Resonance and stability of benzene,Mechanism of electrophilic substitution reactions and Hyperconjugation,Carbocation,RNA,ATP and Mathematics Behind them.

Today i will start from the forces at molecular level and their stabilizing effect responsible for the existence of a particular compound or structure and also how resonance mathematically it is the oscillation of molecule between its all possible combination possible,at molecular level resonance is mainly found in compound having double bond.so what are the forces mainly responsible for stabilizing effects at molecular level and this altering physical property like boiling point,polarity etc.
These interaction includes
1)Covalent interaction  2) Resonance Interaction leading to dispersal of charge 3)Hyperconjugative interaction 3)ionic interaction 4)Hydrogen bond interaction 3)van der wall's Force interaction 4)London Dispersion interaction 5)Electromeric Effect +E Effect and -E effect. etc

Let's start from various domain of bio molecular Science and molecular science where they play vital role.
a)RNA (Ribo nucleic Acid) :RNA is similar to DNA, but with two major chemical differences. First, RNA molecules contain ribose sugars in which the number 2 carbon is bonded to a hydroxyl group. In DNA, this hydroxyl group is replaced by a hydrogen atom. Second, RNA molecules utilize uracil in place of thymine. Uracil has the same structure as thymine, except that one of its carbons lacks a methyl (—CH3) group. Transcribing the DNA message into a chemically different
molecule such as RNA allows the cell to tell which is the original information storage molecule and which is the transcript. DNA molecules are always double-stranded (except
for a few single-stranded DNA viruses)while the RNA molecules transcribed from DNA are typically single-stranded.  
The figure of  DNA and RNA can develop some  motivation here for their stability in terms of fundamental forces of interaction.
In DNA it is hydrogen bond as discussed in the previous article as depicted here

  Although there is no chemical reason why RNA cannot form double helices as DNA does, cells do not possess the enzymes necessary to assemble double strands of RNA, as they do for DNA. Using two different molecules, one single-stranded and the other double-stranded, separates the role of DNA in storing hereditary information from the role of RNA in using this information to specify protein structure.
But my question is which bio molecular interaction is responsible for the stability of single strand ,why doesn't it decompose down?
Let's analyses it in terms of figure 

DNA versus RNA. DNA forms a double helix, uses deoxyribose as the sugar in its sugar-phosphate backbone, and utilizes thymine among its nitrogenous bases. RNA, on the other hand, is usually single-stranded, uses ribose as the sugar in its sugar-phosphate backbone, and utilizes uracil in place of thymine.

Let's come to another instance where these molecular force will stabilize ATP molecule by storing Energy in bond.

 
ATP. Adenosine triphosphate (ATP) contains adenine, a fivecarbon sugar, and three phosphate groups. This molecule serves to transfer energy rather than store genetic information.
What molecular force is responsible for stability of ATP. In addition to serving as subunits of DNA and RNA, nucleotide bases play other critical roles in the life of a cell.
For example, adenine is a key component of the molecule adenosine triphosphate the energy currency of the cell. It also occurs in the molecules nicotinamide adenine dinucleotide (NAD+) and flavin adenine dinucleotide (FAD+), which carry electrons whose energy is used to make ATP. A nucleic acid is a long chain of five-carbon sugars with
an organic base protruding from each sugar. DNA is a
double-stranded helix that stores hereditary information as a specific sequence of nucleotide bases. RNA is a single-stranded molecule that transcribes this information to direct protein synthesis.

Benzene:A completely different phenomenon will come to define the stability of benzene and mathematically it is equivalent to oscillation ie benzene switching on and off between to energy equivalent term and hence the average energy of benzene decreases on an average ie it's bind dissociation enthalpy is in between double and single bond and bond length also between double and single bond.
and it's resonance can be shown as

its Equivalence is as following

We can say that the three pi bond is executing oscillation so the six pi electron is present everywhere the hexagonal ring.


  Its other energetically same structure is as following

The sum up of the above two resonance structure is equivalent to the following hybrid.

The electron free electron density or pi electron density is increasing above and below the hexagonal benzene where each carbon is SP2 hybridized and thus trigonal planar and the unhybrid P orbital oriented perpendicular above and below the hexagonal plane total six having six electron  in this orthogonal p orbital forming pi bond leads to electron density above and below the plane.


I will come to different interactions at molecular level which will lead to stability of molecular structure or system and try to correlate them using mathematics till then wait.

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Hyperconjugation,Resonance Structure: http://t.co/jpzq9LFzAb via @YouTube
— Abraham Malik (@brhmmlk93_malik) February 9, 2015

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