once, and accessing information from the electronic memory is fast. However,
RAM cannot yet store as many integrals as the hard drive. A (currently) respectable
memory of 4 GB can store all the integrals generated by perhaps about 2,000 basis
functions (up to about 100 million); beyond this the computer essentially grinds to a
halt. The capacity of the hard drive is typically considerably greater than that of the
RAM (say, 1,000 GB for a respectable hard drive), and storing all the two-electron
integrals on the hard drive is often a viable option, but suffers from the disadvantage
that the time taken to read data from a mechanical device into the RAM, where it
can be used by the CPU, is much greater (perhaps a millisecond compared to a
nanosecond) than the time needed to access the information were it stored in a
purely electronic device like the RAM (which is the only alternative to direct scf in,
for example, Spartan [ 37 ]). For these reasons, ab initio calculations with many basis
functions (beyond some hundreds, depending on the size of the RAM) nowadays
use direct scf, despite the need to recalculate integrals [ 38 ]. These considerations
will change with improvements in hardware, and the availability of very large
electronic memories may make storage of all the two-electron integrals in RAM the
only choice for ab initio calculations.
5.3.3 Types of Basis Sets and Their Uses..............................
We have met the STO-1G (Sections 5.2.3.6.5 and5.3.2) and STO-3G (Section 5.3.2)
basis sets. We saw that a single Gaussian gives a poor representation of a Slater
function, but that this approximation can be improved by using a linear combination
of Gaussians (Fig.5.12). In this section the basis sets commonly used in ab initio
calculations are described and their domains of utility are outlined. Note that the
STO-1G basis, although it was useful for our illustrative purposes, is not used in
research calculations (Fig.5.12shows how poorly it approximates a Slater func-
tion). We will consider the STO-3G, 3–21G, 6–31G, and 6–311G basis sets,
which, with variations obtained by adding polarization (*) and diffuse (+) func-
tions, are the most widely-used; other sets will be briefly mentioned. Information on
basis sets is summarized in Fig.5.13. Good discussions of currently popular basis
sets are given in, e.g., references [ 1 a, e, i]; the compilations by Hehre et al. [ 39 , 40 ]
are extensive and critically evaluated.
The basis sets described here in most detail are those developed by Pople^3
and coworkers [ 40 ], which are probably the most popular now, but most general-
purpose (those not used just on small molecules or on atoms) basis sets utilize some
sort of contracted Gaussian functions to simulate Slater orbitals. A brief discus-
sion of basis sets and references to many, including the widely-used Dunning
(^3) John Pople, born in Burnham-on-Sea, Somerset, England, 1925. Ph.D. (Mathematics) Cambridge,
- Professor, Carnegie-Mellon University, 1960–1986, Northwestern University (Evanston,
Illinois) 1986–present. Nobel Prize in chemistry 1998 (with Walter Kohn, Chapter 5, Section 7.1).
Died Chicago, 2004.
238 5 Ab initio Calculations