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Chemistry with Relativistic Hamiltonians

Hess, B. A. Dolg, M. Relativistic Quantum Chemistry with Pseudopotentials and Transformed Hamiltonians, Relativistic Effects in Heavy-Element Chemistry and Physics -, Ed. Hess, B. A. Wiley Chichester, 2002, pp. 89-122. [Pg.100]

Relativistic Quantum Chemistry with Pseudopotentials and Transformed Hamiltonians... [Pg.89]

Eqs. (l)-(3), (13), and (19) define the spin-free CGWB-AIMP relativistic Hamiltonian of a molecule. It can be utilised in any standard wavefunction based or Density Functional Theory based method of nonrelativistic Quantum Chemistry. It would work with all-electron basis sets, but it is expected to be used with valence-only basis sets, which are the last ingredient of practical CGWB-AIMP calculations. The valence basis sets are obtained in atomic CGWB-AIMP calculations, via variational principle, by minimisation of the total valence energy, usually in open-shell restricted Hartree-Fock calculations. In this way, optimisation of valence basis sets is the same problem as optimisation of all-electron basis sets, it faces the same difficulties and all the experience already gathered in the latter is applicable to the former. [Pg.424]

In most cases, however, the relativistic effects are rather weak and may be separated into spin-orbit coupling effects and scalar effects. The latter lead to compression and/or expansion of electron shells and can rather accurately be treated by modifying the one-electron part of the non-relativistic many-electron Hamiltonian. With this scalar-relativistic Hamiltonian the (modified) energies and wave functions are computed and subsequently an effective spin-orbit part is added to the Hamiltonian. The effects of the spin-orbit term on the energies and wave functions are commonly estimated using second-order perturbation theory. More information for the interested reader can be found in excellent textbooks on relativistic quantum chemistry [2, 3]. [Pg.37]

In this chapter we will provide a critical review of the use of 2- and 4-component relativistic Hamiltonians combined with all-electron methods and appropriate basis sets for the study of lanthanide and actinide chemistry. These approaches provide in principle the more rigorous treatment of the electronic structure but typically demand large computational resources due to the large basis sets that are required for accurate energetics. A complication is furthermore the open-shell nature of many systems of practical interest that make black box application of conventional methods impossible. Especially for calculations in which electron correlation is explicitly considered one needs to find a balance between the appropriate treatment of the multi-reference nature of the wave function and the practical limitations encountered in the choice of an active space. For density functional theory (DFT) calculations one needs to select the appropriate density functional approximation (DFA) on basis of assessments for lighter elements because little or no high-precision experimental information on isolated molecules is available for the f elements. This increases the demand for reliable theoretical ( benchmark ) data in which all possible errors due to the inevitable approximations are carefully checked. In order to do so we need to understand how f elements differ from the more commonly encountered main group elements and also from the d elements with which they of course share some characteristics. [Pg.55]

The approximation techniques described in the earlier sections apply to any (non-relativistic) quantum system and can be universally used. On the other hand, the specific methods necessary for modeling molecular PES that refer explicitly to electronic wave function (or other possible tools mentioned above adjusted to describe electronic structure) are united under the name of quantum chemistry (QC).15 Quantum chemistry is different from other branches of theoretical physics in that it deals with systems of intermediate numbers of fermions - electrons, which preclude on the one hand the use of the infinite number limit - the number of electrons in a system is a sensitive parameter. This brings one to the position where it is necessary to consider wave functions dependent on spatial r and spin s variables of all N electrons entering the system. In other words, the wave functions sought by either version of the variational method or meant in the frame of either perturbational technique - the eigenfunctions of the electronic Hamiltonian in eq. (1.27) are the functions D(xi,..., xN) where. r, stands for the pair of the spatial radius vector of i-th electron and its spin projection s to a fixed axis. These latter, along with the... [Pg.38]

The eigenfunctions of the zeroth order Hamiltonian define the projection of the DCB equation onto the subspace of electronic solutions. This is a first and necessary step to apply QED theory in quantum chemistry. The resulting second quantized formalism is compatible with the non-relativistic spin-orbital formalism if the connection (unbarred spinors <-> alpha-spinorbitals) and (barred spinors beta spinorbitals) is made. This correspondence allows transfer to the relativistic domain of non-relativistic algorithms after the differences between the two formalism are accounted for. [Pg.303]

There are lots of exehange-eorrelation potentials in the literature. There is an impression that their authors worried most about theory/experiment agreement. We ean hardly admire this kind of seienee, but the alternative (i.e., the practiee of ab initio methods with the intact and holy Hamiltonian operator) has its own disadvantages. This is because finally we have to choose a given atomic basis set, and this influences the results. It is true that we have the variational principle at our disposal, and it is possible to tell which result is more accurate. But more and more often in quantum chemistry, we use some non-variational methods (cf. Ch ter 10). Besides, the Hamiltonian holiness disappears when the theory becomes relativistic (cf. Qiapter 3). [Pg.689]

The life is relativistic and of the same kind should be the quantum chemistry. The four-component calculations involving large number of dynamic correlation are extremely time-consuming. The important thing, however, is that one is now able to formulate the fully equivalent two-component algorithms for those calculations. Since the final philosophy of the two-component calculations is similar to non-relativistic theory and most of mathematics are simply enough to comprehend the routine molecular relativistic calculations are possible. The standard nonrelativistic codes can be used with simple modification of the core Hamiltonian. The future is still in the development of the true two-component codes which will be able to deal with the spin-orbit interaction effect not in a posterior way as it is done nowadays. [Pg.126]

The preceding three chapters have already introduced Hamiltonians of reduced dimension. Particularly successful in variational calculations are the DKH and ZORA approaches. In their scalar-relativistic variant, they can easily be implemented in a computer program for nonrelativistic quantum chemistry so that spin remains a good quantum number leading to great computational advantages (if this approximation is justifiable). Already for these methods we have seen that numerous approximations can be made in order to increase their computational efficiency with little or even no loss of accuracy compared with a four-component reference calculation with the same type of total wave function. [Pg.530]

K. Hirao. Relativistic Multireference Perturbation Theory Complete Active-Space Second-Order Perturbation Theory (CASPT2) With The Four-Component Dirac Hamiltonian. In Radiation Induced Molecular Phenomena in Nucleic Adds, Volume 4 of Challenges and Advances in Computational Chemistry and Physics, p. 157-177. Springer, 2008. [Pg.695]

New transformation formalisms for obtaining two component equations are currently being investigated and being applied to atomic systems. Such studies and others together with implementation of the Douglas-Kroll spin-orbit Hamiltonian, give special importance to this active field of relativistic quantum chemistry. [Pg.127]


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Hamiltonian relativistic

Relativistic Quantum Chemistry with Pseudopotentials and Transformed Hamiltonians

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