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: M06-2X/6-31+G**

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 M06-2X/6-31+G**
 hartrees
Energy at 0K-1592.561470
Energy at 298.15K 
HF Energy-1592.561470
Nuclear repulsion energy348.700725
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 M06-2X/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 A1 521 496 0.00 55.55 0.07 0.13
2 A1 199 189 0.00 0.92 0.63 0.77
3 B1 467 444 0.00 39.32 0.75 0.86
4 B2 325 310 0.14 7.99 0.75 0.86
5 E 445 424 0.00 6.56 0.75 0.86
5 E 445 424 0.00 6.56 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1200.7 cm-1
Scaled (by 0.9522) Zero Point Vibrational Energy (zpe) 1143.3 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 M06-2X/6-31+G**
ABC
0.11632 0.11632 0.06371

See section I.F.4 to change rotational constant units
Geometric Data calculated at M06-2X/6-31+G**

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.438 0.314
S2 0.000 -1.438 0.314
S3 -1.438 0.000 -0.314
S4 1.438 0.000 -0.314

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.87682.12902.1290
S22.87682.12902.1290
S32.12902.12902.8768
S42.12902.12902.8768

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 47.499 S1 S3 S4 47.499
S2 S1 S3 47.499 S2 S4 S3 47.499
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at M06-2X/6-31+G** 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 -50.127 0.000 0.000
y 0.000 -50.127 0.000
z 0.000 0.000 -55.639
Traceless
 xyz
x 2.756 0.000 0.000
y 0.000 2.756 0.000
z 0.000 0.000 -5.511
Polar
3z2-r2-11.022
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 11.246 0.000 0.000
y 0.000 11.246 0.000
z 0.000 0.000 7.584


<r2> (average value of r2) Å2
<r2> 171.187
(<r2>)1/2 13.084

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at M06-2X/6-31+G**
 hartrees
Energy at 0K-1592.573904
Energy at 298.15K 
HF Energy-1592.573904
Nuclear repulsion energy332.082351
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 M06-2X/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 A1 688 655 3.88 35.52 0.11 0.20
2 A1 407 387 7.23 52.74 0.20 0.33
3 A1 125 119 0.59 15.56 0.47 0.64
4 A2 213 203 0.00 1.49 0.75 0.86
5 B2 660 628 190.18 4.99 0.75 0.86
6 B2 337 321 0.19 11.71 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1214.3 cm-1
Scaled (by 0.9522) Zero Point Vibrational Energy (zpe) 1156.2 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 M06-2X/6-31+G**
ABC
0.15691 0.07156 0.04915

See section I.F.4 to change rotational constant units
Geometric Data calculated at M06-2X/6-31+G**

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.047 0.917
S2 0.000 -1.047 0.917
S3 0.000 1.609 -0.917
S4 0.000 -1.609 -0.917

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.09371.91733.2269
S22.09373.22691.9173
S31.91733.22693.2176
S43.22691.91733.2176

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 107.043 S1 S3 S4 72.957
S2 S1 S3 107.043 S2 S4 S3 72.957
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at M06-2X/6-31+G** Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.141      
2 S 0.141      
3 S -0.141      
4 S -0.141      


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 1.854 1.854
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -52.073 0.000 0.000
y 0.000 -55.027 0.000
z 0.000 0.000 -50.558
Traceless
 xyz
x 0.719 0.000 0.000
y 0.000 -3.711 0.000
z 0.000 0.000 2.991
Polar
3z2-r25.983
x2-y22.953
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 6.291 0.000 0.000
y 0.000 20.330 0.000
z 0.000 0.000 11.832


<r2> (average value of r2) Å2
<r2> 204.479
(<r2>)1/2 14.300

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at M06-2X/6-31+G**
 hartrees
Energy at 0K-1592.567506
Energy at 298.15K 
HF Energy-1592.567506
Nuclear repulsion energy335.979322
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 M06-2X/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 Ag 758 722 0.00 43.30 0.18 0.30
2 Ag 314 299 0.00 49.46 0.26 0.41
3 Au 253 241 0.00 0.00 0.00 0.00
4 B1u 696 663 209.80 0.00 0.00 0.00
5 B2u 141i 134i 27.06 0.00 0.00 0.00
6 B3g 344 327 0.00 14.86 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1112.5 cm-1
Scaled (by 0.9522) Zero Point Vibrational Energy (zpe) 1059.3 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 M06-2X/6-31+G**
ABC
0.14714 0.08239 0.05282

See section I.F.4 to change rotational constant units
Geometric Data calculated at M06-2X/6-31+G**

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.946 1.265
S2 0.000 0.946 -1.265
S3 0.000 -0.946 1.265
S4 0.000 -0.946 -1.265

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.52981.89303.1596
S22.52983.15961.8930
S31.89303.15962.5298
S43.15961.89302.5298

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 M06-2X/6-31+G** 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 -52.431 0.000 0.000
y 0.000 -49.816 0.000
z 0.000 0.000 -54.573
Traceless
 xyz
x -0.236 0.000 0.000
y 0.000 3.686 0.000
z 0.000 0.000 -3.450
Polar
3z2-r2-6.899
x2-y2-2.615
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 6.542 0.000 0.000
y 0.000 12.292 0.000
z 0.000 0.000 18.932


<r2> (average value of r2) Å2
<r2> 192.380
(<r2>)1/2 13.870