Scale factor specifying

The remainder of the input file gives the basis set. The line, 1 0, specifies the atom center 1 (the only atom in this case) and is terminated by 0. The next line contains a shell type, S for the Is orbital, tells the system that there is 1 primitive Gaussian, and gives the scale factor as 1.0 (unsealed). The next line gives Y = 0.282942 for the Gaussian function and a contiaction coefficient. This is the value of Y, the Gaussian exponential parameter that we found in Computer Project 6-1, Part B. [The precise value for y comes from the closed solution for this problem S/Oir (McWeeny, 1979).] There is only one function, so the contiaction coefficient is 1.0. The line of asterisks tells the system that the input is complete. 

Temp. ( K), pressure (atmospheres), and scale factor. Isotopes are specified as integers although the program will use the actual value. 

When comparing calculated results to thermodynamic quantities extrapolated to zero Kelvin, the zero point energy needs to be added to the total energy. As with the frequencies themselves, this predicted quantity is scaled to eliminate known systematic errors in frequency calculations. Accordingly, if you have not specified a scale factor via input to the Reodlsotopes option, you will need to multiply the values in the output by the appropriate scale factor (see page 64). 

When comparing energy results to experiments performed at particular temperatures, the thermal energy correction given in the output should be added to the total energy (this sum is also given in the output). In order to apply the appropriate scale factor to a thermal energy correction, you must specify a scale factoi via input to the Readlsotopes option. The quantity reported in the output cannot simply be multiplied by the scale factor itself as it is composed of several terms, only some of which should be scaled. 

Compute the isomerization energy between acetaldehyde and ethylene oxide at STP with the QCISD(T)/6-31G(d) model chemistry, and compare the performance of the various model chemistries. Use HF/6-31G(d) to compute the thermal energy corrections. Remember to specify the scaling factor via the Freq=Recxllso option. (Note that we have already optimized the stmcture of acetaldehyde.)... 

Scale factors, used with D, E, F, and G specifiers to shift the decimal... 

It is usually easiest to carry out the sequence of flow-sheet calculations in the same order as the process steps starting with the raw-material feeds and progressing stage by stage, where possible, through the process to the final product flow. The required production rate will usually be specified in terms of the product, not the raw-material feeds, so it will be necessary to select an arbitrary basis for the calculations, say 100 kmol/h of the principal raw material. The actual flows required can then be calculated by multiplying each flow by a scaling factor determined from the actual production rate required. 

We note the use of t as a scaling factor for reactor size or capacity. In Example 15-2, neither V nor qa is specified. For a given r, if either V or q0 is specified, then the other is known. If either V or q0 is changed, the other changes accordingly, for the specified t and performance (cA or /A). This applies also to a CSTR, and to either constant- or variable-density situations. The residence time t may similarly be used for constant-density, but not variable-density cases. 

The primary optimization target of CLs is the effectiveness factor of Pt utilization, Tcl- It includes a factor, that accounts for statistical limitations of catalyst utilization that arise on a hierarchy of scales, as specified in the following equafion. defermines the exchange current density ... 

To decide which of these many vectors to use, it is usual to specify the points at which the plane intersects the three axes of the material s primitive cell or the conventional cell (either may be used). The reciprocals of these intercepts are then multiplied by a scaling factor that makes each reciprocal an integer and also makes each integer as small as possible. The resulting set of numbers is called the Miller index of the surface. For the example in Fig. 4.4, the plane intersects the z axis of the conventional cell at 1 (in units of the lattice constant) and does not intersect the x and y axes at all. The reciprocals of these intercepts are(l/oo,l/oo,l/l), and thus the surface is denoted (001). No scaling is needed for this set of indices, so the surface shown in the figure is called the (001) surface. 

The thermodynamic state is therefore considered equivalent to specification of the complete set of independent intensive properties 7 1 R2, Rn. The fact that state can be specified without reference to extensive properties is a direct consequence of the macroscopic character of the thermodynamic system, for once this character is established, we can safely assume that system size does not matter except as a trivial overall scale factor. For example, it is of no thermodynamic consequence whether we choose a cup-full or a bucket-full as sample size for a thermodynamic investigation of the normal boiling-point state of water, because thermodynamic properties of the two systems are trivially related. 

This result means that a pitch-scale modification specified by a(f) can be achieved by first performing a time-scale modification whose factor is given by a(/) = dT/dt... 

The. hkl file consists of one line per reflection in FORMAT (3I4,2F8.2,I4) for h, k, 1, Fl, a (Fq), and (optionally) a batch number. This file should be terminated by a record with all items zero individual data sets within the file should not be separated from one another—the batch numbers serve to distinguish among groups of reflections for which separate scale factors are to be refined. The reflection order and the batch number order are unimportant. The. hkl file is read when the hklf instruction (which terminates the. ins file) is encountered. The HKLF instruction specifies the format of the. hkl file, and allows scale factors and a reorientation matrix to be applied. Lorentz, polarization and absorption corrections are assumed to have been applied to the data in the. hkl file. Note that there are special extensions to the. hkl format for Laue and powder data, as well as for twinned crystals that cannot be handled by a TWIN instruction alone. 

As specified in Ref. [50]. Sometimes in molecules with ionic bonding character, the aug -cc-pV(T+d)Z basis set is employed with the same scaling factor RMSD(HFREQ27) fra- that is 32.5 cm" including, and 29.9 cm excluding F2... 

A prototype filter is designed to operate at a cutoff or center frequency of 1 rad/s ( 0.159 Hz) and with a l-f2 load, and so the inductor and capacitor values for the prototype must be scaled for operation of the filter at a specified cutoff or center frequency fc and with a specified load resistance Ri. Frequency scaling produces a frequency scale factor kf, which is the ratio of the cutoff or center frequency fc to 1 rad/s... 

Interpreted in terms of the symmetrical form of the periodic table (Fig. 3), the quantum numbers that define the radial distances of r = n a specify the nodal surfaces of spherical waves that define the electronic shell structure. Knowing the number of electrons in each shell, the density at the crests of the spherical waves that represent periodic shells, i.e., at 1.5,3, etc. (a), can be calculated. This density distribution, shown in Fig. 7, decreases exponentially with Z and, like the TF central-field potential, is valid for all atoms and also requires characteristic scale factors to generate the density functions for specific atoms. The Bohr-Schrodinger... 

In modeling an undamped structure for natural frequency, we may arbitrarily fix two scale factors, since there were two dimensionally independent quantities in connection with Eq. (4.48). It will usually be convenient to use a geometrically similar model, which fixes one scale factor, and to specify identical materials, which fix the other. With these restrictions, we will have a perfect model if ... 

This returns image Y via resizing the indexed image X. scale can either be a numeric scale factor or a vector that specifies the size of the output image ([numrows numcols]). By default, imresize returns a new, optimized colormap newmap with the resized image. 

The description of competitive macrosocieties given in Sect. 6.2 is certainly a minimal one. Nevertheless the model is of considerable complexity. It contains 30 trend parameters, 15 for each society, and two time scaling factors v and , where v is absorbed in the definition (6.36) of the scaled time. The trend parameters in (6.28, 37, 39), which have to be specified for a complete model description of the interaction of the societies ifi and follows ... 

Note that for a given equation of motion, i.e., a specified form of y (t), Eq. (21) does not uniquely specify the scaling factor X(t At). It can be shown that Eq. (20) retains the original accuracy of the leap-frog algorithm if the velocity-scaling factor applied to atom i is chosen as [90]... 

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