Abstract
Electron paramagnetic resonance (EPR) spectroscopy has been proven to be an important technique for studying paramagnetic systems. Probably, the most accessible EPR parameter and the one that provides a significant amount of information about molecular structure and spin density is the hyperfine coupling constant (HFCC). Hence, accurate quantum-chemical modeling of HFCCs is frequently essential to the adequate interpretation of EPR spectra. It requires the precise spin density, which is the difference between the densities of α- and β-electrons, and thus, its quality is expected to reflect the quality of the total electron density. The question of which approximate exchange-correlation density functional yields sufficiently accurate HFCCs, and thus, the spin density remains open. To assess the performance of well-established density functionals for calculating HFCCs, we used a series of 26 small paramagnetic species and compared the obtained results to the CCSD reference values. The performance of DFT was also tested on EPR-studied o-semiquinone radical interacting with water molecules and Mg2+ cation. The HFCCs were additionally calculated by the DLPNO-CCSD method, and this wave function-based technique was found superior to all functionals we tested. Although some functionals were found, on average, to be fairly efficient, we found that the most accurate functional is system-dependent, and therefore, the DLPNO-CCSD method should be preferred for theoretical investigations of the HFCCs and spin density.
Similar content being viewed by others
References
Neese F (2009) Prediction of molecular properties and molecular spectroscopy with density functional theory: from fundamental theory to exchange-coupling. Coord Chem Rev 253:526–563. https://doi.org/10.1016/j.ccr.2008.05.014
Jones RO (2015) Density functional theory: its origins, rise to prominence, and future. Rev Mod Phys 87. https://doi.org/10.1103/RevModPhys.87.897
Kohn W, Sham LJ (1965) Self-consistent equations including exchange and correlation effects. Phys Rev 140:A1133–A1138. https://doi.org/10.1103/PhysRev.140.A1133
Levy M (1979) Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem. Proc Natl Acad Sci U S A 76:6062–6065. https://doi.org/10.1073/pnas.76.12.6062
Perdew JP (2013) Climbing the ladder of density functional approximations. MRS Bull 38:743–750. https://doi.org/10.1557/mrs.2013.178
Medvedev MG, Bushmarinov IS, Sun J, Perdew JP, Lyssenko KA (2017) Density functional theory is straying from the path toward the exact functional. Science 355:49–52. https://doi.org/10.1126/science.aah5975
Su NQ, Zhu Z, Xu X (2018) Doubly hybrid density functionals that correctly describe both density and energy for atoms. Proc Natl Acad Sci 115:2287–2292. https://doi.org/10.1073/pnas.1713047115
Kepp KP (2017) Comment on “density functional theory is straying from the path toward the exact functional”. Science 356:496. https://doi.org/10.1126/science.aam9364
Medvedev MG, Bushmarinov IS, Sun J, Perdew JP, Lyssenko KA (2017) Response to comment on “density functional theory is straying from the path toward the exact functional”. Science 356:496. https://doi.org/10.1126/science.aam9550
Kepp KP (2018) Energy vs. density on paths toward more exact density functionals. Phys Chem Chem Phys 20:7538–7548. https://doi.org/10.1039/c7cp07730k
Ranasinghe DS, Perera A, Bartlett RJ (2017) A note on the accuracy of KS-DFT densities. J Chem Phys 147. https://doi.org/10.1063/1.5001939
Gould T (2017) What makes a density functional approximation good? Insights from the left Fukui function. J Chem Theory Comput 13:2373–2377. https://doi.org/10.1021/acs.jctc.7b00231
