rechkemmer, Y. et al. A four-coordinate Cobalt(II) single-ion magnet with coercivity and a very high energy barrier. Nat. Commun. 7, 10467 (2016).

    Article  ADS  Google Scholar 

  225. Penocchio, E., Piccardo, M. & Barone, V. Semiexperimental equilibrium structures for building blocks of organic and biological molecules: the B2PLYP Route. J. Chem. Theory Comput. 11, 4689–4707 (2015).

    Article  Google Scholar 

  226. Kodrycka, M. & Patkowski, K. Platinum, gold, and silver standards of intermolecular interaction energy calculations. J. Chem. Phys. 151, 070901 (2019).

    Article  ADS  Google Scholar 

  227. Alessandrini, S., Gauss, J. & Puzzarini, C. Accuracy of rotational parameters predicted by high-level quantum-chemical calculations: case study of sulfur-containing molecules of astrochemical interest. J. Chem. Theory Comput. 14, 5360–5371 (2018).

    Article  Google Scholar 

  228. Dral, P. O. Quantum chemistry in the age of machine learning. J. Phys. Chem. Lett. 11, 2336–2347 (2020). This article is a general introduction on the use of machine learning in quantum chemistry.

    Article  Google Scholar 

  229. Liakos, D. G., Guo, Y. & Neese, F. Comprehensive benchmark results for the domain based local pair natural orbital coupled cluster method (DLPNO-CCSD(T)) for closed- and open-shell systems. J. Phys. Chem. A 124, 90–100 (2020).

    Article  Google Scholar 

  230. Nagy, P. R. & Kállay, M. Approaching the basis set limit of CCSD(T) energies for large molecules with local natural orbital coupled-cluster methods. J. Chem. Theory Comput. 15, 5275–5298 (2019).

    Article  Google Scholar 

  231. Sibert III, E. L. Modeling vibrational anharmonicity in infrared spectra of high frequency vibrations of polyatomic molecules. J. Chem. Phys. 150, 090901 (2019).

    Article  ADS  Google Scholar 

  232. Basdogan, Y. et al. Machine learning-guided approach for studying solvation environments. J. Chem. Theory Comput. 16, 633–642 (2020).

    Article  Google Scholar 

  233. Hodecker, M., Biczysko, M., Dreuw, A. & Barone, V. Simulation of vacuum UV absorption and electronic circular dichroism spectra of methyl oxirane: the role of vibrational effects. J. Chem. Theory Comput. 12, 2820–2833 (2016).

    Article  Google Scholar 

  234. Puzzarini, C., Biczysko, M., Bloino, J. & Barone, V. Accurate spectroscopic characterization of oxirane: a valuable route to its identification in Titan’s atmosphere and the assignment of unidentified infrared bands. Astrophys. J. 785, 107 (2014).

    Article  ADS  Google Scholar 

  235. Karton, A., Sylvetsky, N. & Martin, J. M. L. W4-17: aA diverse and high-confidence dataset of atomization energies for benchmarking high-level electronic structure methods. J. Comput. Chem. 38, 2063–2075 (2017).

    Article  Google Scholar 

  236. Mayhall, N. J. & Raghavachari, K. Molecules-in-molecules: an extrapolated fragment-based approach for accurate calculations on large molecules and materials. J. Chem. Theory Comput. 7, 1336–1343 (2011).

    Article  Google Scholar 

  237. Santra, G., Sylvetsky, N. & Martin, J. M. L. Minimally empirical double-hybrid functionals trained against the GMTKN55 database: revDSD-PBEP86-D4, revDOD-PBE-D4, and DOD-SCAN-D4. J. Phys. Chem. A 123, 5129–5143 (2019).

    Article  Google Scholar 

  238. Kussmann, J. & Ochsenfeld, C. Preselective screening for linear-scaling exact exchange-gradient calculations for graphics processing units and general strong-scaling massively parallel calculations. J. Chem. Theory Comput. 11, 918–922 (2015).

    Article  Google Scholar 

  239. Doser, B., Lambrecht, D. S. & Ochsenfeld, C. Tighter multipole-based integral estimates and parallel implementation of linear-scaling AO–MP2 theory. Phys. Chem. Chem. Phys. 10, 3335–3344 (2008).

