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

using model chemistry: wB97X-D/6-31G

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/6-31G
 hartrees
Energy at 0K-1592.500380
Energy at 298.15K 
HF Energy-1592.500380
Nuclear repulsion energy324.874867
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/6-31G
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 472 472 0.00 64.86 0.07 0.14
2 A1 158 158 0.00 7.08 0.74 0.85
3 B1 403 403 0.00 39.77 0.75 0.86
4 B2 288 288 0.50 13.82 0.75 0.86
5 E 391 391 0.02 10.28 0.75 0.86
5 E 391 391 0.02 10.28 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1050.8 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1050.8 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/6-31G
ABC
0.10113 0.10113 0.05507

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

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.547 0.326
S2 0.000 -1.547 0.326
S3 -1.547 0.000 -0.326
S4 1.547 0.000 -0.326

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S13.09432.28342.2834
S23.09432.28342.2834
S32.28342.28343.0943
S42.28342.28343.0943

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 47.345 S1 S3 S4 47.345
S2 S1 S3 47.345 S2 S4 S3 47.345
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at wB97X-D/6-31G 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 -51.704 0.000 0.000
y 0.000 -51.704 0.000
z 0.000 0.000 -56.252
Traceless
 xyz
x 2.274 0.000 0.000
y 0.000 2.274 0.000
z 0.000 0.000 -4.548
Polar
3z2-r2-9.097
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 12.369 0.000 0.000
y 0.000 12.369 0.000
z 0.000 0.000 4.467


<r2> (average value of r2) Å2
<r2> 193.260
(<r2>)1/2 13.902

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at wB97X-D/6-31G
 hartrees
Energy at 0K-1592.501798
Energy at 298.15K 
HF Energy-1592.501798
Nuclear repulsion energy313.365809
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/6-31G
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 602 602 0.00 39.34 0.22 0.36
2 A1 316 316 4.17 40.76 0.25 0.40
3 A1 128 128 3.95 10.43 0.53 0.69
4 A2 186 186 0.00 0.17 0.75 0.86
5 B2 585 585 109.06 1.85 0.75 0.86
6 B2 285 285 0.01 21.03 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1050.7 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1050.7 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/6-31G
ABC
0.13138 0.06851 0.04503

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

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.157 1.002
S2 0.000 -1.157 1.002
S3 0.000 1.584 -1.002
S4 0.000 -1.584 -1.002

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.31502.04823.3953
S22.31503.39532.0482
S32.04823.39533.1676
S43.39532.04823.1676

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 102.013 S1 S3 S4 77.987
S2 S1 S3 102.013 S2 S4 S3 77.987
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at wB97X-D/6-31G Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.049      
2 S 0.049      
3 S -0.049      
4 S -0.049      


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 1.250 1.250
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -52.525 0.000 0.000
y 0.000 -55.854 0.000
z 0.000 0.000 -52.402
Traceless
 xyz
x 1.603 0.000 0.000
y 0.000 -3.391 0.000
z 0.000 0.000 1.788
Polar
3z2-r23.576
x2-y23.329
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 3.319 0.000 0.000
y 0.000 19.224 0.000
z 0.000 0.000 12.716


<r2> (average value of r2) Å2
<r2> 220.830
(<r2>)1/2 14.860

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at wB97X-D/6-31G
 hartrees
Energy at 0K-1592.499909
Energy at 298.15K 
HF Energy-1592.499909
Nuclear repulsion energy315.604263
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/6-31G
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 650 650 0.00 41.52 0.28 0.44
2 Ag 293 293 0.00 44.72 0.29 0.44
3 Au 209 209 0.00 0.00 0.00 0.00
4 B1u 611 611 125.14 0.00 0.00 0.00
5 B2u 108i 108i 15.70 0.00 0.00 0.00
6 B3g 284 284 0.00 23.02 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 968.8 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 968.8 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/6-31G
ABC
0.12811 0.07375 0.04680

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

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.014 1.337
S2 0.000 1.014 -1.337
S3 0.000 -1.014 1.337
S4 0.000 -1.014 -1.337

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.67392.02873.3564
S22.67393.35642.0287
S32.02873.35642.6739
S43.35642.02872.6739

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/6-31G 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 -52.672 0.000 0.000
y 0.000 -52.196 0.000
z 0.000 0.000 -55.279
Traceless
 xyz
x 1.065 0.000 0.000
y 0.000 1.779 0.000
z 0.000 0.000 -2.844
Polar
3z2-r2-5.689
x2-y2-0.476
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 3.303 0.000 0.000
y 0.000 13.134 0.000
z 0.000 0.000 18.297


<r2> (average value of r2) Å2
<r2> 213.587
(<r2>)1/2 14.615