Editorial for PCCP themed issue "Developments in Density Functional Theory".

The present issue presents a state-of-theart collection of articles on density functional theory and celebrates the enormous contributions that Evert Jan Baerends has made to this research field. Density functional theory (DFT) is currently one of the main approaches used in electronic structure theory. The history of the method goes back to the ground breaking work of Hohenberg and Kohn which implies that any ground state expectation value can be written as a functional of the density alone. Since then, DFT has inspired a vast amount of work in electronic structure theory, as it offers a possible approach to calculate the ground state properties of many-electron systems, such as molecules and solids, while bypassing the calculation of the complicated many-particle ground state wavefunction. Much effort has gone into finding explicit expressions for the energy as a functional of the density, the minimisation of which gives the ground state energy and density. By means of the so-called Kohn–Sham method this minimisation problem is reduced to solving effective one-particle equations with an effective potential which contains many-body interactions via the so-called exchange (xc) correlation potential which is the functional derivative of the xc energy functional. Since the quality of a DFT calculation depends on the accuracy of the approximate form of the xc-energy functional, many studies have been devoted to finding more accurate approximate expressions for the xc-energy functional and xc-potential. This is a very hard task due to the complicated nature of the many-body interactions and diversity of systems which the functional should be able to describe. To make this task easier, it is important to understand some basic general features of many-body correlations that are present in a wide variety of systems. And it is exactly to the understanding of this problem that Evert Jan Baerends has made a substantial contribution by elucidating the connection between properties of the xc-potential and that of the so-called exchange–correlation hole. The latter quantity describes the difference between the conditional and unconditional probability for finding an electron at a given position r1 when it is known that there is an electron at r2. This concept has played a very important role in the development of approximate xc-energy functionals. The simplest functional that can be constructed on the basis of the xc-hole is the local density approximation (LDA). The accuracy of the LDA can be improved by means of the so-called generalized gradient approximations (GGAs) which were pioneered on the basis of the xc-hole concept during the 1980s especially by Becke and Perdew. These functionals were successful in improving the bond energies of molecules considerably and this led to a massive interest in DFT methods in the quantum chemistry community during the 1990s. However, at the time, it was still unclear on how well-founded the GGAs were and whether the assumptions made in their derivation were actually satisfied in real molecules. While the use of DFT in chemistry is now undisputed, the search for still better functionals with additional ingredients continues, as is illustrated by the contribution of Maier, Haasler, Arbuznikov and Kaupp (DOI: 10.1039/c6cp00990e) on local hybrid functionals, the contribution of Lani, Di Marino, Gerolin, van Leeuwen and Gori-Giorgi (DOI: 10.1039/c6cp00339g) on functionals derived from the strictly correlated limit, and the work by Grimme and Steinmetz (DOI: 10.1039/c5cp06600j) on double hybrid functionals. Other methods to extend DFT beyond the conventional static Kohn–Sham single-determinant approach include real-time TDDFT by Fuks, Nielsen, Ruggenthaler and Maitra (DOI: 10.1039/c6cp00722h) and a GVB Ansatz to ensemble DFT by Filatov, Martı́nez and Kim (DOI: 10.1039/c6cp00236f). The insight that the exact xc-potential can be studied by accurate wave function a Department of Physics, University of Jyväskylä, Survontie 9 40014 Jyväskylä, Finland. E-mail: robert.vanleeuwen@jyu.fi b Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation (CMTC), Westfälische Wilhelms-Universität Münster, Corrensstrasse 40, 48149 Münster, Germany. E-mail: j.neugebauer@uni-muenster.de c Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling (ACMM), Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands. E-mail: l.visscher@vu.nl E-mail: f.m.bickelhaupt@vu.nl d Institute of Molecules and Materials (IMM), Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands. E-mail: f.m.bickelhaupt@vu.nl DOI: 10.1039/c6cp90143c

[1]  R. Dreizler,et al.  Density Functional Theory: An Advanced Course , 2011 .

[2]  Basic density-functional theory - an overview , 2004 .

[3]  E. Baerends,et al.  Physical Meaning of Virtual Kohn-Sham Orbitals and Orbital Energies: An Ideal Basis for the Description of Molecular Excitations. , 2014, Journal of chemical theory and computation.

