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The 2013, Nobel Prize in Chemistry has been awarded to Martin Karplus, Michael Levitt, Arieh Warshel "for the development of multiscale models for complex chemical systems". Essentially, "Chemistry is an experimental science but today theoretical chemists are providing answers to complex questions". These theorists "are working together with experimentalists to understand [the world around us]". The committee of Nobel Prize in Chemistry wrote: Eric Betzig, Stefan W. Helland William E. Moerner are awarded the Nobel Prize in Chemistry 2014 "for the development of super-resolved fluorescence microscopy". The Nobel committee declared: In what has become known as nanoscopy, scientists visualize the pathways of individual molecules inside living cells. They can see how molecules create synapses between nerve cells in the brain; they can track proteins involved in Parkinson's, Alzheimer's etc. So we believe that with two consecutive Nobel Prizes in Chemistry (theory and experiment) which are opening an investigation promise in future on the mechanism of biochemical reactions or complex chemical systems. In this overview we would like to present some recent obtained results in study and applications of quantum approximation method in chemistry of different fields as examples of this important theoretical method.