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

using model chemistry: B3PW91/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 B3PW91/aug-cc-pVTZ
 hartrees
Energy at 0K-1592.668956
Energy at 298.15K 
HF Energy-1592.668956
Nuclear repulsion energy350.307915
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 B3PW91/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 527 509 0.00 40.61 0.04 0.08
2 A1 203 196 0.00 1.07 0.73 0.84
3 B1 464 448 0.00 16.64 0.75 0.86
4 B2 298 287 0.01 7.11 0.75 0.86
5 E 437 422 0.00 2.99 0.75 0.86
5 E 437 422 0.00 2.99 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1183.3 cm-1
Scaled (by 0.9651) Zero Point Vibrational Energy (zpe) 1142.0 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 B3PW91/aug-cc-pVTZ
ABC
0.11738 0.11738 0.06432

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3PW91/aug-cc-pVTZ

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.432 0.313
S2 0.000 -1.432 0.313
S3 -1.432 0.000 -0.313
S4 1.432 0.000 -0.313

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.86312.11942.1194
S22.86312.11942.1194
S32.11942.11942.8631
S42.11942.11942.8631

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 47.510 S1 S3 S4 47.510
S2 S1 S3 47.510 S2 S4 S3 47.510
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B3PW91/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 -48.774 0.000 0.000
y 0.000 -48.774 0.000
z 0.000 0.000 -54.306
Traceless
 xyz
x 2.766 0.000 0.000
y 0.000 2.766 0.000
z 0.000 0.000 -5.532
Polar
3z2-r2-11.064
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 12.764 0.000 0.000
y 0.000 12.764 0.000
z 0.000 0.000 9.008


<r2> (average value of r2) Å2
<r2> 169.063
(<r2>)1/2 13.002

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at B3PW91/aug-cc-pVTZ
 hartrees
Energy at 0K-1592.694471
Energy at 298.15K 
HF Energy-1592.694471
Nuclear repulsion energy332.345508
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 B3PW91/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 692 667 6.19 31.29 0.06 0.12
2 A1 384 370 5.04 37.31 0.14 0.25
3 A1 113 109 0.48 10.26 0.38 0.55
4 A2 216 209 0.00 0.14 0.75 0.86
5 B2 664 641 116.01 3.77 0.75 0.86
6 B2 336 324 0.14 7.96 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1202.0 cm-1
Scaled (by 0.9651) Zero Point Vibrational Energy (zpe) 1160.1 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 B3PW91/aug-cc-pVTZ
ABC
0.15646 0.07217 0.04939

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3PW91/aug-cc-pVTZ

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.058 0.918
S2 0.000 -1.058 0.918
S3 0.000 1.592 -0.918
S4 0.000 -1.592 -0.918

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.11621.91173.2236
S22.11623.22361.9117
S31.91173.22363.1834
S43.22361.91173.1834

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 106.207 S1 S3 S4 73.793
S2 S1 S3 106.207 S2 S4 S3 73.793
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B3PW91/aug-cc-pVTZ Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.180      
2 S 0.180      
3 S -0.180      
4 S -0.180      


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 1.320 1.320
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -51.299 0.000 0.000
y 0.000 -53.020 0.000
z 0.000 0.000 -48.403
Traceless
 xyz
x -0.588 0.000 0.000
y 0.000 -3.169 0.000
z 0.000 0.000 3.757
Polar
3z2-r27.513
x2-y21.720
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 8.215 0.000 0.000
y 0.000 19.921 0.000
z 0.000 0.000 13.171


<r2> (average value of r2) Å2
<r2> 202.613
(<r2>)1/2 14.234

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at B3PW91/aug-cc-pVTZ
 hartrees
Energy at 0K-1592.689179
Energy at 298.15K 
HF Energy-1592.689179
Nuclear repulsion energy336.379519
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 B3PW91/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 741 715 0.00 37.11 0.09 0.16
2 Ag 300 289 0.00 31.65 0.18 0.30
3 Au 252 243 0.00 0.00 0.00 0.00
4 B1u 684 661 118.26 0.00 0.00 0.00
5 B2u 146i 141i 15.14 0.00 0.00 0.00
6 B3g 342 330 0.00 8.57 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1086.1 cm-1
Scaled (by 0.9651) Zero Point Vibrational Energy (zpe) 1048.2 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 B3PW91/aug-cc-pVTZ
ABC
0.14696 0.08291 0.05300

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3PW91/aug-cc-pVTZ

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.947 1.261
S2 0.000 0.947 -1.261
S3 0.000 -0.947 1.261
S4 0.000 -0.947 -1.261

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.52181.89423.1540
S22.52183.15401.8942
S31.89423.15402.5218
S43.15401.89422.5218

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 B3PW91/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 -51.514 0.000 0.000
y 0.000 -47.716 0.000
z 0.000 0.000 -52.728
Traceless
 xyz
x -1.292 0.000 0.000
y 0.000 4.405 0.000
z 0.000 0.000 -3.113
Polar
3z2-r2-6.227
x2-y2-3.798
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 8.194 0.000 0.000
y 0.000 13.541 0.000
z 0.000 0.000 18.902


<r2> (average value of r2) Å2
<r2> 190.798
(<r2>)1/2 13.813