Abstract
Spectroscopic techniques can probe molecular systems noninvasively and investigate their structure, properties and dynamics in different environments and physicochemical 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 mediumsized 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.
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References
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.
Merkt, F. & Quack, M. Handbook of HighResolution Spectroscopy (Wiley, 2011).
Laane, J. Frontiers of Molecular Spectroscopy (Elsevier, 2008).
Berova, N., Nakanishi, K. & Woody, R. W. Circular Dichroism: Principles and Applications 2nd edn (WileyVCH, 2000).
Rijs, A. M. & Oomens, J. GasPhase IR Spectroscopy and Structure of Biological Molecules. Topics in Current Chemistry Vol. 364 (Springer International, 2015).
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).
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).
Caminati, W. in Handbook of HighResolution Spectroscopy (eds Merkt, F. & Quack, M.) (Wiley, 2011).
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).
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).
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).
Alonso, J. L. & López, J. C. in GasPhase IR Spectroscopy and Structure of Biological Molecules (eds Rijs, A. M. & Oomens, J.) 335–401 (Springer International, 2015).
Atanasov, M. et al. First principles approach to the electronic structure, magnetic anisotropy and spin relaxation in mononuclear 3dtransition metal single molecule magnets. Coord. Chem. Rev. 289290, 177–214 (2015).
Barone, V. in Computational Strategies for Spectroscopy: From Small Molecules to Nano Systems (Wiley, 2011).
Grunenberg, J. in Computational Spectroscopy: Methods, Experiments and Applications (Wiley, 2011).
Jensen, P., Bunker P. R. in Computational Molecular Spectroscopy (Wiley, 2000).
Neese, F. Prediction of molecular properties and molecular spectroscopy with density functional theory: from fundamental theory to exchangecoupling. Coord. Chem. Rev. 253, 526–563 (2009).
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 quantumchemical approaches for the study of transition metal complexes.
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).
Born, M. & Oppenheimer, R. Zur quantentheorie der molekeln. Ann. Phys. 389, 457–484 (1927).
Eckart, C. Some studies concerning rotating axes and polyatomic molecules. Phys. Rev. 47, 552–558 (1935).
Sayvetz, A. The kinetic energy of polyatomic molecules. J. Chem. Phys. 7, 383–389 (1939).
Watson, J. K. G. Simplification of the molecular vibration–rotation Hamiltonian. Mol. Phys. 15, 479–490 (1968).
Watson, J. K. G. The vibration–rotation Hamiltonian of linear molecules. Mol. Phys. 19, 465–487 (1970).
Furtenbacher, T., Császár, A. G. & Tennyson, J. MARVEL: measured active rotational–vibrational energy levels. J. Mol. Spectrosc. 245, 115–125 (2007).
Furtenbacher, T. & Császár, A. G. On employing H_{2}^{16}O, H_{2}^{17}O, H_{2}^{18}O, and D_{2}^{16}O lines as frequency standards in the 15–170 cm^{−1} window. J. Quant. Spectrosc. Radiat. Transfer 109, 1234–1251 (2008).
Aliev, M. R. & Watson, J. K. G. in Molecular Spectroscopy: Modern Research (ed. Narahari Rao, K.) 1–67 (Academic, 1985). This book presents the higherorder effects in the vibration–rotation spectra of semirigid molecules.
Gordy, W. & Cook, R. L. in Microwave Molecular Spectra (ed. Weissberger, A.) (Wiley, 1984).
Watson, J. K. G. in Vibrational Spectra and Structure: A Series of Advances (ed. Durig, J. R.) (Elsevier, 1977).
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).
Barone, V. & Polimeno, A. in Electron Paramagnetic Resonance: A Practitioner’s Toolkit Ch. 7 (eds Brustolon, M. & Giamello, E.) 251–284 (Wiley, 2008).
Jose, K. V. & Raghavachari, K. Fragmentbased 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).
Neese, F. Quantum chemistry and EPR parameters. eMagRes 6, 1–22 (2017). This article presents a recent and exhaustive review on the quantumchemical computation of the parameters involved in the electron paramagnetic resonance spectroscopy.
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.
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).
Nielsen, H. H. The vibration–rotation energies of molecules. Rev. Mod. Phys. 23, 90–136 (1951).
Mills, I. A. in Molecular Spectroscopy: Modern Research (eds Rao, K. N. & Mathews, C. N.) (Academic, 1972).
Barone, V. Anharmonic vibrational properties by a fully automated secondorder perturbative approach. J. Chem. Phys. 122, 14108 (2005).
Bloino, J. & Barone, V. A secondorder 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).
Vázquez, J. & Stanton, J. F. Simple(r) algebraic equation for transition moments of fundamental transitions in vibrational secondorder perturbation theory. Mol. Phys. 104, 377–388 (2006).
Willetts, A., Handy, N. C., Green, W. H. & Jayatilaka, D. Anharmonic corrections to vibrational transition intensities. J. Phys. Chem. 94, 5608–5616 (1990).
