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: B3LYP/6-311G*

19 10 17 12 22

States and conformations

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

Conformer 1 (D2D)

Jump to S1C2 S1C3
Energy calculated at B3LYP/6-311G*
 hartrees
Energy at 0K-1592.804748
Energy at 298.15K 
HF Energy-1592.804748
Nuclear repulsion energy342.556068
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 B3LYP/6-311G*
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 481 464 0.00 57.36 0.08 0.15
2 A1 189 182 0.00 3.88 0.71 0.83
3 B1 408 394 0.00 40.40 0.75 0.86
4 B2 299 289 0.03 10.57 0.75 0.86
5 E 392 379 0.22 7.88 0.75 0.86
5 E 392 379 0.22 7.88 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1080.1 cm-1
Scaled (by 0.9663) Zero Point Vibrational Energy (zpe) 1043.7 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 B3LYP/6-311G*
ABC
0.11226 0.11226 0.06148

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3LYP/6-311G*

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.464 0.320
S2 0.000 -1.464 0.320
S3 -1.464 0.000 -0.320
S4 1.464 0.000 -0.320

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.92852.16722.1672
S22.92852.16722.1672
S32.16722.16722.9285
S42.16722.16722.9285

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 47.497 S1 S3 S4 47.497
S2 S1 S3 47.497 S2 S4 S3 47.497
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B3LYP/6-311G* 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 -50.738 0.000 0.000
y 0.000 -50.738 0.000
z 0.000 0.000 -56.109
Traceless
 xyz
x 2.686 0.000 0.000
y 0.000 2.686 0.000
z 0.000 0.000 -5.371
Polar
3z2-r2-10.742
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 11.228 0.000 0.000
y 0.000 11.228 0.000
z 0.000 0.000 5.693


<r2> (average value of r2) Å2
<r2> 176.563
(<r2>)1/2 13.288

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at B3LYP/6-311G*
 hartrees
Energy at 0K-1592.835603
Energy at 298.15K 
HF Energy-1592.835603
Nuclear repulsion energy325.382391
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 B3LYP/6-311G*
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 649 627 2.22 35.25 0.24 0.39
2 A1 300 290 7.79 37.43 0.25 0.39
3 A1 85 82 2.06 8.05 0.49 0.66
4 A2 207 200 0.00 0.13 0.75 0.86
5 B2 622 601 150.02 3.47 0.75 0.86
6 B2 320 309 0.01 14.91 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1090.9 cm-1
Scaled (by 0.9663) Zero Point Vibrational Energy (zpe) 1054.1 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 B3LYP/6-311G*
ABC
0.15069 0.06923 0.04743

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3LYP/6-311G*

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.114 0.935
S2 0.000 -1.114 0.935
S3 0.000 1.603 -0.935
S4 0.000 -1.603 -0.935

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.22721.93343.2979
S22.22723.29791.9334
S31.93343.29793.2051
S43.29791.93343.2051

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 104.649 S1 S3 S4 75.351
S2 S1 S3 104.649 S2 S4 S3 75.351
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B3LYP/6-311G* Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.108      
2 S 0.108      
3 S -0.108      
4 S -0.108      


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 1.551 1.551
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -52.784 0.000 0.000
y 0.000 -55.675 0.000
z 0.000 0.000 -50.760
Traceless
 xyz
x 0.433 0.000 0.000
y 0.000 -3.903 0.000
z 0.000 0.000 3.470
Polar
3z2-r26.939
x2-y22.891
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 4.559 0.000 0.000
y 0.000 19.641 0.000
z 0.000 0.000 12.090


<r2> (average value of r2) Å2
<r2> 210.996
(<r2>)1/2 14.526

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at B3LYP/6-311G*
 hartrees
Energy at 0K-1592.833977
Energy at 298.15K 
HF Energy-1592.833977
Nuclear repulsion energy328.343237
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 B3LYP/6-311G*
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 692 669 0.00 42.23 0.27 0.43
2 Ag 271 262 0.00 35.74 0.29 0.45
3 Au 234 226 0.00 0.00 0.00 0.00
4 B1u 644 623 156.82 0.00 0.00 0.00
5 B2u 82i 79i 21.54 0.00 0.00 0.00
6 B3g 321 310 0.00 16.09 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1040.1 cm-1
Scaled (by 0.9663) Zero Point Vibrational Energy (zpe) 1005.1 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 B3LYP/6-311G*
ABC
0.14328 0.07706 0.05011

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3LYP/6-311G*

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.959 1.308
S2 0.000 0.959 -1.308
S3 0.000 -0.959 1.308
S4 0.000 -0.959 -1.308

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.61571.91833.2438
S22.61573.24381.9183
S31.91833.24382.6157
S43.24381.91832.6157

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 B3LYP/6-311G* 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 -53.071 0.000 0.000
y 0.000 -50.158 0.000
z 0.000 0.000 -55.118
Traceless
 xyz
x -0.434 0.000 0.000
y 0.000 3.937 0.000
z 0.000 0.000 -3.503
Polar
3z2-r2-7.006
x2-y2-2.914
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 4.529 0.000 0.000
y 0.000 12.538 0.000
z 0.000 0.000 18.823


<r2> (average value of r2) Å2
<r2> 201.319
(<r2>)1/2 14.189