Local-scaling self-consistent field

Global Variational Principle The Concept of Local-Scaling Self-Consistent Field... 

The extensive experience with Gaussian-type basis sets shows that basis set sequences that increase rapidly in accuracy can be constructed in a systematic way [9]. At the same time, a compact description of the wave functions is maintained, and this opens the way for efficient methods to solve for the self consistent field (SCF) equations. Furthermore, as Gaussian functions are localized, the representations of the KS, overlap and density matrix in this basis become sparse with increasing system size [11]. This eventually allows for solving the KS equations using computational resources that scale linearly with system size. 

M. Modi, M. Dolg, P. Fulde, H. Stoll, Analysis of large-scale multi-configuration self-consistent field wavefunctions by expectation values of local operators, J. Chem. Phys., 105, 2353—2363 (1996). 

It should also be noted that this section represents a novel application of irreversible thermodynamics to systems with long-range forces. The local field has been dealt with self-consistently. In the macroscopic theory of Section 13.7 local electroneutrality was imposed through Eq. (13.7.10), whereas in the fluctuation theory there is no constraint of electroneutrality. However because we applied Eq. (13.8.3b) we see that deviations from local electroneutrality decay on the time scale rf1. This is the ionic relaxation time. In Section 9.4 only an approximate theory was presented. 

Basis Sets Correlation Consistent Sets Configuration Interaction Coupled-cluster Theory Density Functional Applications Density Functional Theory Applications to Transition Metal Problems G2 Theory Integrals of Electron Repulsion Integrals Overlap Linear Scaling Methods for Electronic Structure Calculations Localized MO SCF Methods Mpller-Plesset Perturbation Theory Monte Carlo Quantum Methods for Electronic Structure Numerical Hartree-Fock Methods for Molecules Pseudospectral Methods in Ab Initio Quantum Chemistry Self-consistent Reaction Field Methods Symmetry in Hartree-Fock Theory. 

DDFT, which was developed by Fraaije et al. in 1997, is a field-based theoretical method for studying complex fluids, their kinetics and their equilibrium structures at micrometer length and microsecond time scales. DDFT has been applied to the study of the self-assembly of block copolymers in bulk, under shear and in confinement, " and to study polymer blend compatibility. Compared to the DPD method, DDFT is computationally extremely fast since larger elements can be modelled. Moreover, since the fiuid elements can freely penetrate, larger time steps can be used, and furthermore it is less likely to become trapped in a local minimum. Since DPD is a particle-based method, it can provide somewhat more detailed structural information. Nonetheless, they are both powerful tools in simulating phase separated phenomena that occurs at the mesoscale and the consistency of results from the two methods for the same coarse-grain model is evaluated in this work. 

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