Relativistic coupled cluster theory

E. Eliav, U. Kaldor, Y. Ishikawa. Relativistic Coupled Cluster Theory Based on the No-Pair Dirac-Coulomb-Breit Hamiltonian Relativistic Pair Corrdation Energies of the Xe Atom. Int. J. Quantum Chem. Quantum Chem. Symp., 28 (1994) 205-214. 

The static dipole polarizabilities for the Pq ground state of the neutral group-14 elements C, Si, Ge, Sn, Pb, and element Z = 114 have been determined from all-electron relativistic coupled cluster theory. It is shown that the isotropic and anisotropic components of the polarizability increase monotonically with the nuclear charge, except for the spin-orbit coupled /=0 states, which start to decrease from Sn to Pb and even further to element 114. So, spin-orbit coupling leads to a significant reduction of the polarizability of element 114, i.e., from 47.9 a.u. at the scalar-relativistic Douglas-Kroll level to 31.5 a.u. at the Dirac-Coulomb level of theory, which is below the value of Si. The calculations further demonstrate that relativistic and electron correlation effects are nonadditive. The measured dipole polarizabilities of Sn (42.4 11 a.u.) and Pb (47.1 7) are in reasonable agreement with the theoretical values, 52.9 a.u. and 47.3 a.u., respectively. 

A new approach based on the relativistic coupled-cluster theory has been presented to calculate the first-order wavefunctions due to one-electron... 

Schwerdtfeger, P., Bast, R., Gerry, M.C.L., Jacob, C.R., Jansen, M., Kelld, V., Mudring, A.V., Sadlej, A.J., Saue, T, Sdhnel, T. and Wagner, F.E. (2005) The quadrupole moment of the 3 /2 nuclear groimd state of Au from electric field gradient relativistic coupled cluster and density functional theory of small molecules and the solid slide. Journal of Chemical Physics, 122,124317-1-124317-9. 

J. Paldus, Algebraic Approach to Coupled Cluster Theory. In G. L. MaUi (Ed.) Relativistic and Correlation Effects in Mmolecules and Solids, NATO ASI series. Series B Physics, Vol. 318. (Plenum, New York, 1994), pp. 207-282. 

In this paper, the main features of the two-step method are presented and PNC calculations are discussed, both those without accounting for correlation effects (PbF and HgF) and those in which electron correlations are taken into account by a combined method of the second-order perturbation theory (PT2) and configuration interaction (Cl), or PT2/CI [100] (for BaF and YbF), by the relativistic coupled cluster (RCC) method [101, 102] (for TIF, PbO, and HI+), and by the spin-orbit direct-CI method [103, 104, 105] (for PbO). In the ab initio calculations discussed here, the best accuracy of any current method has been attained for the hyperfine constants and P,T-odd parameters regarding the molecules containing heavy atoms. 

Because of its size-extensivity and faster convergence with respect to excitation level Coupled cluster theory has replaced Cl theory as the dominant approach in ab initio correlation calculations. Like MBPT the theory is still mainly applied in cases where the exact wave function is dominated by a single determinant, but multireference methods have been formulated and begin to enter mainstream quantum chemistry. Generalization of the algorithms to the relativistic no-pair level can again be achieved via the spinorbital formulation of the methods. I will first discuss the single reference method and then consider the Fock space method [40] that uses multi-reference wavefiinctions for ionized or excited states. 

The all-orders relativistic many-body perturbation theory approach [82], [83], the combination of this approach with the multiconfiguration Dirac - Fock method [84] or the relativistic coupled-cluster approach [85] allow for the evaluation of the energy levels for valence electrons with accuracy of the order of... 

Bogumil Jeziorski received his M.S. degree in chemistry from the University of Warsaw in 1969. He conducted his graduate work also in Warsaw under the supervision of W. Kolos. After a postdoctoral position at the University of Utah, he was a research associate at the University of Florida and a Visiting Professor at the University of Waterloo, University of Delaware and University of Nijmegen. Since 1990 he has been a Professor of Chemistry at the University of Warsaw. His research has been mainly on the coupled-cluster theory of electronic correlation and on the perturbation theory of intermolecular forces. His other research interests include chemical effects in nuclear beta decay, theory of muonic molecules and relativistic and radiative effects in molecules. 

