Skip to main content

Directions for Use of Density Functional Theory: A Short Instruction Manual for Chemists

  • Reference work entry
  • First Online:

Abstract

Two aspects are quintessential if one seeks to successfully perform DFT calculations: a basic understanding of how the concepts and models underlying the various manifestations of DFT are built and an essential knowledge of what can be expected from DFT calculations and how to achieve the most appropriate results. This chapter expands on the development and philosophy of DFT and aims to illustrate the essentials of DFT in a manner that is intuitively accessible. An analysis of the performance and applicability of DFT focuses on a representative selection of chemical properties, including bond lengths, bond angles, vibrational frequencies, electron affinities and ionization potentials, atomization energies, heats of formation, energy barriers, bond energies, hydrogen bonding, weak interactions, spin states, and excited states.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   1,099.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   1,399.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Bibliography

Books on DFT

  • Fiolhais, C., Nogueira, F., & Marques, M. (Eds.). (2003). A primer in density functional theory (lecture notes in physics). Berlin/New York: Springer.

    Google Scholar 

  • Koch, W., & Holzhausen, M. C. (2002). A chemist’s guide to density functional theory (2nd ed.). Weinheim/New York: Wiley.

    Google Scholar 

  • Marques, M. A. L., Ullrich, C. A., Nogueira, F., Rubio, A., Burke, K., & Gross, E. K. U. (Eds.). (2006). Time-dependent density functional theory (lecture notes in physics). Berlin: Springer.

    Google Scholar 

  • Parr, R. G., & Yang, W. (1989). Density functional theory of atoms and molecules. New York: Oxford University Press.

    Google Scholar 

Reviews and Overviews of DFT

  • Baerends, E. J., & Gritsenko, O. V. (1997). A quantum chemical view of density functional theory. Journal of Physical Chemistry A, 101, 5383–5403.

    Article  CAS  Google Scholar 

  • Becke, A. D. (2014). Perspective: Fifty years of density-functional theory in chemical physics. Journal of Chemical Physics, 140, art. 18A301.

    Google Scholar 

  • Cohen, A. J., Mori-Sánchez, P., & Yang, W. (2012). Challenges for density functional theory. Chemical Reviews, 112, 289–320.

    Article  CAS  Google Scholar 

  • Cramer, C. J., & Truhlar, D. G. (2009). Density functional theory for transition metals and transition metal chemistry. Physical Chemistry Chemical Physics, 11, 10757–10816.

    Article  CAS  Google Scholar 

  • Geerlings, P., De Proft, F., & Langenaeker, W. (2003). Conceptual density functional theory. Chemical Reviews, 103, 1793–1873.

    Article  CAS  Google Scholar 

  • Kohn, W., Becke, A. D., & Parr, R. G. (1996). Density functional theory of electronic structure. Journal of Physical Chemistry, 100, 12974–12980.

    Article  CAS  Google Scholar 

  • Neese, F. (2009). Prediction of molecular properties and molecular spectroscopy with density functional theory: From fundamental theory to exchange-coupling. Coordination Chemistry Reviews, 253, 526–563.

    Article  CAS  Google Scholar 

  • Perdew, J. P., Ruzsinszky, A., Constantin, L. A., Sun, J. W., & Csonka, G. I. (2009). Some fundamental issues in ground-state density functional theory: A guide for the perplexed. Journal of Chemical Theory and Computation, 5, 902–908.

    Article  CAS  Google Scholar 

  • Sousa, S. F., Fernandes, P. A., & Ramos, M. J. (2007). General performance of density functionals. Journal of Physical Chemistry A, 111, 10439–10452.

    Article  CAS  Google Scholar 

  • Ziegler, T. (1991). Approximate density functional theory as practical tool in molecular energetics and dynamics. Chemical Reviews, 91, 651–667.

    Article  CAS  Google Scholar 

  • Ziegler, T. (1995). Density functional theory as practical tool in studies of organometallic energetics and kinetics. Beating the heavy metal blues with DFT. Canadian Journal of Chemistry, 73, 743–761.

