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

using model chemistry: PBE1PBE/cc-pVDZ

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-pVDZ
 hartrees
Energy at 0K-1592.182500
Energy at 298.15K 
HF Energy-1592.182500
Nuclear repulsion energy347.704530
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-pVDZ
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 525 505 0.00 41.28 0.05 0.10
2 A1 197 189 0.00 3.53 0.75 0.86
3 B1 460 442 0.00 23.83 0.75 0.86
4 B2 304 293 0.08 11.30 0.75 0.86
5 E 437 420 0.10 5.65 0.75 0.86
5 E 437 420 0.10 5.65 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1179.4 cm-1
Scaled (by 0.9615) Zero Point Vibrational Energy (zpe) 1134.0 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-pVDZ
ABC
0.11564 0.11564 0.06338

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

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.442 0.316
S2 0.000 -1.442 0.316
S3 -1.442 0.000 -0.316
S4 1.442 0.000 -0.316

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.88422.13532.1353
S22.88422.13532.1353
S32.13532.13532.8842
S42.13532.13532.8842

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/cc-pVDZ 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 -48.918 0.000 0.000
y 0.000 -48.918 0.000
z 0.000 0.000 -54.574
Traceless
 xyz
x 2.828 0.000 0.000
y 0.000 2.828 0.000
z 0.000 0.000 -5.657
Polar
3z2-r2-11.314
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 10.256 0.000 0.000
y 0.000 10.256 0.000
z 0.000 0.000 5.033


<r2> (average value of r2) Å2
<r2> 171.236
(<r2>)1/2 13.086

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at PBE1PBE/cc-pVDZ
 hartrees
Energy at 0K-1592.207339
Energy at 298.15K 
HF Energy-1592.207339
Nuclear repulsion energy331.394619
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-pVDZ
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 703 676 3.21 27.58 0.22 0.36
2 A1 360 346 8.09 34.08 0.22 0.36
3 A1 118 114 1.82 8.03 0.50 0.67
4 A2 222 213 0.00 0.08 0.75 0.86
5 B2 675 649 122.97 2.09 0.75 0.86
6 B2 339 326 0.10 15.06 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1208.1 cm-1
Scaled (by 0.9615) Zero Point Vibrational Energy (zpe) 1161.6 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 PBE1PBE/cc-pVDZ
ABC
0.15181 0.07384 0.04968

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

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.081 0.932
S2 0.000 -1.081 0.932
S3 0.000 1.549 -0.932
S4 0.000 -1.549 -0.932

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.16291.92153.2240
S22.16293.22401.9215
S31.92153.22403.0987
S43.22401.92153.0987

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 104.094 S1 S3 S4 75.906
S2 S1 S3 104.094 S2 S4 S3 75.906
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at PBE1PBE/cc-pVDZ Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.096      
2 S 0.096      
3 S -0.096      
4 S -0.096      


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 1.357 1.357
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -51.297 0.000 0.000
y 0.000 -53.303 0.000
z 0.000 0.000 -48.443
Traceless
 xyz
x -0.424 0.000 0.000
y 0.000 -3.433 0.000
z 0.000 0.000 3.857
Polar
3z2-r27.713
x2-y22.006
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 4.152 0.000 0.000
y 0.000 16.552 0.000
z 0.000 0.000 10.976


<r2> (average value of r2) Å2
<r2> 201.675
(<r2>)1/2 14.201

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at PBE1PBE/cc-pVDZ
 hartrees
Energy at 0K-1592.204042
Energy at 298.15K 
HF Energy-1592.204042
Nuclear repulsion energy333.772747
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-pVDZ
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 746 718 0.00 32.34 0.27 0.42
2 Ag 300 289 0.00 33.64 0.27 0.43
3 Au 250 241 0.00 0.00 0.00 0.00
4 B1u 692 666 132.28 0.00 0.00 0.00
5 B2u 125i 121i 17.00 0.00 0.00 0.00
6 B3g 343 330 0.00 16.64 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1103.6 cm-1
Scaled (by 0.9615) Zero Point Vibrational Energy (zpe) 1061.1 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-pVDZ
ABC
0.14495 0.08147 0.05215

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

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.954 1.272
S2 0.000 0.954 -1.272
S3 0.000 -0.954 1.272
S4 0.000 -0.954 -1.272

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.54401.90723.1796
S22.54403.17961.9072
S31.90723.17962.5440
S43.17961.90722.5440

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-pVDZ 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 -51.588 0.000 0.000
y 0.000 -47.948 0.000
z 0.000 0.000 -53.035
Traceless
 xyz
x -1.097 0.000 0.000
y 0.000 4.364 0.000
z 0.000 0.000 -3.267
Polar
3z2-r2-6.535
x2-y2-3.640
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 4.126 0.000 0.000
y 0.000 11.422 0.000
z 0.000 0.000 15.877


<r2> (average value of r2) Å2
<r2> 193.517
(<r2>)1/2 13.911