Conversion between kcal/mol and eV

[AllanChain]

The kilocalorie per mole is a (kcal/mol) is a unit to measure an amount of energy per number of molecules, atoms, or other similar particles. (https://en.wikipedia.org/wiki/Kilocalorie_per_mole). This unit is commonly used in chemistry and biology. It will be convenient to convert it to other energy units like eV, something like http://wild.life.nctu.edu.tw/class/common/energy-unit-conv-table.html.

Currently, it is impossible to do the conversion:

>>> 1 kcal/mol -> eV
error: while type checking
  ┌─ <input:28>:1:1
  │
1 │ 1 kcal/mol -> eV
  │ ^^^^^^^^^^ -- ^^ Energy or Torque
  │ │          │
  │ │          incompatible dimensions in unit conversion
  │ ChemicalPotential or MolarEnthalpyOfVaporization
  │
  =  left hand side: Length² × Mass × Time⁻² × AmountOfSubstance⁻¹    [= ChemicalPotential, MolarEnthalpyOfVaporization]
    right hand side: Length² × Mass × Time⁻²                          [= Energy, Torque]

    Suggested fix: divide the expression on the right hand side by a `AmountOfSubstance` factor

[sharkdp]

That is possible, but you need to divide by or multiply with N_A accordingly, as the error message suggests:

>>> 1 kcal/mol/N_A -> eV

    = 0.0433641 eV    [Energy or Torque]

>>> 1 eV*N_A -> kcal/mol

    = 23.0605 kcal/mol    [ChemicalPotential or MolarEnthalpyOfVaporization]

[AllanChain]

Thanks for your reply. This makes sense logically, but it might be difficult or unintuitive for beginners. However, the issue isn’t with numbat itself; rather, it is the longstanding, inconsistent conventions people have been using.

I don't have any idea how to improve this. Maybe some casting rules? Another example would be cm^-1, which is widely used as an energy unit.

[suhr]

Electronvolts are also used for temperature in plasma physics.

[sharkdp]

I have just pushed two changes to Numbat, one bugfix and one new function quantity_cast, which would allow us to write a generic conversion function like this (in Numbat itself):

fn magic_energy<D: Dim>(q: D) -> Energy =
    if is_zero(q)
      then 0
    else if is_dimensionless(q / K)  # q is a temperature: E = k_B T
      then k_B quantity_cast(q, K)
    else if is_dimensionless(q / m)  # q is a wavelength: E = ℎ c / λ
      then ℎ c / quantity_cast(q, m)
    else if is_dimensionless(q / g)  # q is a mass: E = m c²
      then quantity_cast(q, g) * c²
    else if is_dimensionless(q / (cal/mol))  # q is energy per mole: E = q / N_A
      then quantity_cast(q, cal/mol) / N_A
    else error("magic_energy: Cannot convert quantity of unit '{unit_name(q)}' to an energy")

This could then be used like:

>>> 1e5 K -> magic_energy -> eV

    = 8.61733 eV    [Energy or Torque]

>>> 500 nm -> magic_energy -> eV

    = 2.47968 eV    [Energy or Torque]

>>> electron_mass -> magic_energy -> keV

    = 510.999 keV    [Energy or Torque]

>>> 1 kcal/mol -> magic_energy -> meV

    = 43.3641 meV    [Energy or Torque]

>>> 1 s -> magic_energy
error: runtime error
 = User error: magic_energy: Cannot convert quantity of unit 's' to an energy

We could provide similar "magic" conversion functions for other target dimensions.

[sharkdp]

Let's actually close this in favor of an older ticket #481