Debashis Mukherjee is a Professor of Physical Chemistry and the Director of the Indian Association for the Cultivation of Science, Calcutta, India. He has been one of the earliest developers of a class of multi-reference coupled cluster theories and also of the coupled cluster based linear response theory. Other contributions by him are in the resolution of the size-extensivity problem for multi-reference theories using an incomplete model space and in the size-extensive intermediate Hamiltonian formalism. His research interests focus on the development and applications of non-relativistic and relativistic theories of many-body molecular electronic structure and theoretical spectroscopy, quantum many-body dynamics and statistical held theory of many-body systems. He is a member of the International Academy of the Quantum Molecular Science, a Fellow of the Third World Academy of Science, the Indian National Science Academy and the Indian Academy of Sciences. He is the recipient of the Shantiswarup Bhatnagar Prize of the Council of Scientihc and Industrial Research of the Government of India. 

The current volume presents the compilation of splendid contributions distributed over 21 chapters. The very first chapter contributed by Istvan Hargittai presents the historical account of development of structural chemistry. It also depicts some historical memories of scientists presented in the form of their pictures. This historical description covers a vast period of time. Intruder states pose serious problem in the multireference formulation based on Rayleigh-Schrodinger expansion. Ivan Hubac and Stephen Wilson discuss the ciurent development and future prospects of Many-Body Brillouin-Wigner theories to avoid the problem of intruder states in the next chapter. The third chapter written by Vladimir Ivanov and collaborators reveals the development of multireference state-specific coupled cluster theory. The next chapter from Maria Barysz discusses the development and application of relativistic effects in chemical problems while the fifth chapter contributed by Manthos Papadopoulos and coworkers describes electronic, vibrational and relativistic contributions to the linear and nonlinear optical properties of molecules. 

Quantum chemistry has nowadays reached such an advanced level that highly accurate results can be achieved for energies and properties of small- to mediumsized molecules. As stressed in the previous section, the requirements for these high-level calculations are efficient treatment of electron correlation via coupled-cluster theory, basis set extrapolation techniques, incorporation of core correlation, and relativistic as well as vibrational effects together with the use of suitable additivity schemes. Nevertheless, despite all the progress made so far, it is still essential to benchmark the results from quantum chemical calculations, and, as pointed out above, rotational spectroscopy offers such an opportunity. 

Field (CASSCF) Second-order Perturbation Theory (CAS-PT2) Configuration Interaction Core-Valence Correlation Effects Coupled-cluster Theory Experimental Data Evaluation and Quality Control G2 Theory Heats of Formation Isoelectronic Isogyric Reactions M0ller-Plesset Perturbation Theory Numerical Hartree-Fock Methods for Molecules r 12-Dependent Wavefunctions Relativistic Theory and Applications Spectroscopy Computational Methods Spin Contamination Transition Metals Applications,... 

Coupled-cluster Theory Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field Relativistic Effective Core Potential Techniques for Molecules Containing Very Heavy Atoms Relativistic Theory and Applications. 

The prerequisites for high accuracy are coupled-cluster calculations with the inclusion of connected triples [e.g., CCSD(T)], either in conjunction with R12 theory or with correlation-consistent basis sets of at least quadruple-zeta quality followed by extrapolation. In addition, harmonic vibrational corrections must always be included. For small molecules, such as those contained in Table 1.11, such calculations have errors of the order of a few kJ/mol. To reduce the error below 1 kJ/mol, connected quadruples must be taken into account, together with anhar-monic vibrational and first-order relativistic corrections. In practice, the approximate treatment of connected triples in the CCSD(T) model introduces an error (relative to CCSDT) that often tends to cancel the... 

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