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

using model chemistry: PBEPBE/6-311+G(3df,2p)

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 PBEPBE/6-311+G(3df,2p)
 hartrees
Energy at 0K-1592.130464
Energy at 298.15K 
HF Energy-1592.130464
Nuclear repulsion energy349.190213
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 PBEPBE/6-311+G(3df,2p)
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 505 501 0.00 35.59 0.04 0.08
2 A1 207 206 0.00 0.85 0.65 0.79
3 B1 421 417 0.00 17.08 0.75 0.86
4 B2 281 278 0.04 7.53 0.75 0.86
5 E 397 393 0.07 2.62 0.75 0.86
5 E 397 393 0.07 2.62 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1103.4 cm-1
Scaled (by 0.9918) Zero Point Vibrational Energy (zpe) 1094.3 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 PBEPBE/6-311+G(3df,2p)
ABC
0.11642 0.11642 0.06423

See section I.F.4 to change rotational constant units
Geometric Data calculated at PBEPBE/6-311+G(3df,2p)

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.433 0.326
S2 0.000 -1.433 0.326
S3 -1.433 0.000 -0.326
S4 1.433 0.000 -0.326

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.86512.12812.1281
S22.86512.12812.1281
S32.12812.12812.8651
S42.12812.12812.8651

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 47.688 S1 S3 S4 47.688
S2 S1 S3 47.688 S2 S4 S3 47.688
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at PBEPBE/6-311+G(3df,2p) 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 -49.098 0.000 0.000
y 0.000 -49.098 0.000
z 0.000 0.000 -54.667
Traceless
 xyz
x 2.785 0.000 0.000
y 0.000 2.785 0.000
z 0.000 0.000 -5.569
Polar
3z2-r2-11.139
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 12.893 0.000 0.000
y 0.000 12.893 0.000
z 0.000 0.000 9.291


<r2> (average value of r2) Å2
<r2> 169.961
(<r2>)1/2 13.037

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at PBEPBE/6-311+G(3df,2p)
 hartrees
Energy at 0K-1592.173423
Energy at 298.15K 
HF Energy-1592.173423
Nuclear repulsion energy331.157523
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 PBEPBE/6-311+G(3df,2p)
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 684 679 3.91 31.25 0.07 0.14
2 A1 317 315 3.87 29.84 0.15 0.26
3 A1 93 92 1.36 5.65 0.42 0.59
4 A2 217 215 0.00 0.14 0.75 0.86
5 B2 654 649 88.44 2.54 0.75 0.86
6 B2 324 321 0.00 8.59 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1144.7 cm-1
Scaled (by 0.9918) Zero Point Vibrational Energy (zpe) 1135.3 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 PBEPBE/6-311+G(3df,2p)
ABC
0.15219 0.07364 0.04963

See section I.F.4 to change rotational constant units
Geometric Data calculated at PBEPBE/6-311+G(3df,2p)

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.098 0.931
S2 0.000 -1.098 0.931
S3 0.000 1.541 -0.931
S4 0.000 -1.541 -0.931

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.19571.91343.2293
S22.19573.22931.9134
S31.91343.22933.0820
S43.22931.91343.0820

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 103.392 S1 S3 S4 76.608
S2 S1 S3 103.392 S2 S4 S3 76.608
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at PBEPBE/6-311+G(3df,2p) Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.051      
2 S 0.051      
3 S -0.051      
4 S -0.051      


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 0.982 0.982
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -51.691 0.000 0.000
y 0.000 -53.050 0.000
z 0.000 0.000 -48.469
Traceless
 xyz
x -0.932 0.000 0.000
y 0.000 -2.970 0.000
z 0.000 0.000 3.901
Polar
3z2-r27.803
x2-y21.359
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 8.150 0.000 0.000
y 0.000 19.377 0.000
z 0.000 0.000 13.304


<r2> (average value of r2) Å2
<r2> 201.890
(<r2>)1/2 14.209

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at PBEPBE/6-311+G(3df,2p)
 hartrees
Energy at 0K-1592.171668
Energy at 298.15K 
HF Energy-1592.171668
Nuclear repulsion energy333.755279
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 PBEPBE/6-311+G(3df,2p)
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 711 705 0.00 36.13 0.09 0.16
2 Ag 278 276 0.00 26.29 0.18 0.30
3 Au 241 239 0.00 0.00 0.00 0.00
4 B1u 664 658 86.11 0.00 0.00 0.00
5 B2u 97i 96i 9.81 0.00 0.00 0.00
6 B3g 328 325 0.00 8.64 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1062.3 cm-1
Scaled (by 0.9918) Zero Point Vibrational Energy (zpe) 1053.6 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 PBEPBE/6-311+G(3df,2p)
ABC
0.14544 0.08116 0.05209

See section I.F.4 to change rotational constant units
Geometric Data calculated at PBEPBE/6-311+G(3df,2p)

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.952 1.274
S2 0.000 0.952 -1.274
S3 0.000 -0.952 1.274
S4 0.000 -0.952 -1.274

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.54891.90403.1815
S22.54893.18151.9040
S31.90403.18152.5489
S43.18151.90402.5489

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 PBEPBE/6-311+G(3df,2p) 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 -51.857 0.000 0.000
y 0.000 -47.939 0.000
z 0.000 0.000 -52.961
Traceless
 xyz
x -1.407 0.000 0.000
y 0.000 4.470 0.000
z 0.000 0.000 -3.063
Polar
3z2-r2-6.125
x2-y2-3.918
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 8.202 0.000 0.000
y 0.000 13.513 0.000
z 0.000 0.000 18.728


<r2> (average value of r2) Å2
<r2> 193.757
(<r2>)1/2 13.920