    Article  CAS  Google Scholar 

  • Zhao, Y., & Truhlar, D. G. (2008a). Density functionals with broad applicability in chemistry. Accounts of Chemical Research, 41, 157–167.

    Article  CAS  Google Scholar 

Conceptual Developments and Applications of DFT

  • Ahlrichs, R., Penco, R., & Scoles, G. (1977). Intermolecular forces in simple systems. Chemical Physics, 19, 119–130.

    Article  CAS  Google Scholar 

  • Baerends, E. J., Ellis, D. E., & Ros, P. (1973). Self-consistent molecular Hartree-Fock-Slater calculations – I. The computational procedure. Chemical Physics, 2, 41–47.

    Article  CAS  Google Scholar 

  • Baerends, E. J., & Ros, P. (1978). Evaluation of the LCAO Hartree-Fock-Slater method – Applications to transition-metal complexes. International Journal of Quantum Chemistry, 12, 169–190.

    CAS  Google Scholar 

  • Bartlett, R. J., Lotrich,V. F., & Schweigert, I. V. (2005). Ab initio density functional theory: The best of both worlds? Journal of Chemical Physics, 123, art. 062205.

    Google Scholar 

  • Becke, A. D. (1988a). Density-functional exchange-energy Approximation with correct asymptotic behavior. Physical Review A, 38, 3098–3100.

    Article  CAS  Google Scholar 

  • Becke, A. D. (1988b). A multicenter numerical-integration scheme for polyatomic molecules. Journal of Chemical Physics, 88, 2547–2553.

    Article  CAS  Google Scholar 

  • Becke, A. D., & Roussel, M. R. (1989). Exchange holes in inhomogeneous systems – A coordinate-space model. Physical Review A, 39, 3761–3767.

    Article  CAS  Google Scholar 

  • Becke, A. D. (1993a). A new mixing of Hartree-Fock and local density-functional theories. Journal of Chemical Physics, 98, 1372–1377.

    Article  CAS  Google Scholar 

  • Becke, A. D. (1993b). Density-functional thermochemistry: 3. The role of exact exchange. Journal of Chemical Physics, 98, 5648–5652.

    Article  CAS  Google Scholar 

  • Boerrigter, P. M., te Velde, G., & Baerends, E. J. (1988). 3-dimensional numerical-integration for electronic-structure calculations. International Journal of Quantum Chemistry, 33, 87–113.

    Article  CAS  Google Scholar 

  • Furche, F. (2008). Developing the random phase approximation into a practical post-Kohn–Sham correlation model. Journal of Chemical Physics, 129, art. 114105.

    Google Scholar 

  • Gill, P. M. W. (2001). Obituary: Density functional theory (1927–1993). Australian Journal of Chemistry, 54, 661–662.

    Article  CAS  Google Scholar 

  • Grimme, S. (2006a). Semiempirical hybrid density functional with perturbative second-order correlation. Journal of Chemical Physics, 124, art. 034108.

    Google Scholar 

  • Hepburn, J., Scoles, G., & Penco, R. (1975). Simple but reliable method for prediction of intermolecular potentials. Chemical Physics Letters, 36, 451–456.

    Google Scholar 

  • Hertwig, R. H., & Koch, W. (1997). On the parameterization of the local correlation functional. What is Becke-3-LYP? Chemical Physics Letters, 268, 345–351.

    Article  CAS  Google Scholar 

  • Hohenberg, P., & Kohn, W. (1964). Inhomogeneous electron gas. Physics Reviews, 136, B646–B871.

    Article  Google Scholar 

  • Kohn, W., & Sham, L. J. (1965). Self-consistent equations including exchange and correlation effects. Physics Reviews, 140, A1133–A1138.

    Article  Google Scholar 

  • Kurth, S., & Perdew, J. P. (2000). Role of the exchange-correlation energy: Nature’s glue. International Journal of Quantum Chemistry, 77, 814–818.

