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<TITLE>C. Examples of geometries using symmetry</TITLE>
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<B> Next:</B> <A NAME="tex2html1848"
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<!--Table of Child-Links-->
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
<UL>
<LI><A NAME="tex2html1849"
HREF="node43.html#SECTION004310000000000000000">C.1 <IMG
WIDTH="22" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img6.gif"
ALT="$C_{s}$"> methanol</A>
<LI><A NAME="tex2html1850"
HREF="node43.html#SECTION004320000000000000000">C.2 <IMG
WIDTH="29" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img7.gif"
ALT="$C_{2v}$"> water</A>
<LI><A NAME="tex2html1851"
HREF="node43.html#SECTION004330000000000000000">C.3 <IMG
WIDTH="32" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img8.gif"
ALT="$D_{2h}$"> acetylene</A>
<LI><A NAME="tex2html1852"
HREF="node43.html#SECTION004340000000000000000">C.4 <IMG
WIDTH="32" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img8.gif"
ALT="$D_{2h}$"> ethylene</A>
<LI><A NAME="tex2html1853"
HREF="node43.html#SECTION004350000000000000000">C.5 <IMG
WIDTH="21" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img9.gif"
ALT="$T_d$"> methane</A>
<LI><A NAME="tex2html1854"
HREF="node43.html#SECTION004360000000000000000">C.6 <IMG
WIDTH="19" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img10.gif"
ALT="$I_h$"> buckminsterfullerene</A>
<LI><A NAME="tex2html1855"
HREF="node43.html#SECTION004370000000000000000">C.7 <IMG
WIDTH="21" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img11.gif"
ALT="$S_4$"> porphyrin</A>
<LI><A NAME="tex2html1856"
HREF="node43.html#SECTION004380000000000000000">C.8 <IMG
WIDTH="32" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img12.gif"
ALT="$D_{3h}$"> iron penta-carbonyl</A>
<LI><A NAME="tex2html1857"
HREF="node43.html#SECTION004390000000000000000">C.9 <IMG
WIDTH="31" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img13.gif"
ALT="$D_{3d}$"> sodium crown ether</A>
<LI><A NAME="tex2html1858"
HREF="node43.html#SECTION0043100000000000000000">C.10 <IMG
WIDTH="29" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img14.gif"
ALT="$C_{3v}$"> ammonia</A>
<LI><A NAME="tex2html1859"
HREF="node43.html#SECTION0043110000000000000000">C.11 <IMG
WIDTH="32" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img15.gif"
ALT="$D_{6h}$"> benzene</A>
<LI><A NAME="tex2html1860"
HREF="node43.html#SECTION0043120000000000000000">C.12 <IMG
WIDTH="30" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img16.gif"
ALT="$C_{3h}$"> <IMG
WIDTH="57" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img17.gif"
ALT="$BO_3H_3$"></A>
<LI><A NAME="tex2html1861"
HREF="node43.html#SECTION0043130000000000000000">C.13 <IMG
WIDTH="31" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img18.gif"
ALT="$D_{5d}$"> ferrocene</A>
<LI><A NAME="tex2html1862"
HREF="node43.html#SECTION0043140000000000000000">C.14 <IMG
WIDTH="29" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img19.gif"
ALT="$C_{4v}$"> <IMG
WIDTH="50" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img20.gif"
ALT="$SF_5Cl$"></A>
<LI><A NAME="tex2html1863"
HREF="node43.html#SECTION0043150000000000000000">C.15 <IMG
WIDTH="30" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img21.gif"
ALT="$C_{2h}$"> trans-dichloroethylene</A>
<LI><A NAME="tex2html1864"
HREF="node43.html#SECTION0043160000000000000000">C.16 <IMG
WIDTH="31" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img22.gif"
ALT="$D_{2d}$"> <IMG
WIDTH="82" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img23.gif"
ALT="$CH_2CCH_2$"></A>
<LI><A NAME="tex2html1865"
HREF="node43.html#SECTION0043170000000000000000">C.17 <IMG
WIDTH="32" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img24.gif"
ALT="$D_{5h}$"> cyclopentadiene anion</A>
<LI><A NAME="tex2html1866"
HREF="node43.html#SECTION0043180000000000000000">C.18 <IMG
WIDTH="32" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img25.gif"
ALT="$D_{4h}$"> gold tetrachloride</A>
</UL>
<!--End of Table of Child-Links-->
<HR>
<H1><A NAME="SECTION004300000000000000000">
C. Examples of geometries using symmetry</A>
</H1>
<A NAME="symexamples"></A>
<P>
Below are examples of the use of the <code>SYMMETRY</code> directive in
the compound <code>GEOMETRY</code> directive (Section <A HREF="node8.html#sec:geom">6</A>).
