Basis sets polarization function

One should mention however that our conclusions have been very recently questionned by Axe and Marynick (42) who carried out calculations on the reaction (3) with various basis sets ranging from split valence to double zeta quality, with and without polarization functions on C, O and H atoms. They found a marked increase in the endothermicity value on going from the unpolarized basis sets ( values ranging between 8.7 and 15.2 kcal/mol) to the polarized basis s.ets (with values between 19.5 and 25.2 kcal/mol, i.e. close to our SD-CI values). We have now carried out calculations adding to our original split valence basis set polarization functions on C, O and H. One polarized set includes the two sets of polarization functions ( = 0.920... 

CEPA is not a variational method, but the high accuracy achieved in the calculated properties suggests that the advantage of furnishing an upper bound to the energy is no so important. In contrast to PNO-CI, the approximate inclusion of unlinked clusters ensures the correct dependence with respect to the number of particles. As with any theoretical approach going beyond the Hartree-Fock level, the portion of the correlation energy accounted for depends on the size of the basis set. Polarization functions were found to be very important because they... 

Split Valence Basis Sets Polarized Basis Sets Diffuse Functions Pseudopotentials... 

A TZ basis set for hydrogen (55/35) was expanded with appropriate sets of polarization functions to balance the heavy atom basis. The polarization function exponents were (H) = 1.50, 0.375 and (H) = 1.00. 

Five different basis sets were used for the calculation at both the RHF and correlated levels, as shown in Tables 5.1 and 5.2, where the notation msins means that on each hydrogen atom m 5-type Gaussians are centered and are divided into n groups (contractions). The exponents and contraction coefficients of the first two sets were taken from the literature, and the exponents of the six 5-type Gaussians from another work.< > In the fourth basis set these functions were supplemented by two 5-type bond functions (2 ) centered in the middle between the hydrogen atoms, while in the fifth basis a set of three p-type atomic polarization functions p, Py, Pz) was used. The contraction coefficients and the exponents of the bond and polarization functions were optimized previously. 

Finally one should point out the occurrence of the basis set superposition effect (each unit cell in a quasi-ID polymer is better described because the basis functions of its neighbours also exert an effect, rather than as a single molecule). The basis set superposition causes only an error if one wants to calculate the cohesion energy of a chain or of a 2D or 3D periodic system, because then one has to calculate the energy difference of the extended system and the sum of its constituents. This basis superposition effect occurs both at the HF and at the correlation corrected (QP) level and causes that already at the MP2 level, if one uses a double basis with polarization functions, and one obtains 70-75% of the correlation energy. 

For all calculations, the choice of AO basis set must be made carefully, keeping in mind the scaling of the two-electron integral evaluation step and the scaling of the two-electron integral transfonuation step. Of course, basis fiinctions that describe the essence of the states to be studied are essential (e.g. Rydberg or anion states require diffuse functions and strained rings require polarization fiinctions). 

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... 

Basis sets can be extended indefinitely. The highest MOs in anions and weakly bound lone pairs, for instance, are very diffuse maybe more so than the most diffuse basis functions in a spht valence basis set. In this case, extra diffuse functions must be added to give a diffuse augmented basis set. An early example of such a basis set is 6-31+G [26]. Basis sets may also be split more than once and have many sets of polarization functions. 

The next step in iin proving a basis set could be to go to triple zeta, quadruple zeta, etc. Ifone goes in this direction rather than adding functions of higher angular quantum number, the basis set would not be well balanced. With a large number of s and p functions only, one finds, for example, that the equilibrium geometry of am monia actually becomes planar. The next step beyond double z.ela n sit ally in voices addin g polarization fn n ciion s, i.e.. addin g d-... 

---