Császár, A. G. Anharmonic molecular force fields. WIREs Comput. Mol. Sci. 2, 273–289 (2012).
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.
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).
Maslen, P. E., Jayatilaka, D., Colwell, S. M., Amos, R. D. & Handy, N. C. Higher analytic derivatives. II. The fourth derivative of selfconsistentfield energy. J. Chem. Phys. 95, 7409–7417 (1991).
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 mediumtolarge molecular systems. Int. J. Quantum Chem. 115, 948–982 (2015).
Roy, T. K. & Gerber, R. B. Vibrational selfconsistent field calculations for spectroscopy of biological molecules: new algorithmic developments and applications. Phys. Chem. Chem. Phys. 15, 9468–9492 (2013).
Neff, M. & Rauhut, G. Toward large scale vibrational configuration interaction calculations. J. Chem. Phys. 131, 124129 (2009).
Christiansen, O. Vibrational coupled cluster theory. J. Chem. Phys. 120, 2149–2159 (2004).
Erfort, S., Tschöpe, M. & Rauhut, G. Toward a fully automated calculation of rovibrational infrared intensities for semirigid polyatomic molecules. J. Chem. Phys. 152, 244104 (2020).
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).
Bloino, J., Biczysko, M., Santoro, F. & Barone, V. General approach to compute vibrationally resolved onephoton electronic spectra. J. Chem. Theory Comput. 6, 1256–1274 (2010).
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).
Franck, J. & Dymond, E. G. Elementary processes of photochemical reactions. Trans. Faraday Society 21, 536–542 (1926).
Condon, E. U. Nuclear motions associated with electron transitions in diatomic molecules. Phys. Rev. 32, 858–872 (1928).
Herzberg, G. & Teller, E. Schwingungsstruktur der Elektronenübergänge bei mehratomigen Molekülen. Z. Phys. Chem. 21B, 410–446 (1933).
Duschinsky, F. Acta Physicochim. 7, 551–566 (URSS, 1937) .
Baiardi, A., Bloino, J. & Barone, V. General formulation of vibronic spectroscopy in internal coordinates. J. Chem. Phys. 144, 084114 (2016).
Reimers, J. R. A practical method for the use of curvilinear coordinates in calculations of normalmodeprojected displacements and Duschinsky rotation matrices for large molecules. J. Chem. Phys. 115, 9103–9109 (2001).
Baiardi, A., Bloino, J. & Barone, V. Simulation of vibronic spectra of flexible systems: hybrid DVRharmonic approaches. J. Chem. Theory Comput. 13, 2804–2822 (2017).
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 visàvis comparison of calculated and experimental spectra instead of the mere computation of spectroscopic parameters.
Bloino, J., Baiardi, A. & Biczysko, M. Aiming at an accurate prediction of vibrational and electronic spectra for mediumtolarge 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.
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).
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).
SrebroHooper, 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.
Stephens, P. J., Devlin, F. J. & Cheeseman, J. R. in VCD Spectroscopy for Organic Chemists (CRC, 2012).
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).
Beer, A. Bestimmung der absorption des rothen lichts in farbigen flüssigkeiten. Ann. Phys. 162, 78–88 (1852).
Polavarapu, P. L. in Chiroptical Spectroscopy: Fundamentals and Applications (CRC, 2016).
Stephens, P. J. & Harada, N. ECD cotton effect approximated by the Gaussian curve and other methods. Chirality 22, 229–233 (2010).
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).
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).
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).
Barron, L. D. in Molecular Light Scattering and Optical Activity (Cambridge Univ. Press, Cambridge, 2004).
Long, D. A. in The Raman Effect: A Unified Treatment of the Theory of Raman Scattering by Molecules (Wiley, 2002).
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).
Dzugan, L. C., DiRisio, R. J., Madison, L. R. & McCoy, A. B. Spectral signatures of proton delocalization in H^{+}(H_{2}O)_{n=1−4} ions. Faraday Discuss 212, 443–466 (2018).
Tanaka, S., Roy, P.N. & Mitas, L. in Recent progress in Quantum Monte Carlo Vol. 1234 (ACS, 2016).
Tanaka, S., Rothstein, S. M. & Lester Jr, W. A. in Advances in Quantum Monte Carlo Vol. 1094 (ACS, 2012).
Anderson, J. B. & Rothstein, S. M. in Advances in Quantum Monte Carlo Vol. 953 (ACS, 2007).
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).
Lester, W. A., Rothstein, S. M. & Tanaka, S. in Recent Advances in Quantum Monte Carlo Methods Recent Advances in Computational Chemistry (World Scientific, 1997).
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).
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.
Anderson, J. B. A randomwalk 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.
Anderson, J. B. Quantum chemistry by random walk. H ^{2}P, H^{+3} D_{3h} ^{1}A′_{1}, H_{2} ^{3}Σ^{+u}, H_{4} ^{1}Σ^{+g}, Be ^{1}S. J. Chem. Phys. 65, 4121–4127 (1976).
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).
