Direct SCF calculation

Direct SCF calculations [J. Almlof, K. Faegri Jr., and K. Korsell, J. Comp. Chem. 3, 385 (1982)] offer a solution to this problem by eliminating the storage of two-electron integrals. This can, however, only be done at the expense of having to recompute integrals for every iteration. 

With the current impressive CPU and main memory capacity of relatively inexpensive desktop PC s, non-direct SCF ab initio calculations involving 300-400 basis functions can be practical. However, to run these kinds of calculation, 20 GBytes of hard disk space might be needed. Such big disk space is unlikely to be available on desktop PCs. A direct SCF calculation can eliminate the need for large disk storage. 

As for the difference of about 0.4 kcal/mol between the old-style and new-style SCF extrapolations in Wlh and W1 theories, comparison with the W2h SCF limits clearly suggests the new-style extrapolation to be the more reliable one. (The two extrapolations yield basically the same result in W2h.) This should not be seen as an indication that the Eoo + A/L5 formula is somehow better founded theoretically, but rather as an example of why reliance on (aug-)cc-pVDZ data should be avoided if at all possible. Users who prefer the geometric extrapolation for the SCF component could consider carrying out a direct SCF calculation in the extra large (i.e. V5Z) basis set and applying the Eoo + A/BL extrapolation to the medium , large , and extra large SCF data. 

Tlie combination of these effects means that the increase in computational time of a direct SCF calculation over a disk based method is less than initially expected. For a medium size SCF calculation which requires say 20 iterations, the increase in CPU time may only be a factor of 2 or 1 Owing to the more efficient screening, however, the direct... 

The total computational effort involved in setting up the shell-pair data increases linearly with the size N of the basis. For tasks such as large Direct SCF calculations [44,45], it is entirely negligible compared with the subsequent work for less computationally demanding tasks, such as finding potential-derived atomic charges [98], it typically constitutes 10% of the job time. 

The horizontal arrows in Figures 1 and 2 correspond to contraction steps and, in typical Direct SCF calculations using PRISM, these account for a significant fraction of the total CPU time (15% in the pentacene run described in Section 4.7). In electrostatic grid calculations, the fraction is even higher. It is therefore very important that they be executed as efficiently as possible. 

Ruud et a/.164 have attempted to introduce an integral screening procedure into direct SCF calculations of the second hyperpolarizabilities of large molecules. The screening simulates the correlation effects that are implicit macroscopically in the introduction of a dielectric constant. The introduction... 

The combination of these effects means that the increase in computational time for a direct SCF calculation compared with a disk-based method is less than initially expected. For a medium-sized SCF calculation that requires say 20 iterations, the increase in CPU time may only be a factor of 2 or 3. Due to the more efficient screening, however, the direct method actually becomes more and more advantageous relative to disk-based methods as the size of the system increases. At some point, direct methods will therefore require less CPU time than a conventional method. Exactly where the cross-over point occurs depends on the way the number of basis functions is increased, the machine type and the efficiency of the integral code. Small compact basis sets in general experience the cross-over point quite early (perhaps around 100 functions) while it occurs later for large extended basis sets. Since conventional disk-based methods are limited to 200-300 basis functions, direct methods are normally the only choice for large calculations. Direct methods are essentially only limited by the available CPU time, and calculations involving up to several thousand basis functions have been reported. 

Reproduced by permission of the American Chemical Society from ACS Symposium Series, 2003, 844, 196 The 3(i-type hole states are based on a coordinate system where the z-axis is perpendicular to the ring planes and where the x-and y-axis are parallel to the diagonals of the C4 ring. The ground and low-lying excited states were obtained from separate direct SCF calculations. 

In direct SCF calculations, each two-electron integral is used a few times and then discarded. For example, in the standard SCF scheme, each integral makes a few contributions to the Fock... 

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