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

using model chemistry: M06-2X/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 M06-2X/daug-cc-pVTZ
 hartrees
Energy at 0K-1592.745758
Energy at 298.15K 
HF Energy-1592.745758
Nuclear repulsion energy351.777536
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/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 542 542 0.00 45.40 0.05 0.09
2 A1 202 202 0.00 1.27 0.72 0.84
3 B1 492 492 0.00 17.44 0.75 0.86
4 B2 308 308 0.01 6.68 0.75 0.86
5 E 465 465 0.02 3.51 0.75 0.86
5 E 465 465 0.02 3.51 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1237.1 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1237.1 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 M06-2X/daug-cc-pVTZ
ABC
0.11835 0.11835 0.06489

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

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.425 0.313
S2 0.000 -1.425 0.313
S3 -1.425 0.000 -0.313
S4 1.425 0.000 -0.313

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.85052.11072.1107
S22.85052.11072.1107
S32.11072.11072.8505
S42.11072.11072.8505

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 47.526 S1 S3 S4 47.526
S2 S1 S3 47.526 S2 S4 S3 47.526
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at M06-2X/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 -49.132 0.000 0.000
y 0.000 -49.132 0.000
z 0.000 0.000 -54.574
Traceless
 xyz
x 2.721 0.000 0.000
y 0.000 2.721 0.000
z 0.000 0.000 -5.441
Polar
3z2-r2-10.883
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 12.812 0.000 0.000
y 0.000 12.812 0.000
z 0.000 0.000 8.982


<r2> (average value of r2) Å2
<r2> 168.105
(<r2>)1/2 12.966

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at M06-2X/daug-cc-pVTZ
 hartrees
Energy at 0K-1592.754910
Energy at 298.15K 
HF Energy-1592.754910
Nuclear repulsion energy334.540811
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/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 702 702 8.70 31.07 0.06 0.11
2 A1 456 456 4.56 66.84 0.16 0.28
3 A1 132 132 0.14 14.99 0.38 0.55
4 A2 219 219 0.00 0.31 0.75 0.86
5 B2 667 667 171.26 5.02 0.75 0.86
6 B2 342 342 0.39 7.95 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1258.4 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1258.4 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/daug-cc-pVTZ
ABC
0.16021 0.07198 0.04967

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

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.026 0.907
S2 0.000 -1.026 0.907
S3 0.000 1.616 -0.907
S4 0.000 -1.616 -0.907

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.05181.90753.2044
S22.05183.20441.9075
S31.90753.20443.2310
S43.20441.90753.2310

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 108.005 S1 S3 S4 71.995
S2 S1 S3 108.005 S2 S4 S3 71.995
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at M06-2X/daug-cc-pVTZ Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.137      
2 S 0.137      
3 S -0.137      
4 S -0.137      


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 1.559 1.559
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -51.717 0.000 0.000
y 0.000 -53.549 0.000
z 0.000 0.000 -48.933
Traceless
 xyz
x -0.477 0.000 0.000
y 0.000 -3.224 0.000
z 0.000 0.000 3.700
Polar
3z2-r27.401
x2-y21.831
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 8.366 0.000 0.000
y 0.000 20.945 0.000
z 0.000 0.000 13.125


<r2> (average value of r2) Å2
<r2> 201.955
(<r2>)1/2 14.211

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at M06-2X/daug-cc-pVTZ
 hartrees
Energy at 0K-1592.744807
Energy at 298.15K 
HF Energy-1592.744807
Nuclear repulsion energy339.755480
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/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 771 771 0.00 36.67 0.10 0.17
2 Ag 325 325 0.00 51.26 0.19 0.32
3 Au 260 260 0.00 0.00 0.00 0.00
4 B1u 697 697 179.59 0.00 0.00 0.00
5 B2u 194i 194i 20.18 0.00 0.00 0.00
6 B3g 351 351 0.00 9.44 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1104.3 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1104.3 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 M06-2X/daug-cc-pVTZ
ABC
0.14896 0.08516 0.05418

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

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.941 1.244
S2 0.000 0.941 -1.244
S3 0.000 -0.941 1.244
S4 0.000 -0.941 -1.244

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.48821.88143.1194
S22.48823.11941.8814
S31.88143.11942.4882
S43.11941.88142.4882

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/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 -51.975 0.000 0.000
y 0.000 -48.155 0.000
z 0.000 0.000 -53.104
Traceless
 xyz
x -1.345 0.000 0.000
y 0.000 4.384 0.000
z 0.000 0.000 -3.039
Polar
3z2-r2-6.078
x2-y2-3.820
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 8.314 0.000 0.000
y 0.000 13.617 0.000
z 0.000 0.000 19.551


<r2> (average value of r2) Å2
<r2> 187.595
(<r2>)1/2 13.697