Overlap integrals, tables

The overlap integrals (Table 8.6) were calculated from the master formulae of Mulliken et al. (1949). 

Use the tables referred to in Problem 15.26c [or one of the other available overlap-integral tables see the reference given after (16.80)] to verify the values of the H2O overlap integrals given in Section 15.7. 

The Q s and i s are coulomb and exchange integrals defined as shown in Table 5-2. Notice that when A is infinitely separated from the B-C pair, Qg, Qc Jb, Jc are all zero, and Eq. (5-15) collapses to = Qa Ja, as it should. Similarly it gives the appropriate result for the other extreme cases. London did not derive Eq. (5-15), but it has since been derived and is known to apply only to s electrons moreover it neglects the overlap integrals. 

Formulas and Numerical Tables for Overlap Integrals R. S. Mulliken, C. A. Rieke, D. Orloff and H. Orloff The Journal of Chemical Physics 17 (1949) 1248-1267... 

Mulliken R, Rieke C, Orloff D, Orloff H (1948) Formulas and numerical tables for overlap integrals. JChemPhys 17 1248... 

Table 1. Double bond lengths X=X [A] p-p(x) overlap integrals S ionization potentials IP [eV] of the dissociation products XH2 T-bond strengths Erot [kcal mol 1] from the barrier of rotation, calculated at the CASSCF(2,2)/6-31G + ZPE (zero point energy) level of theory.

Bond strengths are essentially controlled by valence ionization potentials. In the well established extended Hiickel theory (EHT) products of atomic orbital overlap integrals and valence ionization potentials are used to construct the non-diagonal matrix elements which then appear in the energy eigenvalues. The data in Table 1 fit our second basic rule perfectly. 

Mulliken, R. S., Rieke, A., Orloff, D., and Orloff, H. (1949). Overlap integrals and chemical binding. /. Chem. Phys. 17, 510, and Formulas and numerical tables for overlap integrals, /. Chem. Phys. 17, 1248-1267. These two papers present the basis for calculating overlap integrals and show the extensive tables of calculated values. 

Table 3 Calculated overlap integrals (S) between HOMOs for the cation radical salts the PF6 and BF4 salts. (Reprinted with permission from [35]. Copyright 2008 American Chemical Society)...

Table 5.3. The NBO descriptors of binary B HA H-bonded complexes (see Fig. 5.1), showing net intermolecular charge transfer A0b a, ctah bond ionicity / ah. and PNBO overlap integrals for attractive ri j ctah ( Vncr.) and repulsive iib-ctah (5no ) interactions...

Typical lone pair ionization potential data have been presented before and AO overlap integral data in support of these ideas are given in Table 8. Ab initio results are shown in Table 9 and support the notions that the pi donating ability of heteroatoms is energy gap controlled in CH2X but matrix element controlled in CH2=CHX. 

Table 8. Two center C2pw - Xp overlap integrals (S) computed at the optimum bond distance of t H2X cations...

Table 23. Pi overlap integrals between the substituents in the three possible isomers of disubsti-tuted ethylenesa)...

Table 34 shows calculated overlap integrals for various combinations of hybridized atomic centers. In all cases, the absolute magnitude of the overlap for the anti alignment is greater. 

To a first approximation, the matrix element Hda is proportional to the overlap Sda for d-a distances of interest in DNA. Therefore, the couphng Vda, as given by Eq. 5, is approximately proportional to the overlap Sda- Troisi and Orlandi found an almost hnear relationship between the electronic couphng of nucleobases and the overlap of the pertinent donor and acceptor orbitals. At the level HF/3-21G, the matrix element Vda (in oV) can be estimated as —0.716 Sjj, where Sg is the overlap integral calculated between the HOMOs of the donor and acceptor sites. This approximation obviously can be very useful when combined with MD simulations of DNA fragments. However, two remarks are in order (i) the reference values of Vda should be generated with a more accurate method, e.g., based on Eq. 5 instead of Eq. 6 [32] and (ii) the very small basis set 3-2IG is insufficient for achieving satisfactory reference matrix elements (Table 1). 

Tables of overlap integrals (55-57) involving Slater functions are available, and most of those required in calculations on organometallic molecules may be obtained by interpolation. Details of the calculation of both individual and group overlap integrals are given in Sec. IV.

With the aid of the symmetry classification of Table IX, the interactions of the metal and arene orbitals can be split into those of the same symmetry type. To evaluate the group overlap integral between a given arene tt orbital... 

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