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

using model chemistry: B3LYPultrafine/6-31G*

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 B3LYPultrafine/6-31G*
 hartrees
Energy at 0K-1592.702158
Energy at 298.15K 
HF Energy-1592.702158
Nuclear repulsion energy343.489923
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 B3LYPultrafine/6-31G*
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 485 464 0.00 53.33 0.07 0.13
2 A1 188 180 0.00 3.12 0.75 0.86
3 B1 416 399 0.00 37.19 0.75 0.86
4 B2 304 291 0.26 12.18 0.75 0.86
5 E 397 380 0.21 7.00 0.75 0.86
5 E 397 380 0.21 7.00 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1093.3 cm-1
Scaled (by 0.958) Zero Point Vibrational Energy (zpe) 1047.4 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 B3LYPultrafine/6-31G*
ABC
0.11301 0.11301 0.06162

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3LYPultrafine/6-31G*

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.463 0.311
S2 0.000 -1.463 0.311
S3 -1.463 0.000 -0.311
S4 1.463 0.000 -0.311

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.92512.16002.1600
S22.92512.16002.1600
S32.16002.16002.9251
S42.16002.16002.9251

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 47.383 S1 S3 S4 47.383
S2 S1 S3 47.383 S2 S4 S3 47.383
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B3LYPultrafine/6-31G* 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 -49.757 0.000 0.000
y 0.000 -49.757 0.000
z 0.000 0.000 -55.100
Traceless
 xyz
x 2.672 0.000 0.000
y 0.000 2.672 0.000
z 0.000 0.000 -5.343
Polar
3z2-r2-10.687
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 10.732 0.000 0.000
y 0.000 10.732 0.000
z 0.000 0.000 5.320


<r2> (average value of r2) Å2
<r2> 175.292
(<r2>)1/2 13.240

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at B3LYPultrafine/6-31G*
 hartrees
Energy at 0K-1592.736433
Energy at 298.15K 
HF Energy-1592.736433
Nuclear repulsion energy325.462820
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 B3LYPultrafine/6-31G*
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 662 634 2.01 31.40 0.24 0.38
2 A1 317 304 6.87 32.53 0.23 0.37
3 A1 95 91 1.18 9.47 0.51 0.67
4 A2 206 197 0.00 0.16 0.75 0.86
5 B2 640 613 122.36 2.56 0.75 0.86
6 B2 322 309 0.03 15.83 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1120.8 cm-1
Scaled (by 0.958) Zero Point Vibrational Energy (zpe) 1073.7 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 B3LYPultrafine/6-31G*
ABC
0.15188 0.06859 0.04725

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3LYPultrafine/6-31G*

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.098 0.932
S2 0.000 -1.098 0.932
S3 0.000 1.624 -0.932
S4 0.000 -1.624 -0.932

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.19691.93593.2989
S22.19693.29891.9359
S31.93593.29893.2477
S43.29891.93593.2477

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 105.748 S1 S3 S4 74.252
S2 S1 S3 105.748 S2 S4 S3 74.252
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B3LYPultrafine/6-31G* Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.091      
2 S 0.091      
3 S -0.091      
4 S -0.091      


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 1.446 1.446
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -51.593 0.000 0.000
y 0.000 -54.085 0.000
z 0.000 0.000 -49.831
Traceless
 xyz
x 0.365 0.000 0.000
y 0.000 -3.373 0.000
z 0.000 0.000 3.008
Polar
3z2-r26.016
x2-y22.491
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 4.327 0.000 0.000
y 0.000 18.062 0.000
z 0.000 0.000 11.360


<r2> (average value of r2) Å2
<r2> 210.913
(<r2>)1/2 14.523

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at B3LYPultrafine/6-31G*
 hartrees
Energy at 0K-1592.734065
Energy at 298.15K 
HF Energy-1592.734065
Nuclear repulsion energy328.239206
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 B3LYPultrafine/6-31G*
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 707 677 0.00 38.05 0.28 0.44
2 Ag 270 259 0.00 32.49 0.28 0.44
3 Au 235 225 0.00 0.00 0.00 0.00
4 B1u 661 633 133.03 0.00 0.00 0.00
5 B2u 89i 86i 16.26 0.00 0.00 0.00
6 B3g 323 309 0.00 17.73 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1053.0 cm-1
Scaled (by 0.958) Zero Point Vibrational Energy (zpe) 1008.8 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 B3LYPultrafine/6-31G*
ABC
0.14293 0.07716 0.05011

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3LYPultrafine/6-31G*

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.960 1.307
S2 0.000 0.960 -1.307
S3 0.000 -0.960 1.307
S4 0.000 -0.960 -1.307

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.61401.92073.2438
S22.61403.24381.9207
S31.92073.24382.6140
S43.24381.92072.6140

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 B3LYPultrafine/6-31G* 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 -51.905 0.000 0.000
y 0.000 -49.209 0.000
z 0.000 0.000 -53.684
Traceless
 xyz
x -0.458 0.000 0.000
y 0.000 3.585 0.000
z 0.000 0.000 -3.127
Polar
3z2-r2-6.254
x2-y2-2.696
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 4.288 0.000 0.000
y 0.000 11.906 0.000
z 0.000 0.000 17.112


<r2> (average value of r2) Å2
<r2> 200.581
(<r2>)1/2 14.163