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All results from a given calculation for C6H6 (Benzene)

using model chemistry: PBE1PBE/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 PBE1PBE/6-311+G(3df,2p)
 hartrees
Energy at 0K-232.034673
Energy at 298.15K-232.040992
HF Energy-232.034673
Nuclear repulsion energy204.385237
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 PBE1PBE/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 3211 3211 0.00 407.22 0.10 0.18
2 A1g 1028 1028 0.00 86.70 0.02 0.04
3 A2g 1372 1372 0.00 0.00 0.75 0.86
4 A2u 691 691 112.55 0.00 0.00 0.00
5 B1u 3170 3170 0.00 0.00 0.00 0.00
6 B1u 919 919 0.00 0.00 0.00 0.00
7 B2g 1026 1026 0.00 0.00 0.75 0.86
8 B2g 703 703 0.00 0.00 0.75 0.86
9 B2u 1365 1365 0.00 0.00 0.00 0.00
10 B2u 1169 1169 0.00 0.00 0.00 0.00
11 E1g 872 872 0.00 1.00 0.75 0.86
11 E1g 872 872 0.00 0.98 0.75 0.86
12 E1u 3201 3201 28.11 0.00 0.00 0.00
12 E1u 3201 3201 28.11 0.00 0.00 0.00
13 E1u 1515 1515 7.53 0.00 0.00 0.00
13 E1u 1515 1515 7.53 0.00 0.00 0.00
14 E1u 1069 1069 5.72 0.00 0.00 0.00
14 E1u 1069 1069 5.72 0.00 0.00 0.00
15 E2g 3185 3185 0.00 122.74 0.75 0.86
15 E2g 3185 3185 0.00 122.73 0.75 0.86
16 E2g 1657 1657 0.00 12.31 0.75 0.86
16 E2g 1657 1657 0.00 12.30 0.75 0.86
17 E2g 1197 1197 0.00 5.76 0.75 0.86
17 E2g 1197 1197 0.00 5.77 0.75 0.86
18 E2g 613 613 0.00 3.11 0.75 0.86
18 E2g 613 613 0.00 3.11 0.75 0.86
19 E2u 1001 1001 0.00 0.00 0.00 0.00
19 E2u 1001 1001 0.00 0.00 0.00 0.00
20 E2u 409 409 0.00 0.00 0.00 0.00
20 E2u 409 409 0.00 0.00 0.00 0.00

Unscaled Zero Point Vibrational Energy (zpe) 22044.6 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 22044.6 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 PBE1PBE/6-311+G(3df,2p)
ABC
0.19201 0.19201 0.09600

See section I.F.4 to change rotational constant units
Geometric Data calculated at PBE1PBE/6-311+G(3df,2p)

Point Group is D6h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
C1 0.000 1.388 0.000
C2 1.202 0.694 0.000
C3 1.202 -0.694 0.000
C4 0.000 -1.388 0.000
C5 -1.202 -0.694 0.000
C6 -1.202 0.694 0.000
H7 0.000 2.471 0.000
H8 2.140 1.236 0.000
H9 2.140 -1.236 0.000
H10 0.000 -2.471 0.000
H11 -2.140 -1.236 0.000
H12 -2.140 1.236 0.000

Atom - Atom Distances (Å)
  C1 C2 C3 C4 C5 C6 H7 H8 H9 H10 H11 H12
C11.38772.40362.77552.40361.38771.08372.14573.38583.85913.38582.1457
C21.38771.38772.40362.77552.40362.14571.08372.14573.38583.85913.3858
C32.40361.38771.38772.40362.77553.38582.14571.08372.14573.38583.8591
C42.77552.40361.38771.38772.40363.85913.38582.14571.08372.14573.3858
C52.40362.77552.40361.38771.38773.38583.85913.38582.14571.08372.1457
C61.38772.40362.77552.40361.38772.14573.38583.85913.38582.14571.0837
H71.08372.14573.38583.85913.38582.14572.47144.28064.94284.28062.4714
H82.14571.08372.14573.38583.85913.38582.47142.47144.28064.94284.2806
H93.38582.14571.08372.14573.38583.85914.28062.47142.47144.28064.9428
H103.85913.38582.14571.08372.14573.38584.94284.28062.47142.47144.2806
H113.38583.85913.38582.14571.08372.14574.28064.94284.28062.47142.4714
H122.14573.38583.85913.38582.14571.08372.47144.28064.94284.28062.4714

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 PBE1PBE/6-311+G(3df,2p) 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 -31.708 0.000 0.000
y 0.000 -31.708 0.000
z 0.000 0.000 -39.915
Traceless
 xyz
x 4.103 0.000 0.000
y 0.000 4.103 0.000
z 0.000 0.000 -8.206
Polar
3z2-r2-16.413
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 11.824 0.000 0.000
y 0.000 11.824 0.000
z 0.000 0.000 6.500


<r2> (average value of r2) Å2
<r2> 127.489
(<r2>)1/2 11.291