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

using model chemistry: PBE1PBE/cc-pVTZ

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 PBE1PBE/cc-pVTZ
 hartrees
Energy at 0K-1592.256249
Energy at 298.15K 
HF Energy-1592.256249
Nuclear repulsion energy352.045405
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 PBE1PBE/cc-pVTZ
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 541 520 0.00 39.30 0.04 0.08
2 A1 207 199 0.00 2.32 0.75 0.85
3 B1 480 461 0.00 17.03 0.75 0.86
4 B2 302 291 0.00 8.39 0.75 0.86
5 E 453 435 0.00 4.23 0.75 0.86
5 E 453 435 0.00 4.23 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1217.9 cm-1
Scaled (by 0.961) Zero Point Vibrational Energy (zpe) 1170.4 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 PBE1PBE/cc-pVTZ
ABC
0.11850 0.11850 0.06503

See section I.F.4 to change rotational constant units
Geometric Data calculated at PBE1PBE/cc-pVTZ

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.424 0.314
S2 0.000 -1.424 0.314
S3 -1.424 0.000 -0.314
S4 1.424 0.000 -0.314

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.84752.10932.1093
S22.84752.10932.1093
S32.10932.10932.8475
S42.10932.10932.8475

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 47.549 S1 S3 S4 47.549
S2 S1 S3 47.549 S2 S4 S3 47.549
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at PBE1PBE/cc-pVTZ 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 -48.664 0.000 0.000
y 0.000 -48.664 0.000
z 0.000 0.000 -54.110
Traceless
 xyz
x 2.723 0.000 0.000
y 0.000 2.723 0.000
z 0.000 0.000 -5.446
Polar
3z2-r2-10.892
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 11.283 0.000 0.000
y 0.000 11.283 0.000
z 0.000 0.000 6.635


<r2> (average value of r2) Å2
<r2> 167.581
(<r2>)1/2 12.945

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at PBE1PBE/cc-pVTZ
 hartrees
Energy at 0K-1592.277818
Energy at 298.15K 
HF Energy-1592.277818
Nuclear repulsion energy334.197028
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 PBE1PBE/cc-pVTZ
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 705 677 6.24 26.44 0.15 0.26
2 A1 408 392 5.84 39.51 0.19 0.32
3 A1 119 114 0.52 10.42 0.44 0.61
4 A2 222 213 0.00 0.12 0.75 0.86
5 B2 676 650 121.80 3.50 0.75 0.86
6 B2 342 329 0.20 11.46 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1235.5 cm-1
Scaled (by 0.961) Zero Point Vibrational Energy (zpe) 1187.4 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 PBE1PBE/cc-pVTZ
ABC
0.15731 0.07332 0.05001

See section I.F.4 to change rotational constant units
Geometric Data calculated at PBE1PBE/cc-pVTZ

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.048 0.915
S2 0.000 -1.048 0.915
S3 0.000 1.581 -0.915
S4 0.000 -1.581 -0.915

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.09521.90683.2029
S22.09523.20291.9068
S31.90683.20293.1610
S43.20291.90683.1610

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 106.229 S1 S3 S4 73.771
S2 S1 S3 106.229 S2 S4 S3 73.771
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at PBE1PBE/cc-pVTZ Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.135      
2 S 0.135      
3 S -0.135      
4 S -0.135      


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 1.448 1.448
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -51.078 0.000 0.000
y 0.000 -53.092 0.000
z 0.000 0.000 -48.319
Traceless
 xyz
x -0.372 0.000 0.000
y 0.000 -3.393 0.000
z 0.000 0.000 3.765
Polar
3z2-r27.530
x2-y22.014
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 5.813 0.000 0.000
y 0.000 18.132 0.000
z 0.000 0.000 11.828


<r2> (average value of r2) Å2
<r2> 200.431
(<r2>)1/2 14.157

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at PBE1PBE/cc-pVTZ
 hartrees
Energy at 0K-1592.271569
Energy at 298.15K 
HF Energy-1592.271569
Nuclear repulsion energy338.401246
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 PBE1PBE/cc-pVTZ
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 758 728 0.00 33.46 0.20 0.33
2 Ag 311 299 0.00 36.82 0.24 0.39
3 Au 259 249 0.00 0.00 0.00 0.00
4 B1u 698 671 126.63 0.00 0.00 0.00
5 B2u 160i 154i 18.73 0.00 0.00 0.00
6 B3g 349 336 0.00 13.04 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1107.0 cm-1
Scaled (by 0.961) Zero Point Vibrational Energy (zpe) 1063.8 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 PBE1PBE/cc-pVTZ
ABC
0.14789 0.08441 0.05374

See section I.F.4 to change rotational constant units
Geometric Data calculated at PBE1PBE/cc-pVTZ

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.944 1.250
S2 0.000 0.944 -1.250
S3 0.000 -0.944 1.250
S4 0.000 -0.944 -1.250

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.49921.88823.1323
S22.49923.13231.8882
S31.88823.13232.4992
S43.13231.88822.4992

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 PBE1PBE/cc-pVTZ 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 -51.399 0.000 0.000
y 0.000 -47.661 0.000
z 0.000 0.000 -52.681
Traceless
 xyz
x -1.228 0.000 0.000
y 0.000 4.378 0.000
z 0.000 0.000 -3.151
Polar
3z2-r2-6.301
x2-y2-3.737
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 5.790 0.000 0.000
y 0.000 12.316 0.000
z 0.000 0.000 17.139


<r2> (average value of r2) Å2
<r2> 188.572
(<r2>)1/2 13.732