Petit, A. S., Wellen, B. A. & Mccoy, A. B. Using fixednode diffusion Monte Carlo to investigate the effects of rotationvibration coupling in highly fluxional asymmetric top molecules: application to H_{2}D^{+}. J. Chem. Phys. 138, 034105 (2013).
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).
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).
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).
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).
Puzzarini, C. Extrapolation to the complete basis set limit of structural parameters: comparison of different approaches. J. Phys. Chem. A 113, 14530–14535 (2009).
Puzzarini, C. & Barone, V. Extending the molecular size in accurate quantumchemical calculations: the equilibrium structure and spectroscopic properties of uracil. Phys. Chem. Chem. Phys. 13, 7189–7197 (2011).
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).
Tajti, A. et al. HEAT: high accuracy extrapolated ab initio thermochemistry. J. Chem. Phys. 121, 11599–11613 (2004).
Heckert, M., Kállay, M., Tew, D. P., Klopper, W. & Gauss, J. Basisset extrapolation techniques for the accurate calculation of molecular equilibrium geometries using coupledcluster theory. J. Chem. Phys. 125, 044108 (2006).
Puzzarini, C., Heckert, M. & Gauss, J. The accuracy of rotational constants predicted by highlevel quantumchemical calculations. I. Molecules containing firstrow atoms. J. Chem. Phys. 128, 194108 (2008).
Yu, Q. et al. Structure, anharmonic vibrational frequencies, and intensities of NNHNN^{+}. J. Phys. Chem. A 119, 11623–11631 (2015).
Boese, A. D. et al. W3 theory: robust computational thermochemistry in the kJ/mol accuracy range. J. Chem. Phys. 120, 4129–4141 (2004).
Karton, A., Rabinovich, E., Martin, J. M. L. & Ruscic, B. W4 theory for computational thermochemistry: in pursuit of confident subkJ/mol predictions. J. Chem. Phys. 125, 144108 (2006).
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).
Shavitt, I. & Bartlett, R. J. in ManyBody Methods in Chemistry and Physics: MBPT and CoupledCluster Theory Cambridge Molecular Science (Cambridge Univ. Press, 2009).
Raghavachari, K., Trucks, G. W., Pople, J. A. & HeadGordon, M. A fifthorder perturbation comparison of electron correlation theories. Chem. Phys. Lett. 589, 37–40 (2013).
Kong, L., Bischoff, F. A. & Valeev, E. F. Explicitly correlated R12/F12 methods for electronic structure. Chem. Rev. 112, 75–107 (2012).
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).
Neese, F., Wennmohs, F. & Hansen, A. Efficient and accurate local approximations to coupledelectron 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 quantumchemical methods to large molecular systems.
Becke, A. D. Densityfunctional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 98, 5648–5652 (1993).
Lee, C., Yang, W. & Parr, R. G. Development of the Colle–Salvetti correlationenergy formula into a functional of the electron density. Phys. Rev. B 37, 785–789 (1988).
Grimme, S. Semiempirical hybrid density functional with perturbative secondorder correlation. J. Chem. Phys. 124, 034108 (2006). This key publication reports the introduction of doublehybrid functionals allowing quantitative spectroscopic studies by DFT.
Møller, C. & Plesset, M. S. Note on an approximation treatment for manyelectron systems. Phys. Rev. 46, 618–622 (1934).
Barone, V., Biczysko, M., Bloino, J. & Puzzarini, C. Accurate molecular structures and infrared spectra of trans2,3dideuterooxirane, methyloxirane, and trans2,3dimethyloxirane. J. Chem. Phys. 141, 034107 (2014).
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).
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).
Řezáč, J., Riley, K. E. & Hobza, P. S66: a wellbalanced database of benchmark interaction energies relevant to biomolecular structures. J. Chem. Theory Comput. 7, 2427–2438 (2011).
Řezáč, J., Bím, D., Gutten, O. & Rulíšek, L. Toward accurate conformational energies of smaller peptides and mediumsized macrocycles: MPCONF196 benchmark energy data set. J. Chem. Theory Comput. 14, 1254–1266 (2018).
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).
Biczysko, M., Panek, P., Scalmani, G., Bloino, J. & Barone, V. Harmonic and anharmonic vibrational frequency calculations with the doublehybrid B2PLYP method: analytic second derivatives and benchmark studies. J. Chem. Theory Comput. 6, 2115–2125 (2010).
Barone, V., Biczysko, M. & Bloino, J. Fully anharmonic IR and Raman spectra of mediumsize molecular systems: accuracy and interpretation. Phys. Chem. Chem. Phys. 16, 1759–1787 (2014).
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).
Brémond, É. et al. Benchmarking density functionals on structural parameters of small/mediumsized organic molecules. J. Chem. Theory Comput. 12, 459–465 (2016).
Risthaus, T., Steinmetz, M. & Grimme, S. Implementation of nuclear gradients of rangeseparated hybrid density functionals and benchmarking on rotational constants for organic molecules. J. Comput. Chem. 35, 1509–1516 (2014).
