1# The following definitions are all given in SI and are excerpted from the 

2# kim_units.cpp file created by Prof. Ellad B. Tadmor (UMinn) distributed with 

3# LAMMPS. Note that these values do not correspond to any official CODATA set 

4# already released, but rather to the values used internally by LAMMPS. 

5# 

6# Source: https://physics.nist.gov/cuu/Constants/Table/allascii.txt 

7 

8from numpy import sqrt 

9 

10# Constants 

11boltz_si = 1.38064852e-23 # [J K^-1] Boltzmann's factor (NIST value) 

12Nav = mole_si = 6.022140857e23 # [unitless] Avogadro's number 

13me_si = 9.10938356e-31 # [kg] electron rest mass 

14e_si = 1.6021766208e-19 # [C] elementary charge 

15 

16# Distance units 

17meter_si = 1.0 

18bohr_si = ( 

19 5.2917721067e-11 

20) # [m] Bohr unit (distance between nucleus and electron in H) 

21angstrom_si = 1e-10 # [m] Angstrom 

22centimeter_si = 1e-2 # [m] centimeter 

23micrometer_si = 1e-6 # [m] micrometer (micron) 

24nanometer_si = 1e-9 # [m] nanometer 

25 

26# Mass units 

27kilogram_si = 1.0 

28amu_si = gram_per_mole_si = 1e-3 / Nav # [kg] gram per mole i.e. amu 

29gram_si = 1e-3 # [kg] gram 

30picogram_si = 1e-15 # [kg] picogram 

31attogram_si = 1e-21 # [kg[ attogram 

32 

33# Time units 

34second_si = 1.0 

35atu_si = 2.418884326509e-17 # [s] atomic time unit 

36# ( = hbar/E_h where E_h is the Hartree energy) (NIST value) 

37atu_electron_si = atu_si * sqrt( 

38 amu_si / me_si 

39) # [s] atomic time unit used in electron system 

40microsecond_si = 1e-6 # [s] microsecond 

41nanosecond_si = 1e-9 # [s] nanosecond 

42picosecond_si = 1e-12 # [s] picosecond 

43femtosecond_si = 1e-15 # [s] femtosecond 

44 

45# Density units 

46gram_per_centimetercu_si = ( 

47 gram_si / centimeter_si ** 3 

48) # [kg/m^3] gram/centimeter^3 

49amu_per_bohrcu_si = amu_si / bohr_si ** 3 # [kg/m^3] amu/bohr^3 

50picogram_per_micrometercu_si = ( 

51 picogram_si / micrometer_si ** 3 

52) # [kg/m^3] picogram/micrometer^3 

53attogram_per_nanometercu_si = ( 

54 attogram_si / nanometer_si ** 3 

55) # [kg/m^3] attogram/nanometer^3 

56 

57# Energy/torque units 

58joule_si = 1.0 

59kcal_si = ( 

60 4184.0 

61) # [J] kilocalorie (heat energy involved in warming up one kilogram of 

62# water by one degree Kelvin) 

63ev_si = ( 

64 1.6021766208e-19 

65) # [J] electron volt (amount of energy gained or lost by the 

66# charge of a single electron moving across an electric 

67# potential difference of one volt.) (NIST value) 

68hartree_si = ( 

69 4.359744650e-18 

70) # [J] Hartree (approximately the electric potential energy 

71# of the hydrogen atom in its ground state) (NIST value) 

72kcal_per_mole_si = kcal_si / Nav # [J] kcal/mole 

73erg_si = 1e-7 # [J] erg 

74dyne_centimeter_si = 1e-7 # [J[ dyne*centimeter 

75picogram_micrometersq_per_microsecondsq_si = ( 

76 picogram_si * micrometer_si ** 2 / microsecond_si ** 2 

77) # [J] picogram*micrometer^2/microsecond^2 

78attogram_nanometersq_per_nanosecondsq_si = ( 

79 attogram_si * nanometer_si ** 2 / nanosecond_si ** 2 

80) # [J] attogram*nanometer^2/nanosecond^2 

81 

82# Velocity units 

83meter_per_second_si = 1.0 

84angstrom_per_femtosecond_si = ( 

85 angstrom_si / femtosecond_si 

86) # [m/s] Angstrom/femtosecond 

87angstrom_per_picosecond_si = ( 

88 angstrom_si / picosecond_si 

89) # [m/s] Angstrom/picosecond 

90micrometer_per_microsecond_si = ( 

91 micrometer_si / microsecond_si 

92) # [m/s] micrometer/microsecond 

93nanometer_per_nanosecond_si = ( 

94 nanometer_si / nanosecond_si 

95) # [m/s] nanometer/nanosecond 

96centimeter_per_second_si = centimeter_si # [m/s] centimeter/second 

97bohr_per_atu_si = bohr_si / atu_electron_si # [m/s] bohr/atu 

98 

99# Force units 

100newton_si = 1.0 

101kcal_per_mole_angstrom_si = ( 

102 kcal_per_mole_si / angstrom_si 

103) # [N] kcal/(mole*Angstrom) 