    Article  CAS  Google Scholar 

  • Leininger, T., Stoll, H., Werner, H. J., & Savin, A. (1997). Combining long-range configuration interaction with short-range density functionals. Chemical Physics Letters, 275, 151–160.

    Article  CAS  Google Scholar 

  • Perdew, J. P. (1986). Density-functional approximation for the correlation-energy of the inhomogeneous electron gas. Physical Review B, 33, 8822–8824.

    Article  CAS  Google Scholar 

  • Perdew, J. P., Burke, K., & Ernzerhof, M. (1996). Generalized gradient approximation made simple. Physical Review Letters, 77, 3865–3868.

    Article  CAS  Google Scholar 

  • Perdew, J. P., & Schmidt, K. (2001). Jacob's ladder of density functional approximations for the exchange-correlation energy. Density Functional Theory and Its Applications to Materials, 577, 1–20.

    Article  CAS  Google Scholar 

  • Peverati, R., & Truhlar, D. G. (2014). The quest for a universal density functional: The accuracy of density functionals across a broad spectrum of databases in chemistry and physics. Philosophical Transactions of the Royal Society A, 372, art. 20120476.

    Google Scholar 

  • Slater, J. C. (1951). A simplification of the Hartree-Fock method. Physics Reviews, 81, 385–390.

    Article  CAS  Google Scholar 

  • Tao, J. M., Perdew, J. P., Staroverov, V. N., & Scuseria, G. E. (2003). Climbing the density functional ladder: Nonempirical meta-generalized gradient approximation designed for molecules and solids, Physical Review Letters, 91, art. 146401.

    Google Scholar 

  • Tsuneda, T., & Hirao, K. (2014). Long-range correction for density functional theory. WIREs Computational Molecular Science, 4, 375–390.

    Article  CAS  Google Scholar 

  • Versluis, L., & Ziegler, T. (1988). The determination of molecular structures by density functional theory: The evaluation of analytical energy gradients by numerical integration. Journal of Chemical Physics, 88, 322–328.

    Article  CAS  Google Scholar 

  • Vosko, S. H., Wilk, L., & Nusair, M. (1980). Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis. Canadian Journal of Physics, 58, 1200–1211.

    Article  CAS  Google Scholar 

  • Zope, R. R., & Dunlap, B. I. (2006). The limitations of Slater’s element-dependent exchange functional from analytic density-functional theory, Journal of Chemical Physics, 124, art. 044107.

    Google Scholar 

Practical Developments and Applications of DFT

  • Autschbach, J. (2012). Orbitals: Some fiction and some facts. Journal of Chemical Education, 89, 1032–1040.

    Article  CAS  Google Scholar 

  • Barden, C. J., Rienstra-Kiracofe, J. C., & Schaefer, H. F. (2000). Homonuclear 3d transition-metal diatomics: A systematic density functional theory study. Journal of Chemical Physics, 113, 690–700.

    Article  CAS  Google Scholar 

  • Curtiss, L. A., Raghavachari, K., Redfern, P. C., & Pople, J. A. (1997). Assessment of Gaussian-2 and density functional theories for the computation of enthalpies of formation. Journal of Chemical Physics, 106, 1063–1079.

    Article  CAS  Google Scholar 

  • Curtiss, L. A., Raghavachari, K., Redfern, P. C., & Pople, J. A. (2000). Assessment of Gaussian-3 and density functional theories for a larger experimental test set. Journal of Chemical Physics, 112, 7374–7383.

    Article  CAS  Google Scholar 

  • Ghosh, A. (2006). Transition metal spin state energetics and noninnocent systems: Challenges for DFT in the bioinorganic arena. Journal of Biological Inorganic Chemistry, 11, 712–714.

    Article  CAS  Google Scholar 

  • Grimme, S. (2006b). Semiempirical GGA-type density functional constructed with a long-range dispersion correction. Journal of Computational Chemistry, 27, 1787–1799.

