Direct SCF

The disk space (or memory) requirement can be reduced dramatically by performing the SCF in a direct fashion. In the direct SCF method the integrals are calculated from scratch in each iteration. At first this would appear to involve a computational effort which is larger than a conventional FIF calculation by a factor close to the number of iterations. There are, however, a number of considerations which often make direct SCF methods computationally quite competitive or even advantageous. 

The above integral screening is even more advantageous if the Fock matrix is formed incrementally. Consider two sequential density and Fock matrices in the iterative procedure (eq. (3.52)). 

The change in the Fock matrix depends on the change in the density matrix. Combined 

Although direct methods for small and medium size systems require more CPU time than disk based methods, this is in many cases irrelevant. For the user the determining factor is the time from submitting the calculation to the results being available. Over the years the speed of CPUs has increased much faster than the speed of data transfer to and from disk. Many modem machines have quite slow data transfer to disk compared to CPU speed. Measured by the elapsed wall clock time, disk based HF methods are often the slowest in delivering the results, despite the fact that they require the least CPU time. 

Simply speaking, the CPU may be spending most of its time waiting for data to be transferred from disk. Direct methods, on the other hand, use the CPU with a near 100% efficiency. For machines without fast disk transfer (like workstation type machines) the crossover point for direct vs. conventional methods in terms of wall clock time may be so low that direct methods are always preferred. 

The number of two-electron integrals formally grows as the fourth power of the size of the basis set. Owing to permutation symmetry (the following integrals are identical 

In disk-based methods, only integrals larger than a certain cutoff are saved. In direct methods, it is possible to ignore additional integrals. The contribution to a Fock matrix element is a product of density matrix elements and two-electron integrals. In disk- 

ELECTRONIC STRUCTURE METHODS INDEPENDENT-PARTICLE MODELS 

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Almidf J, Faegri K and Korsell K 1982 Principles for a direct SCF approach to LCAO-MO ah initio calculations J. Comput. Chem. 3 385-99... 

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. 

By de ult, Gaussian will substitute the in-core method for direct SCF when there is enough memory because it is fester. When we ran these computations, we explicitly prevented Gaussian from using the in-core method. When you run your jobs, however, the in-core method will undoubtedly be used for some jobs, and so your values may differ. An in-core job is identified by the following line in the output Two-electron integrals will be kept in memory. 

Selufien The basic strategy behind the direct SCF method is recomputing certain intermediate quantities within the calculation—specifically the two-electron integrals—as needed, rather than storing them on disk. This has the advantage of making it possible to study systems which would require more disk space than is available on the system. 

For this computer system, the crossover point where direct SCF beats the conventional algorithm happens at around 120 basis functions ( N=7). This level may be lower for some vector processors. ... 

In the Direct SCF method, we do. not store the two-electron integrals over the basis functions, we recalculate them on demand every cycle of the HF procedure At first sight, this may seem wasteful, but Conventional methods rely on disk input/output transfer rates whilst Direct methods rely on processor power. There is obviously a balance between processor speed and disk I/O. Just for the record my calculation on aspirin (73 basis functions) took 363 s using the Direct method and 567 s using the Conventional method. 

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. 

Experience has shown that it is not necessary to update the Coulomb matrix (in the inverse operator) every SCF cycle. Therefore we have chosen to compute the internal Coulomb matrix with a direct scf fock matrix builder, thereby avoiding the use of large two electron integral files. 

Fig. 21. Theoretically calculated and experimentally determined Cls core binding energies for 50/50 alternating copolymer of ethylene and tetrafluoroethylene. Also shown are charge distributions obtained by direct SCF computation and from the experimental binding energies by inversion of the charge potential model...

Truhlar, D. G. 2000. Perspective on Principles for a direct SCF approach to LCAO-MO ab initio calculations Theor. Chem. Acc., 103, 349. 

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. 

Calculate the integrals Trs, Vrs for each nucleus, and the two-electron integrals (ru ts) etc. needed for Grs, as well as the overlap integrals Srs for the orthogonalizing matrix derived from S (see step 3). Note in the direct SCF method (Section 5.3) the two-electron integrals are calculated as needed, rather than all at once. 

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