The boltzmann distribution is central to (physical) chemistry. it describes the distribution of energy (states = electronic, vibrational, rotational, conformers, etc). the ratio of populations of various states (energies, conformations) of a molecular system is described by the boltzmann distribution. for example, to describe populated vibrational and rotational energy levels in a molecule. one form of the boltzmann distribution is n2 n1 = e−(e2−e1 )/kt where t is the temperature, and n1 and n2 refers to the ratio of populations in states with energies e1 and e2. here k is the boltzmann constant k = 1.381 x 10-23 j k-1 . if we use molar values for energies (ie j/mol or kj/mol) that must be taken into account. note that na x k = r, the gas constant (8.314 j k-1 mol-1 ). it is clear that the greater the energy difference, the smaller the ratio of populations. it is also clear that the greater the temperature, the greater the proportion of molecules in the higher energy states. if we have a number of energy states, such as conformations of a flexible molecule, then we can use the boltzmann distribution to determine the population of each state. %pop(ni) = e−δei /kt e−δei /kt i ∑ ×100% the energy can be any form of chosen energy, including electronic energy (ee), zpe corrected energy (e0), enthalpy (h) or gibb’s free energy (g). the amino acid alanine is conformationally flexible, and in the gas phase is predicted to have 15 different conformations. note that in the gas phase, amino acids are not chargeseparated zwitterions but standard neutral, covalent compounds. in this exercise, you are going to generate a spreadsheet with appropriate formulas to calculate the percentage population of each conformation as a function of temperature.