Abstract
Linear response methods allow for the calculation of various observables connected to the electronic response to an external perturbation. In this chapter, we give an introduction to density functional perturbation theory (DFPT) and several of its applications. After a general derivation of the central DFPT equations we explicitly discuss the calculation of nuclear magnetic resonance (NMR) chemical shifts for the determination of supramolecular packing motifs. In the last part of our chapter, we outline an approach to the calculation of van der Waals interactions from first principles using DFPT.
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Andersson, Y., Langreth, D. Lundqvist, B.I.: van der Waals interactions in density-functional theory. Phys. Rev. Lett. 76(1), 102–105 (1996)
Baroni, S., De Gironcoli, S., Del Corso, A., Giannozzi, P.: Phonons and related crystal properties from density-functional perturbation theory. Rev. Mod. Phys. 73, 515 (2001)
DiLabio, G.A.: Accurate treatment of van der Waals interactions using standard density functional theory methods with effective core-type potentials: application to carbon-containing dimers. Chem. Phys. Lett. 455(4–6), 348–353 (2008)
Dion, M., Rydberg, H., Schröder, E., Langreth, D.C., Lundqvist, B.I.: Van der Waals density functional for general geometries. Phys. Rev. Lett. 92, 246401 (2004)
Ditchfield, R.: Gauge including atomic orbitals. J. Chem. Phys. 56, 5688 (1972)
Dudenko, D., Kiernowski, A., Shu, J., Pisula, W., Sebastiani, D., Spiess, H.W., Hansen, M.R.: A strategy for revealing the packing in semicrystalline \(\pi \)-conjugated polymers: crystal structure of bulk Poly-3-hexyl-thiophene (P3HT). Angew. Chem. Int. Ed. 51, 11068–11072 (2012)
Gonze, X.: Perturbation expansion of variational-principles at arbitrary order. Phys. Rev. A 52, 1086–1095 (1995)
Gonze, X.: Adiabatic density-functional perturbation theory. Phys. Rev. A 52(5), 1096–1114 (1995)
Gregor, T., Mauri, F., Car, R.: A comparison of methods for the calculation of NMR chemical shifts. J. Chem. Phys. 111, 1815–1822 (1999)
Grimme, S.: Accurate description of van der Waals complexes by density functional theory including empirical corrections. J. Comput. Chem. 25, 1463–1473 (2004)
Grimme, S.: Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comp. Chem. 27(15), 1787–1799 (2006)
Hohenberg, P., Kohn, W.: Inhomogeneous electron gas. Phys. Rev. 136, B864–B871 (1964)
Keith, T.A., Bader, R.F.W.: Calculation of magnetic response properties using atoms in molecules. Chem. Phys. Lett. 194(1–2), 1–8 (1992)
Kohn, W., Sham, L.J.: Self-Consistent Equations Including Exchange and Correlation Effects. Defense Technical Information Center (1965)
Kutzelnigg, W.: Individual Gauges for localized orbitals. Isr. J. Chem. 19, 193 (1980)
Kutzelnigg, W., Fleischer, U., Schindler, M.: The IGLO method. NMR Basic Principles Prog. 23, 165 (1990)
Langreth, D.C., Dion, M., Rydberg, H., Schröder, E., Hyldgaard, P., Van der Lundqvist, B.I.: Waals density functional theory with applications. Int. J. Quant. Chem. 101(5), 599–610 (2005)
Langreth, D.C., Lundqvist, B.I., Chakarova-Käck, S.D., Cooper, V.R., Dion, M., Hyldgaard, P., Thonhauser, T.: A density functional for sparse matter. J. Phys.: Condens. Matter 21(8), 084203 (2009)
Lee, K., Murray, É.D., Kong, L., Lundqvist, B.I., Langreth, D.C.: Higher-accuracy van der Waals density functional. Phys. Rev. B 82(8), 081101 (2010)
