By I. PRIGOGINE, STUART A. RICE
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After obtaining the eigenvalues and eigenvectors of these matrices, Cederbaum and c o - ~ o r k e r then s ~ ~ include the couplings of these eigenvectors to the simple electron removal operators, a,, and a,, by solving a second-order Dyson equation for the one-particle Green’s function. EQUATIONS OF MOTION- GREEN'S FUNCTION METHOD 47 Purvis and Ohm3* have reported calculations of the N, shake-up spectrum using the propagator approach. They diagonalize small blocks of matrix elements between different shake-up operators, to obtain spin- and space-symmetry-adapted operators.
Figure 4 displays the predicted spectrum obtained with a more extensive P-space. , the P-space used in the calculation of Fig. 3). Each peak is fitted with a Gaussian whose total area is given by the calculated cross section. The widths are adjusted arbitrarily. '6. 31*32 The calculated results agree qualitatively with experiment for both peak positions and relative intensities. However, the higher energy peaks in the spectrum appear at too high energy. 0 eV is actually made up of two peaks of nearly equal intensity.
Second quantized operators, whereas the IP- EA theory basis operators have strings of one, three, .. , creation and destruction operators. Thus if an ionization potential calculation employs an operator basis that is truncated to include only operators containing one or three second quantized operators (a common point of truncation), the operator basis is much smaller than in the excitation energy calculation (using the same set or orbitals) employing basis operators with two and four at 's and a, 's ( i can be either hole or particle here).
Advances in Chemical Physics, Vol. 48 by I. PRIGOGINE, STUART A. RICE