Computational scales

Method Variational/size extensive Computational scaling... 

We ve somewhat arbitrarily used the SVWN scale factor for SVWN5 and the B3LYP scale factor for B3PW91, since no one has computed scale fectors for those iunctionals as of this writing. 

Kofraneck and coworkers24 have used the geometries and harmonic force constants calculated for tram- and gauche-butadiene and for traws-hexatriene, using the ACPF (Average Coupled Pair Functional) method to include electron correlation, to compute scaled force fields and vibrational frequencies for trans-polyenes up to 18 carbon atoms and for the infinite chain. 

Even for vanishing cycle times, the ParTAD method introduces an additional approximation into the dynamics compared to regular TAD because the subpatch has a fixed size, concerted processes larger than this size, if they exist, will be suppressed. In exchange, the method gives a very favorable computational scaling with system size, which appears to be roughly order log(AJ) as processors are added in proportion to N [34],... 

The resulting SAPT(DFT) potential energy curves turn out to be very accurate in the wide range of intermolecular separations. For the benzene dimer225,228 the results are very close to those of the much more expensive CCSD(T) treatment. For systems of the size of the benzene dimer and for the triple-zeta quality basis sets, a SAPT(DFT) calculation actually takes less time than a conventional supermolecular DFT calculation. Due to the favorable computational scaling the SAPT(DFT) approach is applicable to much larger molecules than any method used thus far for a reliable calculation of dispersion-dominated interaction potential. 

Fig. 7.6. Numerically computed scaled critical fields (bullets) and experimental 10% threshold fields (squares) (from Moorman and Koch (1992)) as a function of scaled frequency. The full line represents critical fields computed on the basis of Chirikov s overlap criterion. (From Blumel (1994b).)...

This operation thus consists of four parts scale particle coordinates, compute scaled interparticle distances, perform minimum imaging, and unscale the interparticle distances. This procedure is performed inside the subroutine to compute the forces on each particle as described in the following code ... 

The dimension D can again be computed, this time with the exponent a = D/d. Using the values for the spectral dimension, d, obtained from the density of states, we find D for cytochrome c, myoglobin, and GFP to be 2.28 0.12, 2.20 0.10, and 2.12 0.09, respectively. Each of these values matches, within the stated errors, the values of D obtained from the computed scaling of energy diffusion. 

From the G2-computed PA(c-C4Hg) to yield 15, 190.3 kcal moP and the experimental Affl n,(c-C4H6). Computed, scaled MP2(FC)/6-311G(d,p) value. 

The MP2 method has been found to accurately describe the energetics of water clusters, providing that sufficiently flexible atomic basis sets are employed [5,11,20, 67,68]. However, whUe MP2 calculations are feasible for clusters containing up to 30 or so water molecules, the steep 0 N )) computational scaling of conventional MP2 calculations with system size precludes their use in carrying out Monte Carlo or molecular dynamics simulations of water clusters containing six or more monomers. 

The computational scaling properties of the Fourier method are a result of the scaling properties of the FFT algorithm which scales as 0(Nf, log Ng). As a result the phase space volume determines the scaling of the computational effort 0(Y log T). 

In general, the application of an operator to a state vector will scale as 0(N2g). For large grid applications, this scaling becomes prohibitively expensive, and much effort must be dedicated to reduce this computation scaling law. 

The SDEL algorithm has been efficiently parallelized using MPI libraries. In the parallelization scheme each node of a cluster of computers calculates the energy and derivatives for a particular segment of the path [60]. Inter-node communication is not heavy and the computation scales favorable with cluster size. 

Tables 12 and 13 suggest that there is good correspondence between the scaled CIS-computed excitation energies and the CASPT2 excitation energies except for the second transition in uracil and the second and third transitions in thymine. The composite nature of the 205 nm (6.05 eV) band observed in CD spectra of these molecules is also revealed in the CIS computations although the splitting is small. Furthermore, the observed CD spectra in an aqueous solution of thymidine and uridine and the aqueous absorption spectra of uracil and thymine can be easily explained in terms of the computed (scaled) transitions of hydrated uracil and thymine with an accuracy of about...

General programs for computer scaling-up of micro- or bench-scale reactor data to demonstration plant unit... 

---