Question about copper(II) phthalocyanine structure

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The discussion centers on the significance of arrows and dashed lines in the structural diagram of copper(II) phthalocyanine (CuPc). The arrows are interpreted as indicating coordinate bonds, which are formed when nitrogen atoms donate electron pairs to the copper ion. Despite the charge neutrality of the involved atoms, the formation of these bonds is essential for the stability and structure of the coordination complex. The nitrogen atoms, which lose protons in the metal-free form, coordinate to the copper, leading to a stable configuration. The representation of these bonds varies across different sources, with some showing four equal bonds to the copper. The overall understanding emphasizes the role of these bonds in defining the coordination sphere of the metal within the complex.
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I am hoping someone might be able to explain the significance of the arrows in the following structural diagram of copper(II) phthalocyanine (CuPc).

http://upload.wikimedia.org/wikipedia/commons/e/ec/Copper_phthalocyanine.svg

Which I have also seen represented as dashed lines such as on http://www.chem.ox.ac.uk/course/ityeartwo/html/colgate2.htm page (near the bottom).

My background is in physics so my understanding of chemistry is very rudimentary. From what I can recall, copper(II) should take 2 electrons in order to become neutrally charged, while nitrogen should have 3 extra electrons. The two N-Cu bonds without arrows should then make everything charge neutral since these two nitrogens only bond to two carbons, leaving a spare electron on each to bond to Cu with.

What do the arrows (or dashed lines) then indicate? They appear to indicate a bond of some form, but why should copper want to bond, or the nitrogens for that matter, if they are charge neutral? My research seems to indicate that the arrow might represent a co-ordinate bond but, once again, I don't see why the nitrogens should want to give up or even share their electrons if they are already stable, nor why the copper should accept them for the same reasons.

There is either something I'm missing, or I've misunderstood the significance of the arrows. In either case, I hope someone will be able to explain their significance to me.

Thanks in advance
 
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It is commonly described as a coordination complex in the literature, and if you look it up at Sigma-Aldrich they draw it with four equal bonds:

http://www.sigmaaldrich.com/large/structureimages/19/mfcd00010719.png

Once the metal-free phthalocyanine complexes a metal such as copper, all four of the inner nitrogen atoms are included in the coordination sphere. Formally speaking, one convention (in my experience) is to draw the bonds from the nitrogen atoms which lose the protons in the metal-free form and indicate that the other two nitrogen coordinate to the metal either through arrows or a dashed-line.

One of my favorite websites ChemSpider actually has an ionic form of this compound (a +2 charge on the copper, and a -2 charge on the phthalocyanine).
 
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