The work presented in this thesis has broadly established a few findings about the structure¬hyperpolarizability relation in molecular compounds: First, by measuring βHRS of an organic keto-enol tautomer, benzoylacetanilide in a binary solvent, I have shown that the first hyperpolarizability can be manipulated favourably by changing the composition of the solvent or by altering the pH of the solution. BA which exists in the pure keto form in water and as a keto-enol tautomer in ethanol, co-exists in equilibrium with the keto and enol forms at pH 11 in aqueous solution. The β value of the anion form is 709 x 10¬30 esu , whereas that of the enol is 232 x 10-30 esu and of the keto is 88 x 10-30 esu. There is an enhancement of β by ~ 8 times for the anion and ~3 times for the enol compared to the keto form. This opens up the possibility of finding large nonlinearities in organic molecules by simply ionizing it. Second, in organometallic complexes of divalent Ru, the first hyperpolarizability could be manipulated by altering the valence state of the metal center by oxidation or reduction or by introducing highly polarisable halogen atoms as substitutions in ligands attached to the metal center. The enhancement of first hyperpolarizability was observed in mononuclear [RuII(acac)2(CH3CN)2] complex by 1.7 times when the metal center was oxidized from RuII to RuIII. As it is already known that the complexes like [(acac)2Ru-bptz-Ru(acac)2] produce stable mixed valent compound, the enhancement of β by ~1.6 times is appearing because of that species only. Exploring Large Nonlinearity in Tautomers In this thesis I have taken a linear ketone for studying the effect of structure on β via the enol and anion formation mediated by solvent and pH of the medium. In the present study the proton transfer in BA took place in the ground state of the ketone and the enol or anion are produced in the ground states. The proton transfer reaction (tautomerism) can also happen in the excited state as well in some molecules where there is a substantial barrier to the proton transfer reaction in the ground state. In such systems, once the ketone is excited using ultraviolet light the barrier to proton transfer in the medium is overcome and a proton transfer in the excited state takes place and the enol is produced. Since such a system will be at higher energy, it will be interesting to do a two-laser experiment where the excited state hyperpolarizability is measured in a time resolved manner and the β value is determined in the excited state. Building Molecular Nonlinearity in Step-by-Step Electron Transfer In this thesis, I have dealt with a binuclear complex of Ru(II) which in one-step electrochemical oxidation produced a mixed valence compound which had substantially higher β value compared to the unoxidized complex. In this way it is possible to build a multicentered complex and see if sequential one-electron transfer and subsequent oxidation/reduction of the metal centers produce a mixed-valent metal compound with large molecular nonlinearity. The indication from the present study is that such a scheme should double the β value in each one-electron transfer step. Also the linker group/moiety between the successive metal centers will play an important role in dictating the efficiency of electron transfer. If the metal d-electrons in a multinuclear complex are linked through a π-conjugation, one would expect manifold enhancement of β. Such metal arrays can also be designed in 2 or 3 dimensions. The dimensionality of the multinuclear metal complexes can easily be changed by supramolecular design and synthesis strategy. Such metal networks may or may not generate large β molecules since electronic polarization in such systems may not be superimposable in a coherent fashion and may not add in a positive sense. All these remain to be tested and explored in the future.