Su, N. Q. & Xu, X. Beyond energies: geometry predictions with the XYG3 type of doubly hybrid density functionals. Chem. Commun. 52, 13840–13860 (2016).
Witte, J., Goldey, M., Neaton, J. B. & HeadGordon, M. Beyond energies: geometries of nonbonded molecular complexes as metrics for assessing electronic structure approaches. J. Chem. Theory Comput. 11, 1481–1492 (2015).
Yu, H. S., He, X., Li, S. L. & Truhlar, D. G. MN15: a Kohn–Sham globalhybrid exchange–correlation density functional with broad accuracy for multireference and singlereference systems and noncovalent interactions. Chem. Sci. 7, 5032–5051 (2016).
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).
HansonHeine, M. W. D. Benchmarking DFTD dispersion corrections for anharmonic vibrational frequencies and harmonic scaling factors. J. Phys. Chem. A 123, 9800–9808 (2019).
Loos, P.F., Lipparini, F., BoggioPasqua, 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).
Brémond, E., Savarese, M., Adamo, C. & Jacquemin, D. Accuracy of TDDFT geometries: a fresh look. J. Chem. Theory Comput. 14, 3715–3727 (2018).
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).
Bomble, Y. J. et al. Equationofmotion coupledcluster methods for ionized states with an approximate treatment of triple excitations. J. Chem. Phys. 122, 154107 (2005).
Roos, B. O., Lindh, R., Malmqvist, P. Å., Veryazov, V. & Widmark, P.O. in Multiconfigurational Quantum Chemistry (Wiley, 2016).
Auer, A. A. et al. A case study of density functional theory and domainbased 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).
Datta, D., Saitow, M., Sandhöfer, B. & Neese, F. ^{57}Fe Mössbauer parameters from domain based local pairnatural orbital coupledcluster theory. J. Chem. Phys. 153, 204101 (2020).
Sirohiwal, A., BerraudPache, 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).
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.
Andersson, K., Malmqvist, P. Å. & Roos, B. O. Secondorder perturbation theory with a complete active space selfconsistent field reference function. J. Chem. Phys. 96, 1218–1226 (1992).
Andersson, K., Malmqvist, P. A., Roos, B. O., Sadlej, A. J. & Wolinski, K. Secondorder perturbation theory with a CASSCF reference function. J. Phys. Chem. 94, 5483–5488 (1990).
Angeli, C., Cimiraglia, R., Evangelisti, S., Leininger, T. & Malrieu, J.P. Introduction of nelectron valence states for multireference perturbation theory. J. Chem. Phys. 114, 10252–10264 (2001).
Puzzarini, C., Stanton, J. F. & Gauss, J. Quantumchemical 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.
Licari, D., Tasinato, N., Spada, L., Puzzarini, C. & Barone, V. VMSROT: a new module of the virtual multifrequency spectrometer for simulation, interpretation, and fitting of rotational spectra. J. Chem. Theory Comput. 13, 4382–4396 (2017).
Lesarri, A., Mata, S., López, J. C. & Alonso, J. L. A laserablation molecularbeam Fouriertransform microwave spectrometer: the rotational spectrum of organic solids. Rev. Sci. Instrum. 74, 4799–4804 (2003).
Mancini, G., Fusè, M., Lazzari, F., Chandramouli, B. & Barone, V. Unsupervised search of lowlying conformers with spectroscopic accuracy: a twostep algorithm rooted into the island model evolutionary algorithm. J. Chem. Phys. 153, 124110 (2020).
Császár, A. G. et al. The fourth age of quantum chemistry: molecules in motion. Phys. Chem. Chem. Phys. 14, 1085–1106 (2012).
Baiardi, A., Stein, C. J., Barone, V. & Reiher, M. Vibrational density matrix renormalization group. J. Chem. Theory Comput. 13, 3764–3777 (2017).
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).
Begušic´, T. & Vanícˇek, J. Onthefly ab initio semiclassical evaluation of vibronic spectra at finite temperature. J. Chem. Phys. 153, 024105 (2020).
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).
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).
Pracht, P., Bohle, F. & Grimme, S. Automated exploration of the lowenergy chemical space with fast quantum chemical methods. Phys. Chem. Chem. Phys. 22, 7169–7192 (2020).
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).
Panek, P. T. & Jacob, C. R. Anharmonic theoretical vibrational spectroscopy of polypeptides. J. Phys. Chem. Lett. 7, 3084–3090 (2016).
Roy, T. K., Sharma, R. & Gerber, R. B. Firstprinciples anharmonic quantum calculations for peptide spectroscopy: VSCF calculations and comparison with experiments. Phys. Chem. Chem. Phys. 18, 1607–1614 (2016).
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).
Balabin, R. M. Conformational equilibrium in glycine: focalpoint analysis and ab initio limit. Chem. Phys. Lett. 479, 195–200 (2009).
