Cubic response functions in time-dependent density functional theory.

We present density-functional theory for time-dependent response functions up to and including cubic response. The working expressions are derived from an explicit exponential parametrization of the density operator and the Ehrenfest principle, alternatively, the quasienergy ansatz. While the theory retains the adiabatic approximation, implying that the time-dependency of the functional is obtained only implicitly-through the time dependence of the density itself rather than through the form of the exchange-correlation functionals-it generalizes previous time-dependent implementations in that arbitrary functionals can be chosen for the perturbed densities (energy derivatives or response functions). In particular, general density functionals beyond the local density approximation can be applied, such as hybrid functionals with exchange correlation at the generalized-gradient approximation level and fractional exact Hartree-Fock exchange. With our implementation the response of the density can always be obtained using the stated density functional, or optionally different functionals can be applied for the unperturbed and perturbed densities, even different functionals for different response order. As illustration we explore the use of various combinations of functionals for applications of nonlinear optical hyperpolarizabilities of a few centrosymmetric systems; molecular nitrogen, benzene, and the C(60) fullerene. Considering that vibrational, solvent, and local field factors effects are left out, we find in general that very good experimental agreement can be obtained for the second dynamic hyperpolarizability of these systems. It is shown that a treatment of the response of the density beyond the local density approximation gives a significant effect. The use of different functional combinations are motivated and discussed, and it is concluded that the choice of higher order kernels can be of similar importance as the choice of the potential which governs the Kohn-Sham orbitals.

[1]  Dennis R. Salahub,et al.  Dynamic polarizabilities and excitation spectra from a molecular implementation of time‐dependent density‐functional response theory: N2 as a case study , 1996 .

[2]  Benoît Champagne,et al.  Assessment of Conventional Density Functional Schemes for Computing the Polarizabilities and Hyperpolarizabilities of Conjugated Oligomers: An Ab Initio Investigation of Polyacetylene Chains , 1998 .

[3]  Alan K. Burnham,et al.  Measurement of the dispersion in polarizability anisotropies , 1975 .

[4]  Daniel S. Elliott,et al.  Measurements of molecular hyperpolarizabilities for ethylene, butadiene, hexatriene, and benzene , 1978 .

[5]  Parr,et al.  Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. , 1988, Physical review. B, Condensed matter.

[6]  G. Wendin.  Generalization of the RPAE: 4d-photoabsorption in atomic Ba including relaxation effects , 1975 .

[7]  Nonlinear optical properties of fullerenes , 1996 .

[8]  G. Bertsch,et al.  Real-space computation of dynamic hyperpolarizabilities , 2001 .

[9]  S. Dixit,et al.  Microscopic theory of third-harmonic generation and electro-absorption in conjugated polymers , 1992 .

[10]  Bertsch,et al.  Time-dependent local-density approximation in real time. , 1996, Physical review. B, Condensed matter.

[11]  Lucas,et al.  Polarization waves and van der Waals cohesion of C60 fullerite. , 1992, Physical review. B, Condensed matter.

[12]  G. Maroulis.  Accurate electric multipole moment, static polarizability and hyperpolarizability derivatives for N2 , 2003 .

[13]  Julia E. Rice,et al.  The calculation of frequency‐dependent polarizabilities as pseudo‐energy derivatives , 1991 .

[14]  N. Rösch,et al.  An efficient method for calculating molecular excitation energies by time-dependent density-functional theory , 2000 .

[15]  Yi Luo,et al.  Ab initio calculations of the polarizability and the hyperpolarizability of C60 , 1997 .

[16]  G. Scuseria,et al.  An efficient implementation of time-dependent density-functional theory for the calculation of excitation energies of large molecules , 1998 .

[17]  John C. Wright,et al.  Measurement of the resonant third-order nonlinear susceptibility of C60 by nondegenerate four-wave mixing , 1996 .