    Article  Google Scholar 

  240. Ma, Q. & Werner, H.-J. Scalable electron correlation methods. 7. Local open-shell coupled-cluster methods using pair natural orbitals: PNO-RCCSD and PNO-UCCSD. J. Chem. Theory Comput. 16, 3135–3151 (2020).

    Article  Google Scholar 

  241. Becca, F. & Sorella, S. in Quantum Monte Carlo Approaches for Correlated Systems (Cambridge Univ. Press, 2017).

  242. Puzzarini, C. & Barone, V. The challenging playground of astrochemistry: an integrated rotational spectroscopy—quantum chemistry strategy. Phys. Chem. Chem. Phys. 22, 6507–6523 (2020).

    Article  Google Scholar 

  243. Biczysko, M., Krupa, J. & Wierzejewska, M. Theoretical studies of atmospheric molecular complexes interacting with NIR to UV light. Faraday Discuss. 212, 421–441 (2018).

    Article  ADS  Google Scholar 

  244. Raucci, U. et al. Ab-initio molecular dynamics and hybrid explicit-implicit solvation model for aqueous and nonaqueous solvents: GFP chromophore in water and methanol solution as case study. J. Comput. Chem. 46, 2228–2239 (2020).

    Article  Google Scholar 

  245. Zhang, W., Kong, X., Liu, S. & Zhao, Y. Multi-coefficients correlation methods. WIREs Comput. Mol. Sci. 10, e1474 (2020).

    Article  Google Scholar 

  246. Gagliardi, L. et al. Multiconfiguration pair-density functional theory: a new way to treat strongly correlated systems. Acc. Chem. Res. 50, 66–73 (2017).

    Article  Google Scholar 

  247. Bannwarth, C. et al. Extended tight-binding quantum chemistry methods. WIREs Comput. Mol. Sci. 11, e01493 (2020).

    Google Scholar 

  248. Loos, P.-F., Scemama, A. & Jacquemin, D. The quest for highly accurate excitation energies: a computational perspective. J. Phys. Chem. Lett. 11, 2374–2383 (2020). This recent perspective article presents accurate computations of excitation energies.

    Article  Google Scholar 

  249. Casanova-Páez, M. & Goerigk, L. Assessing the Tamm–Dancoff approximation, singlet–singlet, and singlet–triplet excitations with the latest long-range corrected double-hybrid density functionals. J. Chem. Phys. 153, 064106 (2020).

    Article  Google Scholar 

  250. Mutter, S. T. et al. Conformational dynamics of carbohydrates: Raman optical activity of d-glucuronic acid and N-acetyl-d-glucosamine using a combined molecular dynamics and quantum chemical approach. Phys. Chem. Chem. Phys. 17, 6016–6027 (2015).

    Article  Google Scholar 

  251. Lee, V. G. M. & McCoy, A. B. An efficient approach for studies of water clusters using diffusion Monte Carlo. J. Phys. Chem. A 123, 8063–8070 (2019).

    Article  Google Scholar 

  252. Zhao, L. et al. Real-time time-dependent nuclear–electronic orbital approach: dynamics beyond the Born–Oppenheimer approximation. J. Phys. Chem. Lett. 11, 4052–4058 (2020).

    Article  Google Scholar 

  253. Petrenko, T. & Rauhut, G. A general approach for calculating strongly anharmonic vibronic spectra with a high density of states: the X˜2B1 ← X˜1A1 photoelectron spectrum of difluoromethane. J. Chem. Theory Comput. 13, 5515–5527 (2017).

    Article  Google Scholar 

  254. Cerezo, J., Aranda, D., Avila Ferrer, F. J., Prampolini, G. & Santoro, F. Adiabatic-molecular dynamics generalized vertical hessian approach: a mixed quantum classical method to compute electronic spectra of flexible molecules in the condensed phase. J. Chem. Theory Comput. 16, 1215–1231 (2020).

    Article  Google Scholar 

  255. Jasper, A. W., Harding, L. B., Knight, C. & Georgievskii, Y. Anharmonic rovibrational partition functions at high temperatures: tests of reduced-dimensional models for systems with up to three fluxional modes. J. Phys. Chem. A 123, 6210–6228 (2019).