    Article  CAS  Google Scholar 

  • Grimme, S. (2006c). Seemingly simple stereoelectronic effects in alkane isomers and the implications for Kohn-Sham density functional theory. Angewandte Chemie International Edition, 45, 4460–4464.

    Article  CAS  Google Scholar 

  • Güell, M., Luis, J. M., Solà, M., & Swart, M. (2008). Importance of the basis set for the spin-state energetics of iron complexes. Journal of Physical Chemistry A, 112, 6384–6391.

    Article  Google Scholar 

  • Holland, J. P., & Green, J. C. (2010). Evaluation of exchange-correlation functionals for time-dependent density functional theory calculations on metal complexes. Journal of Computational Chemistry, 31, 1008–1014.

    CAS  Google Scholar 

  • Jacquemin, D., Perpete, E. A., Scuseria, G. E., Ciofini, I., & Adamo, C. (2008). TD-DFT performance for the visible absorption spectra of organic dyes: Conventional versus long-range hybrids. Journal of Chemical Theory and Computation, 4, 123–135.

    Article  CAS  Google Scholar 

  • Kelly, R. A., Clavier, H., Giudice, S., Scott, N. M., Stevens, E. D., Bordner, J., Samardjiev, I., Hoff, C. D., Cavallo, L., & Nolan, S. P. (2008). Determination of N-heterocyclic carbene (NHC) steric and electronic parameters using the [(NHC)Ir(CO)(2)Cl] system. Organometallics, 27, 202–210.

    Article  CAS  Google Scholar 

  • Korth, M., & Grimme, S. (2009). “Mindless” DFT Benchmarking. Journal of Chemical Theory and Computation, 5, 993–1003.

    Article  CAS  Google Scholar 

  • Lynch, B. J., & Truhlar, D. G. (2003). Small representative benchmarks for thermochemical calculations. Journal of Physical Chemistry A, 107, 8996–8999.

    Article  CAS  Google Scholar 

  • Pierloot, K,. & Vancoillie, S. J. (2008). Relative energy of the high-(T-5(2g)) and low-((1)A(1g)) spin states of the ferrous complexes [Fe(L)(NHS4)]: CASPT2 versus density functional theory. Journal of Chemical Physics, 128, art. 034104.

    Google Scholar 

  • Reiher, M., Salomon, O., & Hess, B. A. (2001). Reparameterization of hybrid functionals based on energy differences of states of different multiplicity. Theoretical Chemistry Accounts, 107, 48–55.

    Article  CAS  Google Scholar 

  • Riley, K. E., Op’t Holt, B. T., & Merz, K. M. (2007). Critical assessment of the performance of density functional methods for several atomic and molecular properties. Journal of Chemical Theory and Computation, 3, 407–433.

    Article  CAS  Google Scholar 

  • Schultz, N. E., Zhao, Y., & Truhlar, D. G. (2005a). Density functionals for inorganometallic and organometallic chemistry. Journal of Physical Chemistry A, 109, 11127–11143.

    Article  CAS  Google Scholar 

  • Schultz, N. E., Zhao, Y., & Truhlar, D. G. (2005b). Databases for transition element bonding: Metal-metal bond energies and bond lengths and their use to test hybrid, hybrid meta, and meta density functionals and generalized gradient approximations. Journal of Physical Chemistry A, 109, 4388–4403.

    Article  CAS  Google Scholar 

  • Sorkin, A., Iron, M. A., & Truhlar, D. G. (2008). Density functional theory in transition-metal chemistry: Relative energies of low-lying states of iron compounds and the effect of spatial symmetry breaking. Journal of Chemical Theory and Computation, 4, 307–315.

    Article  CAS  Google Scholar 

  • Sponer, J., Jurecka, P., & Hobza, P. (2004). Accurate interaction energies of hydrogen-bonded nucleic acid base pairs. Journal of the American Chemical Society, 126, 10142–10151.

    Article  CAS  Google Scholar 

  • Stowasser, R., & Hoffmann, R. (1999). What do the Kohn-Sham orbitals and eigenvalues mean? Journal of the American Chemical Society, 121, 3414–3420.

