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All results from a given calculation for C6H6 (Benzene)

using model chemistry: PBEPBEultrafine/6-311+G(3df,2p)

19 10 17 12 22

States and conformations

State Conformation minimum conformation conformer description state description
1 1 yes D6H 1A1g
Energy calculated at PBEPBEultrafine/6-311+G(3df,2p)
 hartrees
Energy at 0K-232.009065
Energy at 298.15K-232.015218
HF Energy-232.009065
Nuclear repulsion energy202.991467
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 PBEPBEultrafine/6-311+G(3df,2p)
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 3121 3121 0.00 447.69 0.10 0.18
2 A1g 994 994 0.00 88.47 0.02 0.03
3 A2g 1327 1327 0.00 0.00 0.75 0.86
4 A2u 663 663 105.38 0.00 0.00 0.00
5 B1u 3081 3081 0.00 0.00 0.00 0.00
6 B1u 883 883 0.00 0.00 0.00 0.00
7 B2g 980 980 0.00 0.00 0.75 0.86
8 B2g 683 683 0.00 0.00 0.75 0.86
9 B2u 1342 1342 0.00 0.00 0.00 0.00
10 B2u 1138 1138 0.00 0.00 0.00 0.00
11 E1g 836 836 0.00 0.72 0.75 0.86
11 E1g 836 836 0.00 0.74 0.75 0.86
12 E1u 3111 3111 33.60 0.00 0.00 0.00
12 E1u 3111 3111 33.60 0.00 0.00 0.00
13 E1u 1463 1463 5.88 0.00 0.00 0.00
13 E1u 1463 1463 5.88 0.00 0.00 0.00
14 E1u 1035 1035 5.60 0.00 0.00 0.00
14 E1u 1035 1035 5.60 0.00 0.00 0.00
15 E2g 3095 3095 0.00 135.03 0.75 0.86
15 E2g 3095 3095 0.00 135.03 0.75 0.86
16 E2g 1588 1588 0.00 11.68 0.75 0.86
16 E2g 1588 1588 0.00 11.65 0.75 0.86
17 E2g 1161 1161 0.00 6.41 0.75 0.86
17 E2g 1161 1161 0.00 6.40 0.75 0.86
18 E2g 595 595 0.00 3.07 0.75 0.86
18 E2g 595 595 0.00 3.07 0.75 0.86
19 E2u 955 955 0.00 0.00 0.00 0.00
19 E2u 955 955 0.00 0.00 0.00 0.00
20 E2u 393 393 0.00 0.00 0.00 0.00
20 E2u 393 393 0.00 0.00 0.00 0.00

Unscaled Zero Point Vibrational Energy (zpe) 21338.8 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 21338.8 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 PBEPBEultrafine/6-311+G(3df,2p)
ABC
0.18940 0.18940 0.09470

See section I.F.4 to change rotational constant units
Geometric Data calculated at PBEPBEultrafine/6-311+G(3df,2p)

Point Group is D6h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
C1 0.000 1.397 0.000
C2 1.210 0.699 0.000
C3 1.210 -0.699 0.000
C4 0.000 -1.397 0.000
C5 -1.210 -0.699 0.000
C6 -1.210 0.699 0.000
H7 0.000 2.488 0.000
H8 2.155 1.244 0.000
H9 2.155 -1.244 0.000
H10 0.000 -2.488 0.000
H11 -2.155 -1.244 0.000
H12 -2.155 1.244 0.000

Atom - Atom Distances (Å)
  C1 C2 C3 C4 C5 C6 H7 H8 H9 H10 H11 H12
C11.39732.42012.79452.42011.39731.09112.16043.40903.88563.40902.1604
C21.39731.39732.42012.79452.42022.16041.09112.16043.40903.88563.4090
C32.42011.39731.39732.42022.79453.40902.16041.09112.16043.40903.8856
C42.79452.42011.39731.39732.42013.88563.40902.16041.09112.16043.4090
C52.42012.79452.42021.39731.39733.40903.88563.40902.16041.09112.1604
C61.39732.42022.79452.42011.39732.16043.40903.88563.40902.16041.0911
H71.09112.16043.40903.88563.40902.16042.48834.30994.97674.30992.4883
H82.16041.09112.16043.40903.88563.40902.48832.48834.30994.97674.3099
H93.40902.16041.09112.16043.40903.88564.30992.48832.48834.30994.9767
H103.88563.40902.16041.09112.16043.40904.97674.30992.48832.48834.3099
H113.40903.88563.40902.16041.09112.16044.30994.97674.30992.48832.4883
H122.16043.40903.88563.40902.16041.09112.48834.30994.97674.30992.4883

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 PBEPBEultrafine/6-311+G(3df,2p) Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 C -0.096      
2 C -0.096      
3 C -0.096      
4 C -0.096      
5 C -0.096      
6 C -0.096      
7 H 0.096      
8 H 0.096      
9 H 0.096      
10 H 0.096      
11 H 0.096      
12 H 0.096      


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 -32.195 0.000 0.000
y 0.000 -32.195 0.000
z 0.000 0.000 -39.980
Traceless
 xyz
x 3.892 0.000 0.000
y 0.000 3.892 0.000
z 0.000 0.000 -7.785
Polar
3z2-r2-15.570
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 12.292 0.000 0.000
y 0.000 12.292 0.000
z 0.000 0.000 6.659


<r2> (average value of r2) Å2
<r2> 129.166
(<r2>)1/2 11.365