Time-dependent four-component relativistic density-functional theory for excitation energies. II. The exchange-correlation kernel.

We extend our previous formulation of time-dependent four-component relativistic density-functional theory [J. Gao, W. Liu, B. Song, and C. Liu, J. Chem. Phys. 121, 6658 (2004)] by using a noncollinear form for the exchange-correlation kernel. The new formalism can deal with excited states involving moment (spin)-flipped configurations which are otherwise not accessible with ordinary exchange-correlation functionals. As a first application, the global potential-energy curves of 16 low-lying omega omega-coupled electronic states of the AuH molecule have been investigated. The derived spectroscopic parameters, including the adiabatic and vertical excitation energies, equilibrium bond lengths, harmonic and anharmonic vibrational constants, fundamental frequencies, and dissociation energies, are grossly in good agreement with those of ab initio multireference second-order perturbation theory and the available experimental data.

[1]  W. C. Martin,et al.  Handbook of Basic Atomic Spectroscopic Data , 2005 .

[2]  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.

[3]  Guntram Rauhut,et al.  Energy-consistent pseudopotentials for group 11 and 12 atoms: adjustment to multi-configuration Dirac–Hartree–Fock data , 2005 .

[4]  Tom Ziegler,et al.  The performance of time-dependent density functional theory based on a noncollinear exchange-correlation potential in the calculations of excitation energies. , 2005, The Journal of chemical physics.

[5]  Tom Ziegler,et al.  Time-dependent density functional theory based on a noncollinear formulation of the exchange-correlation potential. , 2004, The Journal of chemical physics.

[6]  Chengbu Liu,et al.  Time-dependent four-component relativistic density functional theory for excitation energies. , 2004, The Journal of chemical physics.

[7]  Lemin Li,et al.  Recent Advances in Relativistic Density Functional Methods , 2004 .

[8]  Wenjian Liu,et al.  Comparison of Different Polarization Schemes in Open‐shell Relativistic Density Functional Calculations , 2003 .

[9]  Fan Wang,et al.  The Beijing Density Functional (BDF) Program Package: Methodologies and Applications , 2003 .

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

[11]  D. Chong.  Recent Advances in Density Functional Methods Part III , 2002 .

[12]  K. Hirao,et al.  Relativistic and correlated all-electron calculations on the ground and excited states of AgH and AuH , 2000 .

[13]  Hans-Joachim Werner,et al.  Multireference perturbation theory for large restricted and selected active space reference wave functions , 2000 .

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

[15]  Benjamin T. Miller,et al.  A parallel implementation of the analytic nuclear gradient for time-dependent density functional theory within the Tamm–Dancoff approximation , 1999 .

[16]  Jenning Y. Seto,et al.  Vibration-rotation emission spectra and combined isotopomer analyses for the coinage metal hydrides: CuH & CuD, AgH & AgD, and AuH & AuD , 1999 .

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

[18]  Michael Dolg,et al.  The Beijing four-component density functional program package (BDF) and its application to EuO, EuS, YbO and YbS , 1997 .

[19]  M. E. Casida.  Time-Dependent Density Functional Response Theory for Molecules , 1995 .

[20]  Rajagopal.  Time-dependent functional theory of coupled electron and electromagnetic fields in condensed-matter systems. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[21]  B. A. Hess,et al.  Relativistic all electron configuration interaction calculation of ground and excited states of the gold hydride molecule , 1989 .

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

[23]  J. Olsen,et al.  Solution of the large matrix equations which occur in response theory , 1988 .

[24]  J. Perdew,et al.  Erratum: Density-functional approximation for the correlation energy of the inhomogeneous electron gas , 1986, Physical review. B, Condensed matter.

[25]  J. Perdew,et al.  Density-functional approximation for the correlation energy of the inhomogeneous electron gas. , 1986, Physical review. B, Condensed matter.

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

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

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

[29]  Allan H. MacDonald,et al.  A relativistic density functional formalism , 1979 .

[30]  A. Rajagopal.  Inhomogeneous relativistic electron gas , 1978 .

[31]  U. Ringström.  Absorption Spectrum of Gold Hydride in the Ultra-violet , 1963, Nature.

[32]  E. Hulthén,et al.  The Absorption Spectra of Some Hydride Compounds in the Ultra-Violet , 1926 .

[33]  T. Heimer.  Der Isotopieeffekt des Goldhydrids (AuH/AuD) , 2005, Naturwissenschaften.

[34]  Lemin Li,et al.  RELATIVISTIC DENSITY FUNCTIONAL THEORY: THE BDF PROGRAM PACKAGE , 2004 .

[35]  K. Hirao,et al.  Recent Advances in Relativistic Molecular Theory , 2004 .

[36]  W. C. Martin,et al.  Handbook of Basic Atomic Spectroscopic Data (version 1.0) , 2003 .

[37]  E. Engel.  Relativistic Density Functional Theory: Foundations and Basic Formalism , 2002 .

[38]  P. Kollman,et al.  Encyclopedia of computational chemistry , 1998 .

[39]  M. Petersilka,et al.  DENSITY FUNCTIONAL THEORY OF TIME-DEPENDENT PHENOMENA , 1996 .

[40]  E. Gross,et al.  Density-Functional Theory , 1990 .

[41]  E. Davidson.  The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices , 1975 .