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

using model chemistry: B3LYP/daug-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 B3LYP/daug-cc-pVTZ
 hartrees
Energy at 0K-1592.869242
Energy at 298.15K 
HF Energy-1592.869242
Nuclear repulsion energy346.691008
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 B3LYP/daug-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 504 504 0.00 43.93 0.05 0.09
2 A1 196 196 0.00 1.19 0.74 0.85
3 B1 441 441 0.00 18.53 0.75 0.86
4 B2 298 298 0.03 7.48 0.75 0.86
5 E 415 415 0.02 3.22 0.75 0.86
5 E 415 415 0.02 3.22 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1134.3 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1134.3 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 B3LYP/daug-cc-pVTZ
ABC
0.11506 0.11506 0.06286

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3LYP/daug-cc-pVTZ

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.448 0.312
S2 0.000 -1.448 0.312
S3 -1.448 0.000 -0.312
S4 1.448 0.000 -0.312

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.89612.14062.1406
S22.89612.14062.1406
S32.14062.14062.8961
S42.14062.14062.8961

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 47.433 S1 S3 S4 47.433
S2 S1 S3 47.433 S2 S4 S3 47.433
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B3LYP/daug-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 -49.304 0.000 0.000
y 0.000 -49.304 0.000
z 0.000 0.000 -54.760
Traceless
 xyz
x 2.728 0.000 0.000
y 0.000 2.728 0.000
z 0.000 0.000 -5.457
Polar
3z2-r2-10.913
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 13.229 0.000 0.000
y 0.000 13.229 0.000
z 0.000 0.000 9.254


<r2> (average value of r2) Å2
<r2> 172.346
(<r2>)1/2 13.128

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at B3LYP/daug-cc-pVTZ
 hartrees
Energy at 0K-1592.897446
Energy at 298.15K 
HF Energy-1592.897446
Nuclear repulsion energy328.617063
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 B3LYP/daug-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 667 667 5.86 31.82 0.06 0.12
2 A1 361 361 4.93 37.95 0.14 0.25
3 A1 107 107 0.34 11.53 0.39 0.56
4 A2 207 207 0.00 0.12 0.75 0.86
5 B2 642 642 120.15 4.06 0.75 0.86
6 B2 328 328 0.16 8.27 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1156.1 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1156.1 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 B3LYP/daug-cc-pVTZ
ABC
0.15587 0.06925 0.04795

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3LYP/daug-cc-pVTZ

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.069 0.920
S2 0.000 -1.069 0.920
S3 0.000 1.632 -0.920
S4 0.000 -1.632 -0.920

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.13811.92353.2680
S22.13813.26801.9235
S31.92353.26803.2646
S43.26801.92353.2646

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 107.026 S1 S3 S4 72.974
S2 S1 S3 107.026 S2 S4 S3 72.974
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B3LYP/daug-cc-pVTZ Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.286      
2 S 0.286      
3 S -0.286      
4 S -0.286      


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 1.334 1.334
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -51.731 0.000 0.000
y 0.000 -53.610 0.000
z 0.000 0.000 -49.069
Traceless
 xyz
x -0.392 0.000 0.000
y 0.000 -3.210 0.000
z 0.000 0.000 3.601
Polar
3z2-r27.203
x2-y21.879
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 8.461 0.000 0.000
y 0.000 20.760 0.000
z 0.000 0.000 13.543


<r2> (average value of r2) Å2
<r2> 208.102
(<r2>)1/2 14.426

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at B3LYP/daug-cc-pVTZ
 hartrees
Energy at 0K-1592.892078
Energy at 298.15K 
HF Energy-1592.892078
Nuclear repulsion energy332.458771
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 B3LYP/daug-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 717 717 0.00 36.74 0.09 0.17
2 Ag 282 282 0.00 33.70 0.17 0.30
3 Au 242 242 0.00 0.00 0.00 0.00
4 B1u 663 663 123.46 0.00 0.00 0.00
5 B2u 139i 139i 14.09 0.00 0.00 0.00
6 B3g 331 331 0.00 8.92 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1047.5 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1047.5 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 B3LYP/daug-cc-pVTZ
ABC
0.14524 0.07997 0.05158

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3LYP/daug-cc-pVTZ

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.953 1.284
S2 0.000 0.953 -1.284
S3 0.000 -0.953 1.284
S4 0.000 -0.953 -1.284

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.56771.90533.1974
S22.56773.19741.9053
S31.90533.19742.5677
S43.19741.90532.5677

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 B3LYP/daug-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 -51.953 0.000 0.000
y 0.000 -48.329 0.000
z 0.000 0.000 -53.229
Traceless
 xyz
x -1.174 0.000 0.000
y 0.000 4.262 0.000
z 0.000 0.000 -3.088
Polar
3z2-r2-6.176
x2-y2-3.624
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 8.440 0.000 0.000
y 0.000 13.969 0.000
z 0.000 0.000 19.604


<r2> (average value of r2) Å2
<r2> 195.530
(<r2>)1/2 13.983