    Article  Google Scholar 

  256. Burd, T. A. H. & Clary, D. C. Analytic route to tunneling splittings using semiclassical perturbation theory. J. Chem. Theory Comput. 16, 3486–3493 (2020).

    Article  Google Scholar 

  257. O’Connor, M. B. et al. Interactive molecular dynamics in virtual reality from quantum chemistry to drug binding: an open-source multi-person framework. J. Chem. Phys. 150, 220901 (2019).

    Article  ADS  Google Scholar 

  258. McArdle, S., Endo, S., Aspuru-Guzik, A., Benjamin, S. C. & Yuan, X. Quantum computational chemistry. Rev. Mod. Phys. 92, 015003 (2020).

    Article  ADS  MathSciNet  Google Scholar 

  259. Barone, V. et al. Implementation and validation of a multi-purpose virtual spectrometer for large systems in complex environments. Phys. Chem. Chem. Phys. 14, 12404–12422 (2012).

    Article  Google Scholar 

  260. Dixon, J. M., Taniguchi, M. & Lindsey, J. S. PhotochemCAD 2: a refined program with accompanying spectral databases for photochemical calculations. Photochem. Photobiol. 81, 212–213 (2005).

    Article  Google Scholar 

  261. Caselli, P., Myers, P. C. & Thaddeus, P. Radio-astronomical spectroscopy of the hyperfine structure of N2H+. Astrophys. J. 455, L77–L80 (1995).

    Article  ADS  Google Scholar 

  262. Neese, F. Sum-over-states based multireference ab initio calculation of EPR spin Hamiltonian parameters for transition metal complexes. A case study. Magn. Reson. Chem. 42, S187–S198 (2004).

    Article  Google Scholar 

Download references

Acknowledgements

In Italy, the work described in this Primer was supported by MIUR PRIN funds (grants 2015F59J3R, 2017A4XRCA), the Italian Space Agency (ASI) (‘Life in Space’ project, N. 2019-3-U.0) and SMART@SNS Laboratory for high-performance computing facilities). F.N. is extremely grateful for generous financial support by the Max Planck Society that enables us to follow curiosity-driven research. The science described in this Primer has also been supported by the German Science Foundation through the cluster of excellence programme Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) im Rahmen der Exzellenzstrategie des Bundes und der Länder — EXC 2033 — Projektnummer 390677874. A.B.M. and R.J.D. thank National Science Foundation (NSF) CHE-1856125; R.J.D. was supported by a fellowship from The Molecular Sciences Software Institute under NSF grant OAC-1547580.

Author information

Authors and Affiliations

  1. Scuola Normale Superiore, Pisa, Italy

    Vincenzo Barone & Silvia Alessandrini

  2. International Centre for Quantum and Molecular Structures, Physics Department, Shanghai University, Shanghai, China

    Malgorzata Biczysko

  3. Gaussian Inc., Wallingford, CT, USA

    James R. Cheeseman

  4. Physical and Theoretical Chemical Laboratory, University of Oxford, Oxford, UK

    David C. Clary

  5. Department of Chemistry, University of Washington, Seattle, WA, USA

    Anne B. McCoy & Ryan J. DiRisio

  6. Max-Planck-Institut für Kohlenforschung, Mülheim an der Ruhr, Germany

    Frank Neese

  7. Department of Chemistry ‘Giacomo Ciamician’, University of Bologna, Bologna, Italy

    Mattia Melosso & Cristina Puzzarini

Authors
  1. Vincenzo Barone
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Silvia Alessandrini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Malgorzata Biczysko
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. James R. Cheeseman
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. David C. Clary
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Anne B. McCoy
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Ryan J. DiRisio
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Frank Neese
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Mattia Melosso
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Cristina Puzzarini
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Introduction (V.B., M.B., F.N. and C.P.); Experimentation (V.B., M.B., J.R.C., A.B.M., F.N. and C.P.); Results (M.M., C.P., V.B., M.B., A.B.M., R.J.D. and J.R.C.); Applications (M.M., C.P., D.C.C. and F.N.); Reproducibility and data deposition (S.A., V.B., M.B., A.B.M. and C.P.); Limitations and optimizations (S.A., V.B., M.B., J.R.C. and C.P.); Outlook (V.B.); Overview of the Primer (C.P.).

