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  physical-constants

 

 

 
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physical constants

The base system for units is SI. (That's the standard, dear physicist.)

The following units 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]            
        kB: Boltzmann constant
 vacuum-permittivity            double   required  ! [As/Vm] = [F/m] 
(exact)  epsilon0: electric constant
 
avogadro-number                double   required  ! [1/mol]                  NA: Avogadro number
$end_physical-constants                  required  !
!--------------------------------------------------!

 

Syntax

 electron-charge              = -1.6021766208e-19    ! [As]    = [C]    ! -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] = [F/m]  ! 
(exact) 8.854187817...e-12
 avogadro-number              =  6.022140857e+23     ! [1/mol]          !  6.022140857(74)e+23

Source: https://physics.nist.gov/cuu/Constants/index.html (2019-05-09)

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 by nextnano 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 by nextnano 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 by nextnano 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 by nextnano 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 nextnano 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 kB, one obtains kBT at room temperature in units of [eV]:
    kBT = 0.02585199101... [eV] (T = 298.15 K = 25C)
    kBT = 0.02569257040... [eV]  (T = 300 K)

 

 For input scaling factors, see $input-scaling-factors.

 

Physical constants are stored in MODULE mod_physical_constants.

!*********************************************!
MODULE mod_physical_constants                 !
!*********************************************!
!---------------------------------------------! SI units
 REAL(8) :: electron_charge                   ! [C]     = [As]
 REAL(8) :: electron_mass                     ! [kg]
 REAL(8) :: planck_constant                   ! [Js]
 REAL(8) :: speed_of_light                    ! [m/s]
 REAL(8) :: boltzmann_constant                ! [J/K]
 REAL(8) :: vacuum_permittivity               ! [As/Vm] = [F/m]
 REAL(8) :: avogadro_number                   ! [-]

 REAL(8) :: reduced_planck_constant           ! [Js]      h/2pi

 REAL(8) :: bohr_radius                       ! [m]
 REAL(8) :: hydrogen_ionization_energy_J      ! [J]
 REAL(8) :: hydrogen_ionization_energy_eV     ! [eV]
 REAL(8) :: Hartree_eV                        ! [eV]

!---------------------------------------------!
!*********************************************!
END MODULE mod_physical_constants             !

!*********************************************!

 

Mathematical constants are stored in MODULE math_constants.
Here, the variable pi is defined:

REAL(8),PARAMETER :: pi = 3.1415926535897932384626433832795029d0

 

 

Conversion factors

  • m <=> eV: h * c / e * 106 = 1.23984197

    Example: 1.23984 / 8.4 m    = 0.1476 eV
          
     1.23984 / 0.1476 eV = 8.4 m
  • m <=> THz: c * 10-6  = 299.792458

    Example: 299.79 / 8.4 m    = 35.69 THz
          
     299.79 / 35.69 THz = 8.4 m
  • 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