Basis sets contracted

The contracted basis set created from the procedure above is listed in Figure 28.3. Note that the contraction coefficients are not normalized. This is not usually a problem since nearly all software packages will renormalize the coefficients automatically. The atom calculation rerun with contracted orbitals is expected to run much faster and have a slightly higher energy. 

There are many different contracted basis sets available in the literature or built into programs, and the average user usually only needs to select a suitable quality basis for the calculation. Below is a short description of some basis sets which often are used in routine calculations. 

McLean and Chandler developed a similar set of contracted basis sets from Huzinaga s primitive optimized set for second row elements. A DZ type basis is derived by contracting (12s8p) —> [5s3p], and a TZ type is derived by contracting (13s9p) —> [6s4p]. The latter contraction is 6,3,1,1,1,1 for tlie s-functions and 4,2,1,1,1 for the p-functions, and is often used in connection with the Pople 6-3IG when second row elements are present. 

All of the above basis sets are of the segmented contraction type. Modem contracted basis sets aimed at producing very accurate wave functions often employ a general contraction scheme. The ANO and cc basis sets below are of die general contraction type. 

Triatomic Vibrational Eigenstates Product or Contracted Basis Sets, Lanczos or Conventional Eigensolvers What Is the Most Efficient Combination ... 

The use of Effective Core Potential operators reduces the computational problem in three ways the primitive basis set can be reduced, the contracted basis set can be reduced and the occupied orbital space can be reduced. The reduction of the occupied orbital space is almost inconsequential in molecular calculations, since it neither affects the number of integrals nor the size of the matrices which has to be diagonalized. The reduction of the primitive basis set is of course more important, but since the integral evaluation time is in general not the bottleneck in molecular calculations, this reduction is still of limited importance. There are some cases where the size of the primitive basis set indeed is important, e.g. in direct SCF procedures. The size of the contracted basis set is very important, however. The bottleneck in normal SCF or Cl calculations is the disc storage and/or the iteration time. Both the disc storage and the iteration time depend strongly on the number of contracted functions. 

For heavy atoms the ECP s quickly become essential. The basis set size at the ECP level does not change if we go to the second or third row TM, while a generally contracted basis set for a second row TM would comprise 45 basis functions. The difference increases even more drastically for the third row TM s where in addition the 4f orbital can be included in the core in the ECP case. 

Nowadays optimized GTF basis sets of various size are available for most atoms of the periodic system. Since they represent a starting point for developing contracted basis sets, they will be noted in more detail in the following section for the sake of compactness. 

In testing a particular contraction for molecular calculations, the first natural step is the atomic SCF calculation . However, it should be kept in mind that although a good contracted basis set sust of necessity yield a satisfactory atomic energy, this alone is not sufficient. The basis set must also be flexible enough to allow for the changes in the valence atomic orbitals which occur upon mole-... 

Modified Intermediate Neglect of Differential Overlap 5.4 Contracted Basis Sets 156... 

McLean and Chandler developed a similar set of contracted basis sets from used, however, the occupation number may have any value between 0 and 2. The ANO ... 

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