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Nonrelativistic Theoretical Methods

Nonrelativistic quantum chemistry has been discussed so far. But transition metal (starting already from the first row) and actinide compounds cannot be studied theoretically without a detailed account of relativity. Thus, the multiconfigurational method needs to be extended to the relativistic regime. Can this be done with enough accuracy for chemical applications without using the four-component Dirac theory Much work has also been done in recent years to develop a reliable and computationally efficient four-component quantum chemistry.25,26 Nowadays it can be combined, for example, with the CC approach for electron correlation. The problem is that an extension to multiconfigurational... [Pg.257]

The most widely used semiempirical quantum chemistry technique for theoretical chemisorption studies is the Extended Hiickel Theory (EHT). The method was first proposed by Hoffmann/95/ in its nonrelativistic form, and by Lohr and Pyykko/96/ and also Messmer/97/ in its relativistic form, based on the molecular orbital theory for calculating molecular electronic and geometric properties. For a cluster the molecular orbitals are expanded as linear combinations of atomic orbitals... [Pg.83]

Finally, four-component methods will reach a high degree of applicability such that the relativistic approaches will become the standard tool for electronic structure calculations in the next decades. The four-component theories provide the general framework, in which more approximate methods—such as elimination methods for the small components, reduction methods to one-component wave functions, and also the nonrelativistic approaches—elegantly fit. This function of the four-component theories as the theoretical basis will certainly be reflected in algorithms and computer codes to be developed. [Pg.88]

Needless to say, many-electron atoms and molecules are much more complicated than one-electron atoms, and the realization of the nonrelativistic limit is not easily accomplished in these cases because of the approximations needed for the description of a complicated many-particle system. However, the signature of relativistic effects (see, for example, Chapter 3 in this book) enables us to identify these effects even without calculation from experimental observation. Two mainly experimentally oriented chapters will report astounding examples of relativistic phenomenology, interpreted by means of the methods of relativistic electronic structure theory. These methods for the theoretical treatment of relativistic effects in many-electron atoms and molecules are the subject of most of the chapters in the present volume, and with the help of this theory relativistic effects can be characterized with high precision. [Pg.325]

In spite of the impressive progress which has been achieved with conventional ab-initio methods as the Configuration-Interaction or Coupled-Cluster schemes in recent years density functional theory (DFT) still represents the method of choice for the study of complex many-electron systems (for an overview of DFT see [1]). Today DFT covers an enormous variety of fields, ranging from atomic [2,3], cluster [4,5] and surface physics [6,7] to the material sciences [8-10]. and theoretical biophysics [11-13]. Moreover, since the introduction of the generalized gradient approximation DFT has become an accepted method also for standard quantum chemical applications [14,15]. Given this tremendous success of nonrelativistic DFT the question for a relativistic extension (RDFT) arises quite naturally in view of the large number of problems in which relativistic effects play an important role (see e.g. Refs.[16,17]). [Pg.524]

An alternative approach to the perturbation theory in treating many-electron systems is the configuration-interaction (Cl) method which is based on the variational principle. Nonrelativistic Cl techniques have been used extensively in atomic and molecular calculations. The generalization to relativistic configuration-interaction (RCI) calculations, however, presents theoretical as well as technical challenges. The problem originates from the many-electron Dirac Hamiltonian commonly used in RCI calculations ... [Pg.163]

Pyykko (1979b) used the Dirac-Hartree-Fock one-centre expansion method for the monohydrides to calculate relativistic values for the lanthanide and actinide contraction, i.e. 0.209 A for LaH to LuH and 0.330A for AcH to LrH. The corresponding nonrelativistic value derived from Hartree-Fock one-center expansions for LaH and LuH is 0.191 A, i.e., for this case 9.4% of the lanthanide contraction is due to relativistic effects. The experimental value of 0.179 A would suggest a correlation contribution of-14.4% to the lanthanide contraction if one assumes that the relativistic theoretical values are close to the Dirac-Hartree-Fock limit, which is certainly not true for the absolute values of the bond lengths themselves. Moreover, it is well known that for heavy elements relativistic and correlation contributions are not exactly additive. Corresponding nonrelativistic calculations for AcH and LrH have not been performed and experimental data are not available to determine relativistic and electron correlation effects for the actinide contraction. Table 8 summarizes values for the lanthanide and actinide contraction derived from theoretical or experimental molecular bond lengths. It is evident from Ihese results... [Pg.625]

Brooks, Johansson and Skriver (1984) investigated the band structure of UC and ThC by nonrelativistic and relativistic (based on the Dirac formalism) LMTO methods. They analysed the electron density changes in the compounds as compared with free atoms, as well as the influence of pressure on the band structure. Crystal pressures as a function of lattice constants (equations of state) were calculated as well as theoretical values of the lattice constants. The calculated trends in the variations of lattice constants and bulk moduli agree well with the available experimental data. Some of the most important results of these calculations are shown in Figs. 2.20 and 2.21. [Pg.52]

For comparison, using the rl2-MR-CI method the value —24.65379 a.u., (also <0.1-10 a.u. accurate) [23] was obtained with a very large basis of Gaussian orbitals. The ab initio result from the Diffusion Monte Carlo method is —24.65357(3)a.u. [6], The estimated nonrelativistic energy using theoretical and experimental data is -24.65391 a.u. [13]. The mentioned calculations are less accurate than a microhartree. The relativistic energy value including mass and Darwin corrections is estimated to be —24.659758 a.u. [Pg.106]

To determine the second virial coefficients to the required acciu acy of about 100 ppm, one needs to know the helium dimer potential to a few mK at the minimum. Consider first the interaction of two hehum atoms in the nonrelativistic Born-Oppenheimer (BO) approximation. The best published calculations using the supermolecular method have estimated error bars of 8 mK [ 150,151]. More recently, improved calculations of this type reached an accuracy of 5 mK [ 158]. Also, the SAPT calculations have been repeated with increased accuracy, resulting in an agreement to 5 mK with the supermolecular method. Furthermore, the upper bound from four-electron exphcitly correlated calculations is 5 mK above the new supermolecular value [159]. All this evidence from three different theoretical models seems to show convinc-... [Pg.96]


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