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Apr 15, 20242 min read

材料系の計算機シミュレーションではそれに適したユニットを用いると10の30乗とかがなくてデータの可視性が少し高まる．電子を基準にするような第一原理計算系では，m_e (mass of an electron) = e (electron charge) = hbar (Planck’s constant/2pi) = 1 のような定義を用いる事が多い．

Mole

  • 1 mol = (number of pure C^{12} atoms of exactly 12 g) = 6.022 141e+23

Energy

  • 1 a.u. (Hartree) = 27.2116 eV = 4.359e-18 J (or N*m)
  • 1 eV = 2.6749e-2 Hartree = 1.602e-19 J =~ 11592 K
  • 1 cal = 4.1868 J
  • 1 kcal/mol = 4.1868 kJ/mol = 2.613e+22 eV/mol = 0.0434 eV =~ 503.1 K
  • 1 K = 8.627e-5 eV = 1.988e-3 kcal/mol
  • 1 dyn*cm = 1e-7 J

Length

  • 1 a.u. (Bohr radius) = 0.5291772 Angstrom = 0.5291772e-10 m
  • 1 Angstrom = 1.88972616 Bohr radius
  • 1 ft = 12 inches = 1/3 yd = 0.304 8 m

Mass/Weight

  • 1 lb (pound) = 12 oz. (ounce) = 0.453 592 37 kg

Time

  • 1 a.u. = 2.41889e-17 sec = 2.41889e-2 fs
  • 1 hour = 3,600 sec
  • 1 day = 86,400 sec
  • 1 week = 604,800 sec

Force

  • 1 a.u. = 1 Hartree/Bohr = 51.4225 eV/Angstrom = 4.359744e-18 J / 0.5291772e-10 m = 82.387 nN
  • 1 eV/Angstrom = 1.99467e-2 Hartree/Bohr

Stress

  • 1 a.u. = 1 Hartree/Bohr^3 = (4.359e-18 J)/(0.5291772e-10 m)^3 = 2.94e+13 Pa = 294 Mbar
  • 1 Mbar = 100 GPa, (1 kBar = 0.1 GPa)
  • 1 eV/Å^3 = 1.602e-19 J / 1e-30 m^3 = 1.602e+11 Pa = 1.602e+2 GPa
  • 1 dyn/cm^2 = 1e-1 J / m^3 = 1e-1 Pa = 1e-10 GPa
  • 1 atm (気圧) = 101325 Pa = 760 Torr

Ion conductivity

  • S = (1/Ohm) = kg^{-1} .m^{-2} .s^3 .A^2 = A/V = C/(s.V)
  • S/cm = C/(s.V.cm) = 1/(1.602e+4) (e/(fs.V.Å))
    • 逆：e/(fs.V.Å) = (1.602e-19 C)/(10^{-15} s . V . 10^{-8} cm) = 1.602e+4 C/(s.V.cm)

Beer

  • 1 pint = 473.176473 ml

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