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

using model chemistry: M06-2X/aug-cc-pVDZ

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/aug-cc-pVDZ
 hartrees
Energy at 0K-1592.666656
Energy at 298.15K 
HF Energy-1592.666656
Nuclear repulsion energy347.950266
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/aug-cc-pVDZ
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 531 531 0.00 47.85 0.05 0.09
2 A1 198 198 0.00 1.08 0.70 0.82
3 B1 470 470 0.00 20.58 0.75 0.86
4 B2 312 312 0.01 7.02 0.75 0.86
5 E 448 448 0.00 3.97 0.75 0.86
5 E 448 448 0.00 3.97 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1203.7 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1203.7 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/aug-cc-pVDZ
ABC
0.11567 0.11567 0.06366

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

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.439 0.323
S2 0.000 -1.439 0.323
S3 -1.439 0.000 -0.323
S4 1.439 0.000 -0.323

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.87792.13502.1350
S22.87792.13502.1350
S32.13502.13502.8779
S42.13502.13502.8779

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 47.625 S1 S3 S4 47.625
S2 S1 S3 47.625 S2 S4 S3 47.625
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at M06-2X/aug-cc-pVDZ 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 -48.958 0.000 0.000
y 0.000 -48.958 0.000
z 0.000 0.000 -55.525
Traceless
 xyz
x 3.283 0.000 0.000
y 0.000 3.283 0.000
z 0.000 0.000 -6.567
Polar
3z2-r2-13.134
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 12.620 0.000 0.000
y 0.000 12.620 0.000
z 0.000 0.000 8.755


<r2> (average value of r2) Å2
<r2> 171.136
(<r2>)1/2 13.082

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at M06-2X/aug-cc-pVDZ
 hartrees
Energy at 0K-1592.677594
Energy at 298.15K 
HF Energy-1592.677594
Nuclear repulsion energy331.937384
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/aug-cc-pVDZ
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 693 693 5.86 34.58 0.06 0.12
2 A1 423 423 5.73 56.08 0.18 0.30
3 A1 129 129 0.38 14.79 0.39 0.56
4 A2 214 214 0.00 0.41 0.75 0.86
5 B2 660 660 163.38 4.78 0.75 0.86
6 B2 336 336 0.35 8.70 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1227.1 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1227.1 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/aug-cc-pVDZ
ABC
0.15524 0.07216 0.04926

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

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.045 0.921
S2 0.000 -1.045 0.921
S3 0.000 1.600 -0.921
S4 0.000 -1.600 -0.921

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.09001.92483.2241
S22.09003.22411.9248
S31.92483.22413.2009
S43.22411.92483.2009

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 106.772 S1 S3 S4 73.228
S2 S1 S3 106.772 S2 S4 S3 73.228
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at M06-2X/aug-cc-pVDZ Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.073      
2 S 0.073      
3 S -0.073      
4 S -0.073      


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 1.520 1.520
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -52.483 0.000 0.000
y 0.000 -53.710 0.000
z 0.000 0.000 -48.674
Traceless
 xyz
x -1.291 0.000 0.000
y 0.000 -3.131 0.000
z 0.000 0.000 4.423
Polar
3z2-r28.845
x2-y21.227
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 7.975 0.000 0.000
y 0.000 20.822 0.000
z 0.000 0.000 12.915


<r2> (average value of r2) Å2
<r2> 203.494
(<r2>)1/2 14.265

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at M06-2X/aug-cc-pVDZ
 hartrees
Energy at 0K-1592.669816
Energy at 298.15K 
HF Energy-1592.669816
Nuclear repulsion energy336.420191
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/aug-cc-pVDZ
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 760 760 0.00 38.58 0.11 0.19
2 Ag 321 321 0.00 49.51 0.22 0.35
3 Au 253 253 0.00 0.00 0.00 0.00
4 B1u 690 690 173.87 0.00 0.00 0.00
5 B2u 174i 174i 19.03 0.00 0.00 0.00
6 B3g 345 345 0.00 10.60 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1097.2 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1097.2 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/aug-cc-pVDZ
ABC
0.14594 0.08357 0.05314

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

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.950 1.256
S2 0.000 0.950 -1.256
S3 0.000 -0.950 1.256
S4 0.000 -0.950 -1.256

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.51191.90083.1500
S22.51193.15001.9008
S31.90083.15002.5119
S43.15001.90082.5119

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/aug-cc-pVDZ 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 -52.815 0.000 0.000
y 0.000 -47.969 0.000
z 0.000 0.000 -53.059
Traceless
 xyz
x -2.301 0.000 0.000
y 0.000 4.968 0.000
z 0.000 0.000 -2.667
Polar
3z2-r2-5.334
x2-y2-4.846
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 7.966 0.000 0.000
y 0.000 13.311 0.000
z 0.000 0.000 19.449


<r2> (average value of r2) Å2
<r2> 190.786
(<r2>)1/2 13.813