Two-component relativistic density functional method for computing nonsingular complex linear response of molecules based on the zeroth order regular approximation.

We report the implementation of a frequency-dependent two-component relativistic density functional theory method based on the zeroth order regular approximation (ZORA) for computations of complex linear response of molecules including spin-orbit coupling. The implementation is based on Slater-type atomic orbital basis functions and makes extensive use of density fitting techniques. The complex response is obtained by applying damping in the computations. The method is validated by computations of the real and imaginary part of the static and dynamic polarizability of group 12 atoms, of a number of heavy-atom diatomic molecules, of a range of two- and three-dimensional gold clusters, and of group 8 oxides and metallocenes. Simulated spectra--a plot of extinction coefficient as a function of frequency--obtained from the isotropic imaginary polarizability are compared to broadened spectra obtained from two-component ZORA excitation energies and oscillator strengths.

[1]  Wenli Zou,et al.  Time-dependent quasirelativistic density-functional theory based on the zeroth-order regular approximation. , 2005, The Journal of chemical physics.

[2]  J. Autschbach,et al.  Study of static and dynamic first hyperpolarizabilities using time-dependent density functional quadratic response theory with local contribution and natural bond orbital analysis. , 2006, The Journal of chemical physics.

[3]  D. Santry,et al.  Non-empirical molecular orbital theory of the electronic structure of molecular crystals , 1975 .

[4]  Trond Saue,et al.  Linear response at the 4-component relativistic level: Application to the frequency-dependent dipole polarizabilities of the coinage metal dimers , 2003 .

[5]  W. J. Stevens,et al.  Dipole polarizabilities of Zn, Cd, and Hg (1S) , 1979 .

[6]  J. Autschbach.  Two-component relativistic hybrid density functional computations of nuclear spin-spin coupling tensors using Slater-type basis sets and density-fitting techniques. , 2008, The Journal of chemical physics.

[7]  B. Fricke,et al.  The electronic structure and properties of group 8 oxides MO4, where M=Ru, Os, and Element 108, Hs , 2001 .

[8]  Evert Jan Baerends,et al.  A density-functional theory study of frequency-dependent polarizabilities and Van der Waals dispersion coefficients for polyatomic molecules , 1995 .

[9]  G. Schatz,et al.  Theory and method for calculating resonance Raman scattering from resonance polarizability derivatives. , 2005, The Journal of chemical physics.

[10]  J. G. Snijders,et al.  Relativistic calculations on the adsorption of CO on the (111) surfaces of Ni, Pd, and Pt within the zeroth-order regular approximation , 1997 .

[11]  D. Santry,et al.  Calculation of frequency-dependent polarizabilities by means of SCF perturbation theory , 1979 .

[12]  U. Hohm,et al.  Dipole-quadrupole and dipole-octopole polarizability of OsO4 from depolarized collision-induced light scattering experiments, ab initio and density functional theory calculations. , 2004, The Journal of chemical physics.

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

[14]  Johannes Grotendorst,et al.  Modern methods and algorithms of quantum chemistry , 2000 .

[15]  Trygve Helgaker,et al.  Density-functional theory calculations of optical rotatory dispersion in the nonresonant and resonant frequency regions. , 2004, The Journal of chemical physics.

[16]  F. Aiga,et al.  Frequency-dependent polarizabilities, hyperpolarizabilities, and excitation energies from time-dependent density-functional theory based on the quasienergy derivative method , 1999 .

[17]  Á. Rubio,et al.  The role of dimensionality on the quenching of spin-orbit effects in the optics of gold nanostructures. , 2008, The Journal of chemical physics.

[18]  R. Leeuwen,et al.  Causality and symmetry in time-dependent density-functional theory , 1998 .

[19]  Robert van Leeuwen,et al.  KEY CONCEPTS IN TIME-DEPENDENT DENSITY-FUNCTIONAL THEORY , 2001 .