[4]  Peter Schwerdtfeger,et al.  Relativistic atomic orbital contractions and expansions: magnitudes and explanations , 1990 .

[5]  Johannes Neugebauer,et al.  Modeling solvent effects on electron-spin-resonance hyperfine couplings by frozen-density embedding. , 2005, The Journal of chemical physics.

[6]  Evert Jan Baerends,et al.  Molecular calculations of excitation energies and (hyper)polarizabilities with a statistical average of orbital model exchange-correlation potentials , 2000 .

[7]  Johannes Neugebauer,et al.  An explicit quantum chemical method for modeling large solvation shells applied to aminocoumarin C151. , 2005, The journal of physical chemistry. A.

[8]  Evert Jan Baerends,et al.  An approximate exchange-correlation hole density as a functional of the natural orbitals , 2002 .

[9]  E. Baerends,et al.  Correct dissociation limit for the exchange‐correlation energy and potential , 2006 .

[10]  E J Baerends,et al.  The Kohn-Sham gap, the fundamental gap and the optical gap: the physical meaning of occupied and virtual Kohn-Sham orbital energies. , 2013, Physical chemistry chemical physics : PCCP.

[11]  A. Warshel,et al.  Frozen density functional approach for ab initio calculations of solvated molecules , 1993 .

[12]  Evert Jan Baerends,et al.  Density-functional-theory response-property calculations with accurate exchange-correlation potentials , 1998 .

[13]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

[14]  R. Leeuwen,et al.  Step structure in the atomic Kohn-Sham potential , 1995 .

[15]  Evert Jan Baerends,et al.  An improved density matrix functional by physically motivated repulsive corrections. , 2005, The Journal of chemical physics.

[16]  Senatore,et al.  Density dependence of the dielectric constant of rare-gas crystals. , 1986, Physical review. B, Condensed matter.

[17]  Trygve Helgaker,et al.  Excitation energies in density functional theory: an evaluation and a diagnostic test. , 2008, The Journal of chemical physics.

[18]  E. Baerends,et al.  Excitation energies with time-dependent density matrix functional theory: Singlet two-electron systems. , 2009, The Journal of chemical physics.

[19]  R. Leeuwen,et al.  Exchange-correlation potential with correct asymptotic behavior. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[20]  E. Baerends,et al.  Time-dependent density-matrix-functional theory , 2007 .

[21]  Cortona,et al.  Self-consistently determined properties of solids without band-structure calculations. , 1991, Physical review. B, Condensed matter.

[22]  E. Baerends,et al.  Atomic and molecular hydrogen interacting with Pt(111). , 1999 .

[23]  E. Baerends,et al.  Excitation energies of dissociating H2: A problematic case for the adiabatic approximation of time-dependent density functional theory , 2000 .

[24]  Johannes Neugebauer,et al.  The merits of the frozen-density embedding scheme to model solvatochromic shifts. , 2005, The Journal of chemical physics.

[25]  Baerends,et al.  Effect of molecular dissociation on the exchange-correlation Kohn-Sham potential. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[26]  E. J. Baerends,et al.  An analytical six-dimensional potential energy surface for dissociation of molecular hydrogen on Cu(100) , 1996 .

[27]  E. Baerends,et al.  Robust normal modes in vibrational circular dichroism spectra. , 2009, Physical chemistry chemical physics : PCCP.

[28]  Johannes Neugebauer,et al.  Exploring the ability of frozen-density embedding to model induced circular dichroism. , 2006, The journal of physical chemistry. A.

[29]  J. G. Snijders,et al.  Towards an order-N DFT method , 1998 .

[30]  G. te Velde,et al.  Three‐dimensional numerical integration for electronic structure calculations , 1988 .

[31]  Samuel Fux,et al.  Analysis of electron density distributions from subsystem density functional theory applied to coordination bonds , 2008 .

[32]  Evert Jan Baerends,et al.  Relativistic regular two-component Hamiltonians. , 1996 .

[33]  E. Baerends,et al.  Effects of complex formation on vibrational circular dichroism spectra. , 2008, The journal of physical chemistry. A.