Corresponding author

Correspondence to Cristina Puzzarini.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information

Nature Reviews Methods Primers thanks M. Hanson-Heine, J. Kästner, J. Tennyson and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Related Links

CFOUR: http://www.cfour.de/

Database of semi-experimental equilibrium structures: https://smart.sns.it/molecules/

Gaussian: https://gaussian.com/

Molpro: https://www.molpro.net

MolSSI workshop: https://molssi.org/2019/08/19/molssi-workshop-rovibrational-molecular-spectroscopy/

NWCHEM: https://nwchemgit.github.io/

ORCA (academic): https://orcaforum.kofo.mpg.de/app.php/portal

ORCA (commercial): https://www.faccts.de

PSI4: http://www.psicode.org

QChem: http://www.q-chem.com/

SMART@SNS Laboratory: http://smart.sns.it

Supplementary information

Glossary

Rotational spectroscopy

Spectroscopy using the microwave region of the electromagnetic field to study the excitation of the rotational states of molecules.

Electron spin resonance

A spectroscopic technique equivalent to NMR but dealing with excitation of the electronic spins in open-shell systems.

Quantum chemistry

The application of quantum mechanics to chemistry.

Conformers

Isomers that can be converted into another by rotation about a formally single bond.

Mössbauer isomer shifts

Shifts in resonance frequency of the nuclear gamma-ray transition in a Mössbauer active isotope (for example, 57Fe) caused by its interaction with the molecular environment.

Infrared spectroscopy

Spectroscopy using the infrared region of the electromagnetic field to study the excitation of the vibrational states of molecules.

Raman spectroscopy

Rotational or vibrational spectroscopy that exploits the Raman effect (inelastic scattering).

Schrödinger equation

Equation associated with the Hamiltonian operator: its resolution provides the allowed energy levels (eigenvalues) and the corresponding wave functions (eigenfunctions).

Diffusion Monte Carlo

A Monte Carlo-based approach for obtaining the exact ground-state solution to Eq. 2.

Absolute configuration

The spatial arrangement of atoms in a chiral system and its stereochemical description.

Energy levels

According to quantum mechanics (see above), the allowed energy for a system bound is not continuous but discretized in energy levels.

Hamiltonian

In quantum mechanics, the operator corresponding to the energy of a system.

Position arrays

Arrays containing the coordinates of the position of a specific point in a multidimensional space.

Wave function

A mathematical description of the quantum state of an isolated quantum system resulting from solving the corresponding Schrödinger equation.

Born–Oppenheimer approximation

The assumption that the motion of atomic nuclei and electrons can be treated separately, based on the much larger mass of nuclei.

Potential energy surface

A multi-dimensional, hyper-surface that describes the variations of the electronic energy of a system in terms of suitable nuclear coordinates.

Normal coordinates

Linear combinations of mass-weighted displacement coordinates (usually Cartesian). The motion described by a normal coordinate is called a normal mode.

Spectroscopic transitions

The passage between two energy levels, that is, from an initial to a final state, detected by a spectroscopic technique.

Ro-vibrational spectroscopy

Spectroscopy dealing with rotational and vibrational states of molecules.

Contact transformation

Unitary transformation with an exponential operator U = exp(iS), where S is Hermitean and antisymmetrical with respect to time reversal, thus ensuring that U is unitary and invariant to time reversal.

Anharmonic

Deviation from the harmonic-oscillator behaviour.

Hyperfine structure

Interactions of the molecular electric and/or magnetic fields with the nuclear or electron (for open-shell species) moments produce a splitting of the rotational energy levels, which in turn leads to a splitting of the rotational transitions. This splitting is called the hyperfine structure.

Coriolis couplings

Interactions between the angular momentum of a vibrational mode and the rotational angular momentum.

Rigid-rotor harmonic-oscillator model

A reference model in which a molecular system as a whole is described in terms of a rigid rotating object and in terms of decoupled harmonic oscillators for its vibrational motion.

Fundamental bands

Vibrational transitions from the vibrational ground state to the first excited state of a given vibrational mode (a one-quanta transition).

