Direct SCF methods

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. 

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. 

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. 

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. 

Shared-memory parallel processing was certainly more successful for QC in earlier applications and continues to play a significant role in high performance computational chemistry. A coarse-grained parallel implementation scheme for the direct SCF method by Liithi et al. allowed for a near-asymptotic speed-up involving a very low parallelization overhead without compromising the vector performance of vector-parallel architectures. 

A Coarse-Grain Parallel Implementation of the Direct SCF Method. 

R. Shepard, Theor. Chim. Acta, 84, 343 (1993). Elimination of the Diagonalization Bottleneck in Parallel Direct-SCF Methods. 

R. Ahlrichs, M. Bar, M. Haser, H. Horn, C. Koknel, Electronic structure calculations on workstation computers The program system Turbomole, Chem. Phys. Lett. 162 (1989) 165 M. Haser, R. Ahlrichs, Improvements on the direct SCF method, J. Comput. Chem. 10 (1989) 104 O. Treutler, R. Ahlrichs, J. Chem. Phys. 102 (1995) 346 R. Bauernschmitt, R. Ahlrichs, Treatment of Electronic Excitations within the Adiabatic Approximation of Time Dependent Density Functional Theory, Chem. Phys. Lett. 256 (1996) 454 S. Grimme, F. Furche, R. Ahlrichs, An improved method for density functional calculations of the frequency-dependent optical rotation, Chem. Phys. Lett. 361 (2002) 321 F. Furche,... 

The testbench in the last section was an implementation of conventional SCF the one-electron and repulsion integrals were computed once and stored for use during the iterations of the SCF procedure. It is just as easy to set up a testbench to demonstrate the other extreme the calculation of the energy integrals as they are required during the SCF iterations the so-called direct SCF method. 

The development of MOLFDIR came to an end in 2001 and some of the developers of this program joined forces with a new Scandinavian program, Dirac, that emerged in the mid 1990s [518]. Dirac contains an elegant implementation of Dirac-Hartree-Fock theory as a direct SCF method [317] in terms of quaternion algebra [318,319]. For the treatment of electron correla-... 

To avoid the use of external storage memory, Almldf developed the direct SCF method (not to be confused with the direct Cl method of Section 16.2), in which no (rs tu) integrals are stored, but each two-electron integral is recomputed each time its value is needed. The direct SCF method allows ab initio calculations of large molecules and is very widely used. 

The proper description of the electronic structure of extended systems by state-of-the-art methods remains a challenging task [1] of quantum chemistry. In the past few years the notion of large molecular systems has undergone a considerable evolution, and species, which seemed almost impossible to treat by ab initio quantum chemistry are now in the domain of routine calculations. This development is mainly due to the revolution of computer technology (vector and/or parallel supercomputers) and new computational techniques, which are better adapted to the new generation of computers, like the direct SCF method [2]. The application of advanced computational techniques made it possible to undertake such spectacular calculations like the ab initio study of the C o Buckminsterfullerene [3] or the largest system ever studied by ab initio SCF calculations, the molecule [4]. It seems that in the... 

M. Haser and R. Ahlrichs,/. Comput. Chem., 10, 104 (1989). Improvements on the Direct SCF Method. R. Ahlrichs, M. Bar, M. Haser, H. Horn, and C. Kolmel, Chem. Phys. Lett., 162, 165 (1989). Electronic Structure Calculations on Workstation Computers The Program System Turbomole. 

Large-scale SCF treatments have been made possible with the direct SCF method developed by Almlof and co-workers. This procedure is based on the evaluation of two-election integrals on die fly whenever they are needed in the construction of the Fock operator (in the matrix representation required in SCF treatments). The efficiency of direct SCF method.s results from the fact that many integrals give negligible contributions and can be safely neglected. This requires reliable estimates for the integral values, TURBOMOLE employs the mathematically best separable bounds for this purpose. ... 

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