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

using model chemistry: PBE1PBE/3-21G

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/3-21G
 hartrees
Energy at 0K-1584.675675
Energy at 298.15K 
HF Energy-1584.675675
Nuclear repulsion energy348.740318
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/3-21G
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 496 477 0.00 47.80 0.07 0.13
2 A1 199 191 0.00 3.55 0.75 0.86
3 B1 424 408 0.00 32.46 0.75 0.86
4 B2 318 306 0.56 12.45 0.75 0.86
5 E 401 385 0.08 7.10 0.75 0.86
5 E 401 385 0.08 7.10 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1119.7 cm-1
Scaled (by 0.9604) Zero Point Vibrational Energy (zpe) 1075.3 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 PBE1PBE/3-21G
ABC
0.11633 0.11633 0.06376

See section I.F.4 to change rotational constant units
Geometric Data calculated at PBE1PBE/3-21G

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.438 0.315
S2 0.000 -1.438 0.315
S3 -1.438 0.000 -0.315
S4 1.438 0.000 -0.315

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.87572.12902.1290
S22.87572.12902.1290
S32.12902.12902.8757
S42.12902.12902.8757

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 47.518 S1 S3 S4 47.518
S2 S1 S3 47.518 S2 S4 S3 47.518
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at PBE1PBE/3-21G 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 -50.294 0.000 0.000
y 0.000 -50.294 0.000
z 0.000 0.000 -55.505
Traceless
 xyz
x 2.606 0.000 0.000
y 0.000 2.606 0.000
z 0.000 0.000 -5.211
Polar
3z2-r2-10.422
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 10.062 0.000 0.000
y 0.000 10.062 0.000
z 0.000 0.000 4.804


<r2> (average value of r2) Å2
<r2> 171.175
(<r2>)1/2 13.083

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at PBE1PBE/3-21G
 hartrees
Energy at 0K-1584.711769
Energy at 298.15K 
HF Energy-1584.711769
Nuclear repulsion energy333.479376
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/3-21G
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 717 688 1.99 29.62 0.25 0.40
2 A1 305 293 6.22 35.86 0.25 0.40
3 A1 97 94 4.14 4.01 0.63 0.78
4 A2 232 223 0.00 0.10 0.75 0.86
5 B2 685 657 129.85 1.65 0.75 0.86
6 B2 348 334 0.01 16.13 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1191.7 cm-1
Scaled (by 0.9604) Zero Point Vibrational Energy (zpe) 1144.5 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 PBE1PBE/3-21G
ABC
0.15363 0.07508 0.05043

See section I.F.4 to change rotational constant units
Geometric Data calculated at PBE1PBE/3-21G

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.094 0.926
S2 0.000 -1.094 0.926
S3 0.000 1.521 -0.926
S4 0.000 -1.521 -0.926

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.18811.90123.2050
S22.18813.20501.9012
S31.90123.20503.0426
S43.20501.90123.0426

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 102.987 S1 S3 S4 77.013
S2 S1 S3 102.987 S2 S4 S3 77.013
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at PBE1PBE/3-21G Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.074      
2 S 0.074      
3 S -0.074      
4 S -0.074      


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 1.265 1.265
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -51.926 0.000 0.000
y 0.000 -54.301 0.000
z 0.000 0.000 -50.074
Traceless
 xyz
x 0.261 0.000 0.000
y 0.000 -3.301 0.000
z 0.000 0.000 3.040
Polar
3z2-r26.079
x2-y22.375
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 3.883 0.000 0.000
y 0.000 16.376 0.000
z 0.000 0.000 10.841


<r2> (average value of r2) Å2
<r2> 199.817
(<r2>)1/2 14.136

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at PBE1PBE/3-21G
 hartrees
Energy at 0K-1584.710936
Energy at 298.15K 
HF Energy-1584.710936
Nuclear repulsion energy333.527332
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/3-21G
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 755 725 0.00 34.15 0.30 0.46
2 Ag 297 286 0.00 33.32 0.28 0.44
3 Au 251 241 0.00 0.00 0.00 0.00
4 B1u 702 674 143.30 0.00 0.00 0.00
5 B2u 53i 51i 15.03 0.00 0.00 0.00
6 B3g 345 331 0.00 17.62 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1148.7 cm-1
Scaled (by 0.9604) Zero Point Vibrational Energy (zpe) 1103.2 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 PBE1PBE/3-21G
ABC
0.14758 0.07966 0.05174

See section I.F.4 to change rotational constant units
Geometric Data calculated at PBE1PBE/3-21G

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.945 1.286
S2 0.000 0.945 -1.286
S3 0.000 -0.945 1.286
S4 0.000 -0.945 -1.286

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.57271.89013.1924
S22.57273.19241.8901
S31.89013.19242.5727
S43.19241.89012.5727

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/3-21G 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 -52.211 0.000 0.000
y 0.000 -49.688 0.000
z 0.000 0.000 -53.886
Traceless
 xyz
x -0.425 0.000 0.000
y 0.000 3.361 0.000
z 0.000 0.000 -2.936
Polar
3z2-r2-5.872
x2-y2-2.524
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 3.841 0.000 0.000
y 0.000 11.269 0.000
z 0.000 0.000 16.049


<r2> (average value of r2) Å2
<r2> 195.494
(<r2>)1/2 13.982