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

using model chemistry: M06-2X/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 M06-2X/6-311G*
 hartrees
Energy at 0K-1592.673924
Energy at 298.15K 
HF Energy-1592.673924
Nuclear repulsion energy348.157825
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/6-311G*
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 521 521 0.00 60.33 0.08 0.15
2 A1 196 196 0.00 3.45 0.67 0.80
3 B1 465 465 0.00 39.76 0.75 0.86
4 B2 318 318 0.08 9.07 0.75 0.86
5 E 445 445 0.00 8.83 0.75 0.86
5 E 445 445 0.00 8.83 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1194.8 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1194.8 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 M06-2X/6-311G*
ABC
0.11589 0.11589 0.06362

See section I.F.4 to change rotational constant units
Geometric Data calculated at M06-2X/6-311G*

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.439 0.318
S2 0.000 -1.439 0.318
S3 -1.439 0.000 -0.318
S4 1.439 0.000 -0.318

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.87892.13302.1330
S22.87892.13302.1330
S32.13302.13302.8789
S42.13302.13302.8789

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 47.558 S1 S3 S4 47.558
S2 S1 S3 47.558 S2 S4 S3 47.558
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at M06-2X/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 -50.670 0.000 0.000
y 0.000 -50.670 0.000
z 0.000 0.000 -55.914
Traceless
 xyz
x 2.622 0.000 0.000
y 0.000 2.622 0.000
z 0.000 0.000 -5.244
Polar
3z2-r2-10.488
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 10.825 0.000 0.000
y 0.000 10.825 0.000
z 0.000 0.000 5.599


<r2> (average value of r2) Å2
<r2> 171.837
(<r2>)1/2 13.109

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at M06-2X/6-311G*
 hartrees
Energy at 0K-1592.682666
Energy at 298.15K 
HF Energy-1592.682666
Nuclear repulsion energy332.279439
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/6-311G*
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 675 675 3.64 37.12 0.19 0.32
2 A1 392 392 8.63 59.49 0.25 0.40
3 A1 127 127 0.89 15.33 0.45 0.62
4 A2 217 217 0.00 0.42 0.75 0.86
5 B2 645 645 218.44 5.48 0.75 0.86
6 B2 338 338 0.16 12.96 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1196.9 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1196.9 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/6-311G*
ABC
0.15636 0.07207 0.04933

See section I.F.4 to change rotational constant units
Geometric Data calculated at M06-2X/6-311G*

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.052 0.918
S2 0.000 -1.052 0.918
S3 0.000 1.597 -0.918
S4 0.000 -1.597 -0.918

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.10391.91563.2235
S22.10393.22351.9156
S31.91563.22353.1947
S43.22351.91563.1947

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 106.542 S1 S3 S4 73.458
S2 S1 S3 106.542 S2 S4 S3 73.458
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at M06-2X/6-311G* 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 1.998 1.998
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -52.635 0.000 0.000
y 0.000 -56.092 0.000
z 0.000 0.000 -50.946
Traceless
 xyz
x 0.884 0.000 0.000
y 0.000 -4.301 0.000
z 0.000 0.000 3.417
Polar
3z2-r26.834
x2-y23.457
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 4.567 0.000 0.000
y 0.000 20.398 0.000
z 0.000 0.000 11.601


<r2> (average value of r2) Å2
<r2> 204.260
(<r2>)1/2 14.292

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at M06-2X/6-311G*
 hartrees
Energy at 0K-1592.676969
Energy at 298.15K 
HF Energy-1592.676969
Nuclear repulsion energy336.381984
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/6-311G*
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 750 750 0.00 44.90 0.26 0.42
2 Ag 317 317 0.00 55.00 0.30 0.47
3 Au 256 256 0.00 0.00 0.00 0.00
4 B1u 686 686 237.31 0.00 0.00 0.00
5 B2u 144i 144i 33.39 0.00 0.00 0.00
6 B3g 344 344 0.00 15.76 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1104.5 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1104.5 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 M06-2X/6-311G*
ABC
0.14773 0.08244 0.05291

See section I.F.4 to change rotational constant units
Geometric Data calculated at M06-2X/6-311G*

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.945 1.264
S2 0.000 0.945 -1.264
S3 0.000 -0.945 1.264
S4 0.000 -0.945 -1.264

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.52891.88923.1567
S22.52893.15671.8892
S31.88923.15672.5289
S43.15671.88922.5289

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/6-311G* 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 -53.034 0.000 0.000
y 0.000 -50.242 0.000
z 0.000 0.000 -55.241
Traceless
 xyz
x -0.293 0.000 0.000
y 0.000 3.896 0.000
z 0.000 0.000 -3.604
Polar
3z2-r2-7.207
x2-y2-2.792
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 12.183 0.000
z 0.000 0.000 19.179


<r2> (average value of r2) Å2
<r2> 192.435
(<r2>)1/2 13.872