Fundamental Physical Constants

The fundamental physical constants used in MOPAC were updated in 1993 to conform with the 1986 CODATA recommendations [71]. The constants used in MOPAC are given in the Table. As a result of this update, all calculated quantities in MOPAC, except molecular weight, will change slightly when compared to earlier MOPACs (MOPAC 6 and earlier). Most of the time, changes in ΔHf are less than 0.1 kcal/mol. It is not anticipated that the physical constants will change again. If they do, however, the effect on calculated properties should be very small.

The derived quantities, AM, AD, AQ, EISOL, DD, and QQ are functions of the fundamental constants. Rather than change all of these, they are evaluated at the start of each calculation. This is a quick operation, taking only about 0.1s, and prevents any mistakes being introduced due to human error.


Table: Fundamental Physical Constants

Physical Constant

Symbol

Value

Units

Speed of Light

c

299 792 458

m sec-1 (Definition)

Planck constant

h

6.626 075 5(40) x10-34

J sec

 

 

6.626 075 5(40) x10-27

erg s

Avogadro constant

N

6.022 136 7(36)x1023

mol-1

Molar gas constant

R

1.987 215 6

cal/mol/degree

 

 

8.314 510(70)

J/mol/K

Volume of 1 mol of gas

V0

22.414 10(19)

l/mol (at 1 atm, 25 C)

Electron volt

eV

1.602 177 33(49)x10-19

J

Electron charge

e

1.602 177 33(49)x10-19

C

Hartree

Eh

27.211 396 1(81)

eV

Electrostatic energy

Ehao

14.399 651 782 565

eV

Bohr radius

$a_{circ}$

0.529 177 249(24)x10-10

m

Boltzmann constant

k = R/N

1.380 658(12)x10-23

J/K

 

 

1.380 658(12)x10-16

erg/K

pi

π

3.141 592 653 589 79

 

Joule

J/cal

4.184

J/cal (Definition)

cm-1

hc/eV

1.239 842 4x10-4

eV

cm-1

hcN/(1000J/cal)

2.859 144x10-3

kcal/mol

cm-1

hcN/(J/cal)

2.859 144

cal/mol

cm-1

 

1.196 266x108

erg = dyne Å-1

Atomic unit (a.u.)

 

8.657 10x10-33

e.s.u.

a.u.

 

2.541 747 8x10-40

Debye

a.u.

 

51.422 082

V m-1

kcal/mol

 

6.947 700x10-13

erg

1 J

 

1.x107

erg

1 eV

 

23.060 542 301 389

kcal/mol

1a.u.

 

627.509 6

kcal/mol

1 atm

 

1.013 25x105

Pa

 

 

1.013 25x106

dyn/cm2 (Definition)

 
Note: The precision of derived constants should not be used as an indication of their accuracy.
The uncertainty in the fundamental constants is given in parenthesis after the value.