The z axis is always the primary rotation axis.
When in doubt about which axes and planes are used for the group
elements, the keyword <code>print</code> may be added to the <code>SYMMETRY</code>
directive to obtain this information.
<P>
<H1><A NAME="SECTION004310000000000000000">
C.1 <IMG
WIDTH="22" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img6.gif"
ALT="$C_{s}$"> methanol</A>
</H1>
<P>
The <IMG
WIDTH="21" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="img338.gif"
ALT="$\sigma_h$"> plane is the xy plane.
<P>
<PRE>
geometry units angstroms
C 0.11931097 -0.66334875 0.00000000
H 1.20599017 -0.87824237 0.00000000
H -0.32267592 -1.15740001 0.89812652
O -0.01716588 0.78143468 0.00000000
H -1.04379735 0.88169812 0.00000000
symmetry cs
end
</PRE>
<P>
<H1><A NAME="SECTION004320000000000000000">
C.2 <IMG
WIDTH="29" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img7.gif"
ALT="$C_{2v}$"> water</A>
</H1>
<P>
The z axis is the <IMG
WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img339.gif"
ALT="$C_2$"> axis and the <IMG
WIDTH="21" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="img340.gif"
ALT="$\sigma_v$"> may be either the xz or the
yz planes.
<P>
<PRE>
geometry units au
O 0.00000000 0.00000000 0.00000000
H 0.00000000 1.43042809 -1.10715266
symmetry group c2v
end
</PRE>
<P>
<H1><A NAME="SECTION004330000000000000000">
C.3 <IMG
WIDTH="32" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img8.gif"
ALT="$D_{2h}$"> acetylene</A>
</H1>
<P>
Although acetylene has symmetry <IMG
WIDTH="38" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img341.gif"
ALT="$D_{\infty h}$"> the subgroup
<IMG
WIDTH="32" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img8.gif"
ALT="$D_{2h}$"> includes all operations that interchange equivalent atoms
which is what determines how much speedup you gain from using symmetry
in building a Fock matrix.
<P>
The <IMG
WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img339.gif"
ALT="$C_2$"> axes are the x, y, and z axes. The <IMG
WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img342.gif"
ALT="$\sigma$"> planes are the xy,
xz and yz planes. Generally, the unique atoms are placed to use the z
as the primary rotational axis and use the xz or yz planes as the <IMG
WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img342.gif"
ALT="$\sigma$">
plane.
<P>
<PRE>
geometry units au
symmetry group d2h
C 0.000000000 0.000000000 -1.115108538
H 0.000000000 0.000000000 -3.106737425
end
</PRE>
<P>
<H1><A NAME="SECTION004340000000000000000">
C.4 <IMG
WIDTH="32" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img8.gif"
ALT="$D_{2h}$"> ethylene</A>
</H1>
<P>
The <IMG
WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img339.gif"
ALT="$C_2$"> axes are the x, y, and z axes. The <IMG
WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img342.gif"
ALT="$\sigma$"> planes are the xy,
xz and yz planes. Generally, the unique atoms are placed to use the z
as the primary rotational axis and use the xz or yz planes as the <IMG
WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img342.gif"
ALT="$\sigma$">
plane.
<P>
<PRE>
geometry units angstroms
C 0 0 0.659250
H 0 0.916366 1.224352
symmetry d2h
end
</PRE>
<P>
<H1><A NAME="SECTION004350000000000000000">
C.5 <IMG
WIDTH="21" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img9.gif"
ALT="$T_d$"> methane</A>
</H1>
<P>
For ease of use, the primary <IMG
WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img343.gif"
ALT="$C_3$"> axis should be the x=y=z axis.
