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

using model chemistry: B3LYPultrafine/3-21G

19 10 17 12 22

States and conformations

State Conformation minimum conformation conformer description state description
1 1 no D2D 1A1
1 2 no C2V 1A1
1 3 yes D2H 1AG

Conformer 1 (D2D)

Jump to S1C2 S1C3
Energy calculated at B3LYPultrafine/3-21G
 hartrees
Energy at 0K-1584.861888
Energy at 298.15K 
HF Energy-1584.861888
Nuclear repulsion energy314.959114
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 B3LYPultrafine/3-21G
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 443 428 0.00 46.08 0.06 0.12
2 A1 147 141 0.00 9.76 0.75 0.86
3 B1 351 339 0.00 29.50 0.75 0.86
4 B2 257 248 0.14 17.28 0.75 0.86
5 E 348 336 0.07 8.94 0.75 0.86
5 E 348 336 0.07 8.94 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 946.8 cm-1
Scaled (by 0.9649) Zero Point Vibrational Energy (zpe) 913.5 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 B3LYPultrafine/3-21G
ABC
0.09472 0.09472 0.05225

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3LYPultrafine/3-21G

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.588 0.361
S2 0.000 -1.588 0.361
S3 -1.588 0.000 -0.361
S4 1.588 0.000 -0.361

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S13.17682.35942.3594
S23.17682.35942.3594
S32.35942.35943.1768
S42.35942.35943.1768

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 47.683 S1 S3 S4 47.683
S2 S1 S3 47.683 S2 S4 S3 47.683
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B3LYPultrafine/3-21G 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 -51.669 0.000 0.000
y 0.000 -51.669 0.000
z 0.000 0.000 -56.622
Traceless
 xyz
x 2.476 0.000 0.000
y 0.000 2.476 0.000
z 0.000 0.000 -4.953
Polar
3z2-r2-9.906
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 12.578 0.000 0.000
y 0.000 12.578 0.000
z 0.000 0.000 4.136


<r2> (average value of r2) Å2
<r2> 203.103
(<r2>)1/2 14.251

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at B3LYPultrafine/3-21G
 hartrees
Energy at 0K-1584.878301
Energy at 298.15K 
HF Energy-1584.878301
Nuclear repulsion energy308.395721
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 B3LYPultrafine/3-21G
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 562 543 0.00 32.79 0.28 0.44
2 A1 287 277 0.00 30.70 0.26 0.42
3 A1 102 98 7.92 0.00 0.49 0.66
4 A2 194 187 0.00 0.00 0.75 0.86
5 B2 530 511 72.33 0.00 0.75 0.86
6 B2 269 259 0.00 21.59 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 971.8 cm-1
Scaled (by 0.9649) Zero Point Vibrational Energy (zpe) 937.7 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 B3LYPultrafine/3-21G
ABC
0.12180 0.07074 0.04475

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3LYPultrafine/3-21G

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.365 1.040
S2 0.000 -1.365 1.040
S3 0.000 1.365 -1.040
S4 0.000 -1.365 -1.040

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.73082.08063.4325
S22.73083.43252.0806
S32.08063.43252.7295
S43.43252.08062.7295

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 89.981 S1 S3 S4 90.019
S2 S1 S3 89.981 S2 S4 S3 90.019
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B3LYPultrafine/3-21G 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 -0.002 0.002
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -53.279 0.000 0.000
y 0.000 -55.159 0.000
z 0.000 0.000 -51.973
Traceless
 xyz
x 0.287 0.000 0.000
y 0.000 -2.533 0.000
z 0.000 0.000 2.246
Polar
3z2-r24.491
x2-y21.880
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 2.781 0.000 0.000
y 0.000 16.919 0.000
z 0.000 0.000 13.141


<r2> (average value of r2) Å2
<r2> 221.915
(<r2>)1/2 14.897

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at B3LYPultrafine/3-21G
 hartrees
Energy at 0K-1584.878301
Energy at 298.15K 
HF Energy-1584.878301
Nuclear repulsion energy308.418439
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 B3LYPultrafine/3-21G
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 563 543 0.00 32.79 0.28 0.44
2 Ag 287 277 0.00 30.69 0.26 0.42
3 Au 194 187 0.00 0.00 0.00 0.00
4 B1u 530 511 72.39 0.00 0.00 0.00
5 B2u 102 98 7.92 0.00 0.00 0.00
6 B3g 269 259 0.00 21.59 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 972.1 cm-1
Scaled (by 0.9649) Zero Point Vibrational Energy (zpe) 937.9 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 B3LYPultrafine/3-21G
ABC
0.12184 0.07074 0.04475

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3LYPultrafine/3-21G

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.040 1.365
S2 0.000 1.040 -1.365
S3 0.000 -1.040 1.365
S4 0.000 -1.040 -1.365

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.73012.08033.4324
S22.73013.43242.0803
S32.08033.43242.7301
S43.43242.08032.7301

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 B3LYPultrafine/3-21G 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 -53.278 0.000 0.000
y 0.000 -51.976 0.000
z 0.000 0.000 -55.158
Traceless
 xyz
x 0.289 0.000 0.000
y 0.000 2.242 0.000
z 0.000 0.000 -2.531
Polar
3z2-r2-5.062
x2-y2-1.302
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 2.781 0.000 0.000
y 0.000 13.138 0.000
z 0.000 0.000 16.919


<r2> (average value of r2) Å2
<r2> 221.895
(<r2>)1/2 14.896