return to home page Computational Chemistry Comparison and Benchmark DataBase Release 22 (May 2022) Standard Reference Database 101 National Institute of Standards and Technology
You are here: Calculated > Energy > Optimized > Energy

All results from a given calculation for S4 (Sulfur tetramer)

using model chemistry: B97D3/3-21G*

19 10 17 12 22

States and conformations

State Conformation minimum conformation conformer description state description
1 1 no D2D 1A1
1 2 no C2V 1A1
1 3 yes D2H 1AG

Conformer 1 (D2D)

Jump to S1C2 S1C3
Energy calculated at B97D3/3-21G*
 hartrees
Energy at 0K-1585.296734
Energy at 298.15K 
HF Energy-1585.296734
Nuclear repulsion energy341.496864
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 B97D3/3-21G*
Mode Number Symmetry Frequency
(cm-1)
Scaled Frequency
(cm-1)
IR Intensities
(km mol-1)
Raman Act
4/u)
Dep P Dep U
1 A1 432 432 0.00 45.88 0.07 0.13
2 A1 187 187 0.00 4.23 0.75 0.86
3 B1 329 329 0.00 33.82 0.75 0.86
4 B2 295 295 0.29 15.38 0.75 0.86
5 E 310 310 0.78 5.89 0.75 0.86
5 E 310 310 0.78 5.89 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 930.8 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 930.8 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 B97D3/3-21G*
ABC
0.11156 0.11156 0.06112

See section I.F.4 to change rotational constant units
Geometric Data calculated at B97D3/3-21G*

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.469 0.321
S2 0.000 -1.469 0.321
S3 -1.469 0.000 -0.321
S4 1.469 0.000 -0.321

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.93712.17402.1740
S22.93712.17402.1740
S32.17402.17402.9371
S42.17402.17402.9371

picture of Sulfur tetramer state 1 conformation 1
More geometry information
Calculated Bond Angles
atom1 atom2 atom3 angle atom1 atom2 atom3 angle
S1 S2 S4 47.508 S1 S3 S4 47.508
S2 S1 S3 47.508 S2 S4 S3 47.508
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B97D3/3-21G* Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.000      
2 S 0.000      
3 S 0.000      
4 S 0.000      


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 -49.721 0.000 0.000
y 0.000 -49.721 0.000
z 0.000 0.000 -55.000
Traceless
 xyz
x 2.640 0.000 0.000
y 0.000 2.640 0.000
z 0.000 0.000 -5.279
Polar
3z2-r2-10.558
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 10.546 0.000 0.000
y 0.000 10.546 0.000
z 0.000 0.000 4.863


<r2> (average value of r2) Å2
<r2> 176.789
(<r2>)1/2 13.296

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at B97D3/3-21G*
 hartrees
Energy at 0K-1585.359419
Energy at 298.15K 
HF Energy-1585.359419
Nuclear repulsion energy325.837758
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 B97D3/3-21G*
Mode Number Symmetry Frequency
(cm-1)
Scaled Frequency
(cm-1)
IR Intensities
(km mol-1)
Raman Act
4/u)
Dep P Dep U
1 A1 702 702 0.00 32.10 0.29 0.44
2 A1 248 248 0.00 27.24 0.27 0.42
3 A1 49 49 8.80 0.00 0.48 0.65
4 A2 223 223 0.00 0.00 0.75 0.86
5 B2 661 661 103.95 0.00 0.75 0.86
6 B2 316 316 0.00 17.11 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1099.5 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1099.5 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 B97D3/3-21G*
ABC
0.14422 0.07411 0.04896

See section I.F.4 to change rotational constant units
Geometric Data calculated at B97D3/3-21G*

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.334 0.956
S2 0.000 -1.334 0.956
S3 0.000 1.334 -0.956
S4 0.000 -1.334 -0.956

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.66741.91203.2818
S22.66743.28181.9120
S31.91203.28182.6672
S43.28181.91202.6672

picture of Sulfur tetramer state 1 conformation 2
More geometry information
Calculated Bond Angles
atom1 atom2 atom3 angle atom1 atom2 atom3 angle
S1 S2 S4 89.998 S1 S3 S4 90.002
S2 S1 S3 89.998 S2 S4 S3 90.002
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B97D3/3-21G* Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S -0.000      
2 S -0.000      
3 S 0.000      
4 S 0.000      


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 -51.679 0.000 0.000
y 0.000 -52.911 0.000
z 0.000 0.000 -49.103
Traceless
 xyz
x -0.672 0.000 0.000
y 0.000 -2.520 0.000
z 0.000 0.000 3.192
Polar
3z2-r26.383
x2-y21.232
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 3.859 0.000 0.000
y 0.000 16.203 0.000
z 0.000 0.000 11.513


<r2> (average value of r2) Å2
<r2> 204.322
(<r2>)1/2 14.294

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at B97D3/3-21G*
 hartrees
Energy at 0K-1585.359419
Energy at 298.15K 
HF Energy-1585.359419
Nuclear repulsion energy325.857072
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 B97D3/3-21G*
Mode Number Symmetry Frequency
(cm-1)
Scaled Frequency
(cm-1)
IR Intensities
(km mol-1)
Raman Act
4/u)
Dep P Dep U
1 Ag 702 702 0.00 32.10 0.29 0.44
2 Ag 248 248 0.00 27.24 0.27 0.42
3 Au 223 223 0.00 0.00 0.00 0.00
4 B1u 661 661 103.96 0.00 0.00 0.00
5 B2u 49 49 8.81 0.00 0.00 0.00
6 B3g 316 316 0.00 17.11 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1099.7 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1099.7 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 B97D3/3-21G*
ABC
0.14423 0.07412 0.04896

See section I.F.4 to change rotational constant units
Geometric Data calculated at B97D3/3-21G*

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.956 1.334
S2 0.000 0.956 -1.334
S3 0.000 -0.956 1.334
S4 0.000 -0.956 -1.334

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.66711.91203.2816
S22.66713.28161.9120
S31.91203.28162.6671
S43.28161.91202.6671

picture of Sulfur tetramer state 1 conformation 3
More geometry information
Calculated Bond Angles
atom1 atom2 atom3 angle atom1 atom2 atom3 angle
S1 S2 S4 90.000 S1 S3 S4 90.000
S2 S1 S3 90.000 S2 S4 S3 90.000
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B97D3/3-21G* Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.000      
2 S 0.000      
3 S 0.000      
4 S 0.000      


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 -51.678 0.000 0.000
y 0.000 -49.103 0.000
z 0.000 0.000 -52.911
Traceless
 xyz
x -0.671 0.000 0.000
y 0.000 3.192 0.000
z 0.000 0.000 -2.520
Polar
3z2-r2-5.041
x2-y2-2.575
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 3.859 0.000 0.000
y 0.000 11.512 0.000
z 0.000 0.000 16.201


<r2> (average value of r2) Å2
<r2> 204.299
(<r2>)1/2 14.293