[34]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[35]  E. Baerends,et al.  Self-consistent approximation to the Kohn-Sham exchange potential. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[36]  Erik Van Lenthe,et al.  Optimized Slater‐type basis sets for the elements 1–118 , 2003, J. Comput. Chem..

[37]  E. Baerends,et al.  Response calculations based on an independent particle system with the exact one-particle density matrix: excitation energies. , 2012, The Journal of chemical physics.

[38]  Baerends,et al.  Analysis of correlation in terms of exact local potentials: Applications to two-electron systems. , 1989, Physical review. A, General physics.

[39]  Evert Jan Baerends,et al.  Self-consistent molecular Hartree—Fock—Slater calculations I. The computational procedure , 1973 .

[40]  M. Head‐Gordon,et al.  Failure of time-dependent density functional theory for long-range charge-transfer excited states: the zincbacteriochlorin-bacteriochlorin and bacteriochlorophyll-spheroidene complexes. , 2004, Journal of the American Chemical Society.

[41]  Carsten A. Ullrich,et al.  Time-Dependent Density-Functional Theory: Concepts and Applications , 2012 .

[42]  E J Baerends,et al.  Charge transfer, double and bond-breaking excitations with time-dependent density matrix functional theory. , 2008, Physical review letters.

[43]  E. Engel,et al.  Density Functional Theory , 2011 .

[44]  Johannes Neugebauer,et al.  Assessment of a simple correction for the long-range charge-transfer problem in time-dependent density-functional theory. , 2006, The Journal of chemical physics.

[45]  Evert Jan Baerends,et al.  Physical interpretation and evaluation of the Kohn-Sham and Dyson components of the epsilon-I relations between the Kohn-Sham orbital energies and the ionization potentials , 2003 .

[46]  Evert Jan Baerends,et al.  Shape corrections to exchange-correlation potentials by gradient-regulated seamless connection of model potentials for inner and outer region , 2001 .

[47]  A. Cohen,et al.  Variational density matrix functional calculations for the corrected Hartree and corrected Hartree–Fock functionals , 2002 .

[48]  E. Baerends,et al.  Coupled-perturbed density-matrix functional theory equations. Application to static polarizabilities. , 2006, The Journal of chemical physics.

[49]  Evert Jan Baerends,et al.  Adiabatic approximation of time-dependent density matrix functional response theory. , 2007, The Journal of chemical physics.

[50]  Evert Jan Baerends,et al.  Relativistic effects on bonding , 1981 .

[51]  Evert Jan Baerends,et al.  A Quantum Chemical View of Density Functional Theory , 1997 .

[52]  E. Baerends,et al.  Away from generalized gradient approximation: orbital-dependent exchange-correlation functionals. , 2005, The Journal of chemical physics.

[53]  E. J. Baerends,et al.  One - determinantal pure state versus ensemble Kohn-Sham solutions in the case of strong electron correlation: CH2 and C2 , 1998 .

[54]  Evert Jan Baerends,et al.  Asymptotic correction of the exchange-correlation kernel of time-dependent density functional theory for long-range charge-transfer excitations. , 2004, The Journal of chemical physics.

[55]  E. J. Baerends,et al.  Benchmark calculations of chemical reactions in density functional theory: comparison of the accurate Kohn-Sham solution with generalized gradient approximations for the H2+H and H2+H2 reactions. , 1999 .

[56]  E. Baerends,et al.  Precise density-functional method for periodic structures. , 1991, Physical review. B, Condensed matter.

[57]  E. J. Baerends,et al.  Orbital structure of the Kohn-Sham exchange potential and exchange kernel and the field-counteracting potential for molecules in an electric field , 2001 .

[58]  E. Baerends,et al.  Reactive and Nonreactive Scattering of H2 from a Metal Surface Is Electronically Adiabatic , 2006, Science.

[59]  F. Matthias Bickelhaupt,et al.  Chemistry with ADF , 2001, J. Comput. Chem..

[60]  R. Dreizler,et al.  Density Functional Theory: An Approach to the Quantum Many-Body Problem , 1991 .

[61]  E. J. Baerends,et al.  Approximation of the exchange-correlation Kohn-Sham potential with a statistical average of different orbital model potentials. , 1999 .