GTO basis sets

Choosing a standard GTO basis set means that the wave function is being described by a finite number of functions. This introduces an approximation into the calculation since an infinite number of GTO functions would be needed to describe the wave function exactly. Dilferences in results due to the quality of one basis set versus another are referred to as basis set effects. In order to avoid the problem of basis set effects, some high-accuracy work is done with numeric basis sets. These basis sets describe the electron distribution without using functions with a predefined shape. A typical example of such a basis set might... 

Most calculations today are done by choosing an existing segmented GTO basis set. These basis sets are identihed by one of a number of notation schemes. These abbreviations are often used as the designator for the basis set in the input to ah initio computational chemistry programs. The following is a look at the notation for identifying some commonly available contracted GTO basis sets. 

Here, n corresponds to the principal quantum number, the orbital exponent is termed and Ylm are the usual spherical harmonics that describe the angular part of the function. In fact as a rule of thumb one usually needs about three times as many GTO than STO functions to achieve a certain accuracy. Unfortunately, many-center integrals such as described in equations (7-16) and (7-18) are notoriously difficult to compute with STO basis sets since no analytical techniques are available and one has to resort to numerical methods. This explains why these functions, which were used in the early days of computational quantum chemistry, do not play any role in modem wave function based quantum chemical programs. Rather, in an attempt to have the cake and eat it too, one usually employs the so-called contracted GTO basis sets, in which several primitive Gaussian functions (typically between three and six and only seldom more than ten) as in equation (7-19) are combined in a fixed linear combination to give one contracted Gaussian function (CGF),... 

GTO basis sets are used unless stated otherwise, for the notation of the basis see Table 11. s) All lengths in (A), all energies in (kcal/mole)... 

The interaction of two formamide molecules with Li+ has been studied by Rode 213> using a small GTO basis set. He considered two types of geometries in both 1 1 and 1 2 complexes. In the most stable structure of the 1 1 complex the Li+ cation is situated on the CO connection line. In a chelate-like structure the Li+ ion occupies a position which is almost equidistant from the 0 and N atoms. Although this type of 1 2 complex is found to be 70 kcal/mole less stable than the other structure with a linear OLiO arrangement it might be important for larger central ions. 

The avoided intersection of the two potential surfaces in the H system was studied in detail in a full Cl calculation by Bauschlicher et a/.338 An uncontracted 5s and 2p GTO basis set was used. The lowest surface was found to be attractive, with a binding energy of 444 kJ mol 1 for H relative to H + and Ha. The second surface which represents H + H+ is reported to be repulsive in nature. 

He + H - HeH+ + H.—Two different approaches of He to the HJ ion were investigated by Edmiston et al.im using the same method they applied to H3.184 20 An uncontracted GTO basis set with polarization functions (6s, 2pt, 3px,y on helium and 4s, 1 pz, 3px,u on each hydrogen) was used and pseudonatural orbitals were calculated for the la2 pair. A 65-configuration Cl followed in which ca. 90% of the correlation energy was accounted for. The energies of 22 different linear He-H-H + geometries were calculated. A minimum which lies about 21 kJ mol 1 below the separated reactants is found at He-H and H-H+ bond distances of ca. 2.0 a.u. 

F + Ha->FH + H.—Bender et al.26S recently reported the results of two different sets of calculations on the potential energy surface for the reaction F + H2-+ FH + H. This work is of interest from three points of view. First, it is truly a rigorous quantum mechanical calculation typifying the current state of the art for systems of this size a GTO basis set of double-zeta quality is used (9s5pj4s) for a total of 32 GTO s, and this is contracted according to the Dunning method51 to... 

A few other studies on these molecules have appeared. BCN was the subject of a calculation with a small GTO basis set,427 and the spin-spin interaction in the ground states of NCN, CNN, and CCO has been computed by Williams, using a STO-4G and an extended 4-31G basis set.428 Results were not in very good agreement with experiment. Although spin-orbit contributions were believed to be the main reason... 

A. AH2 Molecules, inclnding H3.—The simplest of these species is H, which has been the subject of a number of recent studies. Work previous to 1970 is listed by Borkman.426 The ground state is triangular (Dsn) and it has been studied using a basis set of elliptical orbitals. Contracted GTO basis sets were used in near-HF calculations by Harrison et a/.,430 and correlated wavefunctions were computed by Salmon and Poshusta,431 and by Handy.482 In the latter calculation a new form for the correlation factor was used, and the good results suggest that it might be useful for other small molecules. 

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