DIIS method

See if the software documentation suggests any other ways to change the DIIS method. You may have to run hundreds of calculations to become experienced enough with the method to know what works when and by how much to adjust it. 

The extent to which this condition does not occur is a measure of deviance from self-consistency. The DIIS method uses a linear combination of previous Fock matrices to predict a Fock matrix that minimizes [P F]. This new Fock matrix is then used by the SCF calculation. 

The DIIS method is not without cost. A history of Fock matrices must be maintained and appropriate memory allocated. In addition, the computational cost of generating anew Fock matrix is significant. Also, in very rare cases, the solution found by this method is very different from that found in other ways. 

Hence the PC plot suggests that die region between 6 and 10 s (approximately) is one of co-elution. The reason why diis method works is that die spectrum over the chromatogram changes widi elution time. During co-elution the spectral appearance changes most, and PCA uses this information. 

In order to understand diis method further, trilinear PLS1 is performed on die first compound. The main results are given in Table 5.19 (using uncentred data). It can be seen diat three components provide an exact model of die concentration, but diere is... 

In order to make diis method quantitative mixtures of Nitroglycerin and Ethyleneglycol Dinitrate were made up from accurately weighed portions of each and studied in the same manner as were the pure compounds. The curves derived gal e the values in Table EiiS Co... 

The effective Fock matrix (20) is in our implementation [51] the quantity which is averaged in the optimization based on the direct inversion in the iterative subspace (DIIS) method [52],... 

Die very first publication on biofluid NMR spectroscopy was concerned with the detection of cancer. In it Ohsaka et al. reported that 100 MHz NMR spectra of human blood serum showed high lactate levels for patients with malignant tumours. Diis method has not been widely used due to two factors (i) lactate is not 100% NMR visible in blood serum or plasma and (ii) variability in lactate levels due to many factors other than cancer. - However, Nagasawa et al. have also reported analogous results for lactate elevation in the urine from mice with mammary tumours. 

The preparation of 2-nitro alcohols was also achieved by reaction of equimolar amounts of nitroal-kanes and aldehydes in the presence of alumina-supported potassium fluoride without solvent (equation 12). A peculiar feature of diis method were reactions performed with aromatic aldehydes, such as benz-aldehyde and furaldehyde, which allowed preparation of the corresponding 2-nitro alcohols without dehydration of these into nitroalkenes, as observed when nitroaldol reactions were performed with organic bases in homogeneous medium or with alumina alone. 

As described in the next Section, the gentamicins and 3, 4 -dideoxy-kanamycin B show molecular-ion peaks in mass spectrometry, and thus diis method is useful in determining the structures of the inactivated derivatives of these antibiotics. Hiis structure was also consistent with... 

A modification to the DIIS method consists in updating the DIIS basis at every iteration with the vector obtained by moving from the approximated minimum position (4.A.29) in the approximated gradient direction (4.A.30) ... 

Of special interest is die use of protected cyanohydrins in the formation of cartiocyclic rings. Ring ck>-siue of an acyclic intermediate to form a five-membered ring (75-85%) has been described in die synthesis of prostaglandins (equation 17). - In addition diis method is tqqilicable to the formation of cyclopropyl,cyclobutyl and cyclohexyl rings (60-70%). ... 

There are, however, practical limitations to diis method of determining Ti. First, it must be remembered diat the modulation eoil and its assoeiated parasitic capacitance behave as a resonant circuit. The frequency range over whieh the coil may be used will therefore be limited. Second, the receiver diode and the associated selective amplifier also limit the applicable frequency range. And, finally, the typical cavity quality factor of approximately 10 imposes a rather narrow bandpass to the measurement, typically 1 MHz. In practice, then, only spin-lattice re-... 

By additioo of a coordinatively saturated cluster to an unsaturated one via a bridging group (Eq. 13.19). In diis method, we rely on a bridging ligand, such as hydride, to link the coordinatively saturated species to an... 

Tables 1.6 and 1.7 show results obtained for styrene monomer determinations carried out on samples of polystyrene by the direct ultraviolet method and by the distillation modification of diis method. It is seen that the distillation method gives results that are consistently higher than those obtained by direct spectroscopy.

We next iq lied diis method to the synthesis of oligosaccharides. One of the exanqiles is shown above. The binding of Triton X-100 to the polymer-supported ammonium is somehow weaker than that of the crown ether. In... 

Having generated a sequence of optimization steps c , the Direct Inversion of the Iterative Subspace (DIIS) method (Csdszar and Pulay 1984 Hutter et al. 1994 Pulay 1980,1982) is designed to accelerate convergence by finding the best linear combination of stored c, vectors. 

A disadvantage of the DIIS method over the standard SCF method is the need to store previous AO Fock matrices and error vectors. In practice, only the matrices and vectors fiom a few iterations are stored - not only to save disk space and memory but also since the oldest matrices usually carry little information and their inclusion in the averaging may in fact degrade the performance. 

Table 10.4 Convergence of Hartree-Fock calculations on the water molecule in the cc-pVQZ basis using the standard SCF method, the DIIS method and the Newton trust-region method. For each iteration, we have listed the energy relative to the converged energy in Eh. The calculations have been carried out at the geometries Rref and 2/ tef of Section 5.3.3...

In the preceding sections, we discussed the optimization of the Hartree-Fock wave function by the iterative SCF procedure, using an approach based on the diagonalization of the Fock matrix as well as an approach based on the optimization of the AO density matrix. The SCF method, in particular when accelerated with the DIIS scheme, is simple to implement and works well in many cases, especially for closed-shell systems close to the equilibrium geometry. Nevertheless, in some cases, conveigence may be difficult to achieve even with the DIIS method. In such cases, it may be better to use one of the standard methods of numerical analysis. 

---