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

using model chemistry: PBE1PBE/cc-pCVTZ

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-pCVTZ
 hartrees
Energy at 0K-1592.272498
Energy at 298.15K 
HF Energy-1592.272498
Nuclear repulsion energy353.670711
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-pCVTZ
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 544 544 0.00      
2 A1 210 210 0.00      
3 B1 484 484 0.00      
4 B2 302 302 0.00      
5 E 456 456 0.00      
5 E 456 456 0.00      

Unscaled Zero Point Vibrational Energy (zpe) 1225.8 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1225.8 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 PBE1PBE/cc-pCVTZ
ABC
0.11960 0.11960 0.06563

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

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.417 0.313
S2 0.000 -1.417 0.313
S3 -1.417 0.000 -0.313
S4 1.417 0.000 -0.313

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.83452.09962.0996
S22.83452.09962.0996
S32.09962.09962.8345
S42.09962.09962.8345

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 47.547 S1 S3 S4 47.547
S2 S1 S3 47.547 S2 S4 S3 47.547
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at PBE1PBE/cc-pCVTZ 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 -48.558 0.000 0.000
y 0.000 -48.558 0.000
z 0.000 0.000 -53.982
Traceless
 xyz
x 2.712 0.000 0.000
y 0.000 2.712 0.000
z 0.000 0.000 -5.423
Polar
3z2-r2-10.847
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 11.234 0.000 0.000
y 0.000 11.234 0.000
z 0.000 0.000 6.738


<r2> (average value of r2) Å2
<r2> 166.266
(<r2>)1/2 12.894

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at PBE1PBE/cc-pCVTZ
 hartrees
Energy at 0K-1592.295592
Energy at 298.15K 
HF Energy-1592.295592
Nuclear repulsion energy335.337953
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-pCVTZ
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 711 711 7.56      
2 A1 421 421 4.79      
3 A1 117 117 0.28      
4 A2 223 223 0.00      
5 B2 680 680 122.28      
6 B2 346 346 0.22      

Unscaled Zero Point Vibrational Energy (zpe) 1248.6 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1248.6 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-pCVTZ
ABC
0.16004 0.07296 0.05011

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

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.037 0.908
S2 0.000 -1.037 0.908
S3 0.000 1.593 -0.908
S4 0.000 -1.593 -0.908

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.07441.89833.1957
S22.07443.19571.8983
S31.89833.19573.1859
S43.19571.89833.1859

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 107.023 S1 S3 S4 72.977
S2 S1 S3 107.023 S2 S4 S3 72.977
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at PBE1PBE/cc-pCVTZ Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.137      
2 S 0.137      
3 S -0.137      
4 S -0.137      


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 1.430 1.430
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -50.914 0.000 0.000
y 0.000 -52.918 0.000
z 0.000 0.000 -48.296
Traceless
 xyz
x -0.307 0.000 0.000
y 0.000 -3.313 0.000
z 0.000 0.000 3.620
Polar
3z2-r27.240
x2-y22.004
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 5.935 0.000 0.000
y 0.000 18.131 0.000
z 0.000 0.000 11.731


<r2> (average value of r2) Å2
<r2> 200.011
(<r2>)1/2 14.143

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at PBE1PBE/cc-pCVTZ
 hartrees
Energy at 0K-1592.288265
Energy at 298.15K 
HF Energy-1592.288265
Nuclear repulsion energy340.076061
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-pCVTZ
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 763 763 0.00      
2 Ag 312 312 0.00      
3 Au 263 263 0.00      
4 B1u 701 701 124.40      
5 B2u 170i 170i 18.17      
6 B3g 354 354 0.00      

Unscaled Zero Point Vibrational Energy (zpe) 1111.5 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1111.5 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/cc-pCVTZ
ABC
0.14922 0.08534 0.05429

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

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.940 1.243
S2 0.000 0.940 -1.243
S3 0.000 -0.940 1.243
S4 0.000 -0.940 -1.243

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.48571.87983.1164
S22.48573.11641.8798
S31.87983.11642.4857
S43.11641.87982.4857

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-pCVTZ 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 -51.254 0.000 0.000
y 0.000 -47.546 0.000
z 0.000 0.000 -52.592
Traceless
 xyz
x -1.185 0.000 0.000
y 0.000 4.377 0.000
z 0.000 0.000 -3.192
Polar
3z2-r2-6.384
x2-y2-3.708
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 5.912 0.000 0.000
y 0.000 12.243 0.000
z 0.000 0.000 17.038


<r2> (average value of r2) Å2
<r2> 186.910
(<r2>)1/2 13.671