return to home page Computational Chemistry Comparison and Benchmark DataBase Release 22 (May 2022) Standard Reference Database 101 National Institute of Standards and Technology
You are here: Calculated > Energy > Optimized > Energy

All results from a given calculation for C6H6 (Benzene)

using model chemistry: PBEPBE/6-31G(2df,p)

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/6-31G(2df,p)
 hartrees
Energy at 0K-231.950791
Energy at 298.15K-231.956953
HF Energy-231.950791
Nuclear repulsion energy202.566825
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/6-31G(2df,p)
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 3136 3104 0.00 385.53 0.10 0.19
2 A1g 997 987 0.00 54.79 0.08 0.15
3 A2g 1310 1297 0.00 0.00 0.75 0.86
4 A2u 671 664 70.37 0.00 0.00 0.00
5 B1u 3100 3068 0.00 0.00 0.00 0.00
6 B1u 981 971 0.00 0.00 0.00 0.00
7 B2g 969 959 0.00 0.00 0.75 0.86
8 B2g 701 694 0.00 0.00 0.75 0.86
9 B2u 1351 1337 0.00 0.00 0.00 0.00
10 B2u 1137 1125 0.00 0.00 0.00 0.00
11 E1g 839 830 0.00 4.73 0.75 0.86
11 E1g 839 830 0.00 4.73 0.75 0.86
12 E1u 3126 3093 36.93 0.00 0.00 0.00
12 E1u 3126 3093 36.93 0.00 0.00 0.00
13 E1u 1465 1449 6.82 0.00 0.00 0.00
13 E1u 1465 1449 6.82 0.00 0.00 0.00
14 E1u 1037 1027 3.64 0.00 0.00 0.00
14 E1u 1037 1027 3.64 0.00 0.00 0.00
15 E2g 3110 3078 0.00 134.16 0.75 0.86
15 E2g 3110 3078 0.00 134.16 0.75 0.86
16 E2g 1593 1577 0.00 8.94 0.75 0.86
16 E2g 1593 1577 0.00 8.94 0.75 0.86
17 E2g 1163 1151 0.00 10.67 0.75 0.86
17 E2g 1163 1151 0.00 10.67 0.75 0.86
18 E2g 595 589 0.00 3.11 0.75 0.86
18 E2g 595 589 0.00 3.11 0.75 0.86
19 E2u 922 912 0.00 0.00 0.00 0.00
19 E2u 922 912 0.00 0.00 0.00 0.00
20 E2u 395 391 0.00 0.00 0.00 0.00
20 E2u 395 391 0.00 0.00 0.00 0.00

Unscaled Zero Point Vibrational Energy (zpe) 21421.4 cm-1
Scaled (by 0.9897) Zero Point Vibrational Energy (zpe) 21200.8 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/6-31G(2df,p)
ABC
0.18861 0.18861 0.09430

See section I.F.4 to change rotational constant units
Geometric Data calculated at PBEPBE/6-31G(2df,p)

Point Group is D6h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
C1 0.000 1.400 0.000
C2 1.213 0.700 0.000
C3 1.213 -0.700 0.000
C4 0.000 -1.400 0.000
C5 -1.213 -0.700 0.000
C6 -1.213 0.700 0.000
H7 0.000 2.494 0.000
H8 2.160 1.247 0.000
H9 2.160 -1.247 0.000
H10 0.000 -2.494 0.000
H11 -2.160 -1.247 0.000
H12 -2.160 1.247 0.000

Atom - Atom Distances (Å)
  C1 C2 C3 C4 C5 C6 H7 H8 H9 H10 H11 H12
C11.40022.42522.80042.42521.40021.09342.16503.41623.89383.41622.1650
C21.40021.40022.42522.80042.42522.16501.09342.16503.41623.89383.4162
C32.42521.40021.40022.42522.80043.41622.16501.09342.16503.41623.8938
C42.80042.42521.40021.40022.42523.89383.41622.16501.09342.16503.4162
C52.42522.80042.42521.40021.40023.41623.89383.41622.16501.09342.1650
C61.40022.42522.80042.42521.40022.16503.41623.89383.41622.16501.0934
H71.09342.16503.41623.89383.41622.16502.49364.31914.98724.31912.4936
H82.16501.09342.16503.41623.89383.41622.49362.49364.31914.98724.3191
H93.41622.16501.09342.16503.41623.89384.31912.49362.49364.31914.9872
H103.89383.41622.16501.09342.16503.41624.98724.31912.49362.49364.3191
H113.41623.89383.41622.16501.09342.16504.31914.98724.31912.49362.4936
H122.16503.41623.89383.41622.16501.09342.49364.31914.98724.31912.4936

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/6-31G(2df,p) Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 C -0.100      
2 C -0.100      
3 C -0.100      
4 C -0.100      
5 C -0.100      
6 C -0.100      
7 H 0.100      
8 H 0.100      
9 H 0.100      
10 H 0.100      
11 H 0.100      
12 H 0.100      


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 -31.414 0.000 0.000
y 0.000 -31.414 0.000
z 0.000 0.000 -38.304
Traceless
 xyz
x 3.445 0.000 0.000
y 0.000 3.445 0.000
z 0.000 0.000 -6.890
Polar
3z2-r2-13.780
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 11.043 0.000 0.000
y 0.000 11.043 0.000
z 0.000 0.000 3.960


<r2> (average value of r2) Å2
<r2> 128.943
(<r2>)1/2 11.355