In-core SCF

The present work was supported by the National Science Foundation, grant CHE-8610809. We are indebted to Dr Peter Taylor for a copy of his In-core SCF code for the Cray-2. 

The SCF and CPHF equations may also be solved using integrals stored in main memory. This has the same advantages of speed and disadvantages of large memory requirements as for in-core SCF. 

Finally, MP2 can be done with all integrals in memory. A double-length integral list is required, so that twice as much memory is required as for in-core SCF. This is again very CPU-efficient but has even more stringent memory requirements than in-core SCF. 

Figure 10 compares SCF algorithms on vector and scalar machines. For long instruction word machines like the Multiflow, the direct SCF becomes faster than the conventional SCF at ca. 90 basis functions (ratio of direct / conventional less than one). For scalar workstations such as the Sun, the cross-over may be beyond 130 basis functions, depending on the speed of the I/O. For vector machines like the Stardent, direct SCF becomes more efficient for more than 70 basis functions. The third curve in Figure 10 indicates that in-core SCF calculations are always more efficient than conventional SCF. With 48 MB of memory on the Stardent, in-core SCF can be used up to ca. 80 basis functions, beyond which direct SCF is more efficient than conventional SCF. 

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. 

All calculations were performed on the Cray-2 computers at the Minnesota Supercomputer Center. In some cases the two-electron Integrals could be kept in the 256 megaword central memory of the Cray-2, and in these cases an "in-core" integral and SCF code(53) was used. The largest in-core calculations possible in... 

In the SCF complex, Cull forms the core scaffold that associates with Rod at the extreme C-terminal region [3]. At its the amino terminal region, Cull interacts... 

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. 

In the pseudopotential method, core states are omitted from explicit consideration, a plane-wave basis is used, and no shape approximations are made to the potentials. This method works well for complex solids of arbitrary structure (i.e., not necessarily close-packed) so long as an adequate division exists between localized core states and delocalized valence states and the properties to be studied do not depend upon the details of the core electron densities. For materials such as ZnO, and presumably other transition-metal oxides, the 3d orbitals are difficult to accommodate since they are neither completely localized nor delocalized. For example, Chelikowsky (1977) obtained accurate results for the O 2s and O 2p part of the ZnO band structure but treated the Zn 3d orbitals as a core, thus ignoring the Zn 3d participation at the top of the valence region found in MS-SCF-Aa cluster calculations (Tossell, 1977) and, subsequently, in energy-dependent photoemission experiments (Disziulis et al., 1988). 

TUtegrals was the only option. Modem machines often have quite significant amounts off memory, a few Gbytes is not uncommon. For small and medium sized systems it may be possible to store all the integrals in the memory instead of on disk. Such in-core methods are very efficient for performing an HF calculation. The integrals are only calculated once, and each SCF iteration is just a multiplication of the integral tensor... 

In the lowest ionized state of ethylene and acetylene, a n electron belonging to the double or triple C—C bond is removed. It is interesting to compare the calculations reported in Table 6 where all electrons were included in the SCF treatment and the results of non-empirical calculations limited to the n electron system. Approximating the interaction of the Jt electrons with the a core by a rigid GMS potential (see Sect. 5.1) and taking an effective nuclear charge equal to 3.18 for all the atomic... 

A modification of this approach, still at the semiempirical level, has been proposed by Gao et al. [29] under the appellation of generalized hybrid orbital (GHO). In this method, the hybrid orbital of atom Y, which occurs in the SLBO, is explicitly considered and is included in the SCF procedure, which involves now all the orbitals of atom X. The other hybrid orbitals of Y, which would define the bonds with the other neighbors of this atom, are considered to define a core potential of Y, which is reparameterized in the semiempirical scheme to describe the X—Y bond as correctly as possible. The parameterization of the Y atom and the X—Y bond requires the same care as above. 

A double -STO basis (8) was employed for the ns and np shells of the main group elements augmented with a single 3d STO function, except for Hydrogen where a 2p STO was used as polarization. The ns, np, nd, (n + l)s and (n + l)p shells of the transition metals were represented by a triple -STO basis (5). Electrons in shells of lower energy were considered as core and treated according to the procedure due to Baerends et al. (2). The total molecular electron density was fitted in each SCF-iteration by an auxiliary basis (9) of s, p, d, f and g STOs, centred on the different atoms, in order to represent the Coulomb and exchange potentials accurately. 

Frozen-core SCF/DZP and CI-SD/DZP calculations on H2O at its equilibrium geometry gave energies of —76.040542 and -76.243772 hartrees application of the Davidson correction brought the energy to -76.254549 hartrees. Find the coefficient of O in the normalized O-SD wave function. 

---