Limbach, H.-H., Tolstoy, P.M., Perez-Hernandez, N., Guo, J., Shenderovich, I.G., Denisov, G.S.: OHO hydrogen bond geometries and NMR chemical shifts: from equilibrium structures to geometric H/D isotope effects, with applications for water, protonated water, and compressed ice. Isr. J. Chem. 49(2), 199–216 (2009)
Lin, I.-C., Coutinho-Neto, M.M.D., Felsenheimer, C., von Lilienfeld, O.A., Tavernelli, I., Röthlisberger, U.: Library of dispersion-corrected atom-centered potentials for generalized gradient approximation functionals: elements H, C, N, O, He, Ne, Ar, and Kr. Phys. Rev. B 75(20), 205131 (2007)
Lundqvist, B.I., Andersson, Y., Shao, H., Chan, S., Langreth, D.C.: Density functional theory including van der Waals forces. Int. J. Quant. Chem. 56(4), 247–255 (1995)
Mahan, G.D.: Modified Sternheimer equation for polarizability. Phys. Rev. A 22(5), 1780–1785 (1980)
Mahan, G.D.: van der Waals coefficient between closed shell ions. J. Chem. Phys. 76(1), 493–497 (1982)
Mauri, F., Louie, S.: Magnetic susceptibility of insulators from first principles. Phys. Rev. Lett. 76, 4246–4249 (1996)
Mauri, F., Pfrommer, B., Louie, S.: Ab initio theory of NMR chemical shifts in solids and liquids. Phys. Rev. Lett. 77, 5300–5303 (1996)
Nguyen, H.-V., de Gironcoli, S.: Van der Waals coefficients of atoms and molecules from a simple approximationfor the polarizability. Phys. Rev. B 79, 115105 (2009)
Ohno, K., Mauri, F., Louie, S.: Magnetic susceptibility of semiconductors by an all-electron first-principles approach. Phys. Rev. B 56, 1009 (1997)
Pickard, C.J., Mauri, F.: All-electron magnetic response with pseudopotentials: NMR chemical shifts. Phys. Rev. B 63, 245101 (2001)
Putrino, A., Sebastiani, D., Parrinello, M.: Generalized variational density functional perturbation theory. J. Chem. Phys. 113(17), 7102–7109 (2000)
Rydberg, H., Dion, M., Jacobson, N., Schröder, E., Hyldgaard, P., Simak, S.I., Van der Langreth, D.C.: Waals density functional for layered structures. Phys. Rev. Lett. 91, 126402 (2003)
Sebastiani, D., Parrinello, M.: A new ab-initio approach for NMR chemical shifts in periodic systems. J. Phys. Chem. 105, 1951–1958 (2001)
Sebastiani, D.: Ab-initio calculation of nuclear magnetic resonance parameters in condensed phases. Mod. Phys. Lett. B 17, 1301–1319 (2003)
Sebastiani, D., Goward, G.R., Schnell, I., Parrinello, M.: NMR chemical shifts in periodic systems from first principles. Comp. Phys. Commun. 147, 707 (2002)
von Lilienfeld, O.A., Tavernelli, I., Rothlisberger, U., Sebastiani, D.: Optimization of effective atom centered potentials for London dispersion forces in density functional theory. Phys. Rev. Lett. 93(15), 153004 (2004)
Vydrov, O.A., Van Voorhis, T.: Nonlocal van der Waals density functional made simple. Phys. Rev. Lett. 103, 063004 (2009)
Vydrov, O.A., Van Voorhis, T.: Benchmark assessment of the accuracy of several van der Waals density functionals. J. Chem. Theor. Comput. 8(6), 1929–1934 (2012)
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Watermann, T., Scherrer, A., Sebastiani, D. (2014). Linear Response Methods in Quantum Chemistry. In: Bach, V., Delle Site, L. (eds) Many-Electron Approaches in Physics, Chemistry and Mathematics. Mathematical Physics Studies. Springer, Cham. https://doi.org/10.1007/978-3-319-06379-9_5
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