Energy relativistic

The total energy in ab initio theory is given relative to the separated particles, i.e. bare nuclei and electrons. The experimental value for an atom is the sum of all the ionization potentials for a molecule there are additional contributions from the molecular bonds and associated zero-point energies. The experimental value for the total energy of H2O is —76.480 a.u., and the estimated contribution from relativistic effects is —0.045 a.u. Including a mass correction of 0.0028 a.u. (a non-Bom-Oppenheimer effect which accounts for the difference between finite and infinite nuclear masses) allows the experimental non-relativistic energy to be estimated at —76.438 0.003 a.u. ... 

The classical, non-relativistic energy E for a free particle, i.e., a particle in the absence of an external force, is expressed as the sum of the kinetic and potential energies and is given by... 

Generally, it is not required to retain all the terms in the resulting approximate Hamiltonian, except those operators which describe the actual physical processes involved in the problem. For example, in the absence of an external electromagnetic field, the non-relativistic energy calculations only requires... 

The ability to use precisely the same basis set parameters in the relativistic and non-relativistic calculations means that the basis set truncation error in either calculation cancels, to an excellent approximation, when we calculate the relativistic energy correction by taking the difference. The cancellation is not exact, because the relativistic calculation contains additional symmetry-types in the small component basis set, but the small-component overlap density of molecular spinors involving basis functions whose origin of coordinates are located at different centres is so small as to be negligible. The non-relativistic molecular structure calculation is, for all practical purposes, a precise counterpoise correction to the four-component relativistic molecular... 

Comparison of atomic and molecular estimates of relativistic energy corrections... 

Table 2 Values of relativistic energies (E) and differences among relativistic and non-relativistic energies (AE) for neutral atoms in atomic units with the present approach using thefunctional given by Eq. (46) not including (1) or including (2) the term, compared to the results of Engel and Dreizler (ED) [23] using the relativistic Thomas-Fermi-Dirac- Weirsacker approach described in Section 2.6, and to Dirac-Fock values...

Two types of corrections to the Thomas-Fermi-Dirac non-relativistic energy density appear. The first is the correction to the kinetic energy given by the mass-variation term ... 

Note that replacing c 2 by zero in this procedure, we find all the TFD expresions, and if we make C 2 = 0 we supress the relativistic exchange corrections. When we include these in our calculations we have always chosen the value of 3jr/2, the one which matches the weak relativistic limit of the fully relativistic energy functional. 

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