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Calculating the integrals

Living calculated the integrals, we are now ready to start the SCF calculation. To formulate the Fock mahix it is necessary to have an initial guess of the density matrix, P. The simplest approach is to use the null matrix in which all elements are zero. In this initial step the Fock nulrix F is therefore equal to... [Pg.83]

Calculate the integrals H -j. H-f. and tiff that go with the integral calculated in Exercise 8-1. [Pg.259]

In HyperChem, equation (226) is used for calculating the integrated infrared band intensities for the ab initio method and equation (228) is employed for all the semi-empirical methods. All IR lines correspond to transitions from the ground vibrational state to an excited vibrational state that has one additional quantum deposited in a given vibrational mode. [Pg.338]

Selection 2 is a similar calculation using the F-Number method (Section 2.5.3.2) 3 calculates the integral over the Chi-Squared distribution. When selected i nput the upper limit of integration... [Pg.457]

In this calculation the integrals will be calculated in every iteration... [Pg.205]

We have to calculate the integral /(/c) of Eq.(2) which depends on the spherical Bessel functions and is expressed as ... [Pg.486]

It is generally accepted that the centrifugal sudden (CS) approximation is the most reliable approximate method. Its results are usually very close to those obtained by ab initio close coupling (CC) calculations. The integral and differential cross-sections of Ar inelastic scattering on nitrogen were performed for a few low-frequency rotational transitions and four different interaction potentials [205]. Much better agreement of CC with CS results was found than with IOS calculations performed in... [Pg.168]

The idea of MLMI method is to calculate the integration first on the coarse grid (//), and then to evaluate the on the fine grid h) through an interpolation. [Pg.123]

Images were acquired with 5-s exposure time after having fixed the focus. The total intensity of fluorescence was estimated by calculations the integral of the gray-level histogram. [Pg.192]

In this example we deal with gradiometer of type L, shown in Fig. 3.1 Id. Let us assume that the masses at the lever ends are elementary but the mass of the bar connecting them is negligible. Then, it is simple to calculate the integral in Equation (3.184) it is... [Pg.215]

To establish the dependence of quantities py on time it is necessary to determine the dimensionless concentrations Q,-- bonds per monomeric unit. It is sufficient for this purpose to solve Eqs. (33) and to calculate the integral (36). The element Kja of the stoichiometric matrix, according to (41), represents the fraction of all groups Aj in the initial mixture which belong to monomer Ma. [Pg.193]

In this case, to calculate the integral in Eq. (152), we have to take into account that in addition to the condition given by Eq. (151), there is also a restrictive condition for the initial eigenvalues. [Pg.165]

Some physical problems, such as those involving interaction of molecules, are usually formulated as integral equations. Monte Carlo methods are especially well-suited to their solution. This section cannot give a comprehensive treatment of such methods, but their use in calculating the value of an integral will be illustrated. Suppose we wish to calculate the integral... [Pg.54]

An advantage of this technique is that it allows for getting as many sample points as needed at each location along the interval of interest. In particular, it is possible to obtain very good statistics even in transition regions which are rarely visited otherwise. This leads in general to an efficient calculation and small statistical errors. Nevertheless, despite its many successes, this method has some difficulties. First, the system needs to be prepared such that has the desired value (at which dA/d needs to be computed) and an equilibration run needs to be performed at this value of . Second, it is not always obvious to determine how many quadrature points are needed to calculate the integral (deff j<9 ) d . [Pg.122]

For the value FA to be calculated, the integration over the whole Brillouin zone should be performed which yields, in the limiting case of =90°, the value FA -5.44/Qijp (in the framework of the isotropic approximation). [Pg.119]

The following formula is used in proofs and calculations. The integral on the left hand side of the equation is often called the second moment of 8... [Pg.113]

An alternative method of integrating the Gibbs-Duhem equation was developed by Darken and Gurry [10]. In order to calculate the integral more accurately, a new function, a, defined as... [Pg.80]

In the nonadiabatic limit, the coupling F between the two electronic states (called the diabatic states) is weak. One can use perturbation theory to calculate the integral in Eq. (17). [Pg.157]

When implementing the HFW method the extra computational cost incurred is that of evaluating and digesting the correlation integrals. The details (d) of calculating the integrals depends on the choice of G(u, v), and in this... [Pg.29]

The AP values for which the change of volume is significant are quite high, and reference pressure Py (normally / ,= ) can be ignored in the development of calculations. The integrals on pressure in equations 2.94 and 2.95 take the forms... [Pg.155]

Given the 5-matrix, one can calculate the integral cross sections for elastic and inelastic scattering as follows ... [Pg.324]

Calculation of the same contribution with the help of the Braun formula was made in [4]. In the Braun formula approach one also makes the substitution in (3.35) in the propagators of the exchange photons, factorizes external wave functions as was explained above (see Subsect. 5.1.1), subtracts the infrared divergent part of the integral corresponding to the correction of previous order in Za, and then calculates the integral. The result of this calculation [4] nicely coincides with the one in (5.5). ... [Pg.102]

In order to calculate the integral in Eq. (69), one has to determine the form of the functions Aej i2(x). Since the coordinate dependence of the electric field S (x) in the space-charge region is assumed to be known, one has actually to specify the dependence Ae1-2([Pg.321]

How much of the compound has crossed the interface at time tl To calculate the integrated mass flux we have to integrate CA = CA - CA from x = 0 to Thus from Eq. 18-20 ... [Pg.793]

Adsorbed Phase Entropy. Since Equations 7 and 8 can accurately describe the relationship between q, T, and p, we may use them to calculate the integral molar entropy of the adsorbed phase. At temperatures significantly lower than critical for the adsorbate, the entropy of the adsorbed phase is usually compared with the entropy of the liquid at same temperature in order to compare the freedom of each phase. Because our experimental domain was higher, we shall make this comparison with the gaseous phase compressed to the same density p as determined by Equation 8. [Pg.389]

As the Laplace transformed current—potential relationship is a much simpler function than its counterpart in the time domain, it has been suggested [76, 77] that it may be advantageous to analyze experimental data in the Laplace domain. In the present case, this would require some procedure to perform Laplace transformation of current datajF(0> i.e. to calculate the integral, according to eqn. (88)... [Pg.266]


See other pages where Calculating the integrals is mentioned: [Pg.449]    [Pg.338]    [Pg.139]    [Pg.221]    [Pg.77]    [Pg.78]    [Pg.461]    [Pg.89]    [Pg.123]    [Pg.28]    [Pg.441]    [Pg.208]    [Pg.166]    [Pg.12]    [Pg.72]    [Pg.367]    [Pg.375]    [Pg.219]    [Pg.152]    [Pg.225]    [Pg.581]    [Pg.153]    [Pg.28]    [Pg.355]   


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