Ab Initio Design Of Chelating Ligands Relevant To Alzheimer'S Disease: Influence Of Metalloaromaticity

The Journal of Physical Chemistry A

ARTICLE

Information. Geometry optimizations, frequency calculations, and

single-point energy CPCM calculations were performed using

the Gaussian 03 set of programs.

As a structure-based measure of metalloaromaticity, we have

calculated the harmonic oscillator model of aromaticity (HOMA)

55,56

index, deﬁned by Kruszewski and Krygowski as

∑

HOMA ¼ 1 À

ðR

À R

ð1Þ

opt

i ¼ 1

where n is the number of bonds considered and R is an empirical

constant (for CÀC, CÀN, and CÀO bonds R = 257.7, 93.5 and

157.4, respectively) ﬁxed to give HOMA = 0 for a model

nonaromatic system, and HOMA = 1 for a system with all bonds

equal to an optimal value R

(1.388, 1.334, and 1.265 Å for

opt

CÀC, CÀN, and CÀO bonds, respectively), assumed to be

achieved for fully aromatic systems. R

stands for a running bond

length. The calculated HOMA values correspond to the

OCCCN group of atoms of the metallacycle, that is, all pairs of

atoms present in the metalated ring except NÀCu and OÀCu

and R values for these bonds are not available. In

because R

opt

addition, the electronic-based I

index (which estimates the

cyclic overlap of molecular orbitals in a given ring) has also been

calculated for some of the compounds by obtaining the corre-

sponding wave functions of the compounds under analysis. If we

consider a ring structure of N atoms represented by the following

string A = {A

}, for a closed-shell monodeterminantal

, A

, ..., A

wave function, then the multicenter I

index, a normalized

57,58

version of Giambiagi’s

, reads

ring

ðA Þ

occ:MO

∑

½2

ðA

ÞS

ðA

Þ 3 3 3 S

ðA

ÞŠ

1=N

3 3 3 n

4NN

, i

, 3 3 3 , i

ð2Þ

ÀOHn and

Figure 1. Optimized structures of the chelating ligands (N

is the number of π-electrons, S

where N

(A) is the overlap

NÀOH4) and of the Cu(II) complexes ([Cu(N

-On)

] and

between natural orbitals i and j in the atom A, and n

are their

[Cu(NÀO4)

]). X = NH, O, and S; n = 1À3.

value is ∼0.04.

occupancies. For benzene, the I

Although

several atomic partitions may be used for the calculations of the

used.

The total complexation energy (ΔE) corresponds to the

overlap between molecular orbitals i and j within the molecular

reaction of Cu

+ 2 L

f [Cu(L

)] (L being the chelating

61,62

space assigned to atom A,

we have chosen in the present work

ligands), and through EDA it is decomposed into two terms, the

preparation and the interaction energies: ΔE = ΔE

+ ΔE

the partition carried out in the framework of the quantum theory of

prep

int

63,64

atoms-in-molecules (QTAIM) of Bader,

by which atoms are

The preparation energy (ΔE

) is the amount of energy

prep

deﬁned from the condition of zero-ﬂux gradient in the one-electron

required to deform the ligands from their equilibrium structure

density, F(r). Calculation of atomic overlap matrices (AOMs) and

to the geometry that they acquire in the metal complex, whereas

computation of I

have been performed with the AIMPAC

and

the interaction energy (ΔE

) corresponds to the actual energy

int

ESI-3D

collection of programs. For the I

calculations, all atoms

change when these geometrically deformed ligands are combined

with Cu to form the metal complexes. ΔE

present in the metal ring including the Cu atom have been

is analyzed in the

int

considered. For the indices used, it is established that the higher

framework of the KohnÀSham molecular orbital model using a

the HOMA and the I

values the more aromatic the rings.

quantitative decomposition of the bond into electrostatic interaction,

Moreover, to get a better understanding of the bonding

Pauli repulsion, and orbital interactions terms represented as

ΔE

= ΔV

+ ΔE

. ΔE

between Cu(II) and the chelating ligands, an energy decomposition

can be decomposed

int

elstat

Pauli

67À73

70,71

analysis (EDA) has also been carried out.

The Amsterdam

according to the extended transition-state method (ETS)

into the contributions from each irreducible representation Γ of

density functional (ADF)

software has been used for such

purpose, and the EDA analysis has been calculated onto the

the interacting system. In the planar systems, we have performed

the σ/π separation because this symmetry partitioning has been

B3LYP/[10s7p4d1f]-ECP-6-31++G(d,p) ECP optimized geo-

metries by a single-point energy calculation with the B3LYP

proven to be quite informative.

39,40

functional

using the TZ2P basis set that contains an uncon-

tracted set of Slater-type orbitals (STOs) of triple-ζ (TZP)

’ RESULTS AND DISCUSSION

quality with diﬀuse functions and two sets of polarization

functions.

To reduce the computational time needed to carry

Geometries, Reaction Energies, and Stability Constants.

out the calculations, the frozen core approximation has been

As mentioned, metal-ion chelators considered in the present

12661

|J. Phys. Chem. A 2011, 115, 12659–12666

Ab Initio Design Of Chelating Ligands Relevant To Alzheimer'S Disease: Influence Of Metalloaromaticity - Physical Chemisrty Page 3

Related Articles

Related forms

Related Categories