Electron-transfer recurrence relation

In the next step, we transfer Cartesian powers from the first to the second electrcm by the electron-transfer recurrence relation fl4,15]... 

We conclude this subsection by deriving the electron-transfer recurrence relation (9.10.27). As in the derivation of the Obara-Saika recurrence relations, we begin by setting up the translational condition on the integrals ... 

We have now succeeded in setting up a set of recurrence relations by means of which the two-electron Cartesian integrals may be obtained from the Boys function. The resulting expressions are rather complicated, however, involving as many as eight distinct contributions. Unlike the McMurchie-Davidson scheme, the Obara-Saika scheme does not treat the two electrons separately since the recurrences (9.10.24) and (9.10.25), for example, affect the indices of all four orbitals. In Section 9.10.3, we shall see how the Obara-Saika recurrences may be simplified considerably when used in conjunction with two other types of recurrence relations the electron-transfer recurrences and the horizontal recurrences. 

From our discussion of the Obara-Saika scheme three techniques emerge, differing in the use of the electron-transfer and the horizontal recurrence relations see Table 9.5. In the OS4 scheme, no use is made of the transfer and horizontal recurrences - the primitive Cartesian integrals... 

In conclusion, most of the recurrent difficulties can be identified in terms of the contexts in which concepts and procedures are used. Various conceptual difficulties are caused by the prominent impact of the physics particulate context, for instance, students conception that the current flow in the electrolyte corresponds to the transport of electrons. When students try to explain electrochemical cell phenomena, it appeared to be very difficult for them to relate a physics context (transport of particles) to a chemical context (transfer of electrons and ions). 

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