Time-dependent quasirelativistic density-functional theory based on the zeroth-order regular approximation.

A time-dependent quasirelativistic density-functional theory for excitation energies of systems containing heavy elements is developed, which is based on the zeroth-order regular approximation (ZORA) for the relativistic Hamiltonian and a noncollinear form for the adiabatic exchange-correlation kernel. To avoid the gauge dependence of the ZORA Hamiltonian a model atomic potential, instead of the full molecular potential, is used to construct the ZORA kinetic operator in ground-state calculations. As such, the ZORA kinetic operator no longer responds to changes in the density in response calculations. In addition, it is shown that, for closed-shell ground states, time-reversal symmetry can be employed to simplify the eigenvalue equation into an approximate form that is similar to that of time-dependent nonrelativistic density-functional theory. This is achieved by invoking an independent-particle approximation for the induced density matrix. The resulting theory is applied to investigate the global potential-energy curves of low-lying LambdaS- and omega omega-coupled electronic states of the AuH molecule. 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 in good agreement with those of time-dependent four-component relativistic density-functional theory and ab initio multireference second-order perturbation theory. Nonetheless, this two-component relativistic version of time-dependent density-functional theory is only moderately advantageous over the four-component one as far as computational efforts are concerned.

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

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

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

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

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

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

[7]  Häberlen,et al.  Relevance of relativistic exchange-correlation functionals and of finite nuclei in molecular density-functional calculations. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[8]  Wenjian Liu,et al.  Spectroscopic constants of MH and M2 (M=Tl, E113, Bi, E115): Direct comparisons of four- and two-component approaches in the framework of relativistic density functional theory , 2002 .

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

[10]  C. Wüllen.  Relativistic Density Functional Calculations on Small Molecules , 2004 .

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

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

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

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

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

[16]  Wenjian Liu,et al.  Spectroscopic constants of Pb and Eka-lead compounds , 2001 .

[17]  Wenjian Liu,et al.  Spectroscopic constants of gold and eka-gold (element 111) diatomic compounds: The importance of spin–orbit coupling , 1999 .

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

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

[20]  Christoph van Wüllen,et al.  Molecular density functional calculations in the regular relativistic approximation: Method, application to coinage metal diatomics, hydrides, fluorides and chlorides, and comparison with first-order relativistic calculations , 1998 .

[21]  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.

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

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

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

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

[26]  J. G. Snijders,et al.  Electronic Spectra of M(CO)6 (M = Cr, Mo, W) Revisited by a Relativistic TDDFT Approach , 1999 .

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

[28]  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.

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

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

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

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

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

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

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

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

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

[38]  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 .

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

[40]  Evert Jan Baerends,et al.  Relativistic total energy using regular approximations , 1994 .

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