[20]  S. Patchkovskii,et al.  Static and dynamic second hyperpolarizability calculated by time-dependent density functional cubic response theory with local contribution and natural bond orbital analysis. , 2007, The Journal of chemical physics.

[21]  D. M. Bishop,et al.  Near-resonant absorption in the time-dependent self-consistent field and multiconfigurational self-consistent field approximations , 2001 .

[22]  Fast generation of nonresonant and resonant optical rotatory dispersion curves with the help of circular dichroism calculations and Kramers-Kronig transformations. , 2008, Chirality.

[23]  J. Frenkel,et al.  Wave mechanics: Advanced general theory , 1934 .

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

[25]  J. Autschbach,et al.  Calculation of static and dynamic linear magnetic response in approximate time-dependent density functional theory. , 2007, The Journal of chemical physics.

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

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

[28]  R. Mcweeny,et al.  Methods Of Molecular Quantum Mechanics , 1969 .

[29]  J. Autschbach,et al.  Calculation of origin-independent optical rotation tensor components in approximate time-dependent density functional theory. , 2006, The Journal of chemical physics.

[30]  Ph. Durand,et al.  Regular Two-Component Pauli-Like Effective Hamiltonians in Dirac Theory , 1986 .

[31]  Evert Jan Baerends,et al.  The calculation of excitation energies based on the relativistic two-component zeroth-order regular approximation and time-dependent density-functional with full use of symmetry. , 2005, The Journal of chemical physics.

[32]  R. Murray,et al.  Gold nanoelectrodes of varied size: transition to molecule-like charging , 1998, Science.

[33]  J. Autschbach,et al.  Calculation of optical rotation with time-periodic magnetic-field-dependent basis functions in approximate time-dependent density-functional theory. , 2005, The Journal of chemical physics.

[34]  S. Grimme,et al.  Experimental and theoretical study of the dipole polarizability of ferrocene Fe(C5H5)2 , 1997 .

[35]  T. Helgaker,et al.  Static and frequency-dependent dipole-dipole polarizabilities of all closed-shell atoms up to radium: a four-component relativistic DFT study. , 2008, Chemphyschem : a European journal of chemical physics and physical chemistry.

[36]  Pekka Pyykkö,et al.  Relativistic Quantum Chemistry , 1978 .

[37]  Per Jensen,et al.  Computational molecular spectroscopy , 2000, Nature Reviews Methods Primers.

[38]  E. Baerends,et al.  Towards excitation energies and (hyper)polarizability calculations of large molecules. Application of parallelization and linear scaling techniques to time‐dependent density functional response theory , 2000 .

[39]  T. Helgaker,et al.  Linear response at the 4-component relativistic density-functional level: application to the frequency-dependent dipole polarizability of Hg, AuH and PtH2 , 2005 .

[40]  D. M. Bishop,et al.  Nonlinear response theory with relaxation: the first-order hyperpolarizability. , 2005, The Journal of chemical physics.

[41]  Evert Jan Baerends,et al.  Geometry optimizations in the zero order regular approximation for relativistic effects. , 1999 .

[42]  D. Cremer,et al.  Calculation of electric properties using regular approximations to relativistic effects: The polarizabilities of RuO4, OsO4, and HsO4 (Z=108) , 2003 .

[43]  G. Schatz,et al.  Time-dependent density functional calculations of optical rotatory dispersion including resonance wavelengths as a potentially useful tool for determining absolute configurations of chiral molecules. , 2006, The journal of physical chemistry. A.

[44]  Goebel,et al.  Theoretical and experimental determination of the polarizabilities of the zinc 1S0 state. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[45]  Shashi P. Karna,et al.  Nonlinear Optical Materials: Theory and Modeling , 1996 .

[46]  U. Hohm,et al.  DIPOLE POLARIZABILITY, CAUCHY MOMENTS, AND RELATED PROPERTIES OF HG , 1996 .