Bazsó, G., Magyarfalvi, G. & Tarczay, G. Tunneling lifetime of the ttc/VIp conformer of glycine in lowtemperature matrices. J. Phys. Chem. A 116, 10539–10547 (2012).
Stepanian, S. G. et al. Matrixisolation infrared and theoretical studies of the glycine conformers. J. Phys. Chem. A 102, 1041–1054 (1998).
Balabin, R. M. Conformational equilibrium in glycine: experimental jetcooled Raman spectrum. J. Phys. Chem. Lett. 1, 20–23 (2010).
Lockyear, J. F. et al. Isomer specific product detection in the reaction of CH with acrolein. J. Phys. Chem. A 117, 11013–11026 (2013).
Barone, V., Biczysko, M., BorkowskaPanek, M. & Bloino, J. A multifrequency virtual spectrometer for complex bioorganic systems: vibronic and environmental effects on the UV/Vis spectrum of chlorophylla. ChemPhysChem 15, 3355–3364 (2014).
Gouterman, M. Spectra of porphyrins. J. Mol. Spectrosc. 6, 138–163 (1961).
Rätsep, M. et al. Absorptionemission symmetry breaking and the different origins of vibrational structures of the ^{1}Q_{y} and ^{1}Q_{x} electronic transitions of pheophytin a. J. Chem. Phys. 151, 165102 (2019).
Huang, X., Braams, B. J. & Bowman, J. M. Ab initio potential energy and dipole moment surfaces for H_{5}O_{2}^{+}. J. Chem. Phys. 122, 044308 (2005).
Petit, A. S., Ford, J. E. & McCoy, A. B. Simultaneous evaluation of multiple rotationally excited states of H_{3} + , H_{3}O^{+}, and CH_{5}^{+} using diffusion Monte Carlo. J. Phys. Chem. A 118, 7206–7220 (2014).
Petit, A. S. & McCoy, A. B. Diffusion Monte Carlo approaches for evaluating rotationally excited states of symmetric top molecules: application to H_{3}O^{+} and D_{3}O^{+}. J. Phys. Chem. A 113, 12706–12714 (2009).
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).
Paesani, F. & Whaley, K. B. Rotational excitations of N_{2}O in small helium clusters and the role of Bose permutation symmetry. J. Chem. Phys. 121, 5293–5311 (2004).
Cho, H. M. & Singer, S. J. Correlation function quantum Monte Carlo study of the excited vibrational states of H_{5}O_{2}^{+}. J. Phys. Chem. A 108, 8691–8702 (2004).
McCoy, A. B., Diken, E. G. & Johnson, M. A. Generating spectra from groundstate wave functions: unraveling anharmonic effects in the OH^{−}·H_{2}O vibrational predissociation spectrum. J. Phys. Chem. A 113, 7346–7352 (2009).
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).
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).
Fusè, M. et al. Unbiased determination of absolute configurations by visàvis comparison of experimental and simulated spectra: the challenging case of diplopyrone. J. Phys. Chem. B 123, 9230–9237 (2019).
Bogaerts, J. et al. A combined Raman optical activity and vibrational circular dichroism study on artemisinintype 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.
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).
Hopmann, K. H. et al. Determining the absolute configuration of two marine compounds using vibrational chiroptical spectroscopy. J. Org. Chem 77, 858–869 (2012).
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).
Nicu, V. P. & Baerends, E. J. Robust normal modes in vibrational circular dichroism spectra. Phys. Chem. Chem. Phys. 11, 6107–6118 (2009).
Tommasini, M. et al. Mode robustness in Raman optical activity. J. Chem. Theory Comput. 10, 5520–5527 (2014).
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).
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).
Hug, W. Visualizing Raman and Raman optical activity generation in polyatomic molecules. Chem. Phys. 264, 53–69 (2001).
Yamamoto, S. in Introduction to Astrochemistry: Chemical Evolution from Interstellar Clouds to Star and Planet Formation (Springer, 2017).
Jørgensen, J. K., Belloche, A. & Garrod, R. T. Astrochemistry during the formation of stars. Annu. Rev. Astron. Astrophys. 58, 727–778 (2020).
McGuire, B. A. 2018 census of interstellar, circumstellar, extragalactic, protoplanetary disk, and exoplanetary molecules. Astrophys. J., Suppl. Ser. 239, 17 (2018).
Herbst, E. & van Dishoeck, E. F. Complex organic interstellar molecules. Annu. Rev. Astron. Astrophys. 47, 427–480 (2009).
Lattelais, M., Pauzat, F., Ellinger, Y. & Ceccarelli, C. Interstellar complex organic molecules and the minimum energy principle. Astrophys. J. 696, L133–L136 (2009).
Puzzarini, C. & Barone, V. A neverending 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.
Cernicharo, J., Guélin, M., Agúndez, M., McCarthy, M. C. & Thaddeus, P. Detection of C_{5}N^{–} and vibrationally excited C_{6}H in IRC+ 10216. Astrophys. J. 688, L83–L86 (2008).
