Constants and units

Table 9.1: Fundamental constants defining the atomic units.

Bohr radius	$a_0$	0.529 177 2083 D-10 m
Electron Mass	$m_e$	9.10938188D-31 kg
Action	$\hbar$	1.054 571 60D-34 J s
Electron charge	$e$	1.602 176 462D-19 C
Kelvin	$K$
mole	$mol$
radian	$rad$

Table 9.2: A list of the universal constants in atomic units.

Hartree	$E_h$	${{\hbar }^{2}} a_{0}^{-2} {m_e}^{-1}$
Permittivity of vacuum	$\epsilon_0$	$0.07957747154594767 {e^{2}} {a_{0}} {m_e} {{\hbar }^{-2}}$
Permeability of vacuum	$\mu_0$	$0.0006691762496807159{ {a_{0}}\ {m_e}}{{e^{-2}}}$
Impedance of vacuum	$Z_0$	$0.0917012364137738 \hbar e^{-2}$
Speed of light in vacuum	$c_0$	$137.0359996287515 \hbar {a_{0}}^{-1} {m_e}^{-1}$
Proton rest mass	$m_p$	$1836.152663302331 {m_e}$
Neutron rest mass	$m_n$	$1838.685239091107 {m_e}$
Unified atomic mass constant	$m_u$	$1822.888479031408 {m_e}$
Avogadro constant	$N_a$	$6.022141990 \times {{10}^{23}}{{mol}^{-1}}$
Boltzmann constant	$k$	$3.16681520371153 \times {{10}^{-6}} {{\hbar }^{2}} {K}^{-1} a_{0}^{-2}\ {m_e}^{-1}$
Faraday constant	$Faraday$	$6.022141991747723 \times {{10}^{23}}{\ e\ }{{mol}^{-1}}$
Molar gas constant	$R_{gas}$	$1.907101047994109 \times {{10}^{18}} {{\hbar }^{2}} {K}^{-1} {mol}^{-1} a_{0}^{-2}\ {m_e}^{-1}$
Fine structure constant	$\alpha$	$0.007297352522615556$
Rydberg constant	$R_{\infty}$	$0.0005807048641344865{{a_{0}^{-1}}}$
Bohr Magneton	$\mu_B$	$0.5 e\ \hbar {m_e}^{-1}$
Electron magnetic moment	$\mu_e$	$0.5005801751848031{\ e\ \hbar }{{m_e}^{-1}}$
Landé g-factor for
the free electron	$g_e$	$2.002320700739213$
Nuclear magneton	$\mu_N$	$0.0002723085122457884{\ e\ \hbar }{{m_e}^{-1}}$
Proton magnetic moment	$\mu_p$	$0.000760516627687762{ e\ \hbar }{{m_e}^{-1}}$
Proton magnetogiric ratio	$\gamma_p$	$0.001521031723472069{\ e}{{m_e}^{-1}}$
Magnetic moment of
protons in H$_{2}$O	$\mu^\prime$	$0.0007604965645{\ e\ \hbar }{{m_e}^{-1}}$
Proton resonance frequency
per field in H$_{2}$O	$\gamma^\prime$	$0.001520992639504675{ e}{{m_e}^{-1}}$
Stefan-Boltzmann constant		$8.80988087157682 \times {{10}^{-28}} {{\hbar }^{3}} {K}^{-4}\ a_{0}^{-6}\ m_{e}^{-2}$
Magnetic flux quantum	$\phi_0$	${3.141592652725856 \hbar }{e^{-1}}$
Conductance quantum		${0.3183098866547112 {e^{2}}}{\hbar^{-1} }$
Plank mass		$2.38945532716683 \times {{10}^{22}} {m_{e}}$
Plank length		$3.05398157366997 \times {{10}^{-25}} {a_{0}}$
Plank time		$2.228598019457374 \times {{10}^{-27}} {{a_{0}^{2} m_{e}}{{{\hbar }^{-1}}}}$
ElectronVolt	$eV$	$0.03674932587122423 {{\hbar }^{2}} a_{0}^{-2} {m_e}^{-1}$
First radiation constant		$741359.8822745807 {{\hbar }^{3}} a_{0}^{-2} m_{e}^{-2}$
Second radiation constant		$2.718891138368016 \times {{10}^{8}} {K} {a_{0}}$
Quantum of circulation		$3.141592653589793 \hbar {m_e}^{-1}$

Table 9.3: A list of the conversion factors from SI and cgs to atomic units.

