The Calvin cycle, also known as the Calvin-Benson-Bassham cycle, is the set of chemical reactions that take place in chloroplasts during photosynthesis. The cycle is light-independent because it takes place after the energy has been captured from sunlight. The Calvin cycle uses ATP and NADPH as energy sources, and incorporates $\mathrm{CO}_2$ into organic molecules, eventually producing glucose.

The cycle consists of three main stages:

• Carbon fixation
• Reduction phase
• Regeneration of the ribulose-1,5-bisphosphate (RuBP)

In the Calvin cycle:

1. Carbon Fixation: Each $\mathrm{CO}_2$ molecule is attached to a five-carbon sugar named ribulose-1,5-bisphosphate (RuBP). This reaction is catalyzed by the enzyme ribulose-1,5-bisphosphate carboxylase/oxygenase (RuBisCO). The product of this reaction is a six-carbon intermediate that immediately splits into two molecules of 3-phosphoglycerate (3-PGA).
2. Reduction Phase: Each 3-PGA is phosphorylated by ATP (consuming 2 ATP molecules total for two 3-PGA molecules) to form 1,3-bisphosphoglycerate. This molecule is then reduced by NADPH (using 2 NADPH molecules in total) to form glyceraldehyde-3-phosphate (G3P). Out of every six G3P formed, one exits the cycle to contribute towards forming glucose, while the rest are recycled to regenerate RuBP.
3. Regeneration of RuBP: For every three CO₂ molecules fixed, five molecules of G3P are used to regenerate three molecules of RuBP, requiring further ATP input (3 more ATP molecules).

Thus, for each incorporated $\mathrm{CO}_2$ molecule, 3 ATP molecules and 2 NADPH molecules are required:

• 3 ATP molecules (2 for the reduction of two molecules of 3-PGA into 1,3-bisphosphoglycerate and then one for the regeneration phase of RuBP).
• 2 NADPH molecules are used to reduce two molecules of 1,3-bisphosphoglycerate to G3P.

Therefore, the correct answer to the question is Option D: 3 molecules of ATP and 2 molecules of NADPH are required for every molecule of $\mathrm{CO}_2$ fixed in the Calvin cycle.