CGTOs

To overcome the primary weakness of GTO fimetions (i.e. their radial derivatives vanish at the nucleus whereas the derivatives of STOs are non-zero), it is coimnon to combine two, tliree, or more GTOs, with combination coefficients which are fixed and not treated as LCAO-MO parameters, into new functions called contracted GTOs or CGTOs. Typically, a series of tight, medium, and loose GTOs are multiplied by contraction coefficients and suimned to produce a CGTO, which approximates the proper cusp at the nuclear centre. 

A double-zeta (DZ) basis in which twice as many STOs or CGTOs are used as there are core and valence AOs. The use of more basis functions is motivated by a desire to provide additional variational flexibility so the LCAO-MO process can generate MOs of variable difhiseness as the local electronegativity of the atom varies. 

A triple-zeta (TZ) basis in which tlnee times as many STOs or CGTOs are used as the number of core and valence AOs (and, yes, there now are quadniple-zeta (QZ) and higher-zeta basis sets appearing in the literature). 

A minimal basis in which the number of STO or CGTO orbitals is equal to the number of core and valence atomic orbitals in the atom. 

A double-zeta (DZ) basis in which twice as many STOs or CGTOs are used as there are... 

The values of the orbital exponents ( s or as) and the GTO-to-CGTO eontraetion eoeffieients needed to implement a partieular basis of the kind deseribed above have been tabulated in several journal artieles and in eomputer data bases (in partieular, in the data base eontained in the book Handbook of Gaussian Basis Sets A. Compendium for Ab initio Moleeular Orbital Caleulations, R. Poirer, R. Kari, and I. G. Csizmadia, Elsevier Seienee Publishing Co., Ine., New York, New York (1985)). 

Combining the full set of basis functions, known as the primitive GTOs (PGTOs), into a smaller set of functions by forming fixed linear combinations is known as basis set contraction, and the resulting functions are called contracted GTOs (CGTOs). 

In a segmented contraction each primitive as a rule is only used in one contracted function. In some cases it may be necessary to duplicate one or two PGTOs in two adjacent CGTOs. The contraction coefficients can be determined by a variational optimization, for example from an atomic HF calculation. 

These calculations have been conducted on the basis of RHF optimized geometries, considering the 6-31G basis set for the n-alkane compounds (11), and the 6-31G basis set for the polyacene series (12). In both cases, the basis set contention has been checked by comparison with more thorough investigations on small compounds, such as ADC[3] calculations (11a) on n-butane based on the 6-31IG, 6-31G and 6-31G basis, or the MRSDCI ionization spectrum of ethylene as obtained by Murray and Davidson (33) using a 196-CGTO basis set. 

Table 1 Values of the energy of calculated with different CGTO s basis sets.

The field-free atom has the configuration Is the nnpertnrbed wavefnnction is described throngh a Hnzinaga s CGTOs set (the 10 CGTOs one in Ref. 37). We use... 

Five large basis sets have been employed in the present study of benzene basis set 1, which has been taken from Sadlej s tables [37], is a ( ()s6pAdl6sAp) contracted to 5s >p2dl >s2p and contains 210 CGTOs. It has been previously adopted by us in a near Hartree-Fock calculation of electric dipole polarizability of benzene molecule [38]. According to our experience, Sadlej s basis sets [37] provide accurate estimates of first-, second-, and third-order electric properties of large molecules [39]. 

Each CGTO can be considered as an approximation to a single Slater-type orbital (STO) with effective nuclear charge f (zeta). The composition of the basis set can therefore be described in terms of the number of such effective zeta values (or STOs) for each electron. A double-zeta (DZ) basis includes twice as many effective STOs per electron as a single-zeta minimal basis (MB) set, a triple-zeta (TZ) basis three times as many, and so forth. A popular choice, of so-called split-valence type, is to describe core electrons with a minimal set and valence electrons with a more flexible DZ (or higher) set. 

The keyword label of a standard Pople-style split-valence basis specifies the sp sets (groups of CGTOs of s and p symmetry) with distinct zeta values for each atomic shell, as well as the contraction length of each CGTO. The keyword contains the following syntactical components ... 

---