The 3 <IMG
WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img339.gif"
ALT="$C_2$"> axes are the x, y, and z.
<P>
<PRE>
geometry units au
c 0.0000000 0.0000000 0.0000000
h 1.1828637 1.1828637 1.1828637
symmetry group Td
end
</PRE>
<P>
<H1><A NAME="SECTION004360000000000000000">
C.6 <IMG
WIDTH="19" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img10.gif"
ALT="$I_h$"> buckminsterfullerene</A>
</H1>
<P>
One of the <IMG
WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img344.gif"
ALT="$C_5$"> axes is the z axis and the point of inversion is the origin.
<P>
<PRE>
geometry units angstroms # Bonds = 1.4445, 1.3945
symmetry group Ih
c -1.2287651 0.0 3.3143121
end
</PRE>
<P>
<H1><A NAME="SECTION004370000000000000000">
C.7 <IMG
WIDTH="21" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img11.gif"
ALT="$S_4$"> porphyrin</A>
</H1>
<P>
The <IMG
WIDTH="21" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img11.gif"
ALT="$S_4$"> and <IMG
WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img339.gif"
ALT="$C_2$"> rotation axis is the z axis. The reflection plane
for the <IMG
WIDTH="21" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img11.gif"
ALT="$S_4$"> operation is the xy plane.
<P>
<PRE>
geometry units angstroms
symmetry group s4
fe 0.000 0.000 0.000
h 2.242 6.496 -3.320
h 1.542 4.304 -2.811
c 1.947 6.284 -2.433
c 1.568 4.987 -2.084
h 2.252 8.213 -1.695
c 1.993 7.278 -1.458
h 5.474 -1.041 -1.143
c 1.234 4.676 -0.765
h 7.738 -1.714 -0.606
c 0.857 3.276 -0.417
h 1.380 -4.889 -0.413
c 1.875 2.341 -0.234
h 3.629 3.659 -0.234
c 0.493 -2.964 -0.229
c 1.551 -3.933 -0.221
c 5.678 -1.273 -0.198
c 1.656 6.974 -0.144
c 3.261 2.696 -0.100
n 1.702 0.990 -0.035
end
</PRE>
<P>
<H1><A NAME="SECTION004380000000000000000">
C.8 <IMG
WIDTH="32" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img12.gif"
ALT="$D_{3h}$"> iron penta-carbonyl</A>
</H1>
<P>
The <IMG
WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img343.gif"
ALT="$C_3$"> axis is the z axis. The <IMG
WIDTH="21" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="img338.gif"
ALT="$\sigma_h$"> plane is the xy plane. One of
the perpendicular <IMG
WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img339.gif"
ALT="$C_2$"> axes is the x=y axis. One of the <IMG
WIDTH="21" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="img340.gif"
ALT="$\sigma_v$">
planes is the plane containing the x=y axis and the z axis. (The
other axes and planes are generated by the <IMG
WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img343.gif"
ALT="$C_3$"> operation.)
<P>
<PRE>
geometry units au
symmetry group d3h
fe 0.0 0.0 0.0
c 0.0 0.0 3.414358
o 0.0 0.0 5.591323
c 2.4417087 2.4417087 0.0
o 3.9810552 3.9810552 0.0
end
</PRE>
<P>
<H1><A NAME="SECTION004390000000000000000">
C.9 <IMG
WIDTH="31" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img13.gif"
ALT="$D_{3d}$"> sodium crown ether</A>
</H1>
<P>
The <IMG
WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img343.gif"
ALT="$C_3$"> axis is the z axis. The point of inversion is the origin. One of
the perpendicular <IMG
WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img339.gif"
ALT="$C_2$"> axes is the x=y axis. One of the <IMG
WIDTH="21" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="img345.gif"
ALT="$\sigma_d$"> planes
is the plane containing the -x=y axis and the z axis.
<P>
Note that the oxygen atom is rotated in the x-y plane 15
degrees away from the y-axis so that it lies in a mirror
plane. There is a total of six atoms generated from the
unique oxygen, in contrast to twelve from each of the carbon
and hydrogen atoms.
