LCGTO type orbitals

Similarly, expanding the KS potential in an LCAO expansion makes molecular density-functional calculations practical [9]. For metals and similar crystalline solids, it is best to expand the Kohn-Sham potential in momentum space via Fourier coefficients. For molecular solids various real-space method are under investigation. For molecules studied with the big, well-chosen Gaussian basis sets of quantum chemistry, it is undoubtedly best to expand the KS potential in linear-combination-of-Gaussian-type-orbital (LCGTO) form [10]. 

Linear Combinations of Gaussian Type Orbitals (LCGTO-LSD) (22) Gaussian basis fits for density and exchange-correlation most similar to "ab initio" analytical integrals accurate total energy possible... 

Note LCGTO is an abbreviation for linear combination of Gaussian-type orbitals. 

The Linear Combination of Gaussian-Type Orbitals (LCGTO) Implementation... 

Despite the huge increase in computational effort, this direct symmetry-adapted LCAO method was used to study ozone [22], tetrahedral Ni4 [23], and D5h-symmetric ferrocene (Fe(C5H5)2) [24] using molecular orbital (MO) contraction coefficients in the linear-combination-of-Gaussian-type orbital (LCGTO) computer code of [25]. Obviously, symmetry-adapted calculations are important enough to pay an order-TV computational price. The reasons are first, and foremost, that the calculations converge, and second that the wavefunction and one-electron orbitals can be used to address experiment, which typically must first determine the symmetry of the molecule. 

In this chapter, we will review the status of DK schemes in the framework of DF methods [13-16] with particular emphasis on recent method development [17-19]. For a long time, our implementations of this methodology, first in the LCGTO-FF-DF program (linear combination of Gaussian-type orbitals fitting-... 

For the calculations we used the Munich version of the linear combination of Gaussian-type orbital density functional (LCGTO-DF) code. ° The computationally economic local spin-density approximation (LSDA) to the exchange-correlation functional has been successfully used in chemical applications since the seventies. This functional (employed here in the parameterization suggested by Vosko, Wilk, and Nusair, has been shown to describe accurately impor-... 

In deMon2k, the linear combination of Gaussian-type orbital (LCGTO) approximation is used to expand the molecular Kohn-Sham orbitals ... 

C3. Linear combination of Gaussian-type orbitals (LCGTO) — either all-electron or model core potentials [229] (deMon-KS code, introduced in Ref. [265]). Auxiliary Gaussians are used as in C2. Calculations are based on either LDA or GGA. 

Here we use the local spin density (LSD) approximation and expand the molecular orbitals as a linear combination of gaussian type orbitals (LCGTO) for solving the LSD equations. The specific form of the latter depends on the treatment of exchange and correlation in electron-gas calculations. The Xa approach yields the following exchange energy ... 

Once an approximate XC functional has been selected, the need to solve the KS equations remains. Several strategies have emerged, which differ mainly in two ways the type of basis in which the KS orbitals are expanded and the manner in which the electrostatic component the KS equations is handled. The large number feasible DFT approaches is in sharp contrast to the more familiar HF formalism where the linear combination Gaussian-type orbitals (LCGTO) approach clearly dominates. The wide variation in DFT schemes is a direct result of the foct that exchange is no longer a nonlocal phenomenon as... 

The calculations were performed with the linear combination of Gaussian type orbital density functional theory (LCGTO-DFT) deMon2k (Koster et al. 2006) code. In O Fig. 16-1, the crosses refer to all-electron polarizabilities calculated with the local density approximation (LDA) employing the exchange functional from Dirac (1930) in combination with the correlation functional proposed by Vosko, Wilk and Nusair (VWN) (Vosko et al. 1980). The stars denote polarizabilities obtained with the gradient corrected exchange-correlation functional proposed by Perdew, Burke and Ernzerhof (PBE) (Perdew et al. 1996). 

Within the Kohn-Sham method [12], using the variational approximation of the Coulomb potential [13-15], the linear combination of Gaussian-type orbitals (LCGTO) expansion and the electronic density yields the following converged total electronic Kohn-Sham energy [16] of the system ... 

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