Vibrational circular dichroism

Vibrational version of circular dichroism.

Vibrational perturbation theory to the second order

Exploitation of perturbation theory to the second order to treat vibrational motions.

Normal modes

Vibrational motion of molecules where all atoms vibrate in phase with the same frequency but with different amplitudes, and the centre of mass remains fixed.

Overtones

Vibrational transitions involving the excitation of two or more quanta of a given vibration mode (that is, the quantum number describing the vibrational energy levels change varies by two or more).

Combination bands

Observed when two or more vibrations are excited simultaneously.

Double-perturbative approach

Simultaneous perturbative treatment of the energy and one property (for example, the electric dipole moment in infrared spectroscopy) around a stationary point.

Property surface

(Multidimensional). The variations of a property as a function of suitable nuclear coordinates.

Large amplitude motions

Molecular vibrations whose amplitude is so large that the harmonic oscillator model is no longer a reliable zero-order approximation.

Density functional theory

A quantum-mechanical method in which the properties of a many-electron system are determined using functionals (that is, functions of another function) of the spatially dependent electron density and, possibly, its derivatives.

Vibrational self-consistent field

Exploitation of the self-consistent model to treat vibrational motion.

Vibrational configuration interaction

Exploitation of the configuration interaction model to treat vibrational motions.

Vibronic spectroscopy

Spectroscopy involving the simultaneous excitations of vibrational and electronic states of molecules.

One-photon absorption

A spectroscopic technique in which one-photon absorption leads from the electronic ground state to an excited electronic state.

One-photon emission

A spectroscopic technique in which one-photon emission leads from an excited electronic state to a less-excited (lower energy, usually the ground) state.

Electronic circular dichroism

Electronic version of circular dichroism.

Optical rotation

The rotation angle of the polarization plane of polarized light issuing from its passage through a layer or a liquid, determined by the concentration of chiral molecules and their structure in a substance.

Raman optical activity

Vibrational spectroscopy based on the differential Raman scattering of left and right circularly polarized light due to molecular chirality.

Optical rotatory dispersion

The variation of the optical rotation of a substance with a change in the wavelength of light.

Line-shape function

A mathematical function (usually Gaussian, Lorentzian or a combination of both) describing phenomenologically the shape of a spectral band.

Imaginary-time

Time rotated into the imaginary plane via Wick rotation in DMC, τ = it/ℏ.

Coupled-cluster theory

A hierarchy of electron correlation methods that, by means of an exponential Ansatz, systematically converge to the exact solution of the molecular Schrödinger equation starting from the independent particle Hartree–Fock model.

CCSD(T)

A coupled-cluster method that considers full account of single and double excitations and a perturbative treatment of triple excitations.

Electron correlation

The effects of electron–electron interactions beyond the mean field Hartree–Fock model.

Domain-based pair natural orbitals

Electron pair-specific localized natural orbitals expanded in a set of local atomic orbitals belonging to pair-specific domains.

Global-hybrid or double-hybrid density functionals

Families of density functionals including a percentage of Hartree–Fock exchange (hybrid) and MP2-type correlation (only double-hybrid).

Møller–Plesset theory to the second order

Møller–Plesset theory including many-body effects on top of the mean field Hartree–Fock reference wave function up to the second order of perturbation theory.

Equation of motion

In a quantum chemistry context, a methodology for treatment of electronically excited or ionized states.

Density matrix renormalization group

A very efficient numerical variational technique devised to obtain the lowest-energy wave function of a given Hamiltonian expressed in terms of a matrix product state.

CASPT2

A specific generalization of Møller–Plesset theory to the second order to multiconfigurational reference wave functions.

NEVPT2

A variant of second-order multi-reference perturbation theory similar to CASPT2.

CIS

Configuration interaction (that is, mixing of ground and excited electronic states) including only single excitations from a reference Slater determinant.

Multi-reference configuration interaction

Extension of the configuration interaction approach to multi-reference wave functions.

Tamm–Dancoff approximation

From a practical point of view, a synonym of CIS.

Isotopologue

Isotopic species of a molecule.

Harmonic approximation

A model in which the vibrational motion is described in terms of masses attached to a spring, whose energy is governed by a quadratic potential.