<P>
<PRE>
geometry units au
symmetry D3d
NA .0000000000 .0000000000 .0000000000
O 1.3384771885 4.9952647969 .1544089284
H 6.7342048019 -0.6723850379 2.6581562148
C 6.7599180056 -0.4844977035 .6136583870
H 8.6497577017 0.0709194071 .0345361934
end
</PRE>
<P>
<H1><A NAME="SECTION0043100000000000000000">
C.10 <IMG
WIDTH="29" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img14.gif"
ALT="$C_{3v}$"> ammonia</A>
</H1>
<P>
The <IMG
WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img343.gif"
ALT="$C_3$"> axis is the z axis. One of the <IMG
WIDTH="21" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="img340.gif"
ALT="$\sigma_v$"> planes is the
plane containing the x=y axis and the z axis.
<P>
<PRE>
geometry units angstroms
N 0 0 -0.055
H 0.665 0.665 -0.481
symmetry c3v
end
</PRE>
<P>
<H1><A NAME="SECTION0043110000000000000000">
C.11 <IMG
WIDTH="32" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img15.gif"
ALT="$D_{6h}$"> benzene</A>
</H1>
<P>
The <IMG
WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img346.gif"
ALT="$C_6$"> axis is the z axis. The point of inversion is the origin. One
of the 6 perpendicular <IMG
WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img347.gif"
ALT="$C_2'$"> axes is the x=y axis. (-x=y works as a
<IMG
WIDTH="25" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img348.gif"
ALT="$C_2''$"> axis.) The <IMG
WIDTH="21" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="img338.gif"
ALT="$\sigma_h$"> plane is the xy plane. The <IMG
WIDTH="21" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="img345.gif"
ALT="$\sigma_d$">
planes contain the <IMG
WIDTH="25" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img348.gif"
ALT="$C_2''$"> axis and the z axis. The <IMG
WIDTH="21" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="img340.gif"
ALT="$\sigma_v$"> planes
contain the <IMG
WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img347.gif"
ALT="$C_2'$"> axis and the z axis.
<P>
<PRE>
geometry units au
C 1.855 1.855 0
H 3.289 3.289 0
symmetry D6h
end
</PRE>
<P>
<H1><A NAME="SECTION0043120000000000000000">
C.12 <IMG
WIDTH="30" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img16.gif"
ALT="$C_{3h}$"> <IMG
WIDTH="57" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img17.gif"
ALT="$BO_3H_3$"></A>
</H1>
<P>
The <IMG
WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img343.gif"
ALT="$C_3$"> axis is the z axis. The <IMG
WIDTH="21" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="img338.gif"
ALT="$\sigma_h$"> plane is the xy plane.
<P>
<PRE>
geometry units au
b 0 0 0
o 2.27238285 1.19464491 0.00000000
h 2.10895420 2.97347707 0.00000000
symmetry C3h
end
</PRE>
<P>
<H1><A NAME="SECTION0043130000000000000000">
C.13 <IMG
WIDTH="31" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img18.gif"
ALT="$D_{5d}$"> ferrocene</A>
</H1>
<P>
The <IMG
WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img344.gif"
ALT="$C_5$"> axis is the z axis. The center of inversion is the origin.
One of the perpendicular <IMG
WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img339.gif"
ALT="$C_2$"> axes is the x axis. One of the <IMG
WIDTH="21" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="img345.gif"
ALT="$\sigma_d$">
planes is the yz plane.
<P>
<PRE>
geometry units angstroms
symmetry d5d
fe 0 0 0
c 0 1.194 1.789
h 0 2.256 1.789
end
</PRE>
<P>
<H1><A NAME="SECTION0043140000000000000000">
C.14 <IMG
WIDTH="29" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img19.gif"
ALT="$C_{4v}$"> <IMG
WIDTH="50" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img20.gif"
ALT="$SF_5Cl$"></A>
</H1>
<P>
The <IMG
WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img349.gif"
ALT="$C_4$"> axis is the z axis. The <IMG
WIDTH="21" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="img340.gif"
ALT="$\sigma_v$"> planes are the yz and the xz
planes. The <IMG
WIDTH="21" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="img345.gif"
ALT="$\sigma_d$"> planes are: 1) the plane containing the x=y axis and
the z axis and 2) the plane containing the -x=y axis and the z axis.
