Linear combination of Gaussian type orbitals

The second approximation in HF calculations is due to the fact that the wave function must be described by some mathematical function, which is known exactly for only a few one-electron systems. The functions used most often are linear combinations of Gaussian-type orbitals exp(—nr ), abbreviated GTO. The wave function is formed from linear combinations of atomic orbitals or, stated more correctly, from linear combinations of basis functions. Because of this approximation, most HF calculations give a computed energy greater than the Hartree-Fock limit. The exact set of basis functions used is often specified by an abbreviation, such as STO—3G or 6—311++g. Basis sets are discussed further in Chapters 10 and 28. 

We have extended the linear combination of Gaussian-type orbitals local-density functional approach to calculate the total energies and electronic structures of helical chain polymers[35]. This method was originally developed for molecular systems[36-40], and extended to two-dimensionally periodic sys-tems[41,42] and chain polymers[34j. The one-electron wavefunctions here are constructed from a linear combination of Bloch functions c>>, which are in turn constructed from a linear combination of nuclear-centered Gaussian-type orbitals Xylr) (in ihis case, products of Gaussians and the real solid spherical harmonics). The one-electron density matrix is given by... 

Haberlen, O.D. and Rdsch, N. (1992) A scalar-relativistic extension of the linear combination of Gaussian-type orbitals local density functional method application to AuFl, AuCl and Au2. Chemical Physics Letters, 199, 491-496. 

Fournier, R., Andzelm, J., Salahub, D. R., 1989, Analytical Gradient of the Linear Combination of Gaussian-Type Orbitals-Local Spin Density Energy , J. Chem. Phys., 90, 6371. 

Gallant, R. T. and A. St-Amant. 1996. Linear scaling for the charge density fitting procedure of the linear combination of Gaussian-type orbitals density functional method. Chem. Phys. Lett. 256, 569. 

We use an alternative to this method, that enables a fast and accurate evaluation of the two-center integrals. Analytical integration is possible when linear combinations of Gaussian Type Orbitals are used to describe the atomic states [1,9, 10]. Imperfect behavior of such gaussian functions at large distances does not affect the results, since the two-center matrix-elements (7) have an exponential decay for increasing intemuclear distances. For example, for integrals and expressed in cartesian coordinates, one has to evaluate expressions such as... 

R. T. Gallant and A. St-Amant, Chem. Phys. Lett., 256 569 (1996). Linear Scaling for the Charge Density Fitting Procedure of the Linear Combination of Gaussian-Type Orbitals Density Functional Method. 

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 fLCGTO) Xa method (M) is based on the local density functional (LDF) method using the Xa variant ior the exchange potential ... 

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

In this contribution we have reviewed the applicability, accuracy and computational efficiency of the local spin density functional approach to the chemistry of transition metal complexes and clusters using a linear combination of Gaussian-type orbital basis set for the calculation of electronic structures, ground state geometries and vibrational properties. 

We determine the ground-state electronic structure of solids within Density Functional Theory (DFT) and the usual KS variational procedure, all implemented in the computational package gtoff [14]. The results of the all-electron, full-potential calculations are Bloch eigenfunctions p,k(r), expressed as linear combinations of Gaussian Type Orbitals (GTOs), and KS eigenvalues p k-... 

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-... 

Duiilap, B. I., Andzehn, J., Mintmire, J. W. (1990). Local-density-functional total energy gradients in the linear combination of Gaussian-type orbitals method. Phys. Rev. A 42,6354-6358. 

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

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