Wang Y, Wang X, Truhlar DG, He X (2017) How well can the M06 suite of functionals describe the electron densities of ne, Ne6+, and Ne8+? J Chem Theory Comput 13:6068–6077. https://doi.org/10.1021/acs.jctc.7b00865
Brorsen KR, Yang Y, Pak MV, Hammes-Schiffer S (2017) Is the accuracy of density functional theory for atomization energies and densities in bonding regions correlated? J Phys Chem Lett 8:2076–2081. https://doi.org/10.1021/acs.jpclett.7b00774
Hait D, Head-Gordon M (2018) How accurate is density functional theory at predicting dipole moments? An assessment using a new database of 200 benchmark values. J Chem Theory Comput 14:1969–1981. https://doi.org/10.1021/acs.jctc.7b01252
Hammes-Schiffer S (2017) A conundrum for density functional theory. Science 355:28–29. https://doi.org/10.1126/science.aal3442
Korth M (2017) Density functional theory: not quite the right answer for the right reason yet. Angew Chem Int Ed 56:5396–5398. https://doi.org/10.1002/anie.201701894
Gromov OI, Kuzin SV, Golubeva EN (2019) Performance of DFT methods in the calculation of isotropic and dipolar contributions to 14N hyperfine coupling constants of nitroxide radicals. J Mol Model 25:93. https://doi.org/10.1007/s00894-019-3966-y
Improta R, Barone V (2004) Interplay of electronic, environmental, and vibrational effects in determining the hyperfine coupling constants of organic free radicals. Chem Rev 104:1231–1254. https://doi.org/10.1021/cr960085f
Mattar SM, Emwas AH, Stephens AD (2002) Accurate computations of the methyl isotropic hyperfine coupling constants in 2-methyl-1,4-benzosemiquinone radical intermediate. Chem Phys Lett 363:152–160. https://doi.org/10.1016/S0009-2614(02)01136-3
Mattar SM, Stephens AD (2000) UB1LYP hybrid density functional studies of the 2,2,6,6-tetramethyl-4-piperidone-oxyly (TEMPONE) hyperfine tensors. Chem Phys Lett 601–610
Malkin VG, Malkina OL, Zhidomirov GM (2017) Visualization of Electron paramagnetic resonance hyperfine structure coupling pathways. J Phys Chem A 121:3580–3587. https://doi.org/10.1021/acs.jpca.7b01833
Hermosilla L, Calle P, García de la Vega JM (2015) Modeling EPR parameters of nitrogen containing conjugated radical cations. RSC Adv 5:62551–62562. https://doi.org/10.1039/C5RA08758A
Hermosilla L, Calle P, Sieiro C, García N, Tiemblo P, Guzmán J (2007) DFT study of the EPR spectral pattern of propagating methacrylic radicals. Chem Phys 340:237–244. https://doi.org/10.1016/j.chemphys.2007.09.004
Hermosilla L, La Vega JMGD, Sieiro C, Calle P (2011) DFT calculations of isotropic hyperfine coupling constants of nitrogen aromatic radicals: the challenge of nitroxide radicals. J Chem Theory Comput 7:169–179. https://doi.org/10.1021/ct1006136
Kossmann S, Kirchner B, Neese F (2007) Performance of modern density functional theory for the prediction of hyperfine structure: meta-GGA and double hybrid functionals. Mol Phys 105:2049–2071. https://doi.org/10.1080/00268970701604655
Kokorin AI, Zaripov RB, Gromov OI, Hideg K, Kálai T (2018) Tailored nitroxide radicals and biradical containing 13C enriched acetylene groups: ENDOR and DFT investigation. Appl Magn Reson 49:137–149. https://doi.org/10.1007/s00723-017-0942-5
Kaupp M, Bühl M, Malkin VG (2004) Calculation of NMR and EPR parameters. Theory and Applications. Wiley-VCH, Weinheim
Witwicki M, Jezierska J (2015) Toward an understanding of the ambiguous electron paramagnetic resonance spectra of the iminoxy radical from o-fluorobenzaldehyde oxime: density functional theory and ab initio studies. J Phys Chem A 119:9109–9120. https://doi.org/10.1021/acs.jpca.5b06143
