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

using model chemistry: wB97X-D/aug-cc-pVDZ

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 wB97X-D/aug-cc-pVDZ
 hartrees
Energy at 0K-1592.727472
Energy at 298.15K 
HF Energy-1592.727472
Nuclear repulsion energy347.296325
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 wB97X-D/aug-cc-pVDZ
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 531 508 0.00 45.50 0.04 0.08
2 A1 200 191 0.00 1.04 0.74 0.85
3 B1 470 450 0.00 18.39 0.75 0.86
4 B2 309 296 0.01 7.17 0.75 0.86
5 E 449 430 0.00 3.45 0.75 0.86
5 E 449 430 0.00 3.45 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1204.4 cm-1
Scaled (by 0.9573) Zero Point Vibrational Energy (zpe) 1153.0 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 wB97X-D/aug-cc-pVDZ
ABC
0.11537 0.11537 0.06323

See section I.F.4 to change rotational constant units
Geometric Data calculated at wB97X-D/aug-cc-pVDZ

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.444 0.316
S2 0.000 -1.444 0.316
S3 -1.444 0.000 -0.316
S4 1.444 0.000 -0.316

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.88782.13782.1378
S22.88782.13782.1378
S32.13782.13782.8878
S42.13782.13782.8878

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 47.514 S1 S3 S4 47.514
S2 S1 S3 47.514 S2 S4 S3 47.514
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at wB97X-D/aug-cc-pVDZ 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 -48.698 0.000 0.000
y 0.000 -48.698 0.000
z 0.000 0.000 -55.269
Traceless
 xyz
x 3.285 0.000 0.000
y 0.000 3.285 0.000
z 0.000 0.000 -6.570
Polar
3z2-r2-13.141
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 12.587 0.000 0.000
y 0.000 12.587 0.000
z 0.000 0.000 8.762


<r2> (average value of r2) Å2
<r2> 171.621
(<r2>)1/2 13.100

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at wB97X-D/aug-cc-pVDZ
 hartrees
Energy at 0K-1592.739634
Energy at 298.15K 
HF Energy-1592.739634
Nuclear repulsion energy331.594932
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 wB97X-D/aug-cc-pVDZ
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 689 659 5.66 35.25 0.07 0.13
2 A1 422 404 6.14 48.97 0.17 0.29
3 A1 158 152 0.69 14.25 0.38 0.55
4 A2 215 206 0.00 0.34 0.75 0.86
5 B2 656 628 150.05 4.43 0.75 0.86
6 B2 341 326 0.43 8.82 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1240.5 cm-1
Scaled (by 0.9573) Zero Point Vibrational Energy (zpe) 1187.5 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 wB97X-D/aug-cc-pVDZ
ABC
0.15391 0.07262 0.04934

See section I.F.4 to change rotational constant units
Geometric Data calculated at wB97X-D/aug-cc-pVDZ

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.055 0.925
S2 0.000 -1.055 0.925
S3 0.000 1.587 -0.925
S4 0.000 -1.587 -0.925

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.10921.92593.2254
S22.10923.22541.9259
S31.92593.22543.1738
S43.22541.92593.1738

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 106.045 S1 S3 S4 73.955
S2 S1 S3 106.045 S2 S4 S3 73.955
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at wB97X-D/aug-cc-pVDZ Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.100      
2 S 0.100      
3 S -0.100      
4 S -0.100      


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 1.525 1.525
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -52.073 0.000 0.000
y 0.000 -53.492 0.000
z 0.000 0.000 -48.359
Traceless
 xyz
x -1.147 0.000 0.000
y 0.000 -3.276 0.000
z 0.000 0.000 4.424
Polar
3z2-r28.847
x2-y21.419
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 7.972 0.000 0.000
y 0.000 20.535 0.000
z 0.000 0.000 12.986


<r2> (average value of r2) Å2
<r2> 203.032
(<r2>)1/2 14.249

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at wB97X-D/aug-cc-pVDZ
 hartrees
Energy at 0K-1592.730841
Energy at 298.15K 
HF Energy-1592.730841
Nuclear repulsion energy336.001172
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 wB97X-D/aug-cc-pVDZ
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 755 723 0.00 39.42 0.11 0.19
2 Ag 307 294 0.00 43.32 0.21 0.35
3 Au 254 243 0.00 0.00 0.00 0.00
4 B1u 690 660 155.20 0.00 0.00 0.00
5 B2u 209i 200i 21.49 0.00 0.00 0.00
6 B3g 351 336 0.00 10.27 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1073.6 cm-1
Scaled (by 0.9573) Zero Point Vibrational Energy (zpe) 1027.7 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 wB97X-D/aug-cc-pVDZ
ABC
0.14539 0.08348 0.05303

See section I.F.4 to change rotational constant units
Geometric Data calculated at wB97X-D/aug-cc-pVDZ

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.952 1.257
S2 0.000 0.952 -1.257
S3 0.000 -0.952 1.257
S4 0.000 -0.952 -1.257

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.51321.90443.1532
S22.51323.15321.9044
S31.90443.15322.5132
S43.15321.90442.5132

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 wB97X-D/aug-cc-pVDZ 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 -52.344 0.000 0.000
y 0.000 -47.657 0.000
z 0.000 0.000 -52.814
Traceless
 xyz
x -2.108 0.000 0.000
y 0.000 4.922 0.000
z 0.000 0.000 -2.814
Polar
3z2-r2-5.628
x2-y2-4.687
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 7.949 0.000 0.000
y 0.000 13.350 0.000
z 0.000 0.000 19.200


<r2> (average value of r2) Å2
<r2> 190.903
(<r2>)1/2 13.817