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All results from a given calculation for C6H6 (Benzene)

using model chemistry: PBEPBE/6-311G**

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/6-311G**
 hartrees
Energy at 0K-231.991990
Energy at 298.15K-231.998177
HF Energy-231.991990
Nuclear repulsion energy202.615283
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/6-311G**
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 3128 3099 0.00 434.39 0.12 0.22
2 A1g 995 986 0.00 58.73 0.09 0.16
3 A2g 1329 1317 0.00 0.00 0.75 0.86
4 A2u 662 656 108.04 0.00 0.00 0.00
5 B1u 3092 3064 0.00 0.00 0.00 0.00
6 B1u 988 979 0.00 0.00 0.00 0.00
7 B2g 975 966 0.00 0.00 0.75 0.86
8 B2g 702 696 0.00 0.00 0.75 0.86
9 B2u 1347 1335 0.00 0.00 0.00 0.00
10 B2u 1141 1130 0.00 0.00 0.00 0.00
11 E1g 830 822 0.00 1.45 0.75 0.86
11 E1g 830 822 0.00 1.45 0.75 0.86
12 E1u 3117 3089 40.88 0.00 0.00 0.00
12 E1u 3117 3089 40.88 0.00 0.00 0.00
13 E1u 1465 1452 7.65 0.00 0.00 0.00
13 E1u 1465 1452 7.65 0.00 0.00 0.00
14 E1u 1036 1026 5.81 0.00 0.00 0.00
14 E1u 1036 1026 5.81 0.00 0.00 0.00
15 E2g 3102 3074 0.00 152.16 0.75 0.86
15 E2g 3102 3074 0.00 152.16 0.75 0.86
16 E2g 1596 1582 0.00 8.61 0.75 0.86
16 E2g 1596 1582 0.00 8.61 0.75 0.86
17 E2g 1163 1152 0.00 7.54 0.75 0.86
17 E2g 1163 1152 0.00 7.54 0.75 0.86
18 E2g 601 596 0.00 3.81 0.75 0.86
18 E2g 601 596 0.00 3.80 0.75 0.86
19 E2u 939 931 0.00 0.00 0.00 0.00
19 E2u 939 931 0.00 0.00 0.00 0.00
20 E2u 395 392 0.00 0.00 0.00 0.00
20 E2u 395 392 0.00 0.00 0.00 0.00

Unscaled Zero Point Vibrational Energy (zpe) 21423.6 cm-1
Scaled (by 0.9909) Zero Point Vibrational Energy (zpe) 21228.7 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/6-311G**
ABC
0.18869 0.18869 0.09434

See section I.F.4 to change rotational constant units
Geometric Data calculated at PBEPBE/6-311G**

Point Group is D6h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
C1 0.000 1.400 0.000
C2 1.212 0.700 0.000
C3 1.212 -0.700 0.000
C4 0.000 -1.400 0.000
C5 -1.212 -0.700 0.000
C6 -1.212 0.700 0.000
H7 0.000 2.493 0.000
H8 2.159 1.246 0.000
H9 2.159 -1.246 0.000
H10 0.000 -2.493 0.000
H11 -2.159 -1.246 0.000
H12 -2.159 1.246 0.000

Atom - Atom Distances (Å)
  C1 C2 C3 C4 C5 C6 H7 H8 H9 H10 H11 H12
C11.40002.42482.79992.42481.40001.09272.16423.41513.89263.41512.1642
C21.40001.40002.42482.79992.42482.16421.09272.16423.41513.89263.4151
C32.42481.40001.40002.42482.79993.41512.16421.09272.16423.41513.8926
C42.79992.42481.40001.40002.42483.89263.41512.16421.09272.16423.4151
C52.42482.79992.42481.40001.40003.41513.89263.41512.16421.09272.1642
C61.40002.42482.79992.42481.40002.16423.41513.89263.41512.16421.0927
H71.09272.16423.41513.89263.41512.16422.49274.31744.98534.31742.4927
H82.16421.09272.16423.41513.89263.41512.49272.49274.31744.98534.3174
H93.41512.16421.09272.16423.41513.89264.31742.49272.49274.31744.9853
H103.89263.41512.16421.09272.16423.41514.98534.31742.49272.49274.3174
H113.41513.89263.41512.16421.09272.16424.31744.98534.31742.49272.4927
H122.16423.41513.89263.41512.16421.09272.49274.31744.98534.31742.4927

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/6-311G** Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 C -0.097      
2 C -0.097      
3 C -0.097      
4 C -0.097      
5 C -0.097      
6 C -0.097      
7 H 0.097      
8 H 0.097      
9 H 0.097      
10 H 0.097      
11 H 0.097      
12 H 0.097      


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 -31.726 0.000 0.000
y 0.000 -31.726 0.000
z 0.000 0.000 -39.593
Traceless
 xyz
x 3.934 0.000 0.000
y 0.000 3.934 0.000
z 0.000 0.000 -7.867
Polar
3z2-r2-15.735
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 11.349 0.000 0.000
y 0.000 11.349 0.000
z 0.000 0.000 4.234


<r2> (average value of r2) Å2
<r2> 129.289
(<r2>)1/2 11.371