Multicenter indices

An interesting comparison between several aromaticity indices (harmonic oscillator model, nucleus-independent chemical shift, para-delocalization index, aromatic fluctuation index, multicenter indices, atoms-in-molecules theoretical indices and graph-theoretical indices) concluded that the most reliable ones are based on electron delocalization (08JCC1543). 

To define Kab and more general multicenter indices at a post Hartree-Fock level, one must invoke more sophisticated techniques [64-67]. We follow our work [36] in which the full Cl and some approximated models were considered in detail. The conventional definition of the generalized bond index is based on identification of Kab with a charge density fluctuation measured via the second-order joint statistical moment [64] (generally, the joint cumulant) ... 

The amount of electron delocalization has been considered to be a measure of aromaticity. There exist several related aromaticity indices. Giambiagj and coworkers have shown a connection between aromaticity and a multicentre bond index. Bultinck et al7 have used the following multicenter index (MCI) for this purpose,... 

The factor 3 comes from the fact that one should consider also the three possibilities for the first index (here A). Furthermore, one must consider a and P molecular orbitals separately (i,j,k denote molecular orbitals where all are either a molecular orbitals or p). For restricted closed shell molecules, both terms in square brackets are obviously the same. More in general for k centers, the multicenter index is given as ... 

Here /, j,. .. again denote occupied molecular orbitals and A, 5,. .., Z the atoms over which to compute the multicenter index. Ft is a permutation operator that generates all permutations over the atoms. The MCI can be resolved in orbital contributions... 

Structures Located for the Different Compounds with Symmetry, Number of Negative Hessian Eigenvalues ( Neg. EV), Relative Energy (RE, in kj/mol) where Relevant, a Qualitative Structural Representation of the Compound and the Multicenter Index (MCI) Over the 4 Al Atoms... 

Patients taking olanzapine (mean dose 12.6 mg/day n = 71) had significantly more weight gain than those taking ziprasidone (mean dose 135.2 mg/day n = 55) in a 6-month, randomized, double-blind, multicenter study of 126 patients (63c). The mean changes in body weight and body mass index were 5.0 kg and 1.3 kg/m2 respectively with olanzapine and -0.8 kg and -0.6 kg/m2 with ziprasidone. 

An MO multicenter bond index involving the cr + 7t electron population is proposed as a measure of aromaticity. It is related both to the energetic and to the magnetic criteria <2000PGP3381>. 

This index, an invariant in the tensor sense <1984ZNA1259>, gives the electronic population along the AB bond and gives values agreeing with chemical expectation. The multicenter bond index <1990STG423>, an extension of /ab to multicenter bonds, involves the total electron population (despite admitting ct-rt-separation). 

MO multicenter bond index (/ring) involving the a+n electron population (this index is related both to energetic and magnetic criteria) <2000PCP3381> ... 

In a randomized, multicenter study in 94 patients, mesalazine 4 g/day for 12 weeks in a microgranular formulation was as effective as a standard dose of a glucocorticoid (6-methylpredisolone 40 mg/day) in mild to moderate Crohn s ileitis (Crohn s Disease Activity Index 180-350) (9). The group treated with methylpredisolone had a higher number of adverse events than those given mesalazine. The only adverse effect related to mesalazine was acute pancreatitis, which resolved on withdrawal. 

Currently, neither defined performance criteria nor external proficiency testing is available for 2-D laboratories. The absence of such criteria results in an overall lack of standardization that adversely affects Interlaboratory data comparison, which is essential to conduct a large multicenter project such as the Human Protein Index."... 

An MO multicenter bond index involving a- and 7t-electron population is related to both energetic and magnetic criteria. Since aromaticity is certainly related to the mutual simultaneous interaction of all bonds of an aromatic ring, 7,ing is defined as a measure of aromaticity <2000PCP3381>. 7, ng values for 1, 1,2,4- and 1,3,5-triazine are 0.087 5,... 

Bultinck, P Rafat, M Ponec, R., van Gheluwe, B Carbo-Dorca, R and Popelier, P. (2006) Electron delocalization and aromaticity in linear polyacenes atoms in molecules multicenter delocalization index. The Journal of Physical Chemistry A, 110, 7642—7648. 

This index is not, however, very convenient for the direct calculation of similarity index. This is due to the fact that the values of calculated using eq. (138) are not invariant with respect to the distance and the mutual position of the corresponding molecules. The origin of this noninvariance arises from the presence of generally multicenter integrals (139) in which the integration is performed over the orbitals centered on the molecules A and B... 

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