Jerzykiewicz M, Ćwieląg-Piasecka I, Witwicki M, Jezierski A (2011) α-Tocopherol impact on oxy-radical induced free radical decomposition of DMSO: spin trapping EPR and theoretical studies. Chem Phys 383:27–34. https://doi.org/10.1016/j.chemphys.2011.03.028
Malček M, Bučinský L, Valko M, Biskupič S (2015) Calculations of hyperfine coupling constant of copper(II) in aqueous environment. Finite temperature molecular dynamics and relativistic effects. J Mol Model 21:237. https://doi.org/10.1007/s00894-015-2752-8
Tabaka K, Jezierska J (2004) Molecular geometry and hyperfine interactions in iminoxy radicals with CO or CH2 group–DFT and EPR studies in liquid and rigid media. Chem Phys Lett 394:298–306. https://doi.org/10.1016/j.cplett.2004.07.007
Jaszewski AR, Tabaka K, Jezierska J, Kedzierska J (2003) The effect of the carbonyl moiety on the spin density delocalization in the iminoxy radicals. Hybrid density functional studies. Chem Phys Lett 367:678–689. https://doi.org/10.1016/S0009-2614(02)01743-8
Jaszewski AR, Jezierska J (2001) Hybrid density functional approach to the isotropic and anisotropic hyperfine couplings with 14N and 1H nuclei in the blue copper proteins. Chem Phys Lett 343:571–580. https://doi.org/10.1016/S0009-2614(01)00753-9
Jaszewski AR, Jezierska J, Jezierski A (2000) Hybrid density functional approach to the structures and EPR parameters of σ-type iminoxy radicals: the case of 3-oxobutan-2-iminoxyl. Chem Phys Lett 319:611–617. https://doi.org/10.1016/S0009-2614(00)00187-1
Munzarová M, Kaupp M (1999) A critical validation of density functional and coupled-cluster approaches for the calculation of EPR hyperfine coupling constants in transition metal complexes. J Phys Chem A 103:9966–9983. https://doi.org/10.1021/jp992303p
Asher JR, Kaupp M (2007) Hyperfine coupling tensors of the benzosemiquinone radical anion from Car–Parrinello molecular dynamics. ChemPhysChem 8:69–79. https://doi.org/10.1002/cphc.200600325
O’Malley PJ (1998) B3LYP, hybrid density functional studies of the durosemiquinone radical: the effect of symmetrical and asymmetrical hydrogen bonding on spin densities and hyperfine couplings. J Phys Chem A 102:248–253. https://doi.org/10.1021/jp972467a
De Almeida WB, O’Malley PJ (2018) Conformational control of cofactors in nature: the effect of methoxy group orientation on the electronic structure of ubisemiquinone. Chem Phys Lett 695:158–161. https://doi.org/10.1016/j.cplett.2017.12.066
Beal NJ, Corry TA, O’Malley PJ (2017) Comparison between experimental and broken symmetry density functional theory (BS-DFT) calculated electron paramagnetic resonance (EPR) parameters of the S2 state of the oxygen-evolving complex of photosystem II in its native (calcium) and strontium-subst. J Phys Chem B 121:11273–11283. https://doi.org/10.1021/acs.jpcb.7b09498
Beal NJ, Corry TA, O’Malley PJ (2018) A comparison of experimental and broken symmetry density functional theory (BS-DFT) calculated Electron paramagnetic resonance (EPR) parameters for intermediates involved in the S2 to S3 state transition of nature’s oxygen evolving complex. J Phys Chem B 122:1394–1407. https://doi.org/10.1021/acs.jpcb.7b10843
Witwicki M (2018) Density functional theory and ab initio studies on hyperfine coupling constants of phosphinyl radicals. Int J Quantum Chem 118. https://doi.org/10.1002/qua.25779
Barone V, Biczysko M, Bloino J, Egidi F, Puzzarini C (2013) Accurate structure, thermodynamics, and spectroscopy of medium-sized radicals by hybrid coupled cluster/density functional theory approaches: the case of phenyl radical. J Chem Phys 138:234303. https://doi.org/10.1063/1.4810863
Pavone M, Cimino P, Crescenzi O, Sillanpää A, Barone V (2007) Interplay of intrinsic, environmental, and dynamic effects in tuning the EPR parameters of nitroxides: further insights from an integrated computational approach. J Phys Chem B 111:8928–8939. https://doi.org/10.1021/jp0727805
