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

using model chemistry: TPSSh/3-21G*

19 10 17 12 22

States and conformations

State Conformation minimum conformation conformer description state description
1 1 no D2D 1A1
1 2 no C2V 1A1
1 3 yes D2H 1AG

Conformer 1 (D2D)

Jump to S1C2 S1C3
Energy calculated at TPSSh/3-21G*
 hartrees
Energy at 0K-1585.288709
Energy at 298.15K 
HF Energy-1585.288709
Nuclear repulsion energy345.089470
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 TPSSh/3-21G*
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 468 452 0.00 47.66 0.07 0.13
2 A1 195 189 0.00 4.03 0.75 0.86
3 B1 386 373 0.00 32.25 0.75 0.86
4 B2 303 292 0.44 13.76 0.75 0.86
5 E 366 353 0.25 7.10 0.75 0.86
5 E 366 353 0.25 7.10 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1041.1 cm-1
Scaled (by 0.9657) Zero Point Vibrational Energy (zpe) 1005.4 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 TPSSh/3-21G*
ABC
0.11378 0.11378 0.06261

See section I.F.4 to change rotational constant units
Geometric Data calculated at TPSSh/3-21G*

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.451 0.325
S2 0.000 -1.451 0.325
S3 -1.451 0.000 -0.325
S4 1.451 0.000 -0.325

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.90202.15262.1526
S22.90202.15262.1526
S32.15262.15262.9020
S42.15262.15262.9020

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 47.619 S1 S3 S4 47.619
S2 S1 S3 47.619 S2 S4 S3 47.619
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at TPSSh/3-21G* 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


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 10.330 0.000 0.000
y 0.000 10.330 0.000
z 0.000 0.000 4.872


<r2> (average value of r2) Å2
<r2> 173.959
(<r2>)1/2 13.189

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at TPSSh/3-21G*
 hartrees
Energy at 0K-1585.335011
Energy at 298.15K 
HF Energy-1585.335011
Nuclear repulsion energy329.488456
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 TPSSh/3-21G*
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 724 699 0.00 33.31 0.29 0.45
2 A1 283 274 0.00 30.03 0.27 0.43
3 A1 72 70 11.70 0.00 0.75 0.86
4 A2 237 229 0.00 0.00 0.75 0.86
5 B2 677 654 125.52 0.00 0.75 0.86
6 B2 328 316 0.00 17.54 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1160.6 cm-1
Scaled (by 0.9657) Zero Point Vibrational Energy (zpe) 1120.8 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 TPSSh/3-21G*
ABC
0.14546 0.07692 0.05031

See section I.F.4 to change rotational constant units
Geometric Data calculated at TPSSh/3-21G*

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.309 0.952
S2 0.000 -1.309 0.952
S3 0.000 1.309 -0.952
S4 0.000 -1.309 -0.952

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.61871.90393.2372
S22.61873.23721.9039
S31.90393.23722.6176
S43.23721.90392.6176

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 89.983 S1 S3 S4 90.017
S2 S1 S3 89.983 S2 S4 S3 90.017
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at TPSSh/3-21G* 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 -0.002 0.002
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 3.835 0.000 0.000
y 0.000 16.151 0.000
z 0.000 0.000 11.441


<r2> (average value of r2) Å2
<r2> 200.002
(<r2>)1/2 14.142

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at TPSSh/3-21G*
 hartrees
Energy at 0K-1585.335011
Energy at 298.15K 
HF Energy-1585.335011
Nuclear repulsion energy329.462156
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 TPSSh/3-21G*
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 724 699 0.00 33.32 0.29 0.45
2 Ag 283 273 0.00 30.03 0.27 0.43
3 Au 237 229 0.00 0.00 0.00 0.00
4 B1u 676 653 125.45 0.00 0.00 0.00
5 B2u 73 70 11.70 0.00 0.00 0.00
6 B3g 328 316 0.00 17.55 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1160.3 cm-1
Scaled (by 0.9657) Zero Point Vibrational Energy (zpe) 1120.5 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 TPSSh/3-21G*
ABC
0.14542 0.07691 0.05031

See section I.F.4 to change rotational constant units
Geometric Data calculated at TPSSh/3-21G*

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.952 1.309
S2 0.000 0.952 -1.309
S3 0.000 -0.952 1.309
S4 0.000 -0.952 -1.309

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.61821.90413.2374
S22.61823.23741.9041
S31.90413.23742.6182
S43.23741.90412.6182

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 TPSSh/3-21G* 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


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 3.835 0.000 0.000
y 0.000 11.443 0.000
z 0.000 0.000 16.152


<r2> (average value of r2) Å2
<r2> 200.025
(<r2>)1/2 14.143