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

using model chemistry: PBEPBEultrafine/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 PBEPBEultrafine/6-31G(2df,p)
 hartrees
Energy at 0K-1592.015939
Energy at 298.15K 
HF Energy-1592.015939
Nuclear repulsion energy348.414103
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 PBEPBEultrafine/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 512 507 0.00 36.26 0.04 0.08
2 A1 202 200 0.00 1.86 0.75 0.85
3 B1 432 427 0.00 18.96 0.75 0.86
4 B2 277 274 0.00 10.91 0.75 0.86
5 E 407 403 0.25 3.66 0.75 0.86
5 E 407 403 0.25 3.66 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1118.4 cm-1
Scaled (by 0.9897) Zero Point Vibrational Energy (zpe) 1106.9 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 PBEPBEultrafine/6-31G(2df,p)
ABC
0.11599 0.11599 0.06381

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

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.437 0.322
S2 0.000 -1.437 0.322
S3 -1.437 0.000 -0.322
S4 1.437 0.000 -0.322

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.87452.13212.1321
S22.87452.13212.1321
S32.13212.13212.8745
S42.13212.13212.8745

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 47.615 S1 S3 S4 47.615
S2 S1 S3 47.615 S2 S4 S3 47.615
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at PBEPBEultrafine/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
Primitive
 xyz
x -48.505 0.000 0.000
y 0.000 -48.505 0.000
z 0.000 0.000 -53.844
Traceless
 xyz
x 2.669 0.000 0.000
y 0.000 2.669 0.000
z 0.000 0.000 -5.339
Polar
3z2-r2-10.677
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 11.288 0.000 0.000
y 0.000 11.288 0.000
z 0.000 0.000 6.876


<r2> (average value of r2) Å2
<r2> 170.238
(<r2>)1/2 13.048

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at PBEPBEultrafine/6-31G(2df,p)
 hartrees
Energy at 0K-1592.056565
Energy at 298.15K 
HF Energy-1592.056565
Nuclear repulsion energy330.029516
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 PBEPBEultrafine/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 685 678 3.35 28.07 0.17 0.29
2 A1 325 322 5.46 29.53 0.19 0.33
3 A1 94 93 1.65 6.49 0.49 0.66
4 A2 216 213 0.00 0.10 0.75 0.86
5 B2 658 651 87.34 1.79 0.75 0.86
6 B2 323 320 0.01 12.78 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1150.4 cm-1
Scaled (by 0.9897) Zero Point Vibrational Energy (zpe) 1138.6 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 PBEPBEultrafine/6-31G(2df,p)
ABC
0.15080 0.07330 0.04932

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

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.100 0.935
S2 0.000 -1.100 0.935
S3 0.000 1.545 -0.935
S4 0.000 -1.545 -0.935

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.19981.92213.2391
S22.19983.23911.9221
S31.92213.23913.0900
S43.23911.92213.0900

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 103.390 S1 S3 S4 76.610
S2 S1 S3 103.390 S2 S4 S3 76.610
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at PBEPBEultrafine/6-31G(2df,p) Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.099      
2 S 0.099      
3 S -0.099      
4 S -0.099      


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 1.104 1.104
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -50.966 0.000 0.000
y 0.000 -52.432 0.000
z 0.000 0.000 -47.931
Traceless
 xyz
x -0.784 0.000 0.000
y 0.000 -2.983 0.000
z 0.000 0.000 3.767
Polar
3z2-r27.535
x2-y21.466
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 5.924 0.000 0.000
y 0.000 17.389 0.000
z 0.000 0.000 11.951


<r2> (average value of r2) Å2
<r2> 202.545
(<r2>)1/2 14.232

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at PBEPBEultrafine/6-31G(2df,p)
 hartrees
Energy at 0K-1592.054658
Energy at 298.15K 
HF Energy-1592.054658
Nuclear repulsion energy332.921580
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 PBEPBEultrafine/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 713 705 0.00 32.32 0.19 0.33
2 Ag 278 276 0.00 28.83 0.24 0.39
3 Au 240 238 0.00 0.00 0.00 0.00
4 B1u 668 661 88.11 0.00 0.00 0.00
5 B2u 102i 101i 12.22 0.00 0.00 0.00
6 B3g 328 324 0.00 13.57 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1062.5 cm-1
Scaled (by 0.9897) Zero Point Vibrational Energy (zpe) 1051.6 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 PBEPBEultrafine/6-31G(2df,p)
ABC
0.14426 0.08103 0.05188

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

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.956 1.275
S2 0.000 0.956 -1.275
S3 0.000 -0.956 1.275
S4 0.000 -0.956 -1.275

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.55101.91183.1878
S22.55103.18781.9118
S31.91183.18782.5510
S43.18781.91182.5510

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 PBEPBEultrafine/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
Primitive
 xyz
x -51.162 0.000 0.000
y 0.000 -47.468 0.000
z 0.000 0.000 -52.294
Traceless
 xyz
x -1.281 0.000 0.000
y 0.000 4.260 0.000
z 0.000 0.000 -2.979
Polar
3z2-r2-5.958
x2-y2-3.694
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 5.947 0.000 0.000
y 0.000 12.277 0.000
z 0.000 0.000 16.683


<r2> (average value of r2) Å2
<r2> 194.019
(<r2>)1/2 13.929