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

using model chemistry: TPSSh/6-31G(2df,p)

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 TPSSh/6-31G(2df,p)
 hartrees
Energy at 0K-1592.753210
Energy at 298.15K 
HF Energy-1592.753210
Nuclear repulsion energy350.375109
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/6-31G(2df,p)
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 525 507 0.00 38.77 0.04 0.08
2 A1 204 197 0.00 1.82 0.75 0.86
3 B1 461 445 0.00 18.71 0.75 0.86
4 B2 289 278 0.00 9.68 0.75 0.86
5 E 434 419 0.06 4.24 0.75 0.86
5 E 434 419 0.06 4.24 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1173.6 cm-1
Scaled (by 0.965) Zero Point Vibrational Energy (zpe) 1132.5 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/6-31G(2df,p)
ABC
0.11732 0.11732 0.06451

See section I.F.4 to change rotational constant units
Geometric Data calculated at TPSSh/6-31G(2df,p)

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.429 0.319
S2 0.000 -1.429 0.319
S3 -1.429 0.000 -0.319
S4 1.429 0.000 -0.319

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.85892.12002.1200
S22.85892.12002.1200
S32.12002.12002.8589
S42.12002.12002.8589

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 47.602 S1 S3 S4 47.602
S2 S1 S3 47.602 S2 S4 S3 47.602
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at TPSSh/6-31G(2df,p) 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 11.135 0.000 0.000
y 0.000 11.135 0.000
z 0.000 0.000 6.791


<r2> (average value of r2) Å2
<r2> 168.697
(<r2>)1/2 12.988

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at TPSSh/6-31G(2df,p)
 hartrees
Energy at 0K-1592.782411
Energy at 298.15K 
HF Energy-1592.782411
Nuclear repulsion energy331.876965
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/6-31G(2df,p)
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 693 668 4.88 27.34 0.16 0.28
2 A1 364 351 6.05 33.45 0.19 0.32
3 A1 111 107 0.79 8.90 0.47 0.64
4 A2 217 209 0.00 0.17 0.75 0.86
5 B2 666 643 106.89 2.58 0.75 0.86
6 B2 333 321 0.12 12.28 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1191.0 cm-1
Scaled (by 0.965) Zero Point Vibrational Energy (zpe) 1149.3 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 TPSSh/6-31G(2df,p)
ABC
0.15502 0.07254 0.04942

See section I.F.4 to change rotational constant units
Geometric Data calculated at TPSSh/6-31G(2df,p)

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.067 0.922
S2 0.000 -1.067 0.922
S3 0.000 1.580 -0.922
S4 0.000 -1.580 -0.922

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.13481.91403.2261
S22.13483.22611.9140
S31.91403.22613.1592
S43.22611.91403.1592

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 105.522 S1 S3 S4 74.478
S2 S1 S3 105.522 S2 S4 S3 74.478
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at TPSSh/6-31G(2df,p) Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.124      
2 S 0.124      
3 S -0.124      
4 S -0.124      


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 1.334 1.334
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 5.867 0.000 0.000
y 0.000 17.649 0.000
z 0.000 0.000 11.658


<r2> (average value of r2) Å2
<r2> 202.265
(<r2>)1/2 14.222

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at TPSSh/6-31G(2df,p)
 hartrees
Energy at 0K-1592.778128
Energy at 298.15K 
HF Energy-1592.778128
Nuclear repulsion energy334.630105
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/6-31G(2df,p)
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 735 710 0.00 33.32 0.20 0.34
2 Ag 288 278 0.00 32.38 0.25 0.40
3 Au 247 238 0.00 0.00 0.00 0.00
4 B1u 683 659 114.27 0.00 0.00 0.00
5 B2u 133i 129i 15.12 0.00 0.00 0.00
6 B3g 335 323 0.00 13.90 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1077.1 cm-1
Scaled (by 0.965) Zero Point Vibrational Energy (zpe) 1039.4 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/6-31G(2df,p)
ABC
0.14628 0.08154 0.05235

See section I.F.4 to change rotational constant units
Geometric Data calculated at TPSSh/6-31G(2df,p)

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.949 1.271
S2 0.000 0.949 -1.271
S3 0.000 -0.949 1.271
S4 0.000 -0.949 -1.271

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.54301.89853.1735
S22.54303.17351.8985
S31.89853.17352.5430
S43.17351.89852.5430

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/6-31G(2df,p) 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 5.903 0.000 0.000
y 0.000 12.121 0.000
z 0.000 0.000 16.873


<r2> (average value of r2) Å2
<r2> 192.552
(<r2>)1/2 13.876