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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}}$


next up previous contents index
Next: Bibliography Up: Electric, magnetic and optical Previous: Vibrational Frequencies and IR   Contents   Index
Michal Jaszunski 2002-11-10