meter	$\ m$	$1.889726133921252 \times {{10}^{10}} {a_{0}}$
Ångström	Å	$1.889726133921252 {a_{0}}$
micron	$\mu$	$18897.26133921252 {a_{0}}$
x unit	$X$	$0.001893505586189094 {a_{0}}$
fermi	$F$	$0.00001889726133921252 {a_{0}}$
barn	$b$	$3.57106486122496 \times {{10}^{-8}} a_{0}^{2}$
litre	$l$	$6.748334594184675 \times {{10}^{27}} a_{0}^{3}$
second	$s$	${4.134137337414122 \times {{10}^{16}} a_{0}^{2} {m_e}}{\hbar^{-1} }$
minute	$min$	${2.480482402448473 \times {{10}^{18}} a_{0}^{2} {m_e}}{\hbar^{-1} }$
hour	$h$	${1.488289441469084 \times {{10}^{20}} a_{0}^{2} {m_e}}{\hbar^{-1} }$
gram	$g$	$1.097769325266227 \times {{10}^{27}} {m_e}$
Unified Atomic Mass	$u$	$1822.888479031408 {m_e}$
Dalton	$Da$	$1822.888479031408 {m_e}$
coulomb	$C$	$6.241509744511525 \times {{10}^{18}} e$
franklin	$Fr$	$2.081942956418242 \times {{10}^{9}} e$
abcoulomb		$6.241509744511525 \times {{10}^{19}} e$
Charge density	$Cm^{-3}$	${9.24896306992557 \times {{10}^{-13}} e}{a_{0}^{-3}}$
Charge density (ESU)	$Frcm^{-3}$	${3.085121117456655 \times {{10}^{-16}} e}{a_{0}^{-3}}$
Velocity	$ms^{-1}$	$4.571028922573879 \times {{10}^{-7}} \hbar a_{0}^{-1} m_e^{-1}$
Acceleration	$ms^{-2}$	$1.105679020676423 \times {{10}^{-23}} {\hbar }^{2} a_{0}^{-3} m_{e}^{-2}$
Momentum	$kg m s^{-1}$	${5.017935336106338 \times {{10}^{23}} \hbar }{{a_{0}}^{-1}}$
Hertz	$Hz$	$2.418884324306202 \times {{10}^{-17}} \hbar a_{0}^{-2} {m_e}^{-1}$
Newton	$N$	$1.21378051248898 \times {{10}^{7}} {{\hbar }^{2}} a_{0}^{-3} {m_e}^{-1}$
Pascal	$Pa$	$3.398931578276133 \times {{10}^{-14}} {{\hbar }^{2}} a_{0}^{-5} {m_e}^{-1}$
bar	$bar$	$3.398931578276133 \times {{10}^{-9}} {{\hbar }^{2}} a_{0}^{-5} {m_e}^{-1}$
Joule	$J$	$2.293712755294755 \times {{10}^{17}} {{\hbar }^{2}} a_{0}^{-2} {m_e}^{-1}$
erg	$erg$	$2.293712755294755 \times {{10}^{10}} {{\hbar }^{2}} a_{0}^{-2} {m_e}^{-1}$
rydberg	$Ry$	$0.5 {{\hbar }^{2}} a_{0}^{-2} {m_e}^{-1}$
electronvolt	$eV$	$0.03674932587122423 {{\hbar }^{2}} a_{0}^{-2} {m_e}^{-1}$
calorie, thermochemical	$cal_{th}$	$9.59689416815326 \times {{10}^{17}} {{\hbar }^{2}} a_{0}^{-2} {m_e}^{-1}$
Power, P	$W$	$5.548225828243671 {{\hbar }^{3}} a_{0}^{-4} m_{e}^{-2}$
Action, L, J	$Js$	$9.48252354296707 \times {{10}^{33}} \hbar$
Action (ESU)	$erg\ s$	$9.48252354296707 \times {{10}^{26}} \hbar$
Thermodynamic Temperature	$K$	$K$
Entropy, S	$J K^{-1}$	$2.293712755294755 \times {{10}^{17}} {{\hbar }^{2}} {K}^{-1} a_{0}^{-2} {m_e}^{-1}$
Molar Entropy, $S_m$	$S_m$	$2.293712755294755 \times {{10}^{17}} {{\hbar }^{2}} {K}^{-1} {mol}^{-1} a_{0}^{-2} {m_e}^{-1}$
Entropy unit	$e.u.$	$9.59689416815326 \times {{10}^{17}} {{\hbar }^{2}} {K}^{-1} {mol}^{-1} a_{0}^{-2} {m_e}^{-1}$
radian	$rad$	${rad}$
degree	$\deg$	$0.0174532925199433\ {rad}$
minute	$'$	$0.0002908882086657216\ {rad}$
second	$''$	$4.84813681109536 \times {{10}^{-6}}\ {rad}$
Circular frequency	$rad\ s^{-1}$	$2.418884324306202 \times {{10}^{-17}}\ {rad}\ \hbar a_{0}^{-2} {m_e}^{-1}$
Ampere	$A$	$150.9749008100334 e \hbar a_{0}^{-2} {m_e}^{-1}$
Current (ESU)		$5.035980618632953 \times {{10}^{-8}} e \hbar a_{0}^{-2} {m_e}^{-1}$
Current (EMU)=biot	$Bi$	$1509.749008100334 e \hbar a_{0}^{-2} {m_e}^{-1}$
