Relativistic effective core

Unlike semiempirical methods that are formulated to completely neglect the core electrons, ah initio methods must represent all the electrons in some manner. However, for heavy atoms it is desirable to reduce the amount of computation necessary. This is done by replacing the core electrons and their basis functions in the wave function by a potential term in the Hamiltonian. These are called core potentials, elfective core potentials (ECP), or relativistic effective core potentials (RECP). Core potentials must be used along with a valence basis set that was created to accompany them. As well as reducing the computation time, core potentials can include the effects of the relativistic mass defect and spin coupling terms that are significant near the nuclei of heavy atoms. This is often the method of choice for heavy atoms, Rb and up. 

Dolg, M. (2002) Relativistic Effective Core Potentials (ed. P. Schwerdtfeger), Elsevier, Amsterdam. 

Hay, P. J., Martin, R. L., 1998, Theoretical Studies of the Structures and Vibrational Frequencies of Actinide Compounds Using Relativistic Effective Core Potentials With Hartree-Fock and Density Functional Methods ... 

The twin facts that heavy-atom compounds like BaF, T1F, and YbF contain many electrons and that the behavior of these electrons must be treated relati-vistically introduce severe impediments to theoretical treatments, that is, to the inclusion of sufficient electron correlation in this kind of molecule. Due to this computational complexity, calculations of P,T-odd interaction constants have been carried out with relativistic matching of nonrelativistic wavefunctions (approximate relativistic spinors) [42], relativistic effective core potentials (RECP) [43, 34], or at the all-electron Dirac-Fock (DF) level [35, 44]. For example, the first calculation of P,T-odd interactions in T1F was carried out in 1980 by Hinds and Sandars [42] using approximate relativistic wavefunctions generated from nonrelativistic single particle orbitals. 

Correlation Consistent Basis Sets with Relativistic Effective Core Potentials The Transition Metal Elements Y and Hg... 

The present work represents a preliminary attempt to incorporate many of these strategies in conjunction with the use of small-core relativistic effective core potentials for obtaining compact series of correlation consistent basis sets... 

At B3LYP/6-311G(2d,p), pseudo-relativistic effective core potential and a (31/31/1) valence basis set were used for Si, Ge, Sn, Pb, from Ref 40. 

The only calculation we found for CdH is the work of Balasubramanian [68], using Cl with relativistic effective core potentials. The coupled-cluster results are presened in Table 6. Calculated values for R , cOg and Dg agree very well with experiment. Relativity contracts the bond by 0.04 and reduces the binding energy by 0.16 eV. The one- and two-component DK method reproduce the relativistic effects closely. Similar trends are observed for the excited states (Tables 7-9). Comparison with experiment is difficult for these states, since many of the experimental values are based on incomplete or uncertain data [65]. Calculated results for the CdH anion are shown in Table 10. The... 

The results presented here show that quantum-chemistry methods, whose accuracy and sophistication continue to increase, are capable of providing thermochemical data of practical value for modehng organometallic tin chemistry. In particular, the relativistic effective core potential used here appears to provide an adequate description of the electronic structure at tin, based on the favorable comparisons between experimental heats of formation and values predicted by the ECP/BAC-MP4 method. Trends in heats of... 

Slovenia), using the DFT implementation in the Gaussian03 code. Revision C.02 (8). The orbitals were described by a mixed basis set. A fully uncontracted basis set from LANL2DZ was used for the valence electrons of Re (9), augmented by two / functions Q =1.14 and 0.40) in the full optimization. Re core electrons were treated by the Hay-Wadt relativistic effective core potential (ECP) given by the standard LANL2 parameter set (electron-electron and nucleus-electron). The 6-3IG basis set was used to describe the rest of the system. The B3PW91 density functional was used in all calculations. 

Abstract. Investigation of P,T-parity nonconservation (PNC) phenomena is of fundamental importance for physics. Experiments to search for PNC effects have been performed on TIE and YbF molecules and are in progress for PbO and PbF molecules. For interpretation of molecular PNC experiments it is necessary to calculate those needed molecular properties which cannot be measured. In particular, electronic densities in heavy-atom cores are required for interpretation of the measured data in terms of the P,T-odd properties of elementary particles or P,T-odd interactions between them. Reliable calculations of the core properties (PNC effect, hyperfine structure etc., which are described by the operators heavily concentrated in atomic cores or on nuclei) usually require accurate accounting for both relativistic and correlation effects in heavy-atom systems. In this paper, some basic aspects of the experimental search for PNC effects in heavy-atom molecules and the computational methods used in their electronic structure calculations are discussed. The latter include the generalized relativistic effective core potential (GRECP) approach and the methods of nonvariational and variational one-center restoration of correct shapes of four-component spinors in atomic cores after a two-component GRECP calculation of a molecule. Their efficiency is illustrated with calculations of parameters of the effective P,T-odd spin-rotational Hamiltonians in the molecules PbF, HgF, YbF, BaF, TIF, and PbO. 

The first-order perturbation theory estimate of relativistic effects (inclusion of the mass-velocity and one-electron Darwin terms as suggested by Cowan and Griffin) is cheap and easy to compute as a property value at the end of a calculation. It is therefore very valuable as a check on the importance of relativistic effects, and should certainly be included in accurate calculations on, for example, transition-metal compounds. For even heavier elements relativistic effective core potentials should be used. 

All of the measurements employed the technique described above that involves the analysis of the isotope composition of 02 released from the carrier complexes in preequilibrated solutions. In addition, an established DFT method (mPWPW91)34 with the atomic orbital basis functions, Co, Fe, and Cl (the compact relativistic effective core potential basis CEP-31G),35 N and O (6-311G ), P (6-311G ), C(6-31G), and H (STO-3G),36 were used to calculate the 180 EIE in terms of actual and model structures. The latter approach has also been employed for hypothetical intermediates in enzymes as described below. 

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