[18]  Nicholas C. Handy,et al.  On the determination of excitation energies using density functional theory , 2000 .

[19]  Shelton.  Nonlinear-optical susceptibilities of gases measured at 1064 and 1319 nm. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[20]  J. G. Snijders,et al.  Improved density functional theory results for frequency‐dependent polarizabilities, by the use of an exchange‐correlation potential with correct asymptotic behavior , 1996 .

[21]  A. Becke,et al.  Density-functional exchange-energy approximation with correct asymptotic behavior. , 1988, Physical review. A, General physics.

[22]  Senatore,et al.  Nonlinear response of closed-shell atoms in the density-functional formalism. , 1987, Physical review. A, General physics.

[23]  A. Buckingham,et al.  The magnetic susceptibility anisotropy of benzene, 1,3,5-trifluorobenzene and hexafluorobenzene , 1972 .

[24]  Jorge M. Seminario,et al.  Recent developments and applications of modern density functional theory , 1996 .

[25]  Aaron M. Lee,et al.  The determination of hyperpolarizabilities using density functional theory with nonlocal functionals , 1994 .

[26]  D. Shelton.  Dispersion of the nonlinear susceptibility measured for benzene , 1985 .

[27]  A. Becke.  Density-functional thermochemistry. III. The role of exact exchange , 1993 .

[28]  M. Frisch,et al.  Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields , 1994 .

[29]  Paweł Sałek,et al.  Density-functional theory of linear and nonlinear time-dependent molecular properties , 2002 .

[30]  Evert Jan Baerends,et al.  Calculating frequency-dependent hyperpolarizabilities using time-dependent density functional theory , 1998 .

[31]  R. Fleming,et al.  Deposition and characterization of fullerene films , 1991 .

[32]  Fabio Della Sala,et al.  Efficient methods to calculate dynamic hyperpolarizability tensors by time-dependent density-functional theory , 2002 .

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

[34]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[35]  K. Burke,et al.  Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)] , 1997 .

[36]  F. Aiga,et al.  Higher‐order response theory based on the quasienergy derivatives: The derivation of the frequency‐dependent polarizabilities and hyperpolarizabilities , 1993 .

[37]  N. Rösch,et al.  Density- and density-matrix-based coupled Kohn–Sham methods for dynamic polarizabilities and excitation energies of molecules , 1999 .

[38]  G. F. Bertsch,et al.  Optical response of small silver clusters , 1999, physics/9903041.

[39]  J. G. Snijders,et al.  Efficient real-space approach to time-dependent density functional theory for the dielectric response of nonmetallic crystals , 2000 .

[40]  Patrick Norman,et al.  Non-linear electric and magnetic properties obtained from cubic response functions in the random phase approximation , 1996 .

[41]  K. Tsemekhman,et al.  Single and double photoionisation in Xe and Ba above the 4d threshold , 1990 .

[42]  D. Salahub,et al.  Asymptotic correction approach to improving approximate exchange–correlation potentials: Time-dependent density-functional theory calculations of molecular excitation spectra , 2000 .

[43]  J. G. Snijders,et al.  Implementation of time-dependent density functional response equations , 1999 .

[44]  J. G. Snijders,et al.  Application of time-dependent current-density-functional theory to nonlocal exchange-correlation effects in polymers , 2003 .

[45]  M. Grüning,et al.  On the required shape corrections to the local density and generalized gradient approximations to the Kohn-Sham potentials for molecular response calculations of (hyper)polarizabilities and excitation energies , 2002 .

[46]  John P. Perdew,et al.  Electron correlation energies from scaled exchange-correlation kernels: Importance of spatial versus temporal nonlocality , 2000 .

[47]  Wendin,et al.  Many-electron effects in BaC60: Collective response and molecular effects in optical conductivity and photoionization. , 1993, Physical review. B, Condensed matter.

[48]  H. Ågren,et al.  Calculations of two-photon absorption cross sections by means of density-functional theory , 2003 .

