By J. Duchesne
The Advances in Chemical Physics sequence offers the chemical physics and actual chemistry fields with a discussion board for severe, authoritative reviews of advances in each zone of the self-discipline. jam-packed with state of the art learn said in a cohesive demeanour now not stumbled on in different places within the literature, every one quantity of the Advances in Chemical Physics sequence serves because the ideal complement to any complicated graduate type dedicated to the research of chemical physics.
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Additional resources for Advances in Chemical Physics: Structure & Properties of Biomolecules, Volume 7
IA] ELECTRONIC STRUCTURES 33 Since in this method, one works with a H c instead of a He,, the Coulomb integral, a;, and the resonance integral, piq, will be: 4= p;* = 1 J XP (1) H C(1) XP (1) W 1 ) (42) XP (1) H C(1) Xn (1) W 1 ) (43) The introduction of electron repulsion (e2/r12) gives rise to a new type of integral] the two-electron repulsion integrals : &I4 = 1 X Y ( 1 ) X A 1 ) (e2/r12)X r P ) X 8 P ) W)M e ) (44) For an asymmetric hydrocarbon with N atomic orbitals, it is necessary to calculate N*/8 integrals such as (44).
34W These failings are undoubtedly due to the neglect of interelectronic repulsion. (2) Mulliken- Wheland Method This method appears to have been introduced by Mulliken, Rieke, and Brown,82 but was developed extensively by Whelandl24 (which explains its name). This method differs from the Huckel one PT. IA] ELECTRONIC STRUCTURES 29 only in that the overlap between neighbors is not zero, but equal to a constant. 25 is adopted. l0g The values of the one-electron energies are now given by E3. = a+njy (35) where y, a new form of resonance integral, is and y = p-sa nj = mj/(l+mjS) (36) (37) We see then that once mj has been calculated by the Huckel method, a simple step gives the values of nj (37) and hence ej from (35).
A deficiency of the LCAO-MO’s is that they do not satisfy the virial theorem. Step 2. To obtain the best set of coefficients, cjr, for the expansion (26), the variational principle (Section 11) is applied, 6 < H > = 0, leading to the best energy for each molecular orbital. This leads to the system of linear homogeneous equations, c S (HT8-EST8) ‘8 = (27) where E is the eigenvalue of orbital energy associated with Y. In these equations, we have employed the following standard symbols : H,, = J x , H x , d r = a, = ’8, XrXUd“ (28) (30) The integral H,,, called the Coulomb integra1,So depends on the nuclear charge and the type of orbital.
Advances in Chemical Physics: Structure & Properties of Biomolecules, Volume 7 by J. Duchesne