Greenish colouration on copper/bronze coins is often a complex mixture of chemical compounds, depending on the environment which the coin has been exposed to. Typically, it's a mixture of copper hydroxide and copper carbonate; copper oxide is black rather than green. If the copper hydroxide content is too high, the verdigris becomes the more contagious "bronze disease". If salt is present (beach finds, sea salt in the air from living near the ocean, or salty soil the coin is buried in) then copper chloride is a likely component. A high-sulfur environment would generate copper sulfide and copper sulfate.
Development of green colour on copper exposed to the environment is an entirely natural process; the coin is in effect attempting to slowly revert back to the copper ore from whence it came.
Malachite, for example, is a dark green, glossy form of verdigris often seen on long-buried coins.
Verdigris on coins is not to be confused with the mediaeval paint pigment also known as "verdigris", which often turns up in dictionary definitions of that word; this was made from copper acetate derived from exposing copper plates to vinegar vapours. Unless you've been cleaning your coins in vinegar, you shouldn't find any copper acetate on them. There shouldn't be any arsenic in copper corrosion products, either, unless you've been storing your coins in arsenic trioxide for some reason.

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