Basis sets molecular integrals

Orbitals Core, Valence, Polarization, and Diffuse Basis Sets Molecular Integral Evaluation. 

Raffenetti, R.C. General contraction of Gaussian atomic orbitals core, valence, polarization, and diffuse basis sets Molecular integral evaluation, J. Chem. Phys. 1973, 58,4452. 

R. C. Raffenetti, /. Chem. Phys., 58,4452 (1973). General Contraction of Gaussian Atomic Orbitals Core, Valence, Polarization and Dif se Basis Sets Molecular Integral Evaluation. 

Flelgaker T and Taylor P R 1995 Gaussian basis sets and molecular integrals Modem Electronic Structure Theory yo 2, ed D R Yarkony (Singapore World Scientific) section 5.4, pp 725-856... 

Each of these tools has advantages and limitations. Ab initio methods involve intensive computation and therefore tend to be limited, for practical reasons of computer time, to smaller atoms, molecules, radicals, and ions. Their CPU time needs usually vary with basis set size (M) as at least M correlated methods require time proportional to at least M because they involve transformation of the atomic-orbital-based two-electron integrals to the molecular orbital basis. As computers continue to advance in power and memory size, and as theoretical methods and algorithms continue to improve, ab initio techniques will be applied to larger and more complex species. When dealing with systems in which qualitatively new electronic environments and/or new bonding types arise, or excited electronic states that are unusual, ab initio methods are essential. Semi-empirical or empirical methods would be of little use on systems whose electronic properties have not been included in the data base used to construct the parameters of such models. 

ADF uses a STO basis set along with STO fit functions to improve the efficiency of calculating multicenter integrals. It uses a fragment orbital approach. This is, in essence, a set of localized orbitals that have been symmetry-adapted. This approach is designed to make it possible to analyze molecular properties in terms of functional groups. Frozen core calculations can also be performed. 

Ab initio methods are characterized by the introduction of an arbitrary basis set for expanding the molecular orbitals and then the explicit calculation of all required integrals involving this basis set. 

To some other experts the meaning of the term ab initio is rather clear cut. Their response is that "ab initio" simply means that all atomic/molecular integrals are computed analytically, without recourse to empirical parametrization. They insist that it does not mean that the method is exact nor that the basis set contraction coefficients were obtained without recourse to parametrization. Yet others point out that even the integrals need not be evaluated exactly for a method to be called ab initio, given that, for instance, Gaussian employs several asymptotic and other cutoffs to approximate integral evaluation. 

Helgaker, T., Taylor, P. R., 1995, Gaussian Basis Sets and Molecular Integrals in Modem Electronic Structure Theory, Part II, Yarkony, D. R., (ed.), World Scientific, Singapore. 

Representation of each molecular orbital as a linear combination of atomic orbitals (atomic basis sets). Atomic basis sets are usually represented as Slater type orbitals or as combinations of Gaussian functions. The latter is very popular, due to a very fast algorithm for the computation of bielectronic integrals. 

In molecular transport junctions, the Hamiltonian models are usually based on Kohn-Sham density functional theory [46—48]. They use relatively small basis sets because the calculations are sufficiently complicated, they take a number of empirical steps for dealing with the basis sets and their potential integrals, and they... 

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