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Introduction:
Metalloporphyrins (MPs) play an important role in biological systems where they serve as active
species with the ability to bind ligands, facilitate light-harvesting photosynthetic reactions, transfer
electrons, and catalyze enzymatic reactions.! MP oligomers such as zinc(II) complexes are especiallyversatile, as coordination of pyridine and imidazole ligands to the zinc atom facilitates the self assembly of
supramolecular structures. The meso-meso-linked porphyrin arrays have now reached a discrete 128-merwith a molecular length of approximately 108 nm.1 Although the !-electron delocalization is disrupted inmeso-meso-linked porphyrin because of the orthogonal arrangement of neighboring porphyrin units,
electronic structure of excited states exhibits remarkable features for such periodic arrays.2 As the firststep to investigate phenomena connected with elongated MP chains, the ground state properties ofperiodic MPs chains with Mg, Zn, and Ni metals are focused on in the present study.
However, even for ground state, the ab initio study applying periodic boundary conditions (PBC) israther difficult for systems with big unit cells. Nevertheless, recently developed method allows extracting
band structure of polymers from quantum-chemical calculations of arrays with limited number of units3.
In the present research Hartree-Fock (HF) electronic band structures!were built for MPs polymers with Mg,Zn, and Ni metals from GAMMESS calculations of 22 units corresponding oligomers.
Methodology:
Method of building band structure of polymers from finite cluster calculations3 is based on theprojection technique which allows assigning a value for the wave vector k to each molecular orbital (MO)of an oligomer. In this method, delocalized MOs of a chain with M repeated units, written as LCAOs areprojected on real linear combinations of model Bloch functions( ,j "q % r r
X qr * ! C jr ! sin &# + j + j" ,' M ) 1$jj"! ! ! q * 1,2,...M . ! !
!
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(1)( ,j "q % r rr
Yq * ! C jr ! cos &# + j + j"' M ) 1$jj"
Here Cjr are MO's expansion coefficients over a set of atomic orbitals (AO)+ rj where r is the AO in thejth unit. Then, maximum of the value Rq

Rq * !

( X qr ) 2 ) (Yqr ) 2 ! !

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,q ,, q * 1,2,...M , 0 - k - ! !
M )1 aa!

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rdefines integer number q which refers to the wave vector kk*The proposed methodology also involves the systematic elimination of strongly localized states fromwave-vector assignment procedure, which is done by calculating the charge distribution over the chain andtreatment of band crossing. After assignment states of energy bands in reciprocal space, theinterpolation/extrapolation is used to eliminate weakly localized states and continue the bands across theentire Brillouin zone (BZ). Additionally, the method is accommodated for the elongation method4 which
is developed for accurate calculations of huge molecular systems with time and memory advantages
compared to conventional calculations.
Results and discussion:
NNNNMNMNNNNMNNNn-2Figure 1 Molecular structure for MPs(M=Mg, Zn, and Ni) arrays

Energy (eV)The investigated structures are schematically illustrated
in Figure 1. Herein, the dihedral angle between adjacentporphyrin units is 90º, and the central metals are Mg, Zn,and Ni, respectively. These MP chains were elongated up to22 MPs rings that correspond to 11 translated unit cells. Inour HF calculations, 6-31G basis set is used to describe theC, N, and H atoms. To take into account the relativistic
effect, the effective core potential (ECP) withcorresponding valence double zeta (VDZ) basis set isemployed for the metals.
Band structures and local density of states (LDOSs) ofthese MP polymers were calculated with our method basedon finite oligomer calculations. In Figure 2 three valence
and three conductive bands of Zn-P are presented in thefirst BZ as an example. Points refer to MOs of the MP array.
One can see the ambiguity of the k-assignment procedure(double points). The fitted lines on the diagram refer tocontinues bands. All these bands have a clear p nature andmainly formed by contributions from C and N atoms. Themetals give the significant contributions for upper
unoccupied bands. The analysis of bands nature is inagreement with the investigations of electronic structure ofmonomers and dimers.
The behaviors of Mg-P and Ni-P are very similar to thatof Zn-P. From Mg-P, Zn-P to Ni-P, the degenerate linear
valence band shifts down. The fundamental energy gaps ofMg-P, Zn-P, and Ni-P are 5.76, 5.79, and 5.81 eV,
respectively.

1 .00 .80 .60 .40 .20 .0-0 .2-5 .6-5 .8-6 .0-6 .2-6 .4
-6 .6
-6 .8
-7 .0

, * (C , N ), * (C , N ), * (C , N ), . /C 0, . /C 0, . /C , N , Z n 00 .0 0 .2 0 .4 0 .6 0 .8 1 .0
k , , /aFigure 2 Band structure of MP (Zn-P)
polymers extracted from elongation HF/6-31(ECP/DVZ for metals) calculations of 11 unitcells.

References:[1] Aratani, N.; Osuka, A.; Kim, Y. H.; Jeong, D. H.; Kim D. Angew. Chem. Int. Ed. 2000, 39, 1458.
[2] Ohta, N.; Iwaki, Y.; Ito, T.; Yamazaki, I.; Osuka, A. J. Phys. Chem. B 1999, 103, 11242.
[3] Pomogaeva, A.; M.; Kirtman, B.; Gu, F. L.; Aoki, Y. J. Chem. Phys. 2008, 128, 074109.
[4] Pomogaeva, A.; Springborg, M.; Kirtman, B.; Gu, F. L.; Aoki, Y. J. Chem. Phys. 2009, 130, 194106.