104ev_per_angstrom_si = ev_si / angstrom_si # [N] eV/Angstrom 

105dyne_si = dyne_centimeter_si / centimeter_si # [N] dyne 

106hartree_per_bohr_si = hartree_si / bohr_si # [N] hartree/bohr 

107picogram_micrometer_per_microsecondsq_si = ( 

108 picogram_si * micrometer_si / microsecond_si ** 2 

109) # [N] picogram*micrometer/microsecond^2 

110attogram_nanometer_per_nanosecondsq_si = ( 

111 attogram_si * nanometer_si / nanosecond_si ** 2 

112) # [N] attogram*nanometer/nanosecond^2 

113 

114# Temperature units 

115kelvin_si = 1.0 

116 

117# Pressure units 

118pascal_si = 1.0 

119atmosphere_si = 101325.0 # [Pa] standard atmosphere (NIST value) 

120bar_si = 1e5 # [Pa] bar 

121dyne_per_centimetersq_si = ( 

122 dyne_centimeter_si / centimeter_si ** 3 

123) # [Pa] dyne/centimeter^2 

124picogram_per_micrometer_microsecondsq_si = picogram_si / ( 

125 micrometer_si * microsecond_si ** 2 

126) # [Pa] picogram/(micrometer*microsecond^2) 

127attogram_per_nanometer_nanosecondsq_si = attogram_si / ( 

128 nanometer_si * nanosecond_si ** 2 

129) # [Pa] attogram/(nanometer*nanosecond^2) 

130 

131# Viscosity units 

132poise_si = 0.1 # [Pa*s] Poise 

133amu_per_bohr_femtosecond_si = amu_si / ( 

134 bohr_si * femtosecond_si 

135) # [Pa*s] amu/(bohr*femtosecond) 

136picogram_per_micrometer_microsecond_si = picogram_si / ( 

137 micrometer_si * microsecond_si 

138) # [Pa*s] picogram/(micrometer*microsecond) 

139attogram_per_nanometer_nanosecond_si = attogram_si / ( 

140 nanometer_si * nanosecond_si 

141) # [Pa*s] attogram/(nanometer*nanosecond) 

142 

143# Charge units 

144coulomb_si = 1.0 

145echarge_si = e_si # [C] electron charge unit 

146statcoulomb_si = ( 

147 e_si / 4.8032044e-10 

148) # [C] Statcoulomb or esu (value from LAMMPS units documentation) 

149picocoulomb_si = 1e-12 # [C] picocoulomb 

150 

151# Dipole units 

152coulomb_meter_si = 1 

153electron_angstrom_si = echarge_si * angstrom_si # [C*m] electron*angstrom 

154statcoulomb_centimeter_si = ( 

155 statcoulomb_si * centimeter_si 

156) # [C*m] statcoulomb*centimeter 

157debye_si = 1e-18 * statcoulomb_centimeter_si # [C*m] Debye 

158picocoulomb_micrometer_si = ( 

159 picocoulomb_si * micrometer_si 

160) # [C*m] picocoulomb*micrometer 

161electron_nanometer_si = echarge_si * nanometer_si # [C*m] electron*nanometer 

162 

163# Electric field units 

164volt_si = 1.0 

165volt_per_meter_si = 1 

166volt_per_angstrom_si = 1.0 / angstrom_si # [V/m] volt/angstrom 

167statvolt_per_centimeter_si = erg_si / ( 

168 statcoulomb_si * centimeter_si 

169) # [V/m] statvolt/centimeter 

170volt_per_centimeter_si = 1.0 / centimeter_si # [V/m] volt/centimeter 

171volt_per_micrometer_si = 1.0 / micrometer_si # [V/m] volt/micrometer 

172volt_per_nanometer_si = 1.0 / nanometer_si # [V/m] volt/nanometer