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] (elementary
charge)
electron-mass
double
required ! [kg]
planck-constant
double required ! [Js]
speed-of-light
double required ! [m/s] (speed of light in vacuum)
boltzmann-constant
double required ! [J/K]
vacuum-permeability
double required ! [As/Vm]
= [F/m] (electric
constant)
avogadro-number
double required
! [1/mol]
$end_physical-constants
required !
!--------------------------------------------------!
Syntax
electron-charge
= -1.602176487d-19
! [As] = [C] ! -1.602176487(40)d-19
electron-mass
= 9.10938215d-31
! [kg] !
9.10938215(45)d-31
planck-constant
= 6.62606896d-34
! [Js] !
6.62606896(33)d-34
speed-of-light
= 2.99792458d8
! [m/s] !
(exact)
boltzmann-constant
= 1.3806504d-23 ! [J/K]
! 1.3806504(24)d-23
vacuum-permeability
= 8.854187817d-12
! [As/Vm] = [F/m] ! 8.854187817...d-12
avogadro-number
= 6.02214179d23 !
[1/mol]
! 6.02214179(30)d+23
Source:
http://physics.nist.gov/cuu
(2011-01-28)
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 =
1.0545716282518d-34 ! [Js] (calculated by nextnano³ from other constants)
1.054571628(53)d-34 ! [Js] (NIST)
bohr_radius is
calculated internally inside the program:
4 * pi * vacuum_permeability * reduced_planck_constant^2 /
(electron_mass * electron_charge^2)
bohr_radius
= 0.529177208316...d-10 ! [m] (calculated by nextnano³ from other constants)
0.52917720859(36)d-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_permeability^2)
hydrogen_ionization_energy_J = 2.179871971...d-18 !
[J] (calculated by nextnano³ from other constants)
2.17987197(11)d-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 = 13.605691935... !
[eV] (calculated by nextnano³ from other constants)
13.60569193(34) ! [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
= 27.211383869... ! [eV]
(calculated by nextnano³ from other constants)
27.21138386(68) ! [eV] (NIST)
Derived constants
[h_bar^2/(2*m0)]
h2b2m_Jm2 =
reduced_planck_constant^2 / (2*electron_mass) =
=
6.104263169559...d-39 [J m^2]h2b2m_evAA2 = h2b2m_Jm2 /
ABS(electron_charge) * (1d10)^2 =
=
3.809981746136...
[eV AA^2] ! AA = Angstrom
- From the Boltzmann constant kB, one obtains kBT at
room temperature in units of [eV]:
kBT = 0.025692607531... [eV] (T =
298.15 K = 25°C)
0.025852028372702... [eV] (T =
300 K)
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_permeability ! [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
µm <=> eV: h * c / e * 106 =
1.239841906
Example: 1.23984 / 8.4 µm
= 0.1476 eV
1.23984
/ 0.1476 eV = 8.4 µmµm <=> THz: c * 10-6 =
299.792458
Example: 299.79 /
8.4 µm
= 35.69 THz
299.79
/ 35.69 THz = 8.4 µm1018 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 | 