    Article  CAS  Google Scholar 

  • Swart, M. (2008). Accurate spin-state energies for iron complexes. Journal of Chemical Theory and Computation, 4, 2057–2066.

    Article  CAS  Google Scholar 

  • Wang, N. X., & Wilson, A. K. (2004). The behavior of density functionals with respect to basis set. I. The correlation consistent basis sets. Journal of Chemical Physics, 121, 7632–7646.

    Article  CAS  Google Scholar 

  • Wodrich, M. D., Corminboeuf, C., & Schleyer, P. v. R. (2006). Systematic errors in computed alkane energies using B3LYP and other popular DFT functionals. Organic Letters, 8, 3631–3634.

    Article  CAS  Google Scholar 

  • Yang, W. (1991). Direct calculation of electron density in density functional theory. Physical Review Letters, 66, 1438–1441.

    Article  CAS  Google Scholar 

  • Zhao, Y., Pu, J., Lynch, B. J., & Truhlar, D. G. (2004). Tests of second-generation and third-generation density functionals for thermochemical kinetics. Physical Chemistry Chemical Physics, 6, 673–676.

    Article  CAS  Google Scholar 

  • Zhao, Y., & Truhlar, D. G. (2004). Hybrid meta density functional theory methods for thermochemistry, thermochemical kinetics, and noncovalent interactions: The MPW1B95 and MPWB1K models and comparative assessments for hydrogen bonding and van der Waals interactions J. Journal of Physical Chemistry A, 108, 6908–6918.

    Article  CAS  Google Scholar 

  • Zhao, Y., & Truhlar, D. G. (2005a). Design of density functionals that are broadly accurate for thermochemistry, thermochemical kinetics, and nonbonded interactions. Journal of Physical Chemistry A, 109, 5656–5667.

    Article  CAS  Google Scholar 

  • Zhao, Y., & Truhlar, D. G. (2005b). Benchmark databases for nonbonded interactions and their use to test density functional theory. Journal of Chemical Theory and Computation, 1, 415–432.

    Article  CAS  Google Scholar 

  • Zhao, Y., Gonzalez-Garcia, N., & Truhlar, D. G. (2005). Benchmark database of barrier heights for heavy atom transfer, nucleophilic substitution, association, and unimolecular reactions and its use to test theoretical methods. Journal of Physical Chemistry A, 109, 2012–2018.

    Article  CAS  Google Scholar 

  • Zhao, Y., & Truhlar, D. G. (2005c). How well can new-generation density functional methods describe stacking interactions in biological systems? Physical Chemistry Chemical Physics, 7, 2701–2705.

    Article  CAS  Google Scholar 

  • Zhao, Y., Schultz, N. E., & Truhlar, D. G. (2006). Design of density functionals by combining the method of constraint satisfaction with parametrization for thermochemistry, thermochemical kinetics, and noncovalent interactions. Journal of Chemical Theory and Computation, 2, 364–382.

    Article  Google Scholar 

  • Zhao, Y., & Truhlar, D. G. (2008b). The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theoretical Chemistry Accounts, 120, 215–241.

    Article  CAS  Google Scholar 

  • Zhou, M., Andrews, L., & Bauschlicher, C. W. (2001). Spectroscopic and theoretical investigations of vibrational frequencies in binary unsaturated transition-metal carbonyl cations, neutrals, and anions. Chemical Reviews, 101, 1931–1961.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Heiko Jacobsen .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this entry

Cite this entry

Jacobsen, H., Cavallo, L. (2017). Directions for Use of Density Functional Theory: A Short Instruction Manual for Chemists. In: Leszczynski, J., Kaczmarek-Kedziera, A., Puzyn, T., G. Papadopoulos, M., Reis, H., K. Shukla, M. (eds) Handbook of Computational Chemistry. Springer, Cham. https://doi.org/10.1007/978-3-319-27282-5_4

Download citation

Publish with us

Policies and ethics