Time-dependent density functional theory scheme for efficient calculations of dynamic (hyper)polarizabilities.

The authors present an efficient perturbative method to obtain both static and dynamic polarizabilities and hyperpolarizabilities of complex electronic systems. This approach is based on the solution of a frequency-dependent Sternheimer equation, within the formalism of time-dependent density functional theory, and allows the calculation of the response both in resonance and out of resonance. Furthermore, the excellent scaling with the number of atoms opens the way to the investigation of response properties of very large molecular systems. To demonstrate the capabilities of this method, they implemented it in a real-space (basis-set-free) code and applied it to benchmark molecules, namely, CO, H2O, and para-nitroaniline. Their results are in agreement with experimental and previous theoretical studies and fully validate their approach.

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

[2]  P. N. Butcher,et al.  The Elements of Nonlinear Optics , 1990 .

[3]  Gonze,et al.  Perturbation expansion of variational principles at arbitrary order. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[4]  G. Scuseria,et al.  Progress in the development of exchange-correlation functionals , 2005 .

[5]  E. Donley,et al.  A comparison of molecular hyperpolarizabilities from gas and liquid phase measurements , 1998 .

[6]  George F. Bertsch,et al.  Time-dependent local-density approximation in real time , 1996 .

[7]  G. Maroulis.  Electric Polarizability and Hyperpolarizability of Carbon Monoxide , 1996 .

[8]  Kieron Burke,et al.  Basics of TDDFT , 2006 .

[9]  H. Appel,et al.  octopus: a tool for the application of time‐dependent density functional theory , 2006 .

[10]  Poul Jo,et al.  Transition moments and dynamic polarizabilities in a second order polarization propagator approach , 1980 .

[11]  Hermann Stoll,et al.  Results obtained with the correlation energy density functionals of becke and Lee, Yang and Parr , 1989 .

[12]  Á. Rubio,et al.  Assessment of exchange-correlation functionals for the calculation of dynamical properties of small clusters in time-dependent density functional theory , 2001, cond-mat/0102234.

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

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

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

[16]  Brian J. Orr,et al.  Perturbation theory of the non-linear optical polarization of an isolated system , 1971 .

[17]  A. Zangwill.  Density functional theory of nonlinear optical response , 1983 .

[18]  C. E. Brion,et al.  Absolute optical oscillator strengths for discrete and continuum photoabsorption of carbon monoxide (7–200 eV) and transition moments for the X 1Σ+ → A 1Π system , 1993 .

[19]  Rubio,et al.  Density-functional theory of the nonlinear optical susceptibility: Application to cubic semiconductors. , 1996, Physical review. B, Condensed matter.

[20]  Qingshi Zhu,et al.  Linear-scaling density matrix perturbation treatment of electric fields in solids. , 2006, Physical review letters.

[21]  S. Karna,et al.  Frequency-dependent hyperpolarizabilities of haloforms from ab initio SCF calculations , 1990 .

[22]  J. Perdew,et al.  Electrical response of molecular chains from density functional theory. , 2004, Physical review letters.

[23]  E. Gross,et al.  Time-dependent density functional theory. , 2004, Annual review of physical chemistry.

[24]  Kohn,et al.  Density functional and density matrix method scaling linearly with the number of atoms. , 1996, Physical review letters.

[25]  C. Taliani,et al.  Electronic excited states of nitroanilines , 1976 .

[26]  A. Zunger,et al.  Self-interaction correction to density-functional approximations for many-electron systems , 1981 .

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

[28]  Stefano de Gironcoli,et al.  Phonons and related crystal properties from density-functional perturbation theory , 2000, cond-mat/0012092.

[29]  Qin Wu,et al.  Accurate polymer polarizabilities with exact exchange density-functional theory , 2003 .

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

[31]  David P. Shelton,et al.  Measurements and calculations of the hyperpolarizabilities of atoms and small molecules in the gas phase , 1994 .

[32]  N. Hush,et al.  Finite-field method calculations of molecular polarisabilities. I. Theoretical basis and limitations of SCF and Galerkin treatments , 1977 .

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

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

[35]  J. G. Snijders,et al.  Current density functional theory for optical spectra: A polarization functional , 2001 .

[36]  M. Spackman.  Accurate prediction of static dipole polarizabilities with moderately sized basis sets , 1989 .

[37]  G. Iafrate,et al.  Derivation and application of an accurate Kohn-Sham potential with integer discontinuity , 1990 .

[38]  R. Gebauer,et al.  Efficient approach to time-dependent density-functional perturbation theory for optical spectroscopy. , 2005, Physical review letters.

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

[40]  Yang,et al.  Direct calculation of electron density in density-functional theory. , 1991, Physical review letters.

[41]  J. Ward,et al.  Measurements of nonlinear optical polarizabilities for twelve small molecules , 1979 .

[42]  Á. Rubio,et al.  octopus: a first-principles tool for excited electron-ion dynamics. , 2003 .

[43]  Johnson,et al.  Modified Broyden's method for accelerating convergence in self-consistent calculations. , 1988, Physical review. B, Condensed matter.

[44]  H. Ågren,et al.  A comparison of density-functional-theory and coupled-cluster frequency-dependent polarizabilities and hyperpolarizabilities , 2005 .

[45]  X. Gonze,et al.  Density-functional approach to nonlinear-response coefficients of solids. , 1989, Physical review. B, Condensed matter.

[46]  Benoît Champagne,et al.  Electric field dependence of the exchange-correlation potential in molecular chains , 1999 .

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

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

[49]  J. Muenter,et al.  Electric dipole moment of carbon monoxide , 1975 .

[50]  P. W. Langhoff,et al.  Aspects of Time-Dependent Perturbation Theory , 1972 .

[51]  Benoît Champagne,et al.  Density-functional theory (hyper)polarizabilities of push-pull pi-conjugated systems: treatment of exact exchange and role of correlation. , 2005, The Journal of chemical physics.

[52]  Senatore,et al.  Hyperpolarizabilities of closed-shell atoms and ions in the local-density approximation. , 1986, Physical review. A, General physics.

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

[54]  G. Mahan,et al.  Local density theory of ionic hyperpolarizability , 1986 .

[55]  A. Stathopoulos,et al.  Solution of large eigenvalue problems in electronic structure calculations , 1996 .

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

[57]  David P. Shelton,et al.  Problems in the comparison of theoretical and experimental hyperpolarizabilities , 1992 .

[58]  A. Görling,et al.  The role of exchange and correlation in time-dependent density-functional theory for photoionization , 2001 .

[59]  Keith Bonin,et al.  Electric-Dipole Polarizabilities Of Atoms, Molecules, And Clusters , 1997 .

[60]  Görling,et al.  Exact Kohn-Sham scheme based on perturbation theory. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[61]  Stefan Goedecker,et al.  Efficient solution of Poisson's equation with free boundary conditions. , 2006, The Journal of chemical physics.

[62]  Kwang S. Kim,et al.  Theory and applications of computational chemistry : the first forty years , 2005 .

[63]  P. Prasad,et al.  Nonlinear optical properties of p‐nitroaniline: An ab initio time‐dependent coupled perturbed Hartree–Fock study , 1991 .

[64]  S. Goedecker.  Linear scaling electronic structure methods , 1999 .

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

[66]  A. F. Garito,et al.  Dispersion of the nonlinear second-order optical susceptibility of organic systems (A) , 1983 .