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

using model chemistry: M06-2X/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 yes C2V 1A1
1 3 no D2H 1AG

Conformer 1 (D2D)

Jump to S1C2 S1C3
Energy calculated at M06-2X/3-21G*
 hartrees
Energy at 0K-1585.152372
Energy at 298.15K 
HF Energy-1585.152372
Nuclear repulsion energy348.715664
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 M06-2X/3-21G*
Mode Number Symmetry Frequency
(cm-1)
Scaled Frequency
(cm-1)
IR Intensities
(km mol-1)
Raman Act
(Å4/u)
Dep P Dep U
1 A1 502 476 0.00 53.80 0.07 0.13
2 A1 188 178 0.00 3.29 0.74 0.85
3 B1 443 420 0.00 35.45 0.75 0.86
4 B2 329 312 0.42 11.61 0.75 0.86
5 E 416 394 0.00 8.13 0.75 0.86
5 E 416 394 0.00 8.13 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1147.1 cm-1
Scaled (by 0.9472) Zero Point Vibrational Energy (zpe) 1086.5 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 M06-2X/3-21G*
ABC
0.11635 0.11635 0.06369

See section I.F.4 to change rotational constant units
Geometric Data calculated at M06-2X/3-21G*

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.439 0.313
S2 0.000 -1.439 0.313
S3 -1.439 0.000 -0.313
S4 1.439 0.000 -0.313

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.87732.12882.1288
S22.87732.12882.1288
S32.12882.12882.8773
S42.12882.12882.8773

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 47.482 S1 S3 S4 47.482
S2 S1 S3 47.482 S2 S4 S3 47.482
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at M06-2X/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 -50.328 0.000 0.000
y 0.000 -50.328 0.000
z 0.000 0.000 -55.456
Traceless
 xyz
x 2.564 0.000 0.000
y 0.000 2.564 0.000
z 0.000 0.000 -5.128
Polar
3z2-r2-10.256
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 10.227 0.000 0.000
y 0.000 10.227 0.000
z 0.000 0.000 4.813


<r2> (average value of r2) Å2
<r2> 171.238
(<r2>)1/2 13.086

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at M06-2X/3-21G*
 hartrees
Energy at 0K-1585.172407
Energy at 298.15K 
HF Energy-1585.172407
Nuclear repulsion energy334.824223
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 M06-2X/3-21G*
Mode Number Symmetry Frequency
(cm-1)
Scaled Frequency
(cm-1)
IR Intensities
(km mol-1)
Raman Act
(Å4/u)
Dep P Dep U
1 A1 708 671 2.71 31.28 0.20 0.33
2 A1 366 347 7.28 47.48 0.25 0.40
3 A1 120 114 1.39 10.81 0.51 0.68
4 A2 224 212 0.00 0.26 0.75 0.86
5 B2 677 641 173.21 2.94 0.75 0.86
6 B2 348 330 0.11 14.62 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1221.7 cm-1
Scaled (by 0.9472) Zero Point Vibrational Energy (zpe) 1157.2 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 M06-2X/3-21G*
ABC
0.15749 0.07385 0.05027

See section I.F.4 to change rotational constant units
Geometric Data calculated at M06-2X/3-21G*

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.049 0.915
S2 0.000 -1.049 0.915
S3 0.000 1.571 -0.915
S4 0.000 -1.571 -0.915

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.09891.90263.1962
S22.09893.19621.9026
S31.90263.19623.1423
S43.19621.90263.1423

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 105.914 S1 S3 S4 74.086
S2 S1 S3 105.914 S2 S4 S3 74.086
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at M06-2X/3-21G* Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.098      
2 S 0.098      
3 S -0.098      
4 S -0.098      


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 1.629 1.629
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -51.836 0.000 0.000
y 0.000 -54.632 0.000
z 0.000 0.000 -50.318
Traceless
 xyz
x 0.639 0.000 0.000
y 0.000 -3.555 0.000
z 0.000 0.000 2.916
Polar
3z2-r25.833
x2-y22.796
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 3.913 0.000 0.000
y 0.000 17.530 0.000
z 0.000 0.000 10.586


<r2> (average value of r2) Å2
<r2> 200.446
(<r2>)1/2 14.158

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at M06-2X/3-21G*
 hartrees
Energy at 0K-1585.168735
Energy at 298.15K 
HF Energy-1585.168735
Nuclear repulsion energy336.127491
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 M06-2X/3-21G*
Mode Number Symmetry Frequency
(cm-1)
Scaled Frequency
(cm-1)
IR Intensities
(km mol-1)
Raman Act
(Å4/u)
Dep P Dep U
1 Ag 768 727 0.00 36.22 0.30 0.46
2 Ag 319 302 0.00 48.61 0.29 0.45
3 Au 256 242 0.00 0.00 0.00 0.00
4 B1u 702 665 200.24 0.00 0.00 0.00
5 B2u 118i 112i 19.93 0.00 0.00 0.00
6 B3g 350 332 0.00 17.91 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1138.3 cm-1
Scaled (by 0.9472) Zero Point Vibrational Energy (zpe) 1078.2 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 M06-2X/3-21G*
ABC
0.14896 0.08145 0.05266

See section I.F.4 to change rotational constant units
Geometric Data calculated at M06-2X/3-21G*

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.941 1.272
S2 0.000 0.941 -1.272
S3 0.000 -0.941 1.272
S4 0.000 -0.941 -1.272

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.54421.88143.1643
S22.54423.16431.8814
S31.88143.16432.5442
S43.16431.88142.5442

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 M06-2X/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 -52.239 0.000 0.000
y 0.000 -49.785 0.000
z 0.000 0.000 -54.011
Traceless
 xyz
x -0.341 0.000 0.000
y 0.000 3.339 0.000
z 0.000 0.000 -2.999
Polar
3z2-r2-5.997
x2-y2-2.453
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 3.853 0.000 0.000
y 0.000 11.186 0.000
z 0.000 0.000 16.742


<r2> (average value of r2) Å2
<r2> 192.688
(<r2>)1/2 13.881