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

using model chemistry: PBEPBEultrafine/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 no C2V 1A1
1 3 yes D2H 1AG

Conformer 1 (D2D)

Jump to S1C2 S1C3
Energy calculated at PBEPBEultrafine/6-31G**
 hartrees
Energy at 0K-1591.971087
Energy at 298.15K 
HF Energy-1591.971087
Nuclear repulsion energy343.446040
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**
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 477 471 0.00 47.12 0.07 0.13
2 A1 195 192 0.00 3.42 0.75 0.86
3 B1 379 374 0.00 37.13 0.75 0.86
4 B2 285 281 0.32 14.83 0.75 0.86
5 E 369 364 0.86 5.60 0.75 0.86
5 E 369 364 0.86 5.60 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1036.7 cm-1
Scaled (by 0.9863) Zero Point Vibrational Energy (zpe) 1022.5 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 PBEPBEultrafine/6-31G**
ABC
0.11273 0.11273 0.06198

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

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.458 0.325
S2 0.000 -1.458 0.325
S3 -1.458 0.000 -0.325
S4 1.458 0.000 -0.325

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.91672.16272.1627
S22.91672.16272.1627
S32.16272.16272.9167
S42.16272.16272.9167

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 47.599 S1 S3 S4 47.599
S2 S1 S3 47.599 S2 S4 S3 47.599
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at PBEPBEultrafine/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 -49.715 0.000 0.000
y 0.000 -49.715 0.000
z 0.000 0.000 -54.955
Traceless
 xyz
x 2.620 0.000 0.000
y 0.000 2.620 0.000
z 0.000 0.000 -5.240
Polar
3z2-r2-10.479
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 10.734 0.000 0.000
y 0.000 10.734 0.000
z 0.000 0.000 5.466


<r2> (average value of r2) Å2
<r2> 175.037
(<r2>)1/2 13.230

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at PBEPBEultrafine/6-31G**
 hartrees
Energy at 0K-1592.022673
Energy at 298.15K 
HF Energy-1592.022673
Nuclear repulsion energy327.328581
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**
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 692 682 0.00 35.70 0.27 0.43
2 A1 262 259 0.00 27.86 0.27 0.43
3 A1 13 12 12.06 0.00 0.68 0.81
4 A2 229 226 0.00 0.00 0.75 0.86
5 B2 653 644 99.51 0.00 0.75 0.86
6 B2 315 310 0.00 16.82 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1081.6 cm-1
Scaled (by 0.9863) Zero Point Vibrational Energy (zpe) 1066.8 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 PBEPBEultrafine/6-31G**
ABC
0.14164 0.07702 0.04989

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

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.304 0.965
S2 0.000 -1.304 0.965
S3 0.000 1.312 -0.965
S4 0.000 -1.312 -0.965

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.60881.92943.2508
S22.60883.25081.9294
S31.92943.25082.6240
S43.25081.92942.6240

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 90.225 S1 S3 S4 89.775
S2 S1 S3 90.225 S2 S4 S3 89.775
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at PBEPBEultrafine/6-31G** Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.001      
2 S 0.001      
3 S -0.001      
4 S -0.001      


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 0.023 0.023
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -51.816 0.000 0.000
y 0.000 -53.503 0.000
z 0.000 0.000 -49.039
Traceless
 xyz
x -0.545 0.000 0.000
y 0.000 -3.075 0.000
z 0.000 0.000 3.620
Polar
3z2-r27.241
x2-y21.687
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 4.328 0.000 0.000
y 0.000 16.675 0.000
z 0.000 0.000 12.024


<r2> (average value of r2) Å2
<r2> 201.223
(<r2>)1/2 14.185

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at PBEPBEultrafine/6-31G**
 hartrees
Energy at 0K-1592.022673
Energy at 298.15K 
HF Energy-1592.022673
Nuclear repulsion energy327.319586
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**
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 692 682 0.00 35.70 0.27 0.43
2 Ag 262 259 0.00 27.86 0.27 0.43
3 Au 229 226 0.00 0.00 0.00 0.00
4 B1u 653 644 99.56 0.00 0.00 0.00
5 B2u 11 11 12.05 0.00 0.00 0.00
6 B3g 315 310 0.00 16.82 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1080.7 cm-1
Scaled (by 0.9863) Zero Point Vibrational Energy (zpe) 1065.9 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**
ABC
0.14166 0.07701 0.04989

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

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.965 1.308
S2 0.000 0.965 -1.308
S3 0.000 -0.965 1.308
S4 0.000 -0.965 -1.308

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.61661.92933.2510
S22.61663.25101.9293
S31.92933.25102.6166
S43.25101.92932.6166

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** 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 -51.816 0.000 0.000
y 0.000 -49.040 0.000
z 0.000 0.000 -53.500
Traceless
 xyz
x -0.546 0.000 0.000
y 0.000 3.618 0.000
z 0.000 0.000 -3.072
Polar
3z2-r2-6.144
x2-y2-2.776
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 4.328 0.000 0.000
y 0.000 12.024 0.000
z 0.000 0.000 16.677


<r2> (average value of r2) Å2
<r2> 201.239
(<r2>)1/2 14.186