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

using model chemistry: mPW1PW91/3-21G

19 10 17 12 22

States and conformations

State Conformation minimum conformation conformer description state description
1 1 no D2D 1A1
1 2 no C2V 1A1
1 3 yes D2H 1AG

Conformer 1 (D2D)

Jump to S1C2 S1C3
Energy calculated at mPW1PW91/3-21G
 hartrees
Energy at 0K-1584.862628
Energy at 298.15K 
HF Energy-1584.862628
Nuclear repulsion energy318.521672
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 mPW1PW91/3-21G
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 462 441 0.00 48.03 0.06 0.11
2 A1 154 147 0.00 9.82 0.75 0.86
3 B1 371 354 0.00 30.59 0.75 0.86
4 B2 266 254 0.26 16.83 0.75 0.86
5 E 367 350 0.01 9.75 0.75 0.86
5 E 367 350 0.01 9.75 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 993.3 cm-1
Scaled (by 0.9546) Zero Point Vibrational Energy (zpe) 948.2 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 mPW1PW91/3-21G
ABC
0.09676 0.09676 0.05360

See section I.F.4 to change rotational constant units
Geometric Data calculated at mPW1PW91/3-21G

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.568 0.364
S2 0.000 -1.568 0.364
S3 -1.568 0.000 -0.364
S4 1.568 0.000 -0.364

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S13.13632.33432.3343
S23.13632.33432.3343
S32.33432.33433.1363
S42.33432.33433.1363

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 47.795 S1 S3 S4 47.795
S2 S1 S3 47.795 S2 S4 S3 47.795
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at mPW1PW91/3-21G 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 -51.989 0.000 0.000
y 0.000 -51.989 0.000
z 0.000 0.000 -56.797
Traceless
 xyz
x 2.404 0.000 0.000
y 0.000 2.404 0.000
z 0.000 0.000 -4.808
Polar
3z2-r2-9.616
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 12.386 0.000 0.000
y 0.000 12.386 0.000
z 0.000 0.000 4.223


<r2> (average value of r2) Å2
<r2> 199.351
(<r2>)1/2 14.119

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at mPW1PW91/3-21G
 hartrees
Energy at 0K-1584.874049
Energy at 298.15K 
HF Energy-1584.874049
Nuclear repulsion energy312.161337
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 mPW1PW91/3-21G
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 585 559 0.00 33.88 0.28 0.44
2 A1 307 293 0.00 32.61 0.27 0.42
3 A1 103 98 8.88 0.00 0.52 0.69
4 A2 203 194 0.00 0.00 0.75 0.86
5 B2 549 524 81.56 0.00 0.75 0.86
6 B2 279 267 0.00 21.73 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1012.9 cm-1
Scaled (by 0.9546) Zero Point Vibrational Energy (zpe) 966.9 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 mPW1PW91/3-21G
ABC
0.12414 0.07288 0.04592

See section I.F.4 to change rotational constant units
Geometric Data calculated at mPW1PW91/3-21G

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.345 1.030
S2 0.000 -1.345 1.030
S3 0.000 1.345 -1.030
S4 0.000 -1.345 -1.030

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.68962.06093.3884
S22.68963.38842.0609
S32.06093.38842.6898
S43.38842.06092.6898

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 90.002 S1 S3 S4 89.998
S2 S1 S3 90.002 S2 S4 S3 89.998
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at mPW1PW91/3-21G 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 -53.451 0.000 0.000
y 0.000 -55.545 0.000
z 0.000 0.000 -52.285
Traceless
 xyz
x 0.464 0.000 0.000
y 0.000 -2.677 0.000
z 0.000 0.000 2.213
Polar
3z2-r24.427
x2-y22.094
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 2.798 0.000 0.000
y 0.000 16.822 0.000
z 0.000 0.000 13.038


<r2> (average value of r2) Å2
<r2> 217.282
(<r2>)1/2 14.740

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at mPW1PW91/3-21G
 hartrees
Energy at 0K-1584.874049
Energy at 298.15K 
HF Energy-1584.874049
Nuclear repulsion energy312.167882
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 mPW1PW91/3-21G
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 585 559 0.00 33.88 0.28 0.44
2 Ag 307 293 0.00 32.61 0.27 0.42
3 Au 203 194 0.00 0.00 0.00 0.00
4 B1u 549 524 81.56 0.00 0.00 0.00
5 B2u 103 98 8.88 0.00 0.00 0.00
6 B3g 279 267 0.00 21.73 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1013.0 cm-1
Scaled (by 0.9546) Zero Point Vibrational Energy (zpe) 967.0 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 mPW1PW91/3-21G
ABC
0.12415 0.07289 0.04593

See section I.F.4 to change rotational constant units
Geometric Data calculated at mPW1PW91/3-21G

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.030 1.345
S2 0.000 1.030 -1.345
S3 0.000 -1.030 1.345
S4 0.000 -1.030 -1.345

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.68962.06083.3884
S22.68963.38842.0608
S32.06083.38842.6896
S43.38842.06082.6896

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 mPW1PW91/3-21G 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 -53.451 0.000 0.000
y 0.000 -52.285 0.000
z 0.000 0.000 -55.546
Traceless
 xyz
x 0.464 0.000 0.000
y 0.000 2.214 0.000
z 0.000 0.000 -2.678
Polar
3z2-r2-5.355
x2-y2-1.166
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 2.798 0.000 0.000
y 0.000 13.038 0.000
z 0.000 0.000 16.821


<r2> (average value of r2) Å2
<r2> 217.273
(<r2>)1/2 14.740