Scale factor table

Our most recent calculations on malonaldehyde [159] gave excellent agreement with experiment without using scale factors (Table 5). The OH frequency... 

Next the scaling influences need to be identified and a combined scaling factor calculated. These scaling factors are found in Table 3-5. 

Frequencies computed with methods other than Hartree-Fock are also scaled to similarly eliminate known systematic errors in calculated frequencies. The followng table lists the recommended scale factors for frequencies and for zero-point energies and for use in computing thermal energy corrections (the latter two items are discussed later in this chapter), for several important calculation types ... 

Most of the scale factors in this table are from the recent paper of Wong. The HF/6-31G(d) and MP2(Full) scale factors are the traditional ones computed by Pople and coworkers and cited by Wong. Note that the MP2 scale factor used in this book is the one for MP2(Full) even though our jobs are run using the (defriultj frozen core approximation. Scott and Radom computed the MP2(FC) and HF/3-21G entries in the table, but this work came to our attention only just as this book was going to press. 

This part of the table lists type and coordinates for the atom in question, along with the orbital type and orbital scaling factor for each basis function on this atom. Here we have a carbon atom described by 19 basis functions. 

The carbon dioxide zero-point energies in the table are scaled, using the scaling factors listed on page 64. ... 

Most of the tests made so far have used water and Freon-12 (CC12F2), and the scaling factors implied by the various possible sets of scaling laws may be calculated from the physical properties for these two fluids. The appropriate scaling factors based on water at 1000 psia, for which pL/pv = 20.63, are listed in Table VII. As an example of how the scaling factors are calculated, the group Ahjl in Eq. (39) will have the same value for water and Freon-12 if... 

The precise method of making a test is best seen by referring to Fig. 44, which is an actual test of Set 4 of the scaling laws and is reproduced from Barnett (B5). The figure shows experimental data for water in a tube at three different mass velocities. Experiments were carried out on Freon-12 using parametric values for L, d, G, and Ah in accordance with the implied scaling factors shown in Table VII. The burn-out-flux values obtained were then... 

Solution Table 5.1 provides the scaling relationships, throughput and volume scaling factor is A = 128. 

Example 5.11 The results of Table 5.1 suggest that scaling a tubular reactor with constant heat transfer per unit volume is possible, even with the further restriction that the temperature driving force be the same in the large and small units. Find the various scaling factors for this form of scaleup for turbulent liquids and apply them to the pilot reactor in Example 5.10. 

Solution Table 5.1 gives the driving-force scaling factor as. ... 

Table XIV lists comparative SD and /values for fittings of all the sets of Table Xlll with each of the scales of Table V, the FandR values of Swain, and with the single substituent parameter treatment, po y These statistics, coupled with structural considerations, we believe support the usefulness and uniqueness of a scale of limited generality. In general, the / values of Table XIV for the Or scale are smaller than those of the other scales by factors of from 2 to 10. The root-mean-square F values for the other scales are from 2.25 (< j (BA)) to 3 to 4 (S L,, cr (yv)) times that for. Because this analysis has demonstrated that Swain s F and R are generally inferior for the discriminating data for all four types, there appears little to encourage proliferation of these parameters.

Table 8-7. Frequency scaling factors, rms deviation, proportion outside a 10 % error range and listings of problematic cases [cm-1] for several methods employing the 6-31G(d) basis set. Taken from Scott and Radom, 1996.

The performance calculations, using this scaling factor and Figure 10.45a, are set out in the table below ... 

Table 5.3 Variation of graphical scaling factor K with equivalent water pressure... 

Table 1 Scaling factors used to improve the frequency predictions of ab initio and DFT calculations...

By the use of the simplified scaling parameters, the linear scale factor can be changed as shown in Tables 4 and 5. Note that as the linear... 

Table 2. The frequencies f , phases 6 , scaling factors Xn of the effective RF fields and the amplitudes A of the excitation bands created by a Gaussian shaped PIP10 (0°, 144°, 40ps, fi(k), 125) with /i(fc) = 0.1577 exp[ — 0.002 x (k —63)2] kHz and a total phase increment 2nA/r = 2mn...

Table 5. The frequencies / , phases 6 , scaling factors Xn of the effective RF fields, and the amplitudes A of the excitation bands created by a DANTE sequence...

The scaling factors, phases, and amplitudes for n= -10,-5, 0, 5, and 10 are shown in Table 5, along with the results from the computer simulation. As expected, the scaling factors Xn are symmetric while the phases 0n are anti-symmetric. 

Table 6. The frequencies f , field strengths f , phases 9 , and scaling factors of the effective RF fields created by a PIP8(0°,144°, 50 is, 1.3214 kHz, 10) and its antisymmetrized PIP8(0°, 0°-144°-0°, 50 ps, 1.3214 kHz, 11), respectively, where and / are the same for both PIPs...

The anti-symmetrized PIP8(0°, 0°-144°-0°, 50 ps, 1.3213 kHz, 10) (Fig. 8) is taken into account first. Figure 10 shows the inversion profile of the PIP8as and Table 6 lists the scaling factors, RF field strengths, phases, and polarizations for n= — 2 to 2. For the PIP8as, the UPS= —72° for all bands is compensated and a phase inversion occurs if n is odd (Table 6), in agreement with the previous conclusions. Another phase inversion appears for X < 0 (n = — 2 and — 1) as discussed in Section 2.2. 

The scaling factors, phases, and the strengths of the effective RF fields for n = — 2 to 2 are shown in Table 8 and the BSOS for NNA1 to NNA3 is shown... 

Table 8. The frequencies, field strengths /ln, phases d , and scaling factors X of the effective RF fields created by a periodic pulse /iJsin(jr//7) Ix...

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