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All results from a given calculation for C6H6 (Benzene)

using model chemistry: HSEh1PBE/6-31+G**

19 10 17 12 22

States and conformations

State Conformation minimum conformation conformer description state description
1 1 yes D6H 1A1g
Energy calculated at HSEh1PBE/6-31+G**
 hartrees
Energy at 0K-232.000761
Energy at 298.15K-232.007090
HF Energy-232.000761
Nuclear repulsion energy203.498133
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 HSEh1PBE/6-31+G**
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 3233 3087 0.00 425.61 0.12 0.22
2 A1g 1028 982 0.00 84.89 0.02 0.03
3 A2g 1374 1312 0.00 0.00 0.75 0.86
4 A2u 690 659 131.92 0.00 0.00 0.00
5 B1u 3198 3054 0.00 0.00 0.00 0.00
6 B1u 1016 970 0.00 0.00 0.00 0.00
7 B2g 1019 973 0.00 0.00 0.75 0.86
8 B2g 718 686 0.00 0.00 0.75 0.86
9 B2u 1385 1323 0.00 0.00 0.00 0.00
10 B2u 1176 1123 0.00 0.00 0.00 0.00
11 E1g 868 829 0.00 0.74 0.75 0.86
11 E1g 868 829 0.00 0.74 0.75 0.86
12 E1u 3224 3078 34.76 0.00 0.00 0.00
12 E1u 3224 3078 34.77 0.00 0.00 0.00
13 E1u 1521 1452 7.01 0.00 0.00 0.00
13 E1u 1521 1452 7.02 0.00 0.00 0.00
14 E1u 1072 1023 6.94 0.00 0.00 0.00
14 E1u 1072 1023 6.94 0.00 0.00 0.00
15 E2g 3208 3063 0.00 136.33 0.75 0.86
15 E2g 3208 3063 0.00 136.36 0.75 0.86
16 E2g 1667 1592 0.00 12.85 0.75 0.86
16 E2g 1667 1592 0.00 12.86 0.75 0.86
17 E2g 1201 1147 0.00 5.97 0.75 0.86
17 E2g 1201 1147 0.00 5.97 0.75 0.86
18 E2g 618 590 0.00 4.59 0.75 0.86
18 E2g 618 590 0.00 4.59 0.75 0.86
19 E2u 990 945 0.00 0.00 0.00 0.00
19 E2u 990 945 0.00 0.00 0.00 0.00
20 E2u 411 392 0.00 0.00 0.00 0.00
20 E2u 411 392 0.00 0.00 0.00 0.00

Unscaled Zero Point Vibrational Energy (zpe) 22197.9 cm-1
Scaled (by 0.9548) Zero Point Vibrational Energy (zpe) 21194.6 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 HSEh1PBE/6-31+G**
ABC
0.19030 0.19030 0.09515

See section I.F.4 to change rotational constant units
Geometric Data calculated at HSEh1PBE/6-31+G**

Point Group is D6h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
C1 0.000 1.394 0.000
C2 1.207 0.697 0.000
C3 1.207 -0.697 0.000
C4 0.000 -1.394 0.000
C5 -1.207 -0.697 0.000
C6 -1.207 0.697 0.000
H7 0.000 2.481 0.000
H8 2.148 1.240 0.000
H9 2.148 -1.240 0.000
H10 0.000 -2.481 0.000
H11 -2.148 -1.240 0.000
H12 -2.148 1.240 0.000

Atom - Atom Distances (Å)
  C1 C2 C3 C4 C5 C6 H7 H8 H9 H10 H11 H12
C11.39422.41492.78852.41491.39421.08642.15383.39943.87493.39942.1538
C21.39421.39422.41492.78852.41492.15381.08642.15383.39943.87493.3994
C32.41491.39421.39422.41492.78853.39942.15381.08642.15383.39943.8749
C42.78852.41491.39421.39422.41493.87493.39942.15381.08642.15383.3994
C52.41492.78852.41491.39421.39423.39943.87493.39942.15381.08642.1538
C61.39422.41492.78852.41491.39422.15383.39943.87493.39942.15381.0864
H71.08642.15383.39943.87493.39942.15382.48064.29664.96124.29662.4806
H82.15381.08642.15383.39943.87493.39942.48062.48064.29664.96124.2966
H93.39942.15381.08642.15383.39943.87494.29662.48062.48064.29664.9612
H103.87493.39942.15381.08642.15383.39944.96124.29662.48062.48064.2966
H113.39943.87493.39942.15381.08642.15384.29664.96124.29662.48062.4806
H122.15383.39943.87493.39942.15381.08642.48064.29664.96124.29662.4806

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 HSEh1PBE/6-31+G** Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 C -0.154      
2 C -0.154      
3 C -0.154      
4 C -0.154      
5 C -0.154      
6 C -0.154      
7 H 0.154      
8 H 0.154      
9 H 0.154      
10 H 0.154      
11 H 0.154      
12 H 0.154      


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 -31.666 0.000 0.000
y 0.000 -31.666 0.000
z 0.000 0.000 -40.235
Traceless
 xyz
x 4.285 0.000 0.000
y 0.000 4.285 0.000
z 0.000 0.000 -8.569
Polar
3z2-r2-17.138
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 11.526 0.000 0.000
y 0.000 11.527 0.000
z 0.000 0.000 5.965


<r2> (average value of r2) Å2
<r2> 128.464
(<r2>)1/2 11.334