The essential and sufficient condition for enantiomers to exist is the dissymmetry in the molecule.

Enantiomers are a type of stereoisomers that are non-superposable mirror images of each other. They have the same connectivity of atoms but differ in their spatial arrangement. To understand why dissymmetry is the essential and sufficient condition for enantiomers to exist, let's explore the other options mentioned in the question.

a) The presence of double bond in the molecule:
The presence of a double bond does not guarantee the existence of enantiomers. Double bonds can lead to the formation of geometric isomers, where the double bond restricts rotation around the bond axis. Geometric isomers have different spatial arrangements but are not mirror images of each other. Therefore, the presence of a double bond is not sufficient for enantiomers to exist.

c) The presence of asymmetric carbon atom:
An asymmetric carbon atom, also known as a chiral carbon, is a carbon atom that is bonded to four different groups. The presence of an asymmetric carbon atom is indeed a necessary condition for a molecule to have enantiomers. However, it is not a sufficient condition. Molecules with an asymmetric carbon atom can have enantiomers if they also possess dissymmetry.

d) The tendency to form mirror image:
While enantiomers do form mirror images of each other, the tendency to form a mirror image is not the essential and sufficient condition for enantiomers to exist. Molecules can have mirror images without being enantiomers. For example, meso compounds have internal symmetry and possess a plane of symmetry, resulting in mirror images that are superposable.

The essential and sufficient condition for enantiomers to exist is dissymmetry in the molecule.

Dissymmetry refers to the absence of any internal symmetry or plane of symmetry in a molecule. Enantiomers must have a chiral center, such as an asymmetric carbon atom, but they must also lack any internal symmetry. This means that there should not be any plane, axis, or center of symmetry in the molecule that allows for superposition of the mirror images.

In the absence of dissymmetry, the molecule and its mirror image would be superposable, making them identical rather than enantiomers. Dissymmetry ensures that the mirror images cannot be superimposed, resulting in enantiomers.

To determine if a molecule possesses dissymmetry, one can look for the presence of symmetry elements like planes, centers, and axes of symmetry. If any of these symmetry elements are present, the molecule does not possess dissymmetry and cannot have enantiomers.

In conclusion, dissymmetry is the essential and sufficient condition for enantiomers to exist. While the presence of an asymmetric carbon atom is necessary, it is not sufficient without dissymmetry. Other factors like the presence of a double bond or the tendency to form a mirror image are not the essential conditions for enantiomers.