Basics to rez molecules in 3D
Most of the organic molecules could be rez in 2D.
But the carbon have 4 bonds, 4 rods. Methane, ammonium are tetrahedral.
And we must study the geometry of tetrahedron !
For chemistry, Wikipedia say :
“The tetrahedron shape is seen in nature in covalent bonds of molecules. For instance in a methane molecule (CH4) the four hydrogen atoms lie in each corner of a tetrahedron with the carbon atom in the centre. For this reason, one of the leading journals in organic chemistry is called Tetrahedron.”
1) First step : geometry of a triangle
from the positions of triangles to the orientation of covalents bonds.
|
|
|
x |
y |
z |
|
1 |
C |
a |
b |
c |
|
2 |
C |
a+d |
b |
c |
|
3 |
O |
a-d/3 |
b+2*sqr(2)/3*d |
c |
|
4 |
O |
a-d/3 |
b-2*sqr(2)/3*d |
c |
2) Second step : geometry of a tetrahedron
Tetrahedron : differents views…
vertical projection of methane
d: covalent bond & a: side of the terahedron
[More with this source ]
a = 2*sqr(2/3) * d
EF=EG=FG=DE=DF=DG=a
CE=CD=CF=CG=d
AC=d/3
AE=a/sqr(3)
AM=a/[2*sqr(3)]
EM=a*sqr(3)/2
CM=a/[2*sqr(2)]
Side view of the methane
|
|
|
x |
y |
z |
z’ |
|
1 |
C |
a |
b |
c |
|
|
2 |
H |
a+d |
b |
c |
|
|
3 |
H |
a-d/3 |
b |
c+2*sqr(2)/3*d |
c-2*sqr(2)/3*d |
|
4 |
H |
a-d/3 |
b-sqr(2/3)*d |
c-2*sqr(2)/3*d |
c+sqr(2)/3*d |
|
5 |
H |
a-d/3 |
b+sqr(2/3)*d |
c-2*sqr(2)/3*d |
c+sqr(2)/3*d |
3) Data : colors and dimensions
The common colors used for molecular models are those defined by Corey, Pauling and Kultun (the CPK system).
|
Element |
Symbol |
Color |
Hexa code |
SL vector |
Covalent radius (Ǻ) |
|
C |
Clear grey / gris clair |
#c8c8c8 |
<0.784,0.784,0.784> |
0,77 |
|
|
O |
Red / rouge |
#ff0000 |
<1.0,0.0,0.0> |
0,73 |
|
|
H |
White / blanc |
#ffffff |
<1.0,1.0,1.0> |
0,37 |
|
|
N |
Clear blue / bleu clair |
#8f8fff |
<0.5608,0.5608,1.0> |
0,75 |
|
|
S |
Yellow / jaune |
#ffc832 |
<1.0,0.784,0.196> |
1,02 |
|
|
P |
Orange |
#ffa500 |
<1.0,0.647,0.0> |
1,06 |
|
|
Cl |
Green / vert |
#00ff00 |
<0.0,1.0,0.0 > |
0,99 |
|
|
Bromine / brome, Zinc |
Br, Zn |
Brown / marron |
#a52a2a |
<0.647,0.1647,0.1647> |
1,14 , 1,31 |
|
Natrium / sodium |
Na |
Blue / bleu |
#0000ff |
<0.0,0.0,1.0> |
1,54 |
|
Iron / fer |
Fe |
Purple / violet |
#a020f0 |
<0.6275,0.1255,0.9412> |
1,25 |
|
Calcium, métaux |
Ca |
Dark grey / gris foncé |
#808090 |
<0.5,0.5,0.5647> |
1,74 |
|
Unknown |
|
Deep pink / rose foncé |
#ff1493 |
<1.0,0.0784,0.5765 > |
|
d (C/H) = 1,02 Ǻ
d (O/H) = 0,96 Ǻ
d (N/H) = 1,01 Ǻ
d (C/C) = 1,54 Ǻ
d (C//C) = 1,33 Ǻ
d (C///C) = 1,20 Ǻ
d (C//C) benzen = 1,40 Ǻ
d (C/O) = 1,43 Ǻ
d (C//O) = 1,26 Ǻ
d (C/N) = 1,47 Ǻ
d (C///N) = 1,15 Ǻ
d (C/Cl) = 1,77 Ǻ
d (C/Br) = 1,94 Ǻ
d (C/S) = 1,82 Ǻ
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