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

using model chemistry: mPW1PW91/6-31+G**

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 mPW1PW91/6-31+G**
 hartrees
Energy at 0K-1592.718070
Energy at 298.15K 
HF Energy-1592.718070
Nuclear repulsion energy348.571214
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 mPW1PW91/6-31+G**
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 515 491 0.00 49.21 0.07 0.13
2 A1 201 191 0.00 0.90 0.63 0.77
3 B1 451 429 0.00 38.18 0.75 0.86
4 B2 313 298 0.17 8.53 0.75 0.86
5 E 431 410 0.05 5.80 0.75 0.86
5 E 431 410 0.05 5.80 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1170.6 cm-1
Scaled (by 0.9518) Zero Point Vibrational Energy (zpe) 1114.2 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 mPW1PW91/6-31+G**
ABC
0.11626 0.11626 0.06363

See section I.F.4 to change rotational constant units
Geometric Data calculated at mPW1PW91/6-31+G**

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
S12.87852.12962.1296
S22.87852.12962.1296
S32.12962.12962.8785
S42.12962.12962.8785

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 mPW1PW91/6-31+G** 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 -49.839 0.000 0.000
y 0.000 -49.839 0.000
z 0.000 0.000 -55.331
Traceless
 xyz
x 2.746 0.000 0.000
y 0.000 2.746 0.000
z 0.000 0.000 -5.492
Polar
3z2-r2-10.984
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 11.106 0.000 0.000
y 0.000 11.106 0.000
z 0.000 0.000 7.518


<r2> (average value of r2) Å2
<r2> 171.123
(<r2>)1/2 13.081

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at mPW1PW91/6-31+G**
 hartrees
Energy at 0K-1592.745005
Energy at 298.15K 
HF Energy-1592.745005
Nuclear repulsion energy330.324925
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 mPW1PW91/6-31+G**
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 688 655 3.33 33.16 0.13 0.23
2 A1 361 343 7.45 34.71 0.19 0.32
3 A1 106 101 0.99 10.31 0.50 0.67
4 A2 214 204 0.00 0.88 0.75 0.86
5 B2 663 631 142.16 3.82 0.75 0.86
6 B2 335 319 0.05 12.12 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1183.4 cm-1
Scaled (by 0.9518) Zero Point Vibrational Energy (zpe) 1126.3 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 mPW1PW91/6-31+G**
ABC
0.15495 0.07120 0.04879

See section I.F.4 to change rotational constant units
Geometric Data calculated at mPW1PW91/6-31+G**

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.071 0.922
S2 0.000 -1.071 0.922
S3 0.000 1.598 -0.922
S4 0.000 -1.598 -0.922

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.14231.91863.2449
S22.14233.24491.9186
S31.91863.24493.1969
S43.24491.91863.1969

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 105.953 S1 S3 S4 74.047
S2 S1 S3 105.953 S2 S4 S3 74.047
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at mPW1PW91/6-31+G** Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.119      
2 S 0.119      
3 S -0.119      
4 S -0.119      


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 1.603 1.603
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -51.673 0.000 0.000
y 0.000 -54.415 0.000
z 0.000 0.000 -50.113
Traceless
 xyz
x 0.592 0.000 0.000
y 0.000 -3.523 0.000
z 0.000 0.000 2.931
Polar
3z2-r25.862
x2-y22.743
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 6.141 0.000 0.000
y 0.000 19.183 0.000
z 0.000 0.000 11.875


<r2> (average value of r2) Å2
<r2> 205.444
(<r2>)1/2 14.333

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at mPW1PW91/6-31+G**
 hartrees
Energy at 0K-1592.741478
Energy at 298.15K 
HF Energy-1592.741478
Nuclear repulsion energy333.439615
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 mPW1PW91/6-31+G**
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 739 703 0.00 41.63 0.17 0.29
2 Ag 292 278 0.00 32.58 0.25 0.41
3 Au 247 235 0.00 0.00 0.00 0.00
4 B1u 689 655 152.75 0.00 0.00 0.00
5 B2u 111i 106i 21.33 0.00 0.00 0.00
6 B3g 337 320 0.00 13.82 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1095.8 cm-1
Scaled (by 0.9518) Zero Point Vibrational Energy (zpe) 1042.9 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 mPW1PW91/6-31+G**
ABC
0.14580 0.08062 0.05192

See section I.F.4 to change rotational constant units
Geometric Data calculated at mPW1PW91/6-31+G**

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.951 1.279
S2 0.000 0.951 -1.279
S3 0.000 -0.951 1.279
S4 0.000 -0.951 -1.279

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.55731.90173.1869
S22.55733.18691.9017
S31.90173.18692.5573
S43.18691.90172.5573

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 mPW1PW91/6-31+G** 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 -51.998 0.000 0.000
y 0.000 -49.427 0.000
z 0.000 0.000 -54.066
Traceless
 xyz
x -0.251 0.000 0.000
y 0.000 3.604 0.000
z 0.000 0.000 -3.353
Polar
3z2-r2-6.706
x2-y2-2.570
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 6.373 0.000 0.000
y 0.000 12.280 0.000
z 0.000 0.000 18.170


<r2> (average value of r2) Å2
<r2> 194.869
(<r2>)1/2 13.960