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

using model chemistry: wB97X-D/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 wB97X-D/6-31+G**
 hartrees
Energy at 0K-1592.623954
Energy at 298.15K 
HF Energy-1592.623954
Nuclear repulsion energy348.516548
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/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 531 505 0.00 51.73 0.07 0.13
2 A1 198 188 0.00 0.85 0.65 0.79
3 B1 475 453 0.00 36.19 0.75 0.86
4 B2 320 305 0.21 8.11 0.75 0.86
5 E 455 433 0.00 5.74 0.75 0.86
5 E 455 433 0.00 5.74 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1217.0 cm-1
Scaled (by 0.9523) Zero Point Vibrational Energy (zpe) 1158.9 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 wB97X-D/6-31+G**
ABC
0.11634 0.11634 0.06343

See section I.F.4 to change rotational constant units
Geometric Data calculated at wB97X-D/6-31+G**

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.442 0.307
S2 0.000 -1.442 0.307
S3 -1.442 0.000 -0.307
S4 1.442 0.000 -0.307

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.88312.12882.1288
S22.88312.12882.1288
S32.12882.12882.8831
S42.12882.12882.8831

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 47.379 S1 S3 S4 47.379
S2 S1 S3 47.379 S2 S4 S3 47.379
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at wB97X-D/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 -49.770 0.000 0.000
y 0.000 -49.770 0.000
z 0.000 0.000 -55.318
Traceless
 xyz
x 2.774 0.000 0.000
y 0.000 2.774 0.000
z 0.000 0.000 -5.548
Polar
3z2-r2-11.097
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 11.067 0.000 0.000
y 0.000 11.067 0.000
z 0.000 0.000 7.524


<r2> (average value of r2) Å2
<r2> 171.249
(<r2>)1/2 13.086

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at wB97X-D/6-31+G**
 hartrees
Energy at 0K-1592.637923
Energy at 298.15K 
HF Energy-1592.637923
Nuclear repulsion energy331.688347
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/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 679 647 4.05 35.79 0.11 0.20
2 A1 421 401 7.55 46.34 0.19 0.32
3 A1 130 124 0.81 16.07 0.47 0.64
4 A2 214 204 0.00 1.28 0.75 0.86
5 B2 651 620 176.17 4.72 0.75 0.86
6 B2 343 327 0.26 12.03 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1219.8 cm-1
Scaled (by 0.9523) Zero Point Vibrational Energy (zpe) 1161.6 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/6-31+G**
ABC
0.15606 0.07166 0.04911

See section I.F.4 to change rotational constant units
Geometric Data calculated at wB97X-D/6-31+G**

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.052 0.919
S2 0.000 -1.052 0.919
S3 0.000 1.604 -0.919
S4 0.000 -1.604 -0.919

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.10371.91923.2298
S22.10373.22981.9192
S31.91923.22983.2077
S43.22981.91923.2077

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 106.716 S1 S3 S4 73.284
S2 S1 S3 106.716 S2 S4 S3 73.284
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at wB97X-D/6-31+G** Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.138      
2 S 0.138      
3 S -0.138      
4 S -0.138      


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 1.865 1.865
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -51.606 0.000 0.000
y 0.000 -54.681 0.000
z 0.000 0.000 -50.151
Traceless
 xyz
x 0.810 0.000 0.000
y 0.000 -3.802 0.000
z 0.000 0.000 2.992
Polar
3z2-r25.984
x2-y23.075
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 6.192 0.000 0.000
y 0.000 19.960 0.000
z 0.000 0.000 11.807


<r2> (average value of r2) Å2
<r2> 204.348
(<r2>)1/2 14.295

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at wB97X-D/6-31+G**
 hartrees
Energy at 0K-1592.630218
Energy at 298.15K 
HF Energy-1592.630218
Nuclear repulsion energy335.407524
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/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 750 715 0.00 44.01 0.18 0.30
2 Ag 301 287 0.00 43.89 0.26 0.41
3 Au 254 242 0.00 0.00 0.00 0.00
4 B1u 692 659 189.54 0.00 0.00 0.00
5 B2u 169i 161i 28.88 0.00 0.00 0.00
6 B3g 349 333 0.00 14.76 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1088.3 cm-1
Scaled (by 0.9523) Zero Point Vibrational Energy (zpe) 1036.4 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/6-31+G**
ABC
0.14667 0.08209 0.05263

See section I.F.4 to change rotational constant units
Geometric Data calculated at wB97X-D/6-31+G**

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.948 1.267
S2 0.000 0.948 -1.267
S3 0.000 -0.948 1.267
S4 0.000 -0.948 -1.267

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.53431.89603.1651
S22.53433.16511.8960
S31.89603.16512.5343
S43.16511.89602.5343

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/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 -51.933 0.000 0.000
y 0.000 -49.413 0.000
z 0.000 0.000 -54.122
Traceless
 xyz
x -0.165 0.000 0.000
y 0.000 3.614 0.000
z 0.000 0.000 -3.449
Polar
3z2-r2-6.897
x2-y2-2.520
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 6.445 0.000 0.000
y 0.000 12.270 0.000
z 0.000 0.000 18.588


<r2> (average value of r2) Å2
<r2> 192.652
(<r2>)1/2 13.880