Botschwina, P. & Oswald, R. Carbon chains of type C_{2n+1}N^{−} (n = 2–6): a theoretical study of potential interstellar anions. J. Chem. Phys. 129, 044305 (2008).
Cazzoli, G., Cludi, L., Buffa, G. & Puzzarini, C. Precise THz measurements of HCO^{+}, N_{2}H^{+} and CF^{+} for astrophysical observations. Astrophys. J. Suppl. Ser. 203, 11 (2012).
Guzmán, V. et al. The hyperfine structure in the rotational spectrum of CF^{+}. Astron. Astrophys. 548, A94 (2012).
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).
BorregoVarillas, R. et al. Twodimensional UV spectroscopy: a new insight into the structure and dynamics of biomolecules. Chem. Sci. 10, 9907–9921 (2019).
East, K. W. et al. NMR and computational methods for molecular resolution of allosteric pathways in enzyme complexes. Biophys. Rev. 12, 155–174 (2020).
Huang, J., Zhou, Y. & Xie, D. Predicted infrared spectra in the HF stretching band of the H_{2}–HF complex. J. Chem. Phys. 149, 094307 (2018).
Clary, D. C. & Nesbitt, D. J. Calculation of vibration–rotation spectra for rare gas–HCl complexes. J. Chem. Phys. 90, 7000–7013 (1989).
Felker, P. M. & Bacˇic´, Z. H_{2}O–CO and D_{2}O–CO complexes: intra and intermolecular rovibrational states from fulldimensional and fully coupled quantum calculations. J. Chem. Phys. 153, 074107 (2020).
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.
Mukhopadhyay, A., Xantheas, S. S. & Saykally, R. J. The water dimer II: theoretical investigations. Chem. Phys. Lett. 700, 163–175 (2018).
Schwan, R. et al. Observation of the lowfrequency 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).
Cisneros, G. A. et al. Modeling molecular interactions in water: from pairwise to manybody potential energy functions. Chem. Rev. 116, 7501–7528 (2016).
Mallory, J. D. & Mandelshtam, V. A. Diffusion Monte Carlo studies of MBpol (H_{2}O)_{2−6} and (D_{2}O)_{2−6} clusters: structures and binding energies. J. Chem. Phys. 145, 064308 (2016).
Liu, K. et al. Characterization of a cage form of the water hexamer. Nature 381, 501–503 (1996).
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).
Richardson, J. O. et al. Concerted hydrogenbond breaking by quantum tunneling in the water hexamer prism. Science 351, 1310–1313 (2016).
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).
Gaigeot, M. P. Unravelling the conformational dynamics of the aqueous alanine dipeptide with firstprinciple molecular dynamics. J. Phys. Chem. B 113, 10059–10062 (2009).
Clary, D. C., Benoit, D. M. & van Mourik, T. HDensities: a new concept for hydrated molecules. Acc. Chem. Res. 33, 441–447 (2000).
Fornaro, T., Burini, D., Biczysko, M. & Barone, V. Hydrogenbonding effects on infrared spectra from anharmonic computations: uracil–water complexes and uracil dimers. J. Phys. Chem. A 119, 4224–4236 (2015).
Bec´, K. B. & Huck, C. W. Breakthrough potential in nearinfrared 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.
Benoit, D. M. Rationalising the vibrational spectra of biomolecules using atomistic simulations. Front. Biosci. 14, 4229–4241 (2009).
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).
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).
Singh, S. K., Atanasov, M. & Neese, F. Challenges in multireference perturbation theory for the calculations of the gtensor of firstrow transitionmetal complexes. J. Chem. Theory Comput. 14, 4662–4677 (2018).
Maganas, D. et al. First principles calculations of the structure and V Ledge Xray absorption spectra of V_{2}O_{5} using local pair natural orbital coupled cluster theory and spin–orbit coupled configuration interaction approaches. Phys. Chem. Chem. Phys. 15, 7260–7276 (2013).
Roemelt, M., Maganas, D., DeBeer, S. & Neese, F. A combined DFT and restricted openshell configuration interaction method including spinorbit coupling: spplication to transition metal Ledge Xray absorption spectroscopy. J. Chem. Phys. 138, 204101 (2013).
Neese, F. A critical evaluation of DFT, including timedependent DFT, applied to bioinorganic chemistry. J. Biol. Inorg. Chem. 11, 702–711 (2006).
Neese, F. Highlevel spectroscopy, quantum chemistry, and catalysis: not just a passing fad. Angew. Chem. Int. Ed. 56, 11003–11010 (2017).
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).
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).
Neese, F. & Pantazis, D. A. What is not required to make a single molecule magnet. Faraday Discuss. 148, 229–238 (2011).
Suturina, E. A. et al. Magnetostructural 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).
Suturina, E. A., Maganas, D., Bill, E., Atanasov, M. & Neese, F. Magnetostructural correlations in a series of pseudotetrahedral [Co^{II}(XR)_{4}]^{2–} single molecule magnets: an ab initio ligand field study. Inorg. Chem. 54, 9948–9961 (2015).
