Reducing computational cost

Another advantage of PB based pKa calculations is that effects of electrolytes are readily accounted for in the PB equation. The Coulombic contribution in conjunction with salt dependence to the abnormally depressed pAVs of histidine in staphylococcal nuclease has been experimentally tested [56], Recently, the methodology used in the PB calculations (Eqs. 10-11 and 10-12) has been combined with the generalized Born (GB) implicit solvent model [94] to offer pKa predictions at a reduced computational cost [52],... 

It is advantageous to use the doubling property of the autocorrelation function to reduce computational costs. 

An exact determination of the relative values of P for the BPTI and villin simulations is not possible, because some algorithmic developments reduce computational costs (particularly methods that allow one to increase the size of the time step and to efficiently treat long-range interactions), while others increase the costs (e.g., more detailed force fields and appropriate boundary conditions). But we can place reasonable bounds on the historical growth rate of P by using r=l and r=2 as lower and upper limits on the costs of calculating interatomic interactions. 

A modification of G2 by Pople and co-workers was deemed sufficiently comprehensive tliat it is known simply as G3, and its steps are also outlined in Table 7.6. G3 is more accurate titan G2, witli an error for the 148-molecule heat-of-formation test set of 0.9 kcal mol . It is also more efficient, typically being about twice as fast. A particular improvement of G3 over G2 is associated with improved basis sets for tlie third-row nontransition elements (Curtiss et al. 2001). As with G2, a number of minor to major variations of G3 have been proposed to either improve its efficiency or increase its accuracy over a smaller subset of chemical space, e.g., the G3-RAD method of Henry, Sullivan, and Radom (2003) for particular application to radical thermochemistry, the G3(MP2) model of Curtiss et al. (1999), which reduces computational cost by computing basis-set-extension corrections at the MP2 level instead of the MP4 level, and the G3B3 model of Baboul et al. (1999), which employs B3LYP structures and frequencies. 

This approximation should suffice for first, second and third order methods, however, at least four numerical solutions are required on substantially different meshes to determine the coefficients and the extrapolated value, c/>cxt. Three sets of calculations can be used to reduce computational cost by taking one of two following path... 

DFT offers partial treatment of electron correlation at drastically reduced computational cost relative to other post-HE methods. How well does DFT account for acidity DPEs computed using the popular B3LYP method are listed in Table 3.4. As with the other methods, diffuse functions are essential for reasonable estimation of DPEs using B3LYP. With a set of diffuse functions, even the smallest basis set tried (6-31q-G(d)) produced quite satisfactory results the DPEs of acetone and propene are predicted within 2.5 kcal mol of the experimental values, but that of acetic acid is off by 6.5 kcal mol". For a set of 45 acids, the average absolute error for the B3LYP/6-31-l-G(d)-predicted DPEs is... 

Computing the interatomic forces is the most time-consuming part in an MD simulation. The use of a cutoff radius is a standard trick of the trade that reduces computational cost by neglecting interactions between atoms separated by a distance larger than the specified cutoff. As described earlier, this truncation results in a discontinuity of both the potential and the force at the cutoff distance, but the drawback thus entailed can be avoided by implementation of either the shifted-force potential or a taper function. 

The advantage of the correlation function approach is that only the storage of scalar quantities, rather than wave packets, is needed. Thus, the memory requirement is significantly reduced, an issue that may become more important for large systems. The implementation with the Chebyshev propagator takes further advantage of its numerical properties discussed above. In cases where resonances are dominant, the LSFD approach can be used to further reduce computational costs. We note in passing this approach can be extended to the calculation of thermal rate constants. 

In 1989, Knowles introduced81 a modified full Cl procedure which exploits the sparsity of the Hamiltonian matrix and affords approximate full Cl results at a dramatically reduced computational cost. Employing the Davidson method108 (cf. section 3.2.1), the correction to the current Cl vector is given by... 

In model systems, the hydrophilic polymer PVP is frequently used as a stabilizing reagent for Au clusters. Here, to reduce computational costs, the PVP molecule shown in Fig. 19.5 was used as a model molecule to investigate the interactions between Au atoms and PVP. The optimized structure of Au-PVP is displayed in Fig. 19.5. The adsorption energy of this model was estimated to be 3.93 kcal/mol, and the Mulliken charge on the Au atom was —0.214. 

Choosing a more tractable energy expression, by neglecting some of its critical terms at appropriate stages of the minimization, offers another way to reduce computational cost, a strategy followed in PROMET3, where electrostatic interactions are initially left out, and in MOLPAK, which omits the attractive part of the van der Waals interactions. 

The use of methods with a reduced scaling does not necessarily lead to a reduced computational cost for systems that can be studied by the available resources. The cross-over point for when the linear scaling methods becomes competitive with traditional methods may be so high that is it of little practical use. At present, there is little... 

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