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

using model chemistry: HSEh1PBE/STO-3G

19 10 17 12 22

States and conformations

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

Conformer 1 (D2D)

Jump to S1C2 S1C3
Energy calculated at HSEh1PBE/STO-3G
 hartrees
Energy at 0K-1574.654585
Energy at 298.15K 
HF Energy-1574.654585
Nuclear repulsion energy344.780567
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 HSEh1PBE/STO-3G
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 642 567 0.00 24.79 0.09 0.16
2 A1 161 143 0.00 1.76 0.73 0.84
3 B1 586 517 0.00 15.44 0.75 0.86
4 B2 346 305 0.99 6.08 0.75 0.86
5 E 573 506 1.57 3.48 0.75 0.86
5 E 573 506 1.57 3.48 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1440.6 cm-1
Scaled (by 0.8831) Zero Point Vibrational Energy (zpe) 1272.2 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 HSEh1PBE/STO-3G
ABC
0.11470 0.11470 0.06085

See section I.F.4 to change rotational constant units
Geometric Data calculated at HSEh1PBE/STO-3G

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.472 0.257
S2 0.000 -1.472 0.257
S3 -1.472 0.000 -0.257
S4 1.472 0.000 -0.257

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.94372.14402.1440
S22.94372.14402.1440
S32.14402.14402.9437
S42.14402.14402.9437

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 46.646 S1 S3 S4 46.646
S2 S1 S3 46.646 S2 S4 S3 46.646
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at HSEh1PBE/STO-3G 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 -43.846 0.000 0.000
y 0.000 -43.846 0.000
z 0.000 0.000 -45.789
Traceless
 xyz
x 0.972 0.000 0.000
y 0.000 0.972 0.000
z 0.000 0.000 -1.944
Polar
3z2-r2-3.887
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 5.825 0.000 0.000
y 0.000 5.825 0.000
z 0.000 0.000 0.897


<r2> (average value of r2) Å2
<r2> 170.662
(<r2>)1/2 13.064

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at HSEh1PBE/STO-3G
 hartrees
Energy at 0K-1574.621109
Energy at 298.15K 
HF Energy-1574.621109
Nuclear repulsion energy329.753216
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 HSEh1PBE/STO-3G
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 774 684 0.02 15.28 0.20 0.33
2 A1 395 349 6.13 13.98 0.23 0.38
3 A1 133 118 5.33 3.12 0.53 0.69
4 A2 207 183 0.00 0.02 0.75 0.86
5 B2 776 686 30.76 0.55 0.75 0.86
6 B2 340 301 0.46 8.73 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1313.2 cm-1
Scaled (by 0.8831) Zero Point Vibrational Energy (zpe) 1159.7 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 HSEh1PBE/STO-3G
ABC
0.14206 0.07823 0.05045

See section I.F.4 to change rotational constant units
Geometric Data calculated at HSEh1PBE/STO-3G

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.129 0.963
S2 0.000 -1.129 0.963
S3 0.000 1.448 -0.963
S4 0.000 -1.448 -0.963

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.25791.95273.2172
S22.25793.21721.9527
S31.95273.21722.8953
S43.21721.95272.8953

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 99.393 S1 S3 S4 80.607
S2 S1 S3 99.393 S2 S4 S3 80.607
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at HSEh1PBE/STO-3G Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.055      
2 S 0.055      
3 S -0.055      
4 S -0.055      


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 1.066 1.066
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -42.423 0.000 0.000
y 0.000 -45.048 0.000
z 0.000 0.000 -44.736
Traceless
 xyz
x 2.469 0.000 0.000
y 0.000 -1.469 0.000
z 0.000 0.000 -1.000
Polar
3z2-r2-2.001
x2-y22.625
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 1.209 0.000 0.000
y 0.000 9.359 0.000
z 0.000 0.000 6.329


<r2> (average value of r2) Å2
<r2> 194.755
(<r2>)1/2 13.955

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at HSEh1PBE/STO-3G
 hartrees
Energy at 0K-1574.619625
Energy at 298.15K 
HF Energy-1574.619625
Nuclear repulsion energy331.639611
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 HSEh1PBE/STO-3G
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 819 723 0.00 15.62 0.23 0.37
2 Ag 377 333 0.00 16.30 0.26 0.41
3 Au 231 204 0.00 0.00 0.00 0.00
4 B1u 802 708 36.66 0.00 0.00 0.00
5 B2u 122i 108i 20.14 0.00 0.00 0.00
6 B3g 347 306 0.00 9.03 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1226.9 cm-1
Scaled (by 0.8831) Zero Point Vibrational Energy (zpe) 1083.5 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 HSEh1PBE/STO-3G
ABC
0.14022 0.08220 0.05182

See section I.F.4 to change rotational constant units
Geometric Data calculated at HSEh1PBE/STO-3G

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.970 1.266
S2 0.000 0.970 -1.266
S3 0.000 -0.970 1.266
S4 0.000 -0.970 -1.266

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.53261.93923.1898
S22.53263.18981.9392
S31.93923.18982.5326
S43.18981.93922.5326

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 HSEh1PBE/STO-3G 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 -42.428 0.000 0.000
y 0.000 -44.647 0.000
z 0.000 0.000 -44.259
Traceless
 xyz
x 2.025 0.000 0.000
y 0.000 -1.303 0.000
z 0.000 0.000 -0.722
Polar
3z2-r2-1.444
x2-y22.218
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 1.192 0.000 0.000
y 0.000 6.523 0.000
z 0.000 0.000 9.019


<r2> (average value of r2) Å2
<r2> 190.136
(<r2>)1/2 13.789