Gaussian methods correlated calculations

In hybrid DET-Gaussian methods, a Gaussian basis set is used to obtain the best approximation to the three classical or one-election parts of the Schroedinger equation for molecules and DET is used to calculate the election correlation. The Gaussian parts of the calculation are carried out at the restiicted Hartiee-Fock level, for example 6-31G or 6-31 lG(3d,2p), and the DFT part of the calculation is by the B3LYP approximation. Numerous other hybrid methods are currently in use. 

In this section, we describe a theory for calculating observables resulting from incoherent excited state transport among chromophores randomly distributed in low concentration on isolated, flexible polymer chains. The pair correlation function used to describe the distribution of the chromophores is based on a Gaussian chain model. The method for calculating the excitation transfer dynamics is an extension to finite, inhomogeneous systems of a truncated cumulant expansion method developed by Huber for infinite, homogeneous systems (25.26). 

An improved basis set with 36s32p24d22fl0g7h6i uncontracted Gaussian-type orbitals was used and all 119 electrons were correlated, leading to a better estimate of the electron affinity within the Dirac-Coulomb-Breit Hamiltonian, 0.064(2) eV [102]. Since the method for calculating the QED corrections [101] is based on the one-electron orbital picture, the 8s orbital of El 18 was extracted from the correlated wave function by... 

The local MP2 electron-correlation method for nonconducting crystals [109] is an extension to crystalline solids of the local correlation MP2 method for molecules (see Sect. 5.1.5), starting from a local representation of the occupied and virtual HF subspaces. The localized HF crystalline orbitals of the occupied states are provided in the LCAO approximation by the CRYSTAL program [23] and based on a Boys localization criterion. The localization technique was considered in Sect. 3.3.3. The label im of the occupied localized Wannier functions (LWF) Wim = Wj(r — Rm) includes the type of LWF and translation vector Rm, indicating the primitive unit cell, in which the LWF is centered (m = 0 for the reference cell). The index i runs from 1 to A i, the number of filled electron bands used for the localization procedure the correlation calculation is restricted usually to valence bands LWFs. The latter are expressed as a linear combination of the Gaussian-type atomic orbitals (AOs) Xfiif Rn) = Xfin numbered by index = 1,..., M M is the number of AOs in the reference cell) and the cell n translation vector... 

In the present method of calculation, one first notes that any two scattering centers in a crosslinked gel are connected to each other through the network by a very large number of different paths, most of which are so interconnected that the statistics are forbidding to contemplate. Therefore, the first assumption in this method states that only the shortest path between two scattering centers need be considered in the calculation of correlations. The second assumption, that the shortest path between any two scattering centers in the network is a Gaussian chain, is closely related to the first assumption. 

The application of density functional theory to isolated, organic molecules is still in relative infancy compared with the use of Hartree-Fock methods. There continues to be a steady stream of publications designed to assess the performance of the various approaches to DFT. As we have discussed there is a plethora of ways in which density functional theory can be implemented with different functional forms for the basis set (Gaussians, Slater type orbitals, or numerical), different expressions for the exchange and correlation contributions within the local density approximation, different expressions for the gradient corrections and different ways to solve the Kohn-Sham equations to achieve self-consistency. This contrasts with the situation for Hartree-Fock calculations, wlrich mostly use one of a series of tried and tested Gaussian basis sets and where there is a substantial body of literature to help choose the most appropriate method for incorporating post-Hartree-Fock methods, should that be desired. 

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