Cimino P, Pavone M, Barone V (2006) Structural, thermodynamic, and magnetic properties of adducts between TEMPO radical and alcohols in solution: new insights from DFT and discrete–continuum solvent models. Chem Phys Lett 419:106–110. https://doi.org/10.1016/j.cplett.2005.11.067
Maria Jerzykiewicz, Irmina Ćwieląg-Piasecka, Maciej Witwicki, Adam Jezierski, (2010) EPR spin trapping and DFT studies on structure of active antioxidants in biogycerol. Chemical Physics Letters 497 (1-3):135–141
Munzarová M (2004) DFT calculations of EPR hyperfine coupling tensors. In: Kaupp M, Bühl M, Malkin VG (eds) Calculation of NMR and EPR parameters. Theory and Applications, First. Wiley-VCH, Weinheim, pp 463–482
Neese F (2012) The ORCA program system. Wiley Interdiscip Rev Comput Mol Sci 2:73–78. https://doi.org/10.1002/wcms.81
Neese F (2018) Software update: the ORCA program system, version 4.0. Wiley Interdiscip Rev Comput Mol Sci 8:e1327. https://doi.org/10.1002/wcms.1327
Raghavachari K, Trucks GW, Pople JA, Head-Gordon M (1989) A fifth-order perturbation comparison of electron correlation theories. Chem Phys Lett 157:479–483
Dunning TH (1989) Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J Chem Phys 90:1007–1023. https://doi.org/10.1063/1.456153
Witwicki M, Jezierska J (2011) Effects of solvents, ligand aromaticity, and coordination sphere on the g tensor of anionic o-semiquinone radicals complexed by Mg2+ ions: DFT studies. J Phys Chem B 115:3172–3184. https://doi.org/10.1021/jp110515j
Neese F (2001) Theoretical study of ligand superhyperfine structure. Application to cu(II) complexes. J Phys Chem A 105:4290–4299. https://doi.org/10.1021/jp003254f
Vosko SH, Wilk L, Nusair M (1980) Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis. Can J Phys 58:1200–1211. https://doi.org/10.1139/p80-159
Becke AD (1988) Density-functional exchange-energy approximation with correct asymptotic behavior. Phys Rev A 38:3098–3100. https://doi.org/10.1103/PhysRevA.38.3098
Perdew JP (1986) Density-functional approximation for the correlation energy of the inhomogeneous electron gas. Phys Rev B 33:8822–8824. https://doi.org/10.1103/PhysRevB.33.8822
Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple-the PBE functional. Phys Rev Lett 77:3865–3868. https://doi.org/10.1103/PhysRevLett.77.3865
Hoe WM, Cohen AJ, Handy NC (2001) Assessment of a new local exchange functional OPTX. Chem Phys Lett 341:319–328. https://doi.org/10.1016/S0009-2614(01)00581-4
Lee C, Yang W, Parr RG (1988) Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys Rev B 37:785–789. https://doi.org/10.1103/physrevb.37.785
Xu X, Goddard III WA (2004) The X3LYP extended density functional for accurate descriptions of nonbond interactions, spin states, and thermochemical properties. Proc Natl Acad Sci 101:2673–2677. https://doi.org/10.1073/pnas.0308730100
Sun J, Ruzsinszky A, Perdew J (2015) Strongly constrained and appropriately normed semilocal density functional. Phys Rev Lett 115:1–6. https://doi.org/10.1103/PhysRevLett.115.036402
Zhao Y, Truhlar DG (2006) A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions. J Chem Phys 125. https://doi.org/10.1063/1.2370993
Becke AD (1993) Density-functional thermochemistry. III. The role of exact exchange. J Chem Phys 98:5648–5652. https://doi.org/10.1063/1.464913
Stephens PJ, Devlin FJ, Chabalowski CF, Frisch MJ (1994) Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields. J Phys Chem 98:11623–11627. https://doi.org/10.1021/j100096a001
Adamo C, Barone V (1999) Toward reliable density functional methods without adjustable parameters: the PBE0 model. J Chem Phys 110:6158–6170. https://doi.org/10.1063/1.478522
