Much of this is simple nucleophilic addition of an amine across a carbonyl group. You expel water and generate an imine. If you use hydrazine, you make hydrazone. Nothing too fancy. The chemistry is the same whether you add one mole of the amine or two moles.  Addition of 2 moles is easier than one, for control reasons (you could generate a mixture of products when you use one mole).

Any good organic chemistry text book should be sufficient in explaining the chemistry highlighted in this work. 

What follows next after you generate the imine, is simple coordination chemistry.  The chelate effect comes into play and one generates stable metal complexes with this new ligand (derivatized curcumin). Any basic inorganic chemistry text book should explain the role of chelating ligands (monodentate vs multidentate ligands; chelate effect etc.), and how coordination complexes are generated.

I have included a few useful resources from the internet, which I hope will walk you through the basics.

(I am not too sure if this is the answer you need; pardon me, if you wanted something else / more).

http://www.organic-chemistry.org/namedreactions/knoevenagel-condensation.shtm

http://www.chemtube3d.com/hydrazone_formation.html

https://en.wikipedia.org/wiki/Acetylacetone

https://en.wikipedia.org/wiki/Metal_acetylacetonates

https://en.wikipedia.org/wiki/NacNac

http://www.chem.purdue.edu/gchelp/cchem/bis.html

Hi

Curcumin is a bright yellow chemical produced by some plants. It is the principal curcuminoid of turmeric, which is a member of the ginger family (Zingiberaceae). It is sold as an herbal supplement, added to cosmetics, used to flavor food, and as a food coloring and  as a food additive.

It was first discovered about two centuries ago when Vogel and Pelletier reported the isolation of a “yellow coloring-matter” from the rhizomes of Curcuma longa (turmeric) and named it curcumin.

Chemically, curcumin is a diarylheptanoid. Turmeric's other two curcuminoids are desmethoxycurcumin and bis-desmethoxycurcumin. Curcuminoids are natural phenols that are responsible for the yellow color of turmeric. Curcumin can exist in several tautomeric forms, including a 1,3-diketo form and two equivalent enol forms. The enol form is more energetically stable in the solid phase and in organic solvents, while in water the 1,3-diketo dominates.

Synthesis of curcumin schiff base complex Double distilled water has been used throughout the synthesis process. The synthesized pure curcumin (10

mmol) was dissolved in ethanol and stirred well at room temperature. Then aniline (10 mmol) solution was added to the prepared curcumin solution. The obtained orange coloured mixture was stirred and refluxed at 50ο C for 6 hrs in mild acidic condition. After cooling the resulting orange fine precipitate of curcuminaniline schiff base was filtered and washed well with double distilled water repeatedly to remove

any unreacted chemicals then dried in vacuum oven at 100ο C for 1 hr. The obtained orange powdered curcuminaniline was kept in a desiccator over silica gel for further analyses. The full paper of Synthesis, characterization and biological activities of

turmeric curcumin schiff base complex is found in attach.

Good luck

Thank you very much for your reply Dr.Sudarsan and Dr.El-Emary. Actually . Can you tell me the

@ M.Haneefa: your response is incomplete (and I am not a PhD as yet; just M.Sc)