Basis sets Gaussian-orbital

Basis sets-Gaussian orbital versus plane waves... 

Restricted-basis-set Gaussian-orbital SCF calculations on larger molecules. 

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. 

Molecular orbital theories (ab initio methods (23)) were chosen and validated in this study to characterize the interaction energies between methane and water, while electron density functional theories (24) were tested, but found to be inadequate (see below). Four different ab initio methods were used in the validation MP2 (25,26), MP4(SDTQ) (27), QCISD(T) (28) and CCSD(T) (29). Three different DFT methods, BLYP (30Jl), B3LYP (32) and BPW91 (33), were used and the results compared with the ab initio methods. In addition, for each of the above methods, the effect of the size of different basis sets was investigated specifically, 6-31++G(2d,2p), cc-pVDZ, cc-pVTZ and cc-pVQZ were used. 6-31+-i-G(2d,2p) was chosen, because it was reported to yield reasonable results compared with that at near the basis set limit on this system (77). The others were chosen in order to observe the effect of systematically increasing the size of the basis set. Gaussian 94 (22) was used for all the above calculations. 

Atomic natural orbital (ANO) basis sets [44] are fonned by contracting Gaussian fiinctions so as to reproduce the natural orbitals obtained from correlated (usually using a configuration interaction with... 

Flehre W J, Ditchfieid R and Popie J A 1972 Self-consistent molecular-orbital methods XII. Further extension of Gaussian-type basis sets for use in molecular orbital studies of organic molecules J. Chem. Phys. 56 2257-61 Flariharan P C and Popie J A 1973 The influence of polarization functions on molecular orbital hydrogenation energies Theoret. Chim. Acta. 28 213-22... 

To calculate the matrix elements for H2 in the minimal basis set, we approximate the Slater Is orbital with a Gaussian function. That is, we replace the Is radial wave function... 

The solution to this problem is to use more than one basis function of each type some of them compact and others diffuse, Linear combinations of basis Functions of the same type can then produce MOs with spatial extents between the limits set by the most compact and the most diffuse basis functions. Such basis sets arc known as double is the usual symbol for the exponent of the basis function, which determines its spatial extent) if all orbitals arc split into two components, or split ualence if only the valence orbitals arc split. A typical early split valence basis set was known as 6-31G 124], This nomenclature means that the core (non-valence) orbitals are represented by six Gaussian functions and the valence AOs by two sets of three (compact) and one (more diffuse) Gaussian functions. 

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. 

Minimal basis sets in which 3, 4 etc, Gaussian functions are used to represent the atomic orbitals on an atom... 

The remainder of the input file gives the basis set. The line, 1 0, specifies the atom center 1 (the only atom in this case) and is terminated by 0. The next line contains a shell type, S for the Is orbital, tells the system that there is 1 primitive Gaussian, and gives the scale factor as 1.0 (unsealed). The next line gives Y = 0.282942 for the Gaussian function and a contiaction coefficient. This is the value of Y, the Gaussian exponential parameter that we found in Computer Project 6-1, Part B. [The precise value for y comes from the closed solution for this problem S/Oir (McWeeny, 1979).] There is only one function, so the contiaction coefficient is 1.0. The line of asterisks tells the system that the input is complete. 

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