$physical-constants¶
The base system for units is SI.
The following physical constants are used within the nextnano³ code.
$physical-constants required electron-charge double required ! [As] = [C] e: elementary charge electron-mass double required ! [kg] m0: electron mass planck-constant double required ! [Js] h_bar: Planck's constant speed-of-light double required ! [m/s] (exact) c: speed of light in vacuum boltzmann-constant double required ! [J/K] k_B: Boltzmann constant vacuum-permittivity double required ! [As/Vm] = [F/m] (exact) epsilon0: electric constant avogadro-number double required ! [1/mol] N_A: Avogadro number $end_physical-constants required
Example
!-----------------------------------------! $physical-constants ! electron-charge = -1.6021766208e-19 ! [C] = [As] -1.6021766208(98)e-19 electron-mass = 9.10938356e-31 ! [kg] 9.10938356(11)e-31 planck-constant = 6.626070040e-34 ! [Js] 6.626070040(81)e-34 speed-of-light = 2.99792458e+8 ! [m/s] (exact) boltzmann-constant = 1.38064852e-23 ! [J/K] 1.38064852(79)e-23 vacuum-permittivity = 8.854187817e-12 ! [As/Vm] (exact) 8.854187817...e-12 avogadro-number = 6.022140857e+23 ! [] 6.022140857(74)e+23 $end_physical-constants ! !-----------------------------------------!
These SI units were taken on 2019-05-10 from https://physics.nist.gov/cuu/Constants/index.html. The number in parentheses is the numerical value of the standard uncertainty referred to the corresponding last digits of the quoted result.
Further constants
reduced_planck_constant(Planck constant over 2 pi) is calculated internally inside the program:planck-constant/(2pi) = h/2pireduced_planck_constant = 1.054571800139113e-034 ! [Js] (calculated internally from other constants) 1.054571800(13)e-34 ! [Js] (NIST)
bohr_radiusis calculated internally inside the program:4 * pi * vacuum_permittivity * reduced_planck_constant^2 / (electron_mass * electron_charge^2) bohr_radius = 0.5291772105267628e-010 ! [m] (calculated internally from other constants) 0.52917721067(12)e-10 ! [m] (NIST)
hydrogen_ionization_energy_J(Rydberg constant times hc in[J]) is calculated internally inside the program:electron_mass * electron_charge^4 / (32 * pi^2 * reduced_planck_constant^2 * vacuum_permittivity^2) hydrogen_ionization_energy_J = 2.179872325695729e-018 ! [J] (calculated internally from other constants) 2.179872325(27)e-18 ! [J] (NIST)
hydrogen_ionization_energy_eV(Rydberg constant times hc in[eV]) is calculated internally inside the program:hydrogen_ionization_energy_J / electron-charge hydrogen_ionization_energy_eV = 13.6056930140903 ! [eV] (calculated internally from other constants) 13.605693009(84) ! [eV] (NIST) corresponds to hydrogen_ionization_energy_J
Hartree_eV(Hartree energy in[eV]) is calculated internally inside the program:2 * hydrogen_ionization_energy_eV Hartree_eV = 27.2113860281805 ! [eV] (calculated by nextnano³ from other constants) 27.21138602(17) ! [eV] (NIST)
Derived constants
[h_bar^2/(2*m0)]h2b2m_Jm2 = reduced_planck_constant^2 / (2*electron_mass) = = 6.104264214606464e-039 [J m^2] h2b2m_evAA2 = h2b2m_Jm2 / ABS(electron_charge) * (1d10)^2 = = 3.80998208022688 [eV AA^2] ! AA = Angstrom
From the Boltzmann constant \(k_{\text{B}}\), one obtains \(k_{\text{B}}T\) at room temperature in units of
[eV]:kBT = 0.02585199101... [eV] (T = 298.15 K = 25°C) kBT = 0.02569257040... [eV] (T = 300 K)
For input scaling factors, see $input-scaling-factors.
Conversion factors
µm <=> eV: h * c / e * 106 = 1.23984197
Example
1.23984 / 8.4 µm = 0.1476 eV
1.23984 / 0.1476 eV = 8.4 µm
µm <=> THz: c * 10-6 = 299.792458
Example
299.79 / 8.4 µm = 35.69 THz
299.79 / 35.69 THz = 8.4 µm
1018 cm-3 <=> M: 602.21415
Example
30.11 / 602.2 = 0.050 M
0.050 M * 602.2 = 30.11
1018 cm-3 <=> mM: 0.60221415
Example
30.11 / 0.6022 = 50 mM
50 mM * 0.6022 = 30.11