Rechkemmer, Y. et al. A fourcoordinate Cobalt(II) singleion magnet with coercivity and a very high energy barrier. Nat. Commun. 7, 10467 (2016).
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).
Kodrycka, M. & Patkowski, K. Platinum, gold, and silver standards of intermolecular interaction energy calculations. J. Chem. Phys. 151, 070901 (2019).
Alessandrini, S., Gauss, J. & Puzzarini, C. Accuracy of rotational parameters predicted by highlevel quantumchemical calculations: case study of sulfurcontaining molecules of astrochemical interest. J. Chem. Theory Comput. 14, 5360–5371 (2018).
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.
Liakos, D. G., Guo, Y. & Neese, F. Comprehensive benchmark results for the domain based local pair natural orbital coupled cluster method (DLPNOCCSD(T)) for closed and openshell systems. J. Phys. Chem. A 124, 90–100 (2020).
Nagy, P. R. & Kállay, M. Approaching the basis set limit of CCSD(T) energies for large molecules with local natural orbital coupledcluster methods. J. Chem. Theory Comput. 15, 5275–5298 (2019).
Sibert III, E. L. Modeling vibrational anharmonicity in infrared spectra of high frequency vibrations of polyatomic molecules. J. Chem. Phys. 150, 090901 (2019).
Basdogan, Y. et al. Machine learningguided approach for studying solvation environments. J. Chem. Theory Comput. 16, 633–642 (2020).
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).
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).
Karton, A., Sylvetsky, N. & Martin, J. M. L. W417: aA diverse and highconfidence dataset of atomization energies for benchmarking highlevel electronic structure methods. J. Comput. Chem. 38, 2063–2075 (2017).
Mayhall, N. J. & Raghavachari, K. Moleculesinmolecules: an extrapolated fragmentbased approach for accurate calculations on large molecules and materials. J. Chem. Theory Comput. 7, 1336–1343 (2011).
Santra, G., Sylvetsky, N. & Martin, J. M. L. Minimally empirical doublehybrid functionals trained against the GMTKN55 database: revDSDPBEP86D4, revDODPBED4, and DODSCAND4. J. Phys. Chem. A 123, 5129–5143 (2019).
Kussmann, J. & Ochsenfeld, C. Preselective screening for linearscaling exact exchangegradient calculations for graphics processing units and general strongscaling massively parallel calculations. J. Chem. Theory Comput. 11, 918–922 (2015).
Doser, B., Lambrecht, D. S. & Ochsenfeld, C. Tighter multipolebased integral estimates and parallel implementation of linearscaling AO–MP2 theory. Phys. Chem. Chem. Phys. 10, 3335–3344 (2008).
Ma, Q. & Werner, H.J. Scalable electron correlation methods. 7. Local openshell coupledcluster methods using pair natural orbitals: PNORCCSD and PNOUCCSD. J. Chem. Theory Comput. 16, 3135–3151 (2020).
Becca, F. & Sorella, S. in Quantum Monte Carlo Approaches for Correlated Systems (Cambridge Univ. Press, 2017).
Puzzarini, C. & Barone, V. The challenging playground of astrochemistry: an integrated rotational spectroscopy—quantum chemistry strategy. Phys. Chem. Chem. Phys. 22, 6507–6523 (2020).
Biczysko, M., Krupa, J. & Wierzejewska, M. Theoretical studies of atmospheric molecular complexes interacting with NIR to UV light. Faraday Discuss. 212, 421–441 (2018).
Raucci, U. et al. Abinitio molecular dynamics and hybrid explicitimplicit solvation model for aqueous and nonaqueous solvents: GFP chromophore in water and methanol solution as case study. J. Comput. Chem. 46, 2228–2239 (2020).
Zhang, W., Kong, X., Liu, S. & Zhao, Y. Multicoefficients correlation methods. WIREs Comput. Mol. Sci. 10, e1474 (2020).
Gagliardi, L. et al. Multiconfiguration pairdensity functional theory: a new way to treat strongly correlated systems. Acc. Chem. Res. 50, 66–73 (2017).
Bannwarth, C. et al. Extended tightbinding quantum chemistry methods. WIREs Comput. Mol. Sci. 11, e01493 (2020).
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.
CasanovaPáez, M. & Goerigk, L. Assessing the Tamm–Dancoff approximation, singlet–singlet, and singlet–triplet excitations with the latest longrange corrected doublehybrid density functionals. J. Chem. Phys. 153, 064106 (2020).
Mutter, S. T. et al. Conformational dynamics of carbohydrates: Raman optical activity of dglucuronic acid and Nacetyldglucosamine using a combined molecular dynamics and quantum chemical approach. Phys. Chem. Chem. Phys. 17, 6016–6027 (2015).
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).
Zhao, L. et al. Realtime timedependent nuclear–electronic orbital approach: dynamics beyond the Born–Oppenheimer approximation. J. Phys. Chem. Lett. 11, 4052–4058 (2020).
