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

using model chemistry: B97D3/3-21G

19 10 17 12 22

States and conformations

State Conformation minimum conformation conformer description state description
1 1 no D2D 1A1
1 2 no C2V 1A1
1 3 yes D2H 1AG

Conformer 1 (D2D)

Jump to S1C2 S1C3
Energy calculated at B97D3/3-21G
 hartrees
Energy at 0K-1584.878629
Energy at 298.15K 
HF Energy-1584.878629
Nuclear repulsion energy312.753872
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 B97D3/3-21G
Mode Number Symmetry Frequency
(cm-1)
Scaled Frequency
(cm-1)
IR Intensities
(km mol-1)
Raman Act
(Å4/u)
Dep P Dep U
1 A1 424 417 0.00 42.06 0.06 0.11
2 A1 150 148 0.00 10.21 0.75 0.86
3 B1 292 287 0.00 28.03 0.75 0.86
4 B2 248 244 0.10 20.69 0.75 0.86
5 E 311 305 1.06 7.49 0.75 0.86
5 E 311 305 1.06 7.49 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 867.5 cm-1
Scaled (by 0.983) Zero Point Vibrational Energy (zpe) 852.7 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 B97D3/3-21G
ABC
0.09325 0.09325 0.05174

See section I.F.4 to change rotational constant units
Geometric Data calculated at B97D3/3-21G

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.596 0.374
S2 0.000 -1.596 0.374
S3 -1.596 0.000 -0.374
S4 1.596 0.000 -0.374

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S13.19222.37792.3779
S23.19222.37792.3779
S32.37792.37793.1922
S42.37792.37793.1922

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 47.839 S1 S3 S4 47.839
S2 S1 S3 47.839 S2 S4 S3 47.839
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B97D3/3-21G 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 -51.148 0.000 0.000
y 0.000 -51.148 0.000
z 0.000 0.000 -56.081
Traceless
 xyz
x 2.467 0.000 0.000
y 0.000 2.467 0.000
z 0.000 0.000 -4.934
Polar
3z2-r2-9.867
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 12.622 0.000 0.000
y 0.000 12.622 0.000
z 0.000 0.000 4.278


<r2> (average value of r2) Å2
<r2> 204.966
(<r2>)1/2 14.317

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at B97D3/3-21G
 hartrees
Energy at 0K-1584.915867
Energy at 298.15K 
HF Energy-1584.915867
Nuclear repulsion energy305.089113
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 B97D3/3-21G
Mode Number Symmetry Frequency
(cm-1)
Scaled Frequency
(cm-1)
IR Intensities
(km mol-1)
Raman Act
(Å4/u)
Dep P Dep U
1 A1 535 526 0.00 31.22 0.27 0.43
2 A1 272 268 0.00 26.90 0.26 0.41
3 A1 141 139 5.83 0.00 0.68 0.81
4 A2 181 178 0.00 0.00 0.75 0.86
5 B2 507 499 54.83 0.00 0.75 0.86
6 B2 258 253 0.00 20.91 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 947.5 cm-1
Scaled (by 0.983) Zero Point Vibrational Energy (zpe) 931.4 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 B97D3/3-21G
ABC
0.12008 0.06869 0.04370

See section I.F.4 to change rotational constant units
Geometric Data calculated at B97D3/3-21G

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.385 1.048
S2 0.000 -1.385 1.048
S3 0.000 1.385 -1.048
S4 0.000 -1.385 -1.048

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.77082.09543.4737
S22.77083.47372.0954
S32.09543.47372.7703
S43.47372.09542.7703

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 89.993 S1 S3 S4 90.007
S2 S1 S3 89.993 S2 S4 S3 90.007
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B97D3/3-21G 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 -0.001 0.001
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -52.915 0.000 0.000
y 0.000 -54.439 0.000
z 0.000 0.000 -51.273
Traceless
 xyz
x -0.059 0.000 0.000
y 0.000 -2.345 0.000
z 0.000 0.000 2.404
Polar
3z2-r24.807
x2-y21.524
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 2.835 0.000 0.000
y 0.000 16.796 0.000
z 0.000 0.000 13.286


<r2> (average value of r2) Å2
<r2> 226.094
(<r2>)1/2 15.036

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at B97D3/3-21G
 hartrees
Energy at 0K-1584.915867
Energy at 298.15K 
HF Energy-1584.915867
Nuclear repulsion energy305.109731
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 B97D3/3-21G
Mode Number Symmetry Frequency
(cm-1)
Scaled Frequency
(cm-1)
IR Intensities
(km mol-1)
Raman Act
(Å4/u)
Dep P Dep U
1 Ag 535 526 0.00 31.22 0.27 0.43
2 Ag 272 268 0.00 26.90 0.26 0.41
3 Au 181 178 0.00 0.00 0.00 0.00
4 B1u 508 499 54.85 0.00 0.00 0.00
5 B2u 141 139 5.83 0.00 0.00 0.00
6 B3g 258 253 0.00 20.91 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 947.7 cm-1
Scaled (by 0.983) Zero Point Vibrational Energy (zpe) 931.6 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 B97D3/3-21G
ABC
0.12010 0.06870 0.04370

See section I.F.4 to change rotational constant units
Geometric Data calculated at B97D3/3-21G

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.048 1.385
S2 0.000 1.048 -1.385
S3 0.000 -1.048 1.385
S4 0.000 -1.048 -1.385

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.77042.09533.4735
S22.77043.47352.0953
S32.09533.47352.7704
S43.47352.09532.7704

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 B97D3/3-21G 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 -52.914 0.000 0.000
y 0.000 -51.274 0.000
z 0.000 0.000 -54.440
Traceless
 xyz
x -0.057 0.000 0.000
y 0.000 2.403 0.000
z 0.000 0.000 -2.345
Polar
3z2-r2-4.690
x2-y2-1.640
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 2.835 0.000 0.000
y 0.000 13.284 0.000
z 0.000 0.000 16.794


<r2> (average value of r2) Å2
<r2> 226.068
(<r2>)1/2 15.036