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

using model chemistry: wB97X-D/CEP-31G*

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/CEP-31G*
 hartrees
Energy at 0K-40.555586
Energy at 298.15K 
HF Energy-40.555586
Nuclear repulsion energy48.816686
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/CEP-31G*
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 530 530 0.00 54.87 0.06 0.11
2 A1 200 200 0.00 5.30 0.72 0.84
3 B1 480 480 0.00 32.86 0.75 0.86
4 B2 307 307 0.14 11.04 0.75 0.86
5 E 458 458 0.04 8.45 0.75 0.86
5 E 458 458 0.04 8.45 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1216.8 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1216.8 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 wB97X-D/CEP-31G*
ABC
0.11533 0.11533 0.06308

See section I.F.4 to change rotational constant units
Geometric Data calculated at wB97X-D/CEP-31G*

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.446 0.313
S2 0.000 -1.446 0.313
S3 -1.446 0.000 -0.313
S4 1.446 0.000 -0.313

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.89122.13822.1382
S22.89122.13822.1382
S32.13822.13822.8912
S42.13822.13822.8912

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 47.460 S1 S3 S4 47.460
S2 S1 S3 47.460 S2 S4 S3 47.460
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at wB97X-D/CEP-31G* 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 -46.318 0.000 0.000
y 0.000 -46.318 0.000
z 0.000 0.000 -51.973
Traceless
 xyz
x 2.828 0.000 0.000
y 0.000 2.828 0.000
z 0.000 0.000 -5.656
Polar
3z2-r2-11.312
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 10.560 0.000 0.000
y 0.000 10.560 0.000
z 0.000 0.000 4.555


<r2> (average value of r2) Å2
<r2> 82.615
(<r2>)1/2 9.089

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at wB97X-D/CEP-31G*
 hartrees
Energy at 0K-40.568252
Energy at 298.15K 
HF Energy-40.568252
Nuclear repulsion energy46.375607
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/CEP-31G*
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 708 708 4.99 31.99 0.23 0.37
2 A1 415 415 9.13 49.12 0.22 0.37
3 A1 140 140 1.18 12.20 0.48 0.65
4 A2 219 219 0.00 0.07 0.75 0.86
5 B2 681 681 172.41 3.54 0.75 0.86
6 B2 342 342 0.22 17.29 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1251.8 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1251.8 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 wB97X-D/CEP-31G*
ABC
0.15187 0.07211 0.04889

See section I.F.4 to change rotational constant units
Geometric Data calculated at wB97X-D/CEP-31G*

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.068 0.932
S2 0.000 -1.068 0.932
S3 0.000 1.586 -0.932
S4 0.000 -1.586 -0.932

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.13521.93413.2427
S22.13523.24271.9341
S31.93413.24273.1726
S43.24271.93413.1726

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 105.556 S1 S3 S4 74.444
S2 S1 S3 105.556 S2 S4 S3 74.444
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at wB97X-D/CEP-31G* Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.121      
2 S 0.121      
3 S -0.121      
4 S -0.121      


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 1.761 1.761
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -48.493 0.000 0.000
y 0.000 -51.533 0.000
z 0.000 0.000 -46.074
Traceless
 xyz
x 0.310 0.000 0.000
y 0.000 -4.250 0.000
z 0.000 0.000 3.939
Polar
3z2-r27.879
x2-y23.040
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 3.551 0.000 0.000
y 0.000 18.386 0.000
z 0.000 0.000 11.505


<r2> (average value of r2) Å2
<r2> 95.121
(<r2>)1/2 9.753

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at wB97X-D/CEP-31G*
 hartrees
Energy at 0K-40.561788
Energy at 298.15K 
HF Energy-40.561788
Nuclear repulsion energy47.027366
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/CEP-31G*
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 761 761 0.00 40.51 0.28 0.44
2 Ag 308 308 0.00 41.85 0.29 0.45
3 Au 256 256 0.00 0.00 0.00 0.00
4 B1u 708 708 179.61 0.00 0.00 0.00
5 B2u 169i 169i 28.66 0.00 0.00 0.00
6 B3g 352 352 0.00 18.64 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1107.3 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1107.3 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 wB97X-D/CEP-31G*
ABC
0.14376 0.08285 0.05256

See section I.F.4 to change rotational constant units
Geometric Data calculated at wB97X-D/CEP-31G*

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.958 1.261
S2 0.000 0.958 -1.261
S3 0.000 -0.958 1.261
S4 0.000 -0.958 -1.261

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.52281.91513.1673
S22.52283.16731.9151
S31.91513.16732.5228
S43.16731.91512.5228

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/CEP-31G* 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 -48.779 0.000 0.000
y 0.000 -45.361 0.000
z 0.000 0.000 -51.511
Traceless
 xyz
x -0.343 0.000 0.000
y 0.000 4.784 0.000
z 0.000 0.000 -4.441
Polar
3z2-r2-8.882
x2-y2-3.419
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 3.553 0.000 0.000
y 0.000 12.063 0.000
z 0.000 0.000 17.373


<r2> (average value of r2) Å2
<r2> 90.515
(<r2>)1/2 9.514