Petrenko, T. & Rauhut, G. A general approach for calculating strongly anharmonic vibronic spectra with a high density of states: the X˜^{2}B_{1} ← X˜1A^{1} photoelectron spectrum of difluoromethane. J. Chem. Theory Comput. 13, 5515–5527 (2017).
Cerezo, J., Aranda, D., Avila Ferrer, F. J., Prampolini, G. & Santoro, F. Adiabaticmolecular 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).
Jasper, A. W., Harding, L. B., Knight, C. & Georgievskii, Y. Anharmonic rovibrational partition functions at high temperatures: tests of reduceddimensional models for systems with up to three fluxional modes. J. Phys. Chem. A 123, 6210–6228 (2019).
Burd, T. A. H. & Clary, D. C. Analytic route to tunneling splittings using semiclassical perturbation theory. J. Chem. Theory Comput. 16, 3486–3493 (2020).
O’Connor, M. B. et al. Interactive molecular dynamics in virtual reality from quantum chemistry to drug binding: an opensource multiperson framework. J. Chem. Phys. 150, 220901 (2019).
McArdle, S., Endo, S., AspuruGuzik, A., Benjamin, S. C. & Yuan, X. Quantum computational chemistry. Rev. Mod. Phys. 92, 015003 (2020).
Barone, V. et al. Implementation and validation of a multipurpose virtual spectrometer for large systems in complex environments. Phys. Chem. Chem. Phys. 14, 12404–12422 (2012).
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).
Caselli, P., Myers, P. C. & Thaddeus, P. Radioastronomical spectroscopy of the hyperfine structure of N_{2}H^{+}. Astrophys. J. 455, L77–L80 (1995).
Neese, F. Sumoverstates based multireference ab initio calculation of EPR spin Hamiltonian parameters for transition metal complexes. A case study. Magn. Reson. Chem. 42, S187–S198 (2004).
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. 20193U.0) and SMART@SNS Laboratory for highperformance computing facilities). F.N. is extremely grateful for generous financial support by the Max Planck Society that enables us to follow curiositydriven 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) CHE1856125; R.J.D. was supported by a fellowship from The Molecular Sciences Software Institute under NSF grant OAC1547580.
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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.).
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Nature Reviews Methods Primers thanks M. HansonHeine, J. Kästner, J. Tennyson and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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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 openshell 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 gammaray transition in a Mössbauer active isotope (for example, ^{57}Fe) 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 Carlobased approach for obtaining the exact groundstate 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 multidimensional, hypersurface that describes the variations of the electronic energy of a system in terms of suitable nuclear coordinates.
 Normal coordinates

Linear combinations of massweighted 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.
 Rovibrational 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 harmonicoscillator behaviour.
 Hyperfine structure

Interactions of the molecular electric and/or magnetic fields with the nuclear or electron (for openshell 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.
 Rigidrotor harmonicoscillator 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 onequanta 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.
 Doubleperturbative 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 zeroorder approximation.
 Density functional theory

A quantummechanical method in which the properties of a manyelectron system are determined using functionals (that is, functions of another function) of the spatially dependent electron density and, possibly, its derivatives.
 Vibrational selfconsistent field

Exploitation of the selfconsistent 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.
 Onephoton absorption

A spectroscopic technique in which onephoton absorption leads from the electronic ground state to an excited electronic state.
 Onephoton emission

A spectroscopic technique in which onephoton emission leads from an excited electronic state to a lessexcited (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.
 Lineshape function

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

Time rotated into the imaginary plane via Wick rotation in DMC, τ = it/ℏ.
 Coupledcluster 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 coupledcluster 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.
 Domainbased pair natural orbitals

Electron pairspecific localized natural orbitals expanded in a set of local atomic orbitals belonging to pairspecific domains.
 Globalhybrid or doublehybrid density functionals

Families of density functionals including a percentage of Hartree–Fock exchange (hybrid) and MP2type correlation (only doublehybrid).
 Møller–Plesset theory to the second order

Møller–Plesset theory including manybody 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 lowestenergy 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 secondorder multireference 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.
 Multireference configuration interaction

Extension of the configuration interaction approach to multireference 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 zeroorder 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.
 Halfwidth at halfmaximum

Half of the width between the two points where the value of the function is its halfmaximum.
 Zeropoint energy

The lowest energy that a quantum system may have, which, contrary to the classical case, is nonzero 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 electricfield 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 endoverend rotation of a molecule with the nuclear magnetic moment. The nuclear magnetic moment is present when the nuclear spin is nonnull. 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) manyparticle multiplet states of an ion in a d^{n} or f^{n} 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 ‘meanfield’ wave function in terms of the antisymmetrized products of singleelectron 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 righthanded 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.
 Zerofield 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 semiempirical ‘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.
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Barone, V., Alessandrini, S., Biczysko, M. et al. Computational molecular spectroscopy. Nat Rev Methods Primers 1, 38 (2021). https://doi.org/10.1038/s43586021000341
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DOI: https://doi.org/10.1038/s43586021000341