<P>
<PRE>
geometry units au
S 0.00000000 0.00000000 -0.14917600
Cl 0.00000000 0.00000000 4.03279700
F 3.13694200 0.00000000 -0.15321800
F 0.00000000 0.00000000 -3.27074500
symmetry C4v
end
</PRE>
<P>
<H1><A NAME="SECTION0043150000000000000000">
C.15 <IMG
WIDTH="30" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img21.gif"
ALT="$C_{2h}$"> trans-dichloroethylene</A>
</H1>
<P>
The <IMG
WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img339.gif"
ALT="$C_2$"> axis is the z axis. The origin is the inversion center.
The <IMG
WIDTH="21" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="img338.gif"
ALT="$\sigma_h$"> plane is the xy plane.
<P>
<PRE>
geometry units angstroms
C 0.65051239 -0.08305064 0
Cl 1.75249381 1.30491767 0
H 1.14820954 -1.04789741 0
symmetry C2h
end
</PRE>
<P>
<H1><A NAME="SECTION0043160000000000000000">
C.16 <IMG
WIDTH="31" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img22.gif"
ALT="$D_{2d}$"> <IMG
WIDTH="82" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img23.gif"
ALT="$CH_2CCH_2$"></A>
</H1>
<P>
The <IMG
WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img339.gif"
ALT="$C_2$"> axis is the z axis (z is also the <IMG
WIDTH="21" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img11.gif"
ALT="$S_4$"> axis). The x and y axes
are the perpendicular <IMG
WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img347.gif"
ALT="$C_2'$">s. The <IMG
WIDTH="21" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="img345.gif"
ALT="$\sigma_d$"> planes are:
1) the plane containing the x=y axis and the z axis and 2) the plane
containing the -x=y axis and the z axis.
<P>
<PRE>
geometry units angstroms
symmetry d2d
c 0 0 0
c 0 0 1.300
h 0.656 0.656 1.857
end
</PRE>
<P>
<H1><A NAME="SECTION0043170000000000000000">
C.17 <IMG
WIDTH="32" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img24.gif"
ALT="$D_{5h}$"> cyclopentadiene anion</A>
</H1>
<P>
The <IMG
WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img344.gif"
ALT="$C_5$"> axis is the z axis (z is also the <IMG
WIDTH="21" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img350.gif"
ALT="$S_5$"> axis). The y axis is one
of the perpendicular <IMG
WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img339.gif"
ALT="$C_2$"> axes. The <IMG
WIDTH="21" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="img338.gif"
ALT="$\sigma_h$"> plane is the xy plane and
one of the <IMG
WIDTH="21" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="img345.gif"
ALT="$\sigma_d$"> planes is the yz plane.
<P>
<PRE>
charge -1
geometry units angstroms
symmetry d5h
c 0 1.1853 0
h 0 2.2654 0
end
</PRE>
<P>
<H1><A NAME="SECTION0043180000000000000000">
C.18 <IMG
WIDTH="32" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img25.gif"
ALT="$D_{4h}$"> gold tetrachloride</A>
</H1>
<P>
The <IMG
WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img349.gif"
ALT="$C_4$"> axis is the z axis (z is also the <IMG
WIDTH="21" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img11.gif"
ALT="$S_4$"> axis).
The <IMG
WIDTH="23" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img347.gif"
ALT="$C_2'$"> axes are the x and y axes and the <IMG
WIDTH="25" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img348.gif"
ALT="$C_2''$"> axes are the x=y axis
and the x=-y axis. The inversion center is the origin. The <IMG
WIDTH="21" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="img338.gif"
ALT="$\sigma_h$">
plane is the xy plane. The <IMG
WIDTH="21" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="img340.gif"
ALT="$\sigma_v$"> planes are the xz and yz planes and
the <IMG
WIDTH="21" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="img345.gif"
ALT="$\sigma_d$"> planes are 1) the plane containing the x=-y axis and the z axis
and 2) the plane containing the x=y axis and the z axis.
<P>
<PRE>
geometry units au
Au 0 0 0
Cl 0 4.033 0
symmetry D4h
end
</PRE>
<P>
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<ADDRESS>
Edoardo Apra
2004-05-25
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