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

using model chemistry: HSEh1PBE/6-31G**

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 HSEh1PBE/6-31G**
 hartrees
Energy at 0K-1592.154037
Energy at 298.15K 
HF Energy-1592.154037
Nuclear repulsion energy348.640244
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/6-31G**
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 514 490 0.00 51.83 0.07 0.13
2 A1 199 190 0.00 2.83 0.75 0.86
3 B1 448 428 0.00 36.13 0.75 0.86
4 B2 312 298 0.42 11.44 0.75 0.86
5 E 429 409 0.08 7.07 0.75 0.86
5 E 429 409 0.08 7.07 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1164.9 cm-1
Scaled (by 0.9543) Zero Point Vibrational Energy (zpe) 1111.6 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 HSEh1PBE/6-31G**
ABC
0.11631 0.11631 0.06364

See section I.F.4 to change rotational constant units
Geometric Data calculated at HSEh1PBE/6-31G**

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.439 0.313
S2 0.000 -1.439 0.313
S3 -1.439 0.000 -0.313
S4 1.439 0.000 -0.313

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.87832.12912.1291
S22.87832.12912.1291
S32.12912.12912.8783
S42.12912.12912.8783

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 47.473 S1 S3 S4 47.473
S2 S1 S3 47.473 S2 S4 S3 47.473
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at HSEh1PBE/6-31G** 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 -49.829 0.000 0.000
y 0.000 -49.829 0.000
z 0.000 0.000 -55.083
Traceless
 xyz
x 2.627 0.000 0.000
y 0.000 2.627 0.000
z 0.000 0.000 -5.254
Polar
3z2-r2-10.508
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 10.372 0.000 0.000
y 0.000 10.372 0.000
z 0.000 0.000 5.328


<r2> (average value of r2) Å2
<r2> 171.023
(<r2>)1/2 13.078

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at HSEh1PBE/6-31G**
 hartrees
Energy at 0K-1592.185136
Energy at 298.15K 
HF Energy-1592.185136
Nuclear repulsion energy330.133289
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/6-31G**
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 691 659 2.64 30.80 0.23 0.38
2 A1 355 339 7.29 34.36 0.23 0.37
3 A1 106 101 0.97 9.80 0.50 0.67
4 A2 216 207 0.00 0.20 0.75 0.86
5 B2 667 636 130.92 2.69 0.75 0.86
6 B2 336 321 0.04 15.43 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1185.0 cm-1
Scaled (by 0.9543) Zero Point Vibrational Energy (zpe) 1130.8 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 HSEh1PBE/6-31G**
ABC
0.15486 0.07110 0.04873

See section I.F.4 to change rotational constant units
Geometric Data calculated at HSEh1PBE/6-31G**

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.073 0.923
S2 0.000 -1.073 0.923
S3 0.000 1.599 -0.923
S4 0.000 -1.599 -0.923

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.14641.91863.2472
S22.14643.24721.9186
S31.91863.24723.1976
S43.24721.91863.1976

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 105.899 S1 S3 S4 74.101
S2 S1 S3 105.899 S2 S4 S3 74.101
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at HSEh1PBE/6-31G** 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 1.519 1.519
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -51.559 0.000 0.000
y 0.000 -54.239 0.000
z 0.000 0.000 -49.906
Traceless
 xyz
x 0.514 0.000 0.000
y 0.000 -3.506 0.000
z 0.000 0.000 2.992
Polar
3z2-r25.985
x2-y22.680
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 4.342 0.000 0.000
y 0.000 17.696 0.000
z 0.000 0.000 11.161


<r2> (average value of r2) Å2
<r2> 205.547
(<r2>)1/2 14.337

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at HSEh1PBE/6-31G**
 hartrees
Energy at 0K-1592.181827
Energy at 298.15K 
HF Energy-1592.181827
Nuclear repulsion energy332.848848
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/6-31G**
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 740 706 0.00 38.35 0.28 0.44
2 Ag 287 274 0.00 33.43 0.29 0.44
3 Au 248 236 0.00 0.00 0.00 0.00
4 B1u 690 659 144.03 0.00 0.00 0.00
5 B2u 106i 101i 18.61 0.00 0.00 0.00
6 B3g 337 322 0.00 17.44 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1098.0 cm-1
Scaled (by 0.9543) Zero Point Vibrational Energy (zpe) 1047.9 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 HSEh1PBE/6-31G**
ABC
0.14568 0.08010 0.05168

See section I.F.4 to change rotational constant units
Geometric Data calculated at HSEh1PBE/6-31G**

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.951 1.283
S2 0.000 0.951 -1.283
S3 0.000 -0.951 1.283
S4 0.000 -0.951 -1.283

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.56561.90243.1940
S22.56563.19401.9024
S31.90243.19402.5656
S43.19401.90242.5656

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/6-31G** 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 -51.929 0.000 0.000
y 0.000 -49.272 0.000
z 0.000 0.000 -53.889
Traceless
 xyz
x -0.349 0.000 0.000
y 0.000 3.637 0.000
z 0.000 0.000 -3.288
Polar
3z2-r2-6.576
x2-y2-2.657
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 4.300 0.000 0.000
y 0.000 11.722 0.000
z 0.000 0.000 16.819


<r2> (average value of r2) Å2
<r2> 195.515
(<r2>)1/2 13.983