Account of microwave irradiation for accelerating organic by El Sayed H. El Ashry and Ahmed A. Kassem
By El Sayed H. El Ashry and Ahmed A. Kassem
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Additional info for Account of microwave irradiation for accelerating organic reactions
In fact, it is somehow hidden in gv. We shall now calculate gv and thus reintroduce explicitly the appropriate valence electronic kinetic energy T v into the formula describing E v. We begin with Eq. 1) and write, with Eqs. 18) in mind, the following equation: X gE ¼ gv E v þ g c Ekion (4:19) k [The RHS of Eq. 19) is, from Eqs. 18) and comparison with Eq. ] Now use Eqs. 19) and write X (3 À g)E ¼ (3 À gv )E v þ (3 À g c ) Ekion (4:20) k The (3 2 g)E term is well known [see Eq. 7)]. In the latter, ni is the occupation of the orbital is e i.
Evidently, nothing of the like applies to Evalence, but we may well inquire how things are with E v. The key is in the treatment of core – other core and core – other nucleus interactions. Simple approximations were presented in that matter to get Eq. 35). Assuming cv potential is just as though all the core electronic charge Gauss’ theorem—the Vee were lumped at the nuclear position—the same arguments are now invoked for Vkcv , approximated as follows: ð1 X Zl r(r) dr À Nkc (4:38) Vkcv ¼ Nkc R rb,k jr À Rk j l=k kl Direct calculations  made for 1s electrons confirm the validity of Eq.
2) is our starting point. Multiplication from the left by fÃi , integration from rb to 1, and summation over all occupied orbitals i leads to X ð1 X ð1 ^ fi d t ¼ ni fÃi F ni fÃi ei fi d t (3:3) i rb i rb where ni is the occupation of the normalized orbital with eigenvalue e i. Until now, no constraint has been attached to the radius rb defining the boundary surface separating the inner and outer regions. ] Now we transform Eq. 3) into something more practical. Let us begin with its right-hand side.