Correlations Mulliken

Unified Mulliken Correlations of Donor/Acceptor Complexes... 

Fig. 2 Mulliken correlation of the ionization potentials (IP) of various enol silyl ethers with the charge-transfer transition energies (/jvct) of their EDA complexes with chloranil. Reproduced with permission from Ref. 36.

The 1>3S+ excited states of H2 have been discussed by Huestis and Goddard 71 in an important paper dealing with the general construction of excited-state wavefunctions, and the well-known Hund-Mulliken correlation diagrams. One problem with SCF... 

The energy difference AGET° between the vibronically equilibrated reactant and product states can be considered as the difference between the IP of the donor and the EA of the acceptor (in the gas phase) or between the corresponding electrochemical potentials (in solution). For a set of structurally related arene donors in the same solvent, a linear (Mulliken) correlation is usually observed experimentally between the donor strength and the CT energy (due to the relatively small changes in A), i.e. ... 

Figure 1. Mulliken correlation of the charge-transfer transition energy ( cr = hvci) with the ionization potential [IP) of ferrocene and arene donors in 6w(durene)iron(II) complexes. The straight line is arbitrarily drawn with a slope of unity [124].

Since ionization potentials of anionic donors and electron affinities of cationic acceptors are not readily available, Mulliken correlations for charge-transfer ion pairs are generally presented in a modified form using electrochemical oxidation or reduction potentials, respectively. A typical example of such a modified Mulliken plot with unit slope is shown in Figure 2 for the CT ion pairs of TpMo(CO)3 [Tp = hydrido-trM-(3,5-dimethylpyrazolyl)borate] as the donor and various pyr-idinium acceptors [127]. Similar (modified) Mulliken correlations with unit slopes have been found for numerous other ion pairs with pyridinium acceptors and Mn(CO)s [126], Co(CO)4 [118], or V(CO)e [118] as donors. It is important that the Coulombic work term (co) in Eq. 8 is explicitly included in all Mulliken evaluations of ion pairs with different structures since co reflects the electrostatic energy of the (ground-state) ion pair which strongly depends on the inter-ionic distance [125]. 

Molecular complexes of OSO4 with various substituted benzenes, naphthalenes, and anthracenes have been identified by their charge-transfer absorption, which follows the Mulliken correlation in Eq. 8 [114, 161], The arene-0s04 complexes are quite stable when kept in the dark and only very slowly form osmium(VI) cycloadducts by thermal osmylation (Eq. 30). 

Nevertheless, Murrell, Kettle, and Tedder conclude in their book on valence theory57 that there is no correlation between the electric dipole moment of a bond and the electronegativity difference. They have plotted the values of the electric dipole moments of eight bonds against the difference in the values of the Mulliken electronegativity (see Figure 1-2). (The bond moments for OH, NH, PH, NF, and PF are calculated from the... 

Table 1-1 gives the values of the Mulliken electronegativity, the results of dividing these values by 2.69, and the values from The Nature of the Chemical Bond. (The factor 2.69 is the ratio of the sum of the first-row values to the sum of the third-row values.) The second reason for the failure to obtain a correlation is neglect of some of the structural features. Let us consider the factor 2.69 now. 

A good deal of information on small radicals can be obtained from Walsh diagrams (77). These correlation diagrams allow the estimation of molecular geometry from the mere knowledge of the number of valence electrons. The procedure and arguments are similar to those presented by Mulliken (78), who discussed the shapes of ABl molecules in ground and excited states and interpreted their electronic spectra. 

Kier and Hall noticed that the quantity (S -S) jn, where n is the principal quantum number and 5 is computed with Eq. (2), correlates with the Mulliken-Jaffe electronegativities [19, 20]. This correlation suggested an application of the valence delta index to the computation of the electronic state of an atom. The index (5 -5)/n defines the Kier-Hall electronegativity KHE and it is used also to define the hydrogen E-state (HE-state) index. 

A correlation of isomer shift, electronic configuration, and calculated -electron densities for a number of ruthenium complexes in analogy to the Walker-Wertheim-Jaccarino diagram for iron compounds has been reported by Clausen et al. [ 127]. Also useful is the correlation between isomer shift and electronegativity as communicated by Clausen et al. [128] for ruthenium trihalides where the isomer shift appears to increase with increasing Mulliken electronegativity. 

The Woodward-Hoffmann rules have intellectual roots that can be traced back to Wigner-Witmer correlation rules (E. Wigner and E. E. Witmer, Z. Phys. 51 [1928], 859) and general correlation-diagram concepts (R. S. Mulliken, Rev. Mod. Phys. 4 [1932], 1) as employed, e.g., by K. F. Herzfeld, Rev. Mod. Phys. 41 (1949), 527. Alternative MO... 

F. Hund, "Zur Deutung der Molekulspektren. IV," ZP 51 (1928) 759795 R. S. Mulliken, "The Assignment of Quantum Numbers for Electrons in Molecules. II. Correlation of Molecular and Atomic Electron States," Physical Review 32 (1928) 761772 E. Hiickel, "Zur Quantentheorie der Doppelbindung,"... 

We started by generating a data base of inner-shell correlation contributions for some 130 molecules that cover the first two rows of the periodic table. In order to reduce the number of parameters in the model to be fitted, we introduced a Mulliken-type approximation for the parameters Dab (Da+Db)/2. Furthermore we did retain different parameters for single and multiple bonds, but assumed Da=b (3/2)Da=b-... 

Fig. 31 Correlation of Mulliken charge for diaryl telluride radical cations with Data from Ref. 113.

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