volt	$V$	$0.03674932587122423 {{\hbar }^{2}} e^{-1} a_{0}^{-2} {m_e}^{-1}$
Electric Potential (ESU)	$erg\ Fr^{-1}$	$11.01717387704435 {{\hbar }^{2}} e^{-1} a_{0}^{-2} {m_e}^{-1}$
Ohm	$\Omega$	$0.000243413479154821 \hbar {e^{-2}}$
Electric Field	$Vm^{-1}$	$1.944690567144141 \times {{10}^{-12}} {{\hbar }^{2}} e^{-1} a_{0}^{-3} {m_e}^{-1}$
Electric Field (ESU)	$Fr cm^{-2} (4 \pi \epsilon_0)^{-1}$	$5.830034001970176 \times {{10}^{-8}} {{\hbar }^{2}} e^{-1} a_{0}^{-3} {m_e}^{-1}$
Electric Field Gradient	$Vm^{-2}$	$1.02908592532868 \times {{10}^{-22}} {{\hbar }^{2}} e^{-1} a_{0}^{-4} {m_e}^{-1}$
Electric Field
Gradient (ESU)	$Fr cm^{-3}(4 \pi \epsilon_0)^{-1}$	$3.085121117456655 \times {{10}^{-16}} {{\hbar }^{2}} e^{-1} a_{0}^{-4} {m_e}^{-1}$
Electric Dipole Moment	$Cm$	$1.179474407932758 \times {{10}^{29}} e {a_{0}}$
Electric Dipole
Moment (ESU)	$Fr cm$	$3.934302014076826 \times {{10}^{17}} e {a_{0}}$
debye	$D$	$0.3934302014076827 e {a_{0}}$
Electric Quadrupole
Moment	$Cm^{2}$	$2.228883612961829 \times {{10}^{39}} e a_{0}^{2}$
Electric Quadrupole
Moment (ESU)	$Fr cm^{2}$	$7.434753334739994 \times {{10}^{25}} e a_{0}^{2}$
Electric Dipole Polarizability	$J^{-1}C^{2}m^{2}$	${6.065100679049756 \times {{10}^{40}} {e^{2}} a_{0}^{4} {m_e}}{{{\hbar }^{-2}}}$
Electric Dipole
Polarizability (ESU)	$(4 \pi \epsilon_0 ) cm^{3}$	${6.748334594184674 \times {{10}^{24}} {e^{2}} a_{0}^{4} {m_e}}{{{\hbar }^{-2}}}$
First Electric Dipole
Hyperpolarizability	$J^{-2}C^{3}m^{3}$	${3.118799865397922 \times {{10}^{52}} {e^{3}} a_{0}^{7} m_{e}^{2}}{{{\hbar }^{-4}}}$
First Electric Dipole
Hyperpolarizability (ESU)	$erg^{-2} Fr^{3} cm^{3}$	${1.157510731627746 \times {{10}^{32}} {e^{3}} a_{0}^{7} m_{e}^{2}}{{{\hbar }^{-4}}}$
Second Electric Dipole
Hyperpolarizability	$J^{-3}C^{4}m^{4}$	${1.603751217849538 \times {{10}^{64}} {e^{4}} a_{0}^{10} m_{e}^{3}}{{{\hbar }^{-6}}}$
Second Electric Dipole
Hyperpolarizability (ESU)	$erg^{-3}Fr^{4}cm^{4}$	${1.985425939776565 \times {{10}^{39}} {e^{4}} a_{0}^{10} m_{e}^{3}}{{{\hbar }^{-6}}}$
Electric Displacement	$Cm^{-2}$	${0.01747800722491089 e}{a_{0}^{-2}}$
siemens	$S$	${4108.235926260923 {e^{2}}}{\hbar^{-1}}$
farad	$F$	${1.698401153366137 \times {{10}^{20}} {e^{2}} a_{0}^{2} {m_e}}{{{\hbar }^{-2}}}$
tesla	$T$	$4.254382547308656 \times {{10}^{-6}} \hbar e^{-1} a_{0}^{-2}$
gauss	$\ G$	$4.254382547308656 \times {{10}^{-10}} \hbar e^{-1} a_{0}^{-2}$
weber	$Wb$	${1.519267602090268 \times {{10}^{15}} \hbar }{e^{-1}}$
maxwell	$Mx$	$1.191348438809734 \times {{10}^{-26}} \hbar e a_{0}^{-4}$
henry	$H$	${1.00630475260382 \times {{10}^{13}} a_{0}^{2} {m_e}}{{e^{-2}}}$
Magnetic Field	$Am^{-1}$	$7.989247653402288 \times {{10}^{-9}} e \hbar a_{0}^{-3} {m_e}^{-1}$
oersted	$Oe$	$7.989247653402288 \times {{10}^{-6}} e \hbar a_{0}^{-3} {m_e}^{-1}$
Magnetic Dipole Moment	$JT^{-1}$	${5.391411632096341 \times {{10}^{22}} e \hbar }{{m_e}^{-1}}$
Magnetic Dipole
Moment (EMU)	$erg\ G^{-1}$	${5.39141163209634 \times {{10}^{19}} e \hbar }{{m_e}^{-1}}$
Magnetizability	$JT^{-2}$	${1.267260659365711 \times {{10}^{28}} {e^{2}} a_{0}^{2}}{{m_e}^{-1}}$