[47]  Evert Jan Baerends,et al.  Density functional calculations of nuclear magnetic shieldings using the zeroth-order regular approximation (ZORA) for relativistic effects: ZORA nuclear magnetic resonance , 1999 .

[48]  Trond Saue,et al.  An infinite-order two-component relativistic Hamiltonian by a simple one-step transformation. , 2007, The Journal of chemical physics.

[49]  J. Autschbach,et al.  Calculation of circular dichroism spectra from optical rotatory dispersion, and vice versa, as complementary tools for theoretical studies of optical activity using time-dependent density functional theory. , 2006, The Journal of chemical physics.

[50]  J. Autschbach,et al.  Calculation of Verdet constants with time-dependent density functional theory: implementation and results for small molecules. , 2005, The Journal of chemical physics.

[51]  Hideo Sekino,et al.  Frequency dependent nonlinear optical properties of molecules , 1986 .

[52]  Jochen Autschbach,et al.  Nuclear spin–spin coupling constants from regular approximate relativistic density functional calculations. II. Spin–orbit coupling effects and anisotropies , 2000 .

[53]  Goebel,et al.  Dispersion of the refractive index of cadmium vapor and the dipole polarizability of the atomic cadmium 1S0 state. , 1995, Physical review. A, Atomic, molecular, and optical physics.

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

[55]  D. Santry.  Application of second-order SCF perturbation theory to the solution of time-dependent Hartree—Fock equations , 1979 .

[56]  Wenli Zou,et al.  Time-dependent four-component relativistic density-functional theory for excitation energies. II. The exchange-correlation kernel. , 2005, The Journal of chemical physics.

[57]  Evert Jan Baerends,et al.  Relativistic regular two‐component Hamiltonians , 1993 .

[58]  A. D. McLACHLAN,et al.  Time-Dependent Hartree—Fock Theory for Molecules , 1964 .

[59]  L Jensen,et al.  Finite lifetime effects on the polarizability within time-dependent density-functional theory. , 2005, The Journal of chemical physics.

[60]  S. Karna,et al.  Frequency dependent nonlinear optical properties of molecules: Formulation and implementation in the HONDO program , 1991 .

[61]  P. Pyykkö,et al.  Finite-difference Dirac-Fock calculations of electric dipole polarisabilities for (ns)1 and (ns)2 atoms , 1981 .

[62]  Jin-ming Dong,et al.  Bulk fragment and tubelike structures of Au N ( N = 2 − 26 ) , 2005, cond-mat/0504622.

[63]  Chensheng Lin,et al.  Remarkable second-order optical nonlinearity of nano-sized Au20 cluster: a TDDFT study , 2004 .

[64]  Trygve Helgaker,et al.  Hartree-Fock limit magnetizabilities from London orbitals , 1993 .

[65]  J. Olsen,et al.  Vibrational Raman optical activity calculations using London atomic orbitals , 1994 .

[66]  N. Kaltsoyannis,et al.  Time dependent DFT study of the electronic transition energies of RuO4 and OsO4 , 2005 .

[67]  S. H. Vosko,et al.  Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis , 1980 .

[68]  Laurence D. Barron,et al.  Molecular Light Scattering and Optical Activity: Second Edition, revised and enlarged , 1983 .

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

[70]  P. Norman.  Applications of Response Theory with Relaxation , 2007 .

[71]  P. Norman,et al.  Quadratic response functions in the time-dependent four-component Hartree-Fock approximation. , 2004, The Journal of chemical physics.

[72]  Jinlan Wang,et al.  Static polarizabilities and optical absorption spectra of gold clusters ( Au n , n = 2 – 14 and 20) from first principles , 2007 .

[73]  Harry F. King,et al.  Analytic computation of energy derivatives. Relationships among partial derivatives of a variationally determined function , 1986 .

[74]  Theodore E. Simos,et al.  Computational Methods in Science and Engineering: Theory and Computation Old Problems and New Challenges. Lectures Presented at the International Conference ... Physics , 2007 .