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Density Integral Transform application

Equation (41a) means that the function B( r) is equivalent to the volume integral of the density matrix y(ri, ri) under the condition of r = r - r, and Eq. (41b) means that B(r) is the autocorrelation function of the position wave function (r). The latter is an application of the Wiener-Khintchin theorem (Jennison, 1961 Bracewell, 1965 Champeney, 1973), which states that the Fourier transform of the power spectrum is equal to the autocorrelation function of a function. Equation (41c) implies not only that B(r) is simply the overlap integral of a wave function with itself separated by the distance r (Thulstrup, 1976 Weyrich et al., 1979), but also that the momentum density p(p) and the overlap integral S(r) are a pair of the Fourier transform. The one-dimensional distribution along the z axis, B(0, 0, z), for example, satisfies... [Pg.193]

W i) is an integral operator with kernel W p, p ) and V p, p ) is the Fourier-transformed external potential. Hess s code has been implemented in several program codes like TURBOMOLE or MOLCAS3. Most of the applications are carried out scalar (one-component) without spin-orbit coupling and usually the two-electron operator is chosen as the simple Coulomb operator. This scheme (extended to spin-orbit coupling it necessary) leads to very accurate molecular properties for even the heaviest elements. A large number of applications in the chemistry of heavy elements are carried out by using either the scalar relativistic pseudopotential or density functional approximations. The pseudopotentials most widely used are linear... [Pg.2484]


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See also in sourсe #XX -- [ Pg.275 , Pg.276 , Pg.290 , Pg.291 , Pg.292 , Pg.293 ]




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