[49]  P. Dugourd,et al.  Direct measurement of the electric polarizability of isolated C60 molecules , 1999 .

[50]  C. Hättig,et al.  Coupled cluster calculations of the frequency-dependent second hyperpolarizabilities of Ne, Ar, N2, and CH4 , 1998 .

[51]  K. Burke,et al.  Several Theorems in Time-Dependent Density Functional Theory , 1999 .

[52]  Yi Luo,et al.  Density functional response theory calculations of three-photon absorption. , 2004, The Journal of chemical physics.

[53]  Horst Weiss,et al.  A direct algorithm for self‐consistent‐field linear response theory and application to C60: Excitation energies, oscillator strengths, and frequency‐dependent polarizabilities , 1993 .

[54]  Malcolm J. Stott,et al.  Linear-response theory within the density-functional formalism: Application to atomic polarizabilities , 1980 .

[55]  Herman Vanherzeele,et al.  Dispersion of the third-order optical nonlinearity of C60. A third-harmonic generation study , 1992 .

[56]  Patrick Norman,et al.  CUBIC RESPONSE FUNCTIONS IN THE MULTICONFIGURATION SELF-CONSISTENT FIELD APPROXIMATION , 1996 .

[57]  Roger D. Amos,et al.  Geometric derivatives of excitation energies using SCF and DFT , 1999 .

[58]  M. Head‐Gordon,et al.  Configuration interaction singles, time-dependent Hartree-Fock, and time-dependent density functional theory for the electronic excited states of extended systems , 1999 .

[59]  Andrew Zangwill,et al.  Density-functional approach to local-field effects in finite systems: Photoabsorption in the rare gases , 1980 .

[60]  Nicholas C. Handy,et al.  Exchange functionals and potentials , 1996 .

[61]  Jerzy Cioslowski,et al.  Electronic Structure Calculations on Fullerenes and Their Derivatives , 1995 .

[62]  Poul Jørgensen,et al.  Response functions from Fourier component variational perturbation theory applied to a time-averaged quasienergy , 1998 .

[63]  Trygve Helgaker,et al.  Hartree–Fock and Kohn–Sham atomic-orbital based time-dependent response theory , 2000 .

[64]  Görling,et al.  Density-functional theory for excited states. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[65]  Paweł Sałek,et al.  Density functional theory of nonlinear triplet response properties with applications to phosphorescence , 2003 .

[66]  V. Chernyak,et al.  Resonant nonlinear polarizabilities in the time-dependent density functional theory , 2003 .

[67]  S. Grimme,et al.  A COMBINATION OF KOHN-SHAM DENSITY FUNCTIONAL THEORY AND MULTI-REFERENCE CONFIGURATION INTERACTION METHODS , 1999 .

[68]  Branislav Jansik,et al.  Calculations of static and dynamic polarizabilities of excited states by means of density functional theory. , 2004, The Journal of chemical physics.

[69]  K. Ruud,et al.  The dispersion of the polarizability of C60: A confirmation of recent experimental results through theoretical calculations , 2001 .

[70]  R. Ahlrichs,et al.  Treatment of electronic excitations within the adiabatic approximation of time dependent density functional theory , 1996 .

[71]  Á. Nagy,et al.  Density functional. Theory and application to atoms and molecules , 1998 .

[72]  J. Olsen,et al.  Linear and nonlinear response functions for an exact state and for an MCSCF state , 1985 .

[73]  Filipp Furche,et al.  On the density matrix based approach to time-dependent density functional response theory , 2001 .

[74]  E. Gross,et al.  Density-Functional Theory for Time-Dependent Systems , 1984 .

[75]  J. G. Snijders,et al.  Time-dependent density functional result for the dynamic hyperpolarizabilities of C60. , 1997 .

[76]  J. Autschbach,et al.  Calculating molecular electric and magnetic properties from time-dependent density functional response theory , 2002 .