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

using model chemistry: PBEPBEultrafine/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 PBEPBEultrafine/cc-pVTZ
 hartrees
Energy at 0K-1592.138551
Energy at 298.15K 
HF Energy-1592.138551
Nuclear repulsion energy347.449158
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/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 505 501 0.00 37.65 0.04 0.08
2 A1 201 200 0.00 2.54 0.75 0.86
3 B1 422 419 0.00 17.61 0.75 0.86
4 B2 278 276 0.01 10.37 0.75 0.86
5 E 399 396 0.24 3.84 0.75 0.86
5 E 399 396 0.24 3.84 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1101.3 cm-1
Scaled (by 0.9931) Zero Point Vibrational Energy (zpe) 1093.7 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 PBEPBEultrafine/cc-pVTZ
ABC
0.11531 0.11531 0.06353

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

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.440 0.325
S2 0.000 -1.440 0.325
S3 -1.440 0.000 -0.325
S4 1.440 0.000 -0.325

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.88102.13842.1384
S22.88102.13842.1384
S32.13842.13842.8810
S42.13842.13842.8810

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 47.652 S1 S3 S4 47.652
S2 S1 S3 47.652 S2 S4 S3 47.652
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at PBEPBEultrafine/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 -48.732 0.000 0.000
y 0.000 -48.732 0.000
z 0.000 0.000 -54.082
Traceless
 xyz
x 2.675 0.000 0.000
y 0.000 2.675 0.000
z 0.000 0.000 -5.350
Polar
3z2-r2-10.701
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 11.637 0.000 0.000
y 0.000 11.637 0.000
z 0.000 0.000 6.823


<r2> (average value of r2) Å2
<r2> 171.114
(<r2>)1/2 13.081

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at PBEPBEultrafine/cc-pVTZ
 hartrees
Energy at 0K-1592.179695
Energy at 298.15K 
HF Energy-1592.179695
Nuclear repulsion energy329.856218
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/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 682 677 2.76 28.65 0.17 0.29
2 A1 307 305 5.20 30.98 0.20 0.33
3 A1 91 90 2.61 4.90 0.50 0.66
4 A2 218 216 0.00 0.04 0.75 0.86
5 B2 652 648 88.98 1.77 0.75 0.86
6 B2 321 319 0.00 12.46 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1135.5 cm-1
Scaled (by 0.9931) Zero Point Vibrational Energy (zpe) 1127.6 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 PBEPBEultrafine/cc-pVTZ
ABC
0.14912 0.07419 0.04954

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

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.117 0.940
S2 0.000 -1.117 0.940
S3 0.000 1.519 -0.940
S4 0.000 -1.519 -0.940

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.23301.92293.2374
S22.23303.23741.9229
S31.92293.23743.0375
S43.23741.92293.0375

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 102.075 S1 S3 S4 77.925
S2 S1 S3 102.075 S2 S4 S3 77.925
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at PBEPBEultrafine/cc-pVTZ Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.090      
2 S 0.090      
3 S -0.090      
4 S -0.090      


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 1.030 1.030
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -51.268 0.000 0.000
y 0.000 -52.769 0.000
z 0.000 0.000 -48.036
Traceless
 xyz
x -0.866 0.000 0.000
y 0.000 -3.116 0.000
z 0.000 0.000 3.982
Polar
3z2-r27.964
x2-y21.500
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 5.879 0.000 0.000
y 0.000 17.775 0.000
z 0.000 0.000 12.400


<r2> (average value of r2) Å2
<r2> 201.938
(<r2>)1/2 14.210

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at PBEPBEultrafine/cc-pVTZ
 hartrees
Energy at 0K-1592.178479
Energy at 298.15K 
HF Energy-1592.178479
Nuclear repulsion energy332.108361
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/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 706 702 0.00 32.31 0.19 0.32
2 Ag 278 276 0.00 30.02 0.23 0.38
3 Au 238 237 0.00 0.00 0.00 0.00
4 B1u 661 657 89.08 0.00 0.00 0.00
5 B2u 89i 88i 12.06 0.00 0.00 0.00
6 B3g 325 323 0.00 12.81 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1059.7 cm-1
Scaled (by 0.9931) Zero Point Vibrational Energy (zpe) 1052.3 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 PBEPBEultrafine/cc-pVTZ
ABC
0.14392 0.08041 0.05159

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

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.957 1.280
S2 0.000 0.957 -1.280
S3 0.000 -0.957 1.280
S4 0.000 -0.957 -1.280

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.56071.91413.1970
S22.56073.19701.9141
S31.91413.19702.5607
S43.19701.91412.5607

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/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 -51.450 0.000 0.000
y 0.000 -47.676 0.000
z 0.000 0.000 -52.569
Traceless
 xyz
x -1.327 0.000 0.000
y 0.000 4.333 0.000
z 0.000 0.000 -3.006
Polar
3z2-r2-6.012
x2-y2-3.773
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 5.868 0.000 0.000
y 0.000 12.675 0.000
z 0.000 0.000 17.226


<r2> (average value of r2) Å2
<r2> 195.112
(<r2>)1/2 13.968