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

using model chemistry: mPW1PW91/aug-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 mPW1PW91/aug-cc-pVTZ
 hartrees
Energy at 0K-1592.883962
Energy at 298.15K 
HF Energy-1592.883962
Nuclear repulsion energy351.523390
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/aug-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 537 514 0.00 40.31 0.04 0.08
2 A1 206 197 0.00 1.07 0.72 0.84
3 B1 477 457 0.00 16.38 0.75 0.86
4 B2 303 290 0.01 6.78 0.75 0.86
5 E 450 431 0.00 3.01 0.75 0.86
5 E 450 431 0.00 3.01 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1210.1 cm-1
Scaled (by 0.9581) Zero Point Vibrational Energy (zpe) 1159.4 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 mPW1PW91/aug-cc-pVTZ
ABC
0.11819 0.11819 0.06477

See section I.F.4 to change rotational constant units
Geometric Data calculated at mPW1PW91/aug-cc-pVTZ

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.427 0.313
S2 0.000 -1.427 0.313
S3 -1.427 0.000 -0.313
S4 1.427 0.000 -0.313

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.85312.11212.1121
S22.85312.11212.1121
S32.11212.11212.8531
S42.11212.11212.8531

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 47.514 S1 S3 S4 47.514
S2 S1 S3 47.514 S2 S4 S3 47.514
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at mPW1PW91/aug-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 -48.801 0.000 0.000
y 0.000 -48.801 0.000
z 0.000 0.000 -54.341
Traceless
 xyz
x 2.770 0.000 0.000
y 0.000 2.770 0.000
z 0.000 0.000 -5.540
Polar
3z2-r2-11.080
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 12.651 0.000 0.000
y 0.000 12.651 0.000
z 0.000 0.000 8.938


<r2> (average value of r2) Å2
<r2> 168.128
(<r2>)1/2 12.966

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at mPW1PW91/aug-cc-pVTZ
 hartrees
Energy at 0K-1592.905286
Energy at 298.15K 
HF Energy-1592.905286
Nuclear repulsion energy333.697581
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/aug-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 700 670 6.87 30.91 0.06 0.11
2 A1 405 388 4.96 39.98 0.15 0.25
3 A1 118 113 0.39 10.80 0.38 0.55
4 A2 219 210 0.00 0.16 0.75 0.86
5 B2 671 643 122.63 4.03 0.75 0.86
6 B2 341 326 0.18 7.81 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1226.4 cm-1
Scaled (by 0.9581) Zero Point Vibrational Energy (zpe) 1175.0 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/aug-cc-pVTZ
ABC
0.15766 0.07271 0.04976

See section I.F.4 to change rotational constant units
Geometric Data calculated at mPW1PW91/aug-cc-pVTZ

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.048 0.914
S2 0.000 -1.048 0.914
S3 0.000 1.590 -0.914
S4 0.000 -1.590 -0.914

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.09591.90743.2098
S22.09593.20981.9074
S31.90743.20983.1798
S43.20981.90743.1798

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 106.507 S1 S3 S4 73.493
S2 S1 S3 106.507 S2 S4 S3 73.493
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at mPW1PW91/aug-cc-pVTZ Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.184      
2 S 0.184      
3 S -0.184      
4 S -0.184      


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 1.371 1.371
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -51.321 0.000 0.000
y 0.000 -53.100 0.000
z 0.000 0.000 -48.466
Traceless
 xyz
x -0.538 0.000 0.000
y 0.000 -3.206 0.000
z 0.000 0.000 3.744
Polar
3z2-r27.488
x2-y21.779
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 8.170 0.000 0.000
y 0.000 19.879 0.000
z 0.000 0.000 13.059


<r2> (average value of r2) Å2
<r2> 201.371
(<r2>)1/2 14.191

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at mPW1PW91/aug-cc-pVTZ
 hartrees
Energy at 0K-1592.898858
Energy at 298.15K 
HF Energy-1592.898858
Nuclear repulsion energy337.977820
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/aug-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 753 721 0.00 37.22 0.09 0.16
2 Ag 308 296 0.00 32.57 0.18 0.30
3 Au 257 246 0.00 0.00 0.00 0.00
4 B1u 693 664 125.52 0.00 0.00 0.00
5 B2u 160i 154i 16.55 0.00 0.00 0.00
6 B3g 348 333 0.00 8.55 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1099.0 cm-1
Scaled (by 0.9581) Zero Point Vibrational Energy (zpe) 1053.0 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/aug-cc-pVTZ
ABC
0.14782 0.08402 0.05357

See section I.F.4 to change rotational constant units
Geometric Data calculated at mPW1PW91/aug-cc-pVTZ

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.944 1.253
S2 0.000 0.944 -1.253
S3 0.000 -0.944 1.253
S4 0.000 -0.944 -1.253

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.50501.88873.1372
S22.50503.13721.8887
S31.88873.13722.5050
S43.13721.88872.5050

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/aug-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 -51.546 0.000 0.000
y 0.000 -47.747 0.000
z 0.000 0.000 -52.806
Traceless
 xyz
x -1.270 0.000 0.000
y 0.000 4.429 0.000
z 0.000 0.000 -3.159
Polar
3z2-r2-6.318
x2-y2-3.799
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 8.147 0.000 0.000
y 0.000 13.446 0.000
z 0.000 0.000 18.829


<r2> (average value of r2) Å2
<r2> 189.139
(<r2>)1/2 13.753