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

using model chemistry: B3LYP/CEP-121G*

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/CEP-121G*
 hartrees
Energy at 0K-40.546397
Energy at 298.15K 
HF Energy-40.546397
Nuclear repulsion energy48.214724
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/CEP-121G*
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 499 484 0.00 51.52 0.06 0.12
2 A1 191 185 0.00 2.10 0.75 0.86
3 B1 432 419 0.00 34.85 0.75 0.86
4 B2 297 288 0.04 10.89 0.75 0.86
5 E 414 402 0.20 6.50 0.75 0.86
5 E 414 402 0.20 6.50 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1123.9 cm-1
Scaled (by 0.9694) Zero Point Vibrational Energy (zpe) 1089.5 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/CEP-121G*
ABC
0.11247 0.11247 0.06158

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3LYP/CEP-121G*

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.463 0.319
S2 0.000 -1.463 0.319
S3 -1.463 0.000 -0.319
S4 1.463 0.000 -0.319

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.92602.16522.1652
S22.92602.16522.1652
S32.16522.16522.9260
S42.16522.16522.9260

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 47.492 S1 S3 S4 47.492
S2 S1 S3 47.492 S2 S4 S3 47.492
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B3LYP/CEP-121G* 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 -46.278 0.000 0.000
y 0.000 -46.278 0.000
z 0.000 0.000 -51.996
Traceless
 xyz
x 2.859 0.000 0.000
y 0.000 2.859 0.000
z 0.000 0.000 -5.718
Polar
3z2-r2-11.436
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 11.271 0.000 0.000
y 0.000 11.271 0.000
z 0.000 0.000 6.340


<r2> (average value of r2) Å2
<r2> 83.909
(<r2>)1/2 9.160

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at B3LYP/CEP-121G*
 hartrees
Energy at 0K-40.573692
Energy at 298.15K 
HF Energy-40.573692
Nuclear repulsion energy45.634486
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/CEP-121G*
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 659 639 2.95 34.25 0.20 0.34
2 A1 337 326 7.10 34.62 0.22 0.36
3 A1 94 91 1.06 10.29 0.47 0.64
4 A2 205 199 0.00 0.24 0.75 0.86
5 B2 636 617 128.03 2.83 0.75 0.86
6 B2 317 308 0.04 15.18 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1124.0 cm-1
Scaled (by 0.9694) Zero Point Vibrational Energy (zpe) 1089.6 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 B3LYP/CEP-121G*
ABC
0.14931 0.06894 0.04716

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3LYP/CEP-121G*

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.100 0.940
S2 0.000 -1.100 0.940
S3 0.000 1.617 -0.940
S4 0.000 -1.617 -0.940

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.19931.94913.3033
S22.19933.30331.9491
S31.94913.30333.2341
S43.30331.94913.2341

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 105.395 S1 S3 S4 74.605
S2 S1 S3 105.395 S2 S4 S3 74.605
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B3LYP/CEP-121G* Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.116      
2 S 0.116      
3 S -0.116      
4 S -0.116      


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 1.482 1.482
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -48.672 0.000 0.000
y 0.000 -51.032 0.000
z 0.000 0.000 -46.118
Traceless
 xyz
x -0.097 0.000 0.000
y 0.000 -3.637 0.000
z 0.000 0.000 3.734
Polar
3z2-r27.468
x2-y22.360
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 5.197 0.000 0.000
y 0.000 18.991 0.000
z 0.000 0.000 11.969


<r2> (average value of r2) Å2
<r2> 97.436
(<r2>)1/2 9.871

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at B3LYP/CEP-121G*
 hartrees
Energy at 0K-40.570826
Energy at 298.15K 
HF Energy-40.570826
Nuclear repulsion energy46.151975
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/CEP-121G*
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 704 683 0.00 41.79 0.24 0.39
2 Ag 278 269 0.00 33.77 0.28 0.44
3 Au 236 229 0.00 0.00 0.00 0.00
4 B1u 657 637 135.74 0.00 0.00 0.00
5 B2u 107i 103i 18.76 0.00 0.00 0.00
6 B3g 321 311 0.00 16.77 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1044.8 cm-1
Scaled (by 0.9694) Zero Point Vibrational Energy (zpe) 1012.9 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 B3LYP/CEP-121G*
ABC
0.14109 0.07820 0.05031

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3LYP/CEP-121G*

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.967 1.298
S2 0.000 0.967 -1.298
S3 0.000 -0.967 1.298
S4 0.000 -0.967 -1.298

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.59661.93323.2372
S22.59663.23721.9332
S31.93323.23722.5966
S43.23721.93322.5966

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/CEP-121G* 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 -48.966 0.000 0.000
y 0.000 -45.439 0.000
z 0.000 0.000 -50.878
Traceless
 xyz
x -0.808 0.000 0.000
y 0.000 4.483 0.000
z 0.000 0.000 -3.675
Polar
3z2-r2-7.350
x2-y2-3.528
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 5.190 0.000 0.000
y 0.000 12.447 0.000
z 0.000 0.000 17.971


<r2> (average value of r2) Å2
<r2> 93.124
(<r2>)1/2 9.650