Localized orbital methods

Ab initio calculations involving electron correlation essentially always build on a set of canonical HF orbitals. As illustrated in this chapter, this leads to a computational effort which increases as a rather high power of the system size, i.e. Considering that 

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To circumvent problems associated with the link atoms different approaches have been developed in which localized orbitals are added to model the bond between the QM and MM regions. Warshel and Levitt [17] were the first to suggest the use of localized orbitals in QM/MM studies. In the local self-consistent field (LSCF) method the QM/MM frontier bond is described with a strictly localized orbital, also called a frozen orbital [43]. These frozen orbitals are parameterized by use of small model molecules and are kept constant in the SCF calculation. The frozen orbitals, and the localized orbital methods in general, must be parameterized for each quantum mechanical model (i.e. energy-calculation method and basis set) to achieve reliable treatment of the boundary [34]. This restriction is partly circumvented in the generalized hybrid orbital (GHO) method [44], In this method, which is an extension of the LSCF method, the boundary MM atom is described by four hybrid orbitals. The three hybrid orbitals that would be attached to other MM atoms are fixed. The remaining hybrid orbital, which represents the bond to a QM atom, participates in the SCF calculation of the QM part. In contrast with LSCF approach the added flexibility of the optimized hybrid orbital means that no specific parameterization of this orbital is needed for each new system. 

An early example implementing the general approach to take into account first the intrabond correlation, is presented by the PCILO - perturbational configuration interaction of localized orbitals method [121,122], As one of its authors, J.-P. Malrieu mentions in [122], the PCILO method opposes the majority of the QC methods in all the fundamental concepts. In contrast to the majority of the methods based on the variational principle, the PCILO method is based on estimating the energy by perturbation theory. Also, the majority of the QC methods use one-electron HFR approximation, at least as an intermediate construct, whereas the PCILO is claimed to addresses directly the V-electron wave function and takes into account all surviving matrix elements of the electron-electron interactions. In contrast with other QC... 

Localized orbital methods, 227 Moments of inertia, 300 qeiec, partition function, 302 ... 

S. Louie, New localized-orbital method for calculating the electronic structure of molecules and solids covalent semiconductors, Phys. Rev. B22, 1933 (1980). 

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... 

It is also worth mentioning an alternative approach [77] to describe the localized character of njr excitations. It based on the PCILO (Perturbative Configuration Interaction using Localized Orbitals) method where Cl calculations are carried out in a basis of locally excited determinants. Accordingly, the local structure of nn — excitations is detected by the weights of the appropriate determinant. At the same time, our approach includes no localization procedure for MOs, and excited state local properties arise directly from the main indices (14.35), (14.37), and (14.38). Moreover, the PCILO method is somewhat outdated at least its extension to the DPT methodology seems not reasonable. We cite work [77] as the first paper where the localization phenomena otnn — transitions were discussed from a quantum-chemical viewpoint. 

An alternative CNDO procedure for Cl, developed at the same time as CNDO/S but oriented toward ground-state properties is the PCILO (perturbative configuration interaction using localized orbitals) method of Malrieu, Claverie, Diner, and co-workers. °" Its major strength and weakness lie in the use of intuitively construaed hybrid atomic orbitals as zeroeth-order localized MOs. This leads to conceptually appealing interpretations at the expense of some arbitrariness in the treatment. 

Localized Orbital Methods for Wavefunction-based Electron Correlation Calculations... 

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