Self-consistency cycle

The Kohn-Sham-Dirac equation (28) has to be solved self consistently, since the crystal potential and the XC-field depend via the (magnetization) density on its solutions. For a local orbital method it is advantageous to use a strictly local language for all relevant quantities, so that computationally expensive transformations between different numerical representations are avoided during the self consistency cycle. In the (R)FPLO method, the density n(r) and the magnetization density m(r) = m r)z are represented as lattice sums... 

As starting point for the self consistency cycle we use a density n(r) and a magnetization density m r) represented as lattice sum (29). These initial densities may be either obtained from an atomic or a scalar-relativistic band... 

QM-EFP polarization is obtained self-consistently with electronic wave function of the QM part and induced dipoles of the EFP part. In practice, this is achieved in two included self-consistent cycles, the outer one for the electronic wave function, i.e., a standard SCF procedure, and the inner one for the EFP induced dipoles at the instantaneous value of the field due to electronic wave function. The Hqm mm for polarization includes two parts the one-electron contribution to the electronic Hamiltonian (Eq. 5.11) and the polarization energy added to the EFP subsystem (Eq. 5.12) ... 

Additional tests not reported here, have also shown that the subspace filtering method is robust with respect to the initial subspace. Besides self-consistency, it can be used together with molecular dynamics or structural optimization, provided that atoms move by a small amount. Even after atomic displacements of a fraction of the Bohr radius, the CheFSI method was able to bring the initial subspace to the subspace of self-consistent Kohn-Sham eigenvectors for the current position of atoms, with no substantial increase in the number of self-consistent cycles needed. 

Here, we explicitly write the averaging as a sum over the BZ. Hence, the imposed self-consistency condition is that the Gbath put into Eq. (35) should equal the Gbath extracted from Eq. (38) with Eq. (36). This is usually obtained via an iteration process (the DMFT self-consistency cycle). 

Using a time reversible BO scheme as discussed in Sect. 2.5 allows for efficient and stable dynamics. However, a sufficient accuracy of the nuclear forces is stiU needed. In systems with slow convergence this will require many self-consistency cycles and therefore it will slow down the simulation. For such systems, an algorithm that would allow for less stringent convergence criteria on the forces could bring considerable gains in efficiency. 

If the parameter yp can be kept small, the Langevin method not only generates the correct canonical distribution but also dynamical properties are accurately described [60]. In order to achieve this goal, the error of the forces can be consistently reduced by noting that the last self-consistent cycle can be interpreted as a Harris functiOTial. The missing force Fbo — F c can then be approximated to a high degree by... 

We have now all the ingredients to obtain the electronic density from (6.2). The self-consistency cycle is stopped when some convergence criterion is reached. The two most common criteria are based on the difference of total energies or densities from iteration i and i - 1, i.e., the cycle is stopped when < t]e or fd r ( - ) < where and... 

During the last 40 years it has been possible to witness an important evolution on the way the environment around a solute molecule is described. The reaction field approach, the effect a continuous dielectric medium has on the charge distribution of a molecule that polarizes back the dielectric and generates a reaction potential, is a standard scheme to consider the solvent effects on many molecular properties. Most modem continuum models obtain through a self-consistent cycle the wave function of the molecule affected by the reaction potential thus the self-consistent reaction field acronym (SCRF). Solvatochromic effects have been more or less successfully explained using from Onsager s to more refined models like Nancy SCRF [44], Tomasi s polarizable continuum model (PCM) [45], Cramer and Tmhlar s SMx models [46]. 

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