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All results from a given calculation for C6H6 (Benzene)

using model chemistry: PBEPBE/3-21G

19 10 17 12 22

States and conformations

State Conformation minimum conformation conformer description state description
1 1 yes D6H 1A1g
Energy calculated at PBEPBE/3-21G
 hartrees
Energy at 0K-230.663502
Energy at 298.15K-230.669777
HF Energy-230.663502
Nuclear repulsion energy201.946707
The energy at 298.15K was derived from the energy at 0K and an integrated heat capacity that used the calculated vibrational frequencies.
Vibrational Frequencies calculated at PBEPBE/3-21G
Mode Number Symmetry Frequency
(cm-1)
Scaled Frequency
(cm-1)
IR Intensities
(km mol-1)
Raman Act
4/u)
Dep P Dep U
1 A1g 3151 3123 0.00 327.89 0.10 0.18
2 A1g 993 984 0.00 50.89 0.11 0.20
3 A2g 1385 1372 0.00 0.00 0.75 0.86
4 A2u 670 664 125.58 0.00 0.00 0.00
5 B1u 3112 3084 0.00 0.00 0.00 0.00
6 B1u 1028 1019 0.00 0.00 0.00 0.00
7 B2g 999 989 0.00 0.00 0.75 0.86
8 B2g 729 722 0.00 0.00 0.75 0.86
9 B2u 1319 1307 0.00 0.00 0.00 0.00
10 B2u 1194 1183 0.00 0.00 0.00 0.00
11 E1g 841 833 0.00 6.63 0.75 0.86
11 E1g 841 833 0.00 6.63 0.75 0.86
12 E1u 3138 3109 30.32 0.00 0.00 0.00
12 E1u 3138 3109 30.32 0.00 0.00 0.00
13 E1u 1490 1477 11.60 0.00 0.00 0.00
13 E1u 1490 1477 11.60 0.00 0.00 0.00
14 E1u 1043 1034 4.67 0.00 0.00 0.00
14 E1u 1043 1034 4.67 0.00 0.00 0.00
15 E2g 3121 3093 0.00 121.33 0.75 0.86
15 E2g 3121 3093 0.00 121.33 0.75 0.86
16 E2g 1582 1567 0.00 11.53 0.75 0.86
16 E2g 1582 1567 0.00 11.53 0.75 0.86
17 E2g 1203 1192 0.00 8.83 0.75 0.86
17 E2g 1203 1192 0.00 8.83 0.75 0.86
18 E2g 625 619 0.00 3.44 0.75 0.86
18 E2g 625 619 0.00 3.44 0.75 0.86
19 E2u 960 951 0.00 0.00 0.00 0.00
19 E2u 960 951 0.00 0.00 0.00 0.00
20 E2u 404 400 0.00 0.00 0.00 0.00
20 E2u 404 400 0.00 0.00 0.00 0.00

Unscaled Zero Point Vibrational Energy (zpe) 21695.6 cm-1
Scaled (by 0.9909) Zero Point Vibrational Energy (zpe) 21498.2 cm-1
See section III.C.1 List or set vibrational scaling factors to change the scale factors used here.
See section III.C.2 Calculate a vibrational scaling factor for a given set of molecules to determine the least squares best scaling factor.
Rotational Constants (cm-1) from geometry optimized at PBEPBE/3-21G
ABC
0.18737 0.18737 0.09368

See section I.F.4 to change rotational constant units
Geometric Data calculated at PBEPBE/3-21G

Point Group is D6h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
C1 0.000 1.405 0.000
C2 1.217 0.703 0.000
C3 1.217 -0.703 0.000
C4 0.000 -1.405 0.000
C5 -1.217 -0.703 0.000
C6 -1.217 0.703 0.000
H7 0.000 2.498 0.000
H8 2.164 1.249 0.000
H9 2.164 -1.249 0.000
H10 0.000 -2.498 0.000
H11 -2.164 -1.249 0.000
H12 -2.164 1.249 0.000

Atom - Atom Distances (Å)
  C1 C2 C3 C4 C5 C6 H7 H8 H9 H10 H11 H12
C11.40532.43412.81062.43411.40531.09322.16943.42473.90383.42472.1694
C21.40531.40532.43412.81062.43412.16941.09322.16943.42473.90383.4247
C32.43411.40531.40532.43412.81063.42472.16941.09322.16943.42473.9038
C42.81062.43411.40531.40532.43413.90383.42472.16941.09322.16943.4247
C52.43412.81062.43411.40531.40533.42473.90383.42472.16941.09322.1694
C61.40532.43412.81062.43411.40532.16943.42473.90383.42472.16941.0932
H71.09322.16943.42473.90383.42472.16942.49854.32754.99704.32752.4985
H82.16941.09322.16943.42473.90383.42472.49852.49854.32754.99704.3275
H93.42472.16941.09322.16943.42473.90384.32752.49852.49854.32754.9970
H103.90383.42472.16941.09322.16943.42474.99704.32752.49852.49854.3275
H113.42473.90383.42472.16941.09322.16944.32754.99704.32752.49852.4985
H122.16943.42473.90383.42472.16941.09322.49854.32754.99704.32752.4985

picture of Benzene state 1 conformation 1
More geometry information
Calculated Bond Angles
atom1 atom2 atom3 angle atom1 atom2 atom3 angle
C1 C2 C3 120.000 C1 C2 H8 120.000
C1 C6 C5 120.000 C1 C6 H12 120.000
C2 C1 C6 120.000 C2 C1 H7 120.000
C2 C3 C4 120.000 C2 C3 H9 120.000
C3 C2 H8 120.000 C3 C4 C5 120.000
C3 C4 H10 120.000 C4 C3 H9 120.000
C4 C5 C6 120.000 C4 C5 H11 120.000
C5 C4 H10 120.000 C5 C6 H12 120.000
C6 C1 H7 120.000 C6 C5 H11 120.000
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at PBEPBE/3-21G Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 C -0.197      
2 C -0.197      
3 C -0.197      
4 C -0.197      
5 C -0.197      
6 C -0.197      
7 H 0.197      
8 H 0.197      
9 H 0.197      
10 H 0.197      
11 H 0.197      
12 H 0.197      


Electric dipole moments
Electric dipole components in Debye
(What's a Debye? See section VII.A.3)
  x y z Total
  0.000 0.000 0.000 0.000
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -30.905 0.000 0.000
y 0.000 -30.905 0.000
z 0.000 0.000 -40.093
Traceless
 xyz
x 4.594 0.000 0.000
y 0.000 4.594 0.000
z 0.000 0.000 -9.188
Polar
3z2-r2-18.376
x2-y20.000
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 10.235 0.000 0.000
y 0.000 10.235 0.000
z 0.000 0.000 2.337


<r2> (average value of r2) Å2
<r2> 129.766
(<r2>)1/2 11.392