Basis sets Gaussian type orbitals

Spatial orbitals are typically (but not necessarily) expanded in a basis set. The choice of the latter expansion is somewhat arbitrary, but the quality of the possible choices can be judged by considering completeness of the basis set and how quickly the basis converges to eigenfunctions of the Hamiltonian. Alternatives include plane-wave basis sets. Slater-type orbitals (STO), Gaussian-type orbitals (GTO), and numerical orbitals. 

Minimum basis sets (Slater-type orbitals, three Gaussian (STO-3G)) tend to underestimate bond lengths by 0.05 A at SCF and overestimate by 0.05 A with electron correlation, with an uncertainty of 10° in the bond angle. 

Because th e calculation of m n Iti-ceiiter in tegrals that are in evitable for ah iniiio method is very difficult and time-con sum in g. Ilyper-Chem uses Gaussian Type Orbital (GTO) for ah initio methods. In truly reflecting a atomic orbital. STO may he better than GTO. so HyperC hem uses several GTOs to construct a STO. The number of GTOs depends on the basis sets. For example, in the minimum STO-3G basis set IlyperGhem uses three GTOs to construct a STO. 

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. 

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. 

Minimal basis sets use fixed-size atomic-type orbitals. The STO-3G basis set is a minimal basis set (although it is not the smallest possible basis set). It uses three gaussian primitives per basis function, which accounts for the 3G in its name. STO stands for Slater-type orbitals, and the STO-3G basis set approximates Slater orbitals with gaussian functions. ... 

The quantum mechanical polarizability is calculated using the DFT, with B3P86 (Becke s three-parameter functional [53] with the non-local correlation provided by Perdew [54]). The basis set used for the water molecules is 6-311 + +G. Because of the very diffuse nature of the anion F, the basis set used is the specially designed, and very extensive, fully uncontracted 14s 9p 6d 2f Gaussian-type orbitals [55]. All the QM calculations were made with the Gaussian98 program [56]. 

Large basis sets of Gaussian-type orbitals (up to 35s21p2ld9g6h4i) were used, taken from the universal basis set ofMalli etal. [55]. Many electrons were correlated (5 in B,... 

Dahle, P., Helgaker, T., Jonsson, D., Taylor, RR. Accurate quantum-chemical calculations using Gaussian-type geminal and Gaussian-type orbital basis sets applications to atoms and diatomics. Phys. Chem. Chem. Phys. 2007, 9, 3112-26. 

STO-3G. A Minimal Basis Set. Each atomic orbital is written in terms of a sum of three Gaussian functions taken as best fits to Slater-type (exponential) functions. 

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]. 

Triple-Zeta Basis Set of Gaussian-Type Orbitals for Pb... 

Two different basis sets were used (1) basis set I was medium size, and (2) split-valence basis set II taken from Huzinaga [24] (9s and 5p gaussian-type orbital contracted into [3s, lp] for the C,N,0 atoms). In basis set II, more flexibility has been allowed to the description of the valence shells by adapting a triple- contraction completed with one p type (for hydrogen) or one d type (for C,N,0) polarization function. Then two ab initio calculations were carried out (1) all atoms were described with basis set I, and (2) basis set II was used for all the atoms but those belonging to the methyl and phenyl substituents due to computer limitations. 

All calculations employed extended basis sets constructed from contracted Gaussian type orbitals. Basis sets were, in general, taken from the work of Huzlnaga (26) and Dunning and Hay (27). 

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