Cohen AJ, Handy NC (2001) Dynamic correlation. Mol Phys 99:607–615. https://doi.org/10.1080/00268970010023435
Tao J, Perdew JP, Staroverov VN, Scuseria GE (2003) Climbing the density functional ladder: nonempirical meta–generalized gradient approximation designed for molecules and solids. Phys Rev Lett 91:146401. https://doi.org/10.1103/PhysRevLett.91.146401
Grimme S (2005) Accurate calculation of the heats of formation for large main group compounds with spin-component scaled MP2 methods. J Phys Chem A 109:3067–3077. https://doi.org/10.1021/jp050036j
Quintal MM, Karton A, Iron MA, Boese AD, Martin JML (2006) Benchmark study of DFT functionals for late-transition-metal reactions †. J Phys Chem A 110:709–716. https://doi.org/10.1021/jp054449w
Zhao Y, Truhlar DG (2008) The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other function. Theor Chem Accounts 120:215–241. https://doi.org/10.1007/s00214-007-0310-x
Yanai T, Tew DP, Handy NC (2004) A new hybrid exchange-correlation functional using the Coulomb-attenuating method (CAM-B3LYP). Chem Phys Lett 393:51–57. https://doi.org/10.1016/j.cplett.2004.06.011
Da Chai J, Head-Gordon M (2008) Systematic optimization of long-range corrected hybrid density functionals. J Chem Phys 128:084106. https://doi.org/10.1063/1.2834918
Mardirossian N, Head-Gordon M (2014) ωb97X-V: a 10-parameter, range-separated hybrid, generalized gradient approximation density functional with nonlocal correlation, designed by a survival-of-the-fittest strategy. Phys Chem Chem Phys 16:9904–9924. https://doi.org/10.1039/c3cp54374a
Mardirossian N, Head-Gordon M (2016) ω B97M-V: a combinatorially optimized, range-separated hybrid, meta-GGA density functional with VV10 nonlocal correlation. J Chem Phys 144:214110. https://doi.org/10.1063/1.4952647
Grimme S (2006) Semiempirical hybrid density functional with perturbative second-order correlation. J Chem Phys 124:034108. https://doi.org/10.1063/1.2148954
Schwabe T, Grimme S (2006) Towards chemical accuracy for the thermodynamics of large molecules: new hybrid density functionals including non-local correlation effects. Phys Chem Chem Phys 8:4398. https://doi.org/10.1039/b608478h
Kozuch S, Gruzman D, Martin JML (2010) DSD-BLYP: a general purpose double hybrid density functional including spin component scaling and dispersion correction. J Phys Chem C 114:20801–20808. https://doi.org/10.1021/jp1070852
Neese F (2004) Definition of corresponding orbitals and the diradical character in broken symmetry DFT calculations on spin coupled systems. J Phys Chem Solids 65:781–785. https://doi.org/10.1016/j.jpcs.2003.11.015
Neese F (2006) Importance of direct spin - spin coupling and spin-flip excitations for the zero-field splittings of transition metal complexes: a case study. J Am Chem Soc 128:10213–10222. https://doi.org/10.1021/ja061798a
Saitow M, Becker U, Riplinger C, Valeev EF, Neese F (2017) A new near-linear scaling, efficient and accurate, open-shell domain-based local pair natural orbital coupled cluster singles and doubles theory. J Chem Phys 146:164105. https://doi.org/10.1063/1.4981521
Datta D, Kossmann S, Neese F (2016) Analytic energy derivatives for the calculation of the first-order molecular properties using the domain-based local pair-natural orbital coupled-cluster theory. J Chem Phys 145:114101. https://doi.org/10.1063/1.4962369
Pinski P, Riplinger C, Valeev EF, Neese F (2015) Sparse maps—a systematic infrastructure for reduced-scaling electronic structure methods. I. an efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals. J Chem Phys 143:034108. https://doi.org/10.1063/1.4926879
