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Atomic Units

Definition of atomic units

e = me = h/2p = 1

numerical values of atomic units

Energy E (Hartree) e2/a0(4pe0) 4.3597482 10-18 J
27.2113961 eV
219474.63068 cm-1
2 Rydbergs
Length a0 (4pe0) (h/2p)2/mee2 5.291772527 10-11 m
Mass me 9.1093897 10-31 kg
5.4857990 10-4 a.m.u.
Velocity v0 e2/(h/2p)(4pe0) 2.1876926 106 m sec-1
Time t0 a0/v0 2.418884326 10-17 sec
Polarizability a0 a03 1.481847466 10-31 m3
van der Waals potentail C6 Eh a06 5.9752740 10-61 eV m6
6.92005197 mK nm6
van der Waals potentail C3 Eh a03 *.***** 10-** eV m3
4.679276443 104 mK nm3

expression by atomic units

Speed of Light c 1/a 137.03599976 au

Physical Constants

Physical Constants

c = 2.99792458 108 m sec-1 Speed of Light
m0 = 1.2566370614... 10-8 H m-1 magnetic constant
e0 = 8.854187817... 10-12 F m-1 electric constant
G = 6.673(10) 10-11 N m2 kg-2 gravitational constant
h = 6.62606876(52) 10-34 J sec Planck constant
h/2p = 1.054571596(82) 10-34 J sec
e = 1.602176462(63) 10-19 C electron charge
mB = 9.27400899(37) 10-24 J T-1 Bohr magneton
me = 9.10938188(72) 10-31 kg electron mass
mp = 1.67262158(13) 10-27 kg proton mass
mn = 1.67492716(13) 10-27 kg neutron mass
g = 2.0023193043737(82) -- g-factor of electron
a0 = 0.5291772083(19) 10-10 m Bohr constant
R00 = 1.0973731568548(83) 107 m-1 Rydberg constant
a = 7.297352533(27) 10-3 -- fine structure constant
1/a = 137.03599976(50) -- --
kB = 1.3806503(24) 10-23 J K-1 Boltzmann constant
mu = 1.66053873(13) 10-27 kg Atomic Mass Constant
NA = 6.02214199(47) 1023 mol-1 Avogadro constant
R = 8.314472(15) J mol-1 K-1 gas constant

See also: "Rika-Nenpyo, 2002 edition, p. 434 (Japanese),

and/or CRC Handbook of Chemistry and Physics, 72nd edition, p. 1-18.

Definition non-SI units

1 cal = 4.184 J (def.) calorie
1 erg = 1 10-7 J (def.) erg
1 A = 1 10-10 m (def.) Angstrom

Energy Conversion

Energy Conversion Table (numerical)

Eh eV cm-1 Hz K J J/mol
Eh 1 2.7211396 101 2.1947463 105 6.5796839 1015 3.1577322 105 4.3597482 10-18 2.6255000 106
eV 3.6749309 10-2 1 8.0655409 103 2.4179883 1014 1.1604448 104 1.6021773 10-19 9.6485309 104
cm-1 4.5563353 10-6 1.2398424 10-4 1 2.9979246 1010 1.4387687 1.9864475 10-23 1.1962658 101
Hz 1.5198299 10-16 4.1356692 10-15 3.3356410 10-11 1 4.7992157 10-11 6.6260755 10-34 3.9903132 10-10
K 3.1668297 10-6 8.6173857 10-5 6.9503877 10-1 2.0836738 1010 1 1.3806580 10-23 8.3145112
J 2.2937104 1017 6.2415064 1018 5.0341125 1022 1.5091890 1033 7.2429233 1022 1 6.0221367 1023
J/mol 3.8087983 10-7 1.0364272 10-5 8.3593461 10-2 2.5060689 109 1.2027165 10-1 1.6605402 10-24 1

Frequently-Used

1 mK = 20.836738 MHz
1 cm-1 = 29.979246 GHz
1 eV = 11604.448 K

Energy Conversion Table (analytical)

Eh eV cm-1 Hz K J J/mol
Eh 1 2R00hc/e 2R00/100 2R00c 2R00hc/k 2R00hc 2R00hcN
eV e/(2R00hc) 1 e/(100hc) e/h e/k e eN
cm-1 100(2R00) 100hc/e 1 100c 100hc/k 100hc 100hcN
Hz 1/(2R00c) h/e 1/(100c) 1 h/k h hN
K k/(2R00hc) k/e k/(100hc) k/h 1 k kN
J 1/(2R00hc) 1/e 1/(100hc) 1/h 1/k 1 N
J/mol 1/(2R00hcN) 1/eN 1/(100hcN) 1/(hN) 1/(kN) 1/N 1

Others

Atomic masses (including electrons) of most abundant isotope in a.m.u.

1H 1.007825
2D 2.0140
4He 4.0026
12C 12
14N 14.00307
16O 15.99491462
19F 18.9984
23Na 22.989768
32S 31.97207
35Cl 34.96885
40Ar 39.962383124
40Ca 40.08
85Rb 85.4678
133Cs 132.90545
174Yb 173.04

Prefixes for use in S.I. units.

amount prefix symbol

10-24

yocto

y

10-21

zepto

z

10-18

atto

a

10-15

femto

f

10-12

pico

p

10-9

nano

n

10-6

micro

m

10-3

milli

m

10-2

centi

c

10-1

deci

d

101

deca

da

102

hecto

h

103

kilo

k

106

mega

M

109

giga

G

1012

tera

T

1015

peta

P

1018

exa

E

1021

zetta

Z

1024

yotta

Y

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