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All results from a given calculation for C6H6 (Benzene)

using model chemistry: HSEh1PBE/3-21G

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/3-21G
 hartrees
Energy at 0K-230.710564
Energy at 298.15K-230.717027
HF Energy-230.710564
Nuclear repulsion energy203.570980
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/3-21G
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 3245 3125 0.00 312.65 0.10 0.18
2 A1g 1029 992 0.00 50.88 0.11 0.20
3 A2g 1433 1381 0.00 0.00 0.75 0.86
4 A2u 703 677 139.92 0.00 0.00 0.00
5 B1u 3205 3088 0.00 0.00 0.00 0.00
6 B1u 1067 1027 0.00 0.00 0.00 0.00
7 B2g 1058 1020 0.00 0.00 0.75 0.86
8 B2g 759 731 0.00 0.00 0.75 0.86
9 B2u 1349 1299 0.00 0.00 0.00 0.00
10 B2u 1231 1186 0.00 0.00 0.00 0.00
11 E1g 886 853 0.00 5.62 0.75 0.86
11 E1g 886 853 0.00 5.62 0.75 0.86
12 E1u 3231 3113 25.38 0.00 0.00 0.00
12 E1u 3231 3113 25.37 0.00 0.00 0.00
13 E1u 1545 1488 14.23 0.00 0.00 0.00
13 E1u 1545 1488 14.23 0.00 0.00 0.00
14 E1u 1079 1040 5.11 0.00 0.00 0.00
14 E1u 1079 1040 5.11 0.00 0.00 0.00
15 E2g 3215 3097 0.00 115.13 0.75 0.86
15 E2g 3215 3097 0.00 115.13 0.75 0.86
16 E2g 1650 1589 0.00 11.63 0.75 0.86
16 E2g 1650 1589 0.00 11.63 0.75 0.86
17 E2g 1243 1197 0.00 7.91 0.75 0.86
17 E2g 1243 1197 0.00 7.90 0.75 0.86
18 E2g 648 624 0.00 3.47 0.75 0.86
18 E2g 648 624 0.00 3.47 0.75 0.86
19 E2u 1018 981 0.00 0.00 0.00 0.00
19 E2u 1018 981 0.00 0.00 0.00 0.00
20 E2u 422 407 0.00 0.00 0.00 0.00
20 E2u 422 407 0.00 0.00 0.00 0.00

Unscaled Zero Point Vibrational Energy (zpe) 22474.6 cm-1
Scaled (by 0.9633) Zero Point Vibrational Energy (zpe) 21649.8 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 HSEh1PBE/3-21G
ABC
0.19040 0.19040 0.09520

See section I.F.4 to change rotational constant units
Geometric Data calculated at HSEh1PBE/3-21G

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 2.479 0.000
H8 2.147 1.239 0.000
H9 2.147 -1.239 0.000
H10 0.000 -2.479 0.000
H11 -2.147 -1.239 0.000
H12 -2.147 1.239 0.000

Atom - Atom Distances (Å)
  C1 C2 C3 C4 C5 C6 H7 H8 H9 H10 H11 H12
C11.39412.41462.78822.41461.39411.08452.15213.39743.87273.39742.1521
C21.39411.39412.41462.78812.41462.15211.08452.15213.39743.87273.3974
C32.41461.39411.39412.41462.78813.39742.15211.08452.15213.39743.8727
C42.78822.41461.39411.39412.41463.87273.39742.15211.08452.15213.3974
C52.41462.78812.41461.39411.39413.39743.87273.39742.15211.08452.1521
C61.39412.41462.78812.41461.39412.15213.39743.87273.39742.15211.0845
H71.08452.15213.39743.87273.39742.15212.47864.29314.95724.29312.4786
H82.15211.08452.15213.39743.87273.39742.47862.47864.29314.95724.2931
H93.39742.15211.08452.15213.39743.87274.29312.47862.47864.29314.9572
H103.87273.39742.15211.08452.15213.39744.95724.29312.47862.47864.2931
H113.39743.87273.39742.15211.08452.15214.29314.95724.29312.47862.4786
H122.15213.39743.87273.39742.15211.08452.47864.29314.95724.29312.4786

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/3-21G Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 C -0.219      
2 C -0.219      
3 C -0.219      
4 C -0.219      
5 C -0.219      
6 C -0.219      
7 H 0.219      
8 H 0.219      
9 H 0.219      
10 H 0.219      
11 H 0.219      
12 H 0.219      


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 -30.758 0.000 0.000
y 0.000 -30.758 0.000
z 0.000 0.000 -40.220
Traceless
 xyz
x 4.731 0.000 0.000
y 0.000 4.731 0.000
z 0.000 0.000 -9.462
Polar
3z2-r2-18.925
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 9.936 0.000 0.000
y 0.000 9.936 0.000
z 0.000 0.000 2.271


<r2> (average value of r2) Å2
<r2> 128.006
(<r2>)1/2 11.314