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

using model chemistry: M06-2X/cc-pCVTZ

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/cc-pCVTZ
 hartrees
Energy at 0K-1592.762603
Energy at 298.15K 
HF Energy-1592.762603
Nuclear repulsion energy353.200268
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/cc-pCVTZ
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 545 545 0.00      
2 A1 205 205 0.00      
3 B1 496 496 0.00      
4 B2 308 308 0.00      
5 E 468 468 0.01      
5 E 468 468 0.01      

Unscaled Zero Point Vibrational Energy (zpe) 1244.4 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1244.4 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/cc-pCVTZ
ABC
0.11932 0.11932 0.06540

See section I.F.4 to change rotational constant units
Geometric Data calculated at M06-2X/cc-pCVTZ

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.420 0.311
S2 0.000 -1.420 0.311
S3 -1.420 0.000 -0.311
S4 1.420 0.000 -0.311

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.83942.10212.1021
S22.83942.10212.1021
S32.10212.10212.8394
S42.10212.10212.8394

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 47.517 S1 S3 S4 47.517
S2 S1 S3 47.517 S2 S4 S3 47.517
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at M06-2X/cc-pCVTZ 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 -48.876 0.000 0.000
y 0.000 -48.876 0.000
z 0.000 0.000 -54.313
Traceless
 xyz
x 2.719 0.000 0.000
y 0.000 2.719 0.000
z 0.000 0.000 -5.438
Polar
3z2-r2-10.875
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 11.392 0.000 0.000
y 0.000 11.392 0.000
z 0.000 0.000 6.697


<r2> (average value of r2) Å2
<r2> 166.857
(<r2>)1/2 12.917

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at M06-2X/cc-pCVTZ
 hartrees
Energy at 0K-1592.774415
Energy at 298.15K 
HF Energy-1592.774415
Nuclear repulsion energy335.796712
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/cc-pCVTZ
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 709 709 9.16      
2 A1 466 466 4.50      
3 A1 133 133 0.10      
4 A2 222 222 0.00      
5 B2 673 673 172.57      
6 B2 347 347 0.44      

Unscaled Zero Point Vibrational Energy (zpe) 1274.7 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1274.7 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 M06-2X/cc-pCVTZ
ABC
0.16232 0.07208 0.04992

See section I.F.4 to change rotational constant units
Geometric Data calculated at M06-2X/cc-pCVTZ

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.019 0.901
S2 0.000 -1.019 0.901
S3 0.000 1.618 -0.901
S4 0.000 -1.618 -0.901

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.03771.89943.1943
S22.03773.19431.8994
S31.89943.19433.2368
S43.19431.89943.2368

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 108.400 S1 S3 S4 71.600
S2 S1 S3 108.400 S2 S4 S3 71.600
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at M06-2X/cc-pCVTZ Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.155      
2 S 0.155      
3 S -0.155      
4 S -0.155      


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 1.633 1.633
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -51.296 0.000 0.000
y 0.000 -53.473 0.000
z 0.000 0.000 -48.736
Traceless
 xyz
x -0.192 0.000 0.000
y 0.000 -3.458 0.000
z 0.000 0.000 3.649
Polar
3z2-r27.299
x2-y22.177
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 5.935 0.000 0.000
y 0.000 19.202 0.000
z 0.000 0.000 11.696


<r2> (average value of r2) Å2
<r2> 200.966
(<r2>)1/2 14.176

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at M06-2X/cc-pCVTZ
 hartrees
Energy at 0K-1592.763382
Energy at 298.15K 
HF Energy-1592.763382
Nuclear repulsion energy341.115786
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/cc-pCVTZ
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 777 777 0.00      
2 Ag 326 326 0.00      
3 Au 265 265 0.00      
4 B1u 702 702 181.72      
5 B2u 197i 197i 22.40      
6 B3g 356 356 0.00      

Unscaled Zero Point Vibrational Energy (zpe) 1114.0 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1114.0 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/cc-pCVTZ
ABC
0.15018 0.08583 0.05462

See section I.F.4 to change rotational constant units
Geometric Data calculated at M06-2X/cc-pCVTZ

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.937 1.239
S2 0.000 0.937 -1.239
S3 0.000 -0.937 1.239
S4 0.000 -0.937 -1.239

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.47851.87373.1070
S22.47853.10701.8737
S31.87373.10702.4785
S43.10701.87372.4785

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/cc-pCVTZ 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 -51.717 0.000 0.000
y 0.000 -47.944 0.000
z 0.000 0.000 -52.951
Traceless
 xyz
x -1.269 0.000 0.000
y 0.000 4.390 0.000
z 0.000 0.000 -3.121
Polar
3z2-r2-6.242
x2-y2-3.772
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 5.913 0.000 0.000
y 0.000 12.299 0.000
z 0.000 0.000 17.857


<r2> (average value of r2) Å2
<r2> 186.233
(<r2>)1/2 13.647