What subatomic particle is specifically responsible for combining the atoms together to form a new substance?

Electron 

Atoms, compounds, and molecules undergo chemical reactions to form new substances. In general, reactions proceed to produce products which are have more stability. 

These chemical reactions are possible because of the ability of substances to form chemical bonds with other substances. These formation of bonds are primarily attributed to electronic interactions (i.e. the valence or outer electrons of the atoms). of substances. 

Atoms are able to form new substances by gaining, losing, or sharing electrons with other atoms. 

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