Saitow M, Neese F (2018) Accurate spin-densities based on the domain-based local pair-natural orbital coupled-cluster theory. J Chem Phys 149. https://doi.org/10.1063/1.5027114
Kaupp M, Arbuznikov AV, Heelmann A, Görling A (2010) Hyperfine coupling constants of the nitrogen and phosphorus atoms: a challenge for exact-exchange density-functional and post-Hartree-Fock methods. J Chem Phys 132:1–10. https://doi.org/10.1063/1.3417985
Witwicki M, Jezierska J, Ozarowski A (2009) Solvent effect on EPR, molecular and electronic properties of semiquinone radical derived from 3,4-dihydroxybenzoic acid as model for humic acid transient radicals: high-field EPR and DFT studies. Chem Phys Lett 473:160–166. https://doi.org/10.1016/j.cplett.2009.03.035
Neese F (2017) Quantum chemistry and EPR parameters. eMagRes 6:1–22. https://doi.org/10.1002/9780470034590.emrstm1505
Puzzarini C, Barone V (2010) Toward spectroscopic accuracy for open-shell systems: molecular structure and hyperfine coupling constants of H2 CN, H2 CP, NH 2, and PH2 as test cases. J Chem Phys 133:184301. https://doi.org/10.1063/1.3503763
Grimme S, Hansen A (2015) A practicable real-space measure and visualization of static electron-correlation effects. Angew Chem Int Ed 54:12308–12313. https://doi.org/10.1002/anie.201501887
Vydrov OA, Van Voorhis T (2010) Nonlocal van der Waals density functional: the simpler the better. J Chem Phys 133:244103. https://doi.org/10.1063/1.3521275
Witwicki M, Jezierska J (2013) DFT insight into o-semiquinone radicals and Ca2+ ion interaction: structure, g tensor, and stability. Theor Chem Accounts 132:1383. https://doi.org/10.1007/s00214-013-1383-3
Cossi M, Rega N, Scalmani G, Barone V, Chimica D, Ii F, Angelo CMS (2003) Energies, structures, and electronic properties of molecules in solution with the C-PCM solvation model. J Comput Chem 24:669–681. https://doi.org/10.1002/jcc.10189
Barone V, Cossi M (1998) Quantum calculation of molecular energies and energy gradients in solution by a conductor solvent model. J Phys Chem A 102:1995–2001. https://doi.org/10.1021/jp9716997
Taguchi AT, O’Malley PJ, Wraight CA, Dikanov SA (2017) Determination of the complete spin density distribution in 13 C-labeled protein-bound radical intermediates using advanced 2D electron paramagnetic resonance spectroscopy and density functional theory. J Phys Chem B 121:10256–10268. https://doi.org/10.1021/acs.jpcb.7b10036
Sinnecker S, Reijerse E, Neese F, Lubitz W (2004) Hydrogen bond geometries from electron paramagnetic resonance and electron-nuclear double resonance parameters: density functional study of quinone radical anion-solvent interactions. J Am Chem Soc 126:3280–3290. https://doi.org/10.1021/ja0392014
Acknowledgments
This paper is dedicated to Professor Zdzisław Latajka, honoring his many contributions to chemistry, on the occasion of his 70th birthday.
Funding
This work was financially supported by the National Science Centre, Poland (Narodowe Centrum Nauki, nr rej. 2018/02/X/ST5/01186). All computations were performed using computers of the Wroclaw Center for Networking and Supercomputing (Grant No. 47).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This paper belongs to Topical Collection on Zdzislaw Latajka 70th Birthday Festschrift
Electronic supplementary material
ESM 1
(PDF 368 kb)
Rights and permissions
About this article
Cite this article
Witwicki, M., Walencik, P.K. & Jezierska, J. How accurate is density functional theory in predicting spin density? An insight from the prediction of hyperfine coupling constants. J Mol Model 26, 10 (2020). https://doi.org/10.1007/s00894-019-4268-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00894-019-4268-0