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

using model chemistry: PBE1PBE/aug-cc-pVTZ

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/aug-cc-pVTZ
 hartrees
Energy at 0K-1592.259070
Energy at 298.15K 
HF Energy-1592.259070
Nuclear repulsion energy352.014258
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/aug-cc-pVTZ
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 540 519 0.00 39.67 0.04 0.08
2 A1 208 200 0.00 1.06 0.72 0.84
3 B1 479 461 0.00 16.19 0.75 0.86
4 B2 302 291 0.01 6.72 0.75 0.86
5 E 453 435 0.00 2.99 0.75 0.86
5 E 453 435 0.00 2.99 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1217.2 cm-1
Scaled (by 0.9615) Zero Point Vibrational Energy (zpe) 1170.4 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/aug-cc-pVTZ
ABC
0.11848 0.11848 0.06502

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

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.424 0.314
S2 0.000 -1.424 0.314
S3 -1.424 0.000 -0.314
S4 1.424 0.000 -0.314

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.84772.10952.1095
S22.84772.10952.1095
S32.10952.10952.8477
S42.10952.10952.8477

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 47.548 S1 S3 S4 47.548
S2 S1 S3 47.548 S2 S4 S3 47.548
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at PBE1PBE/aug-cc-pVTZ 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 -48.921 0.000 0.000
y 0.000 -48.921 0.000
z 0.000 0.000 -54.428
Traceless
 xyz
x 2.753 0.000 0.000
y 0.000 2.753 0.000
z 0.000 0.000 -5.507
Polar
3z2-r2-11.014
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 12.654 0.000 0.000
y 0.000 12.654 0.000
z 0.000 0.000 8.958


<r2> (average value of r2) Å2
<r2> 167.780
(<r2>)1/2 12.953

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at PBE1PBE/aug-cc-pVTZ
 hartrees
Energy at 0K-1592.280230
Energy at 298.15K 
HF Energy-1592.280230
Nuclear repulsion energy334.111186
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/aug-cc-pVTZ
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 6.96 30.72 0.06 0.11
2 A1 409 393 4.94 40.01 0.15 0.25
3 A1 118 114 0.42 10.61 0.38 0.55
4 A2 220 212 0.00 0.16 0.75 0.86
5 B2 674 648 121.51 3.97 0.75 0.86
6 B2 341 328 0.18 7.82 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1233.1 cm-1
Scaled (by 0.9615) Zero Point Vibrational Energy (zpe) 1185.6 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/aug-cc-pVTZ
ABC
0.15752 0.07313 0.04994

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

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.047 0.915
S2 0.000 -1.047 0.915
S3 0.000 1.584 -0.915
S4 0.000 -1.584 -0.915

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.09361.90683.2044
S22.09363.20441.9068
S31.90683.20443.1680
S43.20441.90683.1680

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 106.364 S1 S3 S4 73.636
S2 S1 S3 106.364 S2 S4 S3 73.636
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at PBE1PBE/aug-cc-pVTZ Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.180      
2 S 0.180      
3 S -0.180      
4 S -0.180      


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 1.364 1.364
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -51.418 0.000 0.000
y 0.000 -53.218 0.000
z 0.000 0.000 -48.567
Traceless
 xyz
x -0.526 0.000 0.000
y 0.000 -3.226 0.000
z 0.000 0.000 3.752
Polar
3z2-r27.504
x2-y21.800
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 8.177 0.000 0.000
y 0.000 19.821 0.000
z 0.000 0.000 13.089


<r2> (average value of r2) Å2
<r2> 200.808
(<r2>)1/2 14.171

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at PBE1PBE/aug-cc-pVTZ
 hartrees
Energy at 0K-1592.273850
Energy at 298.15K 
HF Energy-1592.273850
Nuclear repulsion energy338.443856
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/aug-cc-pVTZ
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 756 727 0.00 37.24 0.09 0.16
2 Ag 311 299 0.00 32.28 0.17 0.30
3 Au 258 248 0.00 0.00 0.00 0.00
4 B1u 696 669 124.06 0.00 0.00 0.00
5 B2u 161i 155i 16.60 0.00 0.00 0.00
6 B3g 349 335 0.00 8.54 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1104.2 cm-1
Scaled (by 0.9615) Zero Point Vibrational Energy (zpe) 1061.7 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/aug-cc-pVTZ
ABC
0.14789 0.08446 0.05376

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

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.944 1.249
S2 0.000 0.944 -1.249
S3 0.000 -0.944 1.249
S4 0.000 -0.944 -1.249

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.49861.88823.1318
S22.49863.13181.8882
S31.88823.13182.4986
S43.13181.88822.4986

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/aug-cc-pVTZ 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 -51.637 0.000 0.000
y 0.000 -47.850 0.000
z 0.000 0.000 -52.950
Traceless
 xyz
x -1.237 0.000 0.000
y 0.000 4.443 0.000
z 0.000 0.000 -3.206
Polar
3z2-r2-6.413
x2-y2-3.787
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 8.152 0.000 0.000
y 0.000 13.464 0.000
z 0.000 0.000 18.791


<r2> (average value of r2) Å2
<r2> 188.664
(<r2>)1/2 13.736