Contracted basis sets dependence

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. 

The choice of basis sets is a particularly important technical issue for this type of calculation. Specifically, the small, highly contracted basis sets such as used in Ref. [16] generally are insufficient to calculate the real parts of dielectric functions and, consequently, the energy loss functions. We started from Partridge s 16sllp set [17], contracted the seven tightest s-functions and the four tightest p-functions, removed the most diffuse s and the two most diffuse p-functions to avoid approximate linear dependencies, and added a full set of three d-functions with exponents equal to those of the... 

A test of the basis-set effects on the excitation energy and transition moments of vertically excited singlet states in pyrazine has been published [43]. Table IV shows some recent data on the basis-set dependency of the excitation energy for the lowest vertically excited singlet states of neutral butadiene and its positive and negative ions. In accord with the previous results, we conclude that basis sets of the contracted size (4s3pld/2s)... 

The discussion above applies to uncontracted basis sets. Contracted basis sets present a few further problems. To properly represent the spin-orbit splitting, the two spin-orbit components should be contracted separately. The contraction is now j -dependent, rather than f-dependent, and can only be represented directly in a 2-spinor basis. The problem is not now confined to the small component. If the large-component scalar basis set includes contractions for both spin-orbit components, the product of the contracted basis functions for each spin-orbit component with the spin functions generates a representation for both spin-orbit components. Thus there is a duplication of the basis set that is close to linearly dependent, and some kind of scheme to project out linearly dependent components, either numerically or by conversion to a 2-spinor basis, is mandatory. The same applies to the small component. For example, the contracted p sets for the large-component and d sets both span the same space, but because of the contraction the (i-generated set cannot be made a subset of the -generated set, even if a dual family basis set is used. 

The orthogonal subspace used in Table I is spanned by the large basis 0=19sl4p8d6f4g3h2i, H=9s6p4d3f2g. The number of basis functions of the large basis that are (nearly) linearly dependent on the cc-pVnZ basis is drastically increased with the cc-pVnZ basis sets. We observe that the externally contracted MP2 calculations converge faster to the MP2 limit. As expected, the energies from the externally contracted MP2 method lie between the standard... 

The greater dependence on basis-set quality of correlated calculations compared to those of the HF variety has prompted many developers of basis sets to optimize contractions via some scheme that includes evaluating results from the former. For instance, the correlation consistent prefix of the cc-pVnZ basis sets discussed in Chapter 6 highlights this feature. 

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