$physical-constants

The base system for units is SI.

The following physical constants are used within nextnano³.

$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/2pi

    reduced_planck_constant      =  1.054571800139113e-034   ! [Js] (calculated internally from other constants)
                                    1.054571800(13)e-34      ! [Js] (NIST)
    
  • bohr_radius is 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