Small amplitude motions

Molecular vibrations whose amplitude is small enough that the harmonic oscillator is a reliable zero-order approximation.

Innocent solvents

Solvents that do not establish specific interactions, for example, hydrogen bonds with the solute.

Polarizable continuum model

A description of bulk solvent effects in terms of a polarizable continuum in which the solute is fully embedded.

Cybotactic region

The region around a solute molecule including solvent molecules belonging to the first solvation shell, that is, showing close solute–solvent contacts.

0–0 transition

The transition between the vibrational ground states of initial and final electronic states.

Half-width at half-maximum

Half of the width between the two points where the value of the function is its half-maximum.

Zero-point energy

The lowest energy that a quantum system may have, which, contrary to the classical case, is non-zero due to the Heisenberg uncertainty principle.

Ensemble of walkers

A large number of virtual copies of a single particle moving randomly over a given potential energy surface.

Nuclear quadrupole coupling

Interaction between the quadrupole moment of a nucleus and the electric-field gradient at this nucleus. Nuclei have a quadrupole moment when the nuclear spin is greater than 1/2. This interaction produces a hyperfine structure in the rotational spectra.

Spin–rotation interaction

The interaction between the weak magnetic field generated by the end-over-end rotation of a molecule with the nuclear magnetic moment. The nuclear magnetic moment is present when the nuclear spin is non-null. This interaction produces a hyperfine structure in the rotational spectra.

Molecular mechanics

Classical model to predict the energy of a molecule as a function of its conformation.

Orbital splittings

Splittings of specific orbitals due to external factors (for example, electric or magnetic field).

Crystal field theory

The splitting of the (relativistic) many-particle multiplet states of an ion in a dn or fn configuration incurred by the electrostatic interaction with its coordinating ligands that are treated as point charges.

Multiplets

An ensemble of many particle states that arise from the distribution of a given number of electrons among sets of degenerate atomic or molecular orbitals under the action of the electron–electron (and perhaps the spin–orbit coupling) interaction.

Spin–orbit coupling

The coupling between the spin and the orbital angular momenta.

Slater determinant

Representation of a many particle ‘mean-field’ wave function in terms of the antisymmetrized products of single-electron wave functions (molecular orbitals).

Circular dichroism

Dichroism (splitting of a beam of light into two beams with different wavelengths) involving circularly polarized light, that is, the differential absorption of left and right-handed light.

Magnetic circular dichroism

Circular dichroism induced by a static, longitudinal external magnetic field.

SQUID

A magnetometer based on superconducting loops used to measure very low magnetic fields.

Electron paramagnetic resonance

A synonym of electron spin resonance.

Zero-field splitting

The lifting of the degeneracy of the 2S + 1 magnetic sublevels of a spin multiplet with total spin S in the absence of a magnetic field, caused by the effects of spin–orbit coupling and electron–electron spin–spin interactions.

Ab initio ligand field theory

A method connecting the results of ab initio calculations with the parameters entering ligand field theory.

Ligand field theory

A semi-empirical ‘perturbed ion’ model, based on crystal field theory, that describes the electronic structure and properties of transition metal complexes.

Template approach

A model in which the structure of a molecular system is refined with reference to suitable fragments, whose structures are accurately known.

Force constants

Derivatives of the potential energy with respect to nuclear coordinates evaluated at the minimum structure, for example, the quadratic force constant is the second derivative.

QM/QM′

A fundamental theory of contemporary physics that provides a description of the properties of the matter at the atomic and subatomic level. The slash is used to denote that two levels of treatments are employed and implies a partitioning of the system (QM′, a different quantum mechanics level).

Perturbed matrix method

A perturbative model in which the environmental effects on a quantum centre are described in terms of the CIS (configuration interaction singles) method, whose elements are the energies of the isolated solute perturbed by the electric field produced by the different configurations of the solvent issuing from a molecular dynamics simulation.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Barone, V., Alessandrini, S., Biczysko, M. et al. Computational molecular spectroscopy. Nat Rev Methods Primers 1, 38 (2021). https://doi.org/10.1038/s43586-021-00034-1

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1038/s43586-021-00034-1

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing