Exact-exchange time-dependent density-functional theory for static and dynamic polarizabilities So Hirata, * Stanislav Ivanov, and Rodney J. Bartlett ² Quantum Theory Project, Department of Chemistry, University of Florida, Gainesville, Florida 32611-8435, USA Ireneusz Grabowski Institute of Physics, Nicolaus Copernicus University, Toruń 87-100, Poland sReceived 16 November 2004; published 21 March 2005d Time-dependent density-functional theory sTDDFTd employing the exact-exchange functional has been formulated on the basis of the optimized-effective-potential sOEPd method of Talman and Shadwick for second-order molecular properties and implemented into a Gaussian-basis-set, trial-vector algorithm. The only approximation involved, apart from the lack of correlation effects and the use of Gaussian-type basis functions, was the consistent use of the adiabatic approximation in the exchange kernel and in the linear response function. The static and dynamic polarizabilities and their anisotropy predicted by the TDDFT with exact exchange sTDOEPd agree accurately with the corresponding values from time-dependent Hartree-Fock theory, the exact-exchange counterpart in the wave function theory. The TDOEP is free from the nonphysical asymptotic decay of the exchange potential of most conventional density functionals or from any other mani- festations of the incomplete cancellation of the self-interaction energy. The systematic overestimation of the absolute values and dispersion of polarizabilities that plagues most conventional TDDFT cannot be seen in the TDOEP. DOI: 10.1103/PhysRevA.71.032507 PACS numberssd: 31.15.Ew, 31.101z, 31.70.Hq, 33.15.Kr I. INTRODUCTION In spite of their remarkable success, Hohenberg-Kohn f1g and Kohn-Sham sKSdf2g density-functional theories sDFT’sd have been criticized as not being a constructive theory, of- fering neither analytically nor numerically tractable a path to the exact exchange-correlation functional. However, this situation has changed dramatically in recent years when a number of rigorous theoretical approaches f3–22g to define converging approximations to the exact exchange-correlation functional have been proposed and have become subject to numerical scrutiny. One such approach consists of the one-particle KS equa- tion with a local, multiplicative exchange-correlation poten- tial defined as the functional derivative of a nonlocal orbital- dependent exchange-correlation functional with respect to electron density f11,16,18–21g. The functionals are those es- tablished in ab initio wave function theory sWFTd such as many-body perturbation theory sMBPTdf11,16,18–20g and coupled-cluster sCCdf21g theory energy functionals. This ap- proach therefore makes use of the variational theorem that is the centerpiece of KS DFT. Others include the Görling-Levy sGLdf8,9g and related f20–22g perturbation theories and the method of the Sham-Schlüter sSSd equation f5,7,10,12g. The GL perturbation theory invokes the premise that the exact one-electron KS orbitals must give rise to the electron den- sity of the exact many-electron wave function. Accordingly, the GL perturbation theory insists that the electron density from the KS orbitals at a given order of the GL perturbation expansion of the exact exchange-correlation functional be correct through that order. In the SS method, a nonlocal self- energy operator in the Dyson equation is projected onto a local operator which is interpreted as the exchange- correlation potential in the KS equation. Collectively, these methods can be called ab initio DFT f20–23g in distinction to other conventional DFT’s that embrace semiempiricism or nonsystematic approximations. The essential features common to all ab initio DFT real- izations are the use of systematic orbital-dependent exchange-correlation functionals and the locality ansatz of the corresponding exchange-correlation potentials. While much of the simplicity afforded by the conventional, non- orbital-dependent functionals may be lost in ab initio DFT, the latter provides a number of critical theoretical and prac- tical advantages over the former. Principally, it gives an un- ambiguous theoretical route to the exact exchange- correlation functional. Second, it suggests a spectrum of new, useful methods as approximations to the exact exchange- correlation functional. Third, various analytical conditions and theorems that hold generally for KS DFT can be applied to the calculated quantities of ab initio DFT se.g., Janak’s theorem f24,25g for the ionization potentiald. While the lo- cality ansatz has been introduced only to relate these meth- ods to KS DFT, the local correlation potential embeds the correlation effects into orbitals and orbital energies and thereby can make the convergence of approximations in ab initio DFT potentially more rapid than the corresponding se- ries in ab initio WFT f19–23gscf. the use of natural f26g or Brueckner f27g orbitals in ab initio WFTd. However, when carried through to the exact limit, ab initio DFT will be as expensive as the full configuration interaction method of ab initio WFT, in spite of the opposite assertion often made in favor of exact DFT. While the different ab initio DFT methods may give rise *Author to whom correspondence should be addressed. Electronic mail: hirata@qtp.ufl.edu ² Also at the Department of Physics. PHYSICAL REVIEW A 71, 032507 s2005d 1050-2947/2005/71s3d/032507s7d/$23.00 ©2005 The American Physical Society 032507-1