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

using model chemistry: B3LYP/LANL2DZ

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 B3LYP/LANL2DZ
 hartrees
Energy at 0K-40.329786
Energy at 298.15K 
HF Energy-40.329786
Nuclear repulsion energy43.940990
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 B3LYP/LANL2DZ
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 423 406 0.00 46.44 0.06 0.11
2 A1 142 136 0.00 13.83 0.73 0.84
3 B1 335 322 0.00 29.24 0.75 0.86
4 B2 257 247 0.08 17.76 0.75 0.86
5 E 328 315 0.11 9.05 0.75 0.86
5 E 328 315 0.11 9.05 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 905.3 cm-1
Scaled (by 0.9612) Zero Point Vibrational Energy (zpe) 870.1 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 B3LYP/LANL2DZ
ABC
0.09348 0.09348 0.05105

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3LYP/LANL2DZ

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.607 0.345
S2 0.000 -1.607 0.345
S3 -1.607 0.000 -0.345
S4 1.607 0.000 -0.345

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S13.21392.37492.3749
S23.21392.37492.3749
S32.37492.37493.2139
S42.37492.37493.2139

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 47.420 S1 S3 S4 47.420
S2 S1 S3 47.420 S2 S4 S3 47.420
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B3LYP/LANL2DZ 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 -49.127 0.000 0.000
y 0.000 -49.127 0.000
z 0.000 0.000 -53.784
Traceless
 xyz
x 2.328 0.000 0.000
y 0.000 2.328 0.000
z 0.000 0.000 -4.657
Polar
3z2-r2-9.314
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 12.840 0.000 0.000
y 0.000 12.840 0.000
z 0.000 0.000 2.670


<r2> (average value of r2) Å2
<r2> 96.482
(<r2>)1/2 9.823

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at B3LYP/LANL2DZ
 hartrees
Energy at 0K-40.351078
Energy at 298.15K 
HF Energy-40.351078
Nuclear repulsion energy42.977752
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 B3LYP/LANL2DZ
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 569 547 0.00 32.77 0.27 0.43
2 A1 270 260 0.00 27.75 0.26 0.42
3 A1 86 83 6.32 0.00 0.54 0.70
4 A2 187 180 0.00 0.00 0.75 0.86
5 B2 540 519 81.73 0.00 0.75 0.86
6 B2 262 252 0.00 22.76 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 957.2 cm-1
Scaled (by 0.9612) Zero Point Vibrational Energy (zpe) 920.1 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 B3LYP/LANL2DZ
ABC
0.12085 0.06872 0.04381

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3LYP/LANL2DZ

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.385 1.044
S2 0.000 -1.385 1.044
S3 0.000 1.385 -1.044
S4 0.000 -1.385 -1.044

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.77002.08883.4693
S22.77003.46932.0888
S32.08883.46932.7700
S43.46932.08882.7700

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 89.999 S1 S3 S4 90.001
S2 S1 S3 89.999 S2 S4 S3 90.001
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B3LYP/LANL2DZ 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 -50.219 0.000 0.000
y 0.000 -52.776 0.000
z 0.000 0.000 -48.942
Traceless
 xyz
x 0.640 0.000 0.000
y 0.000 -3.196 0.000
z 0.000 0.000 2.556
Polar
3z2-r25.112
x2-y22.557
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 1.659 0.000 0.000
y 0.000 16.969 0.000
z 0.000 0.000 13.195


<r2> (average value of r2) Å2
<r2> 103.848
(<r2>)1/2 10.191

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at B3LYP/LANL2DZ
 hartrees
Energy at 0K-40.351078
Energy at 298.15K 
HF Energy-40.351078
Nuclear repulsion energy42.981561
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 B3LYP/LANL2DZ
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 570 548 0.00 32.78 0.27 0.43
2 Ag 270 260 0.00 27.75 0.26 0.42
3 Au 187 180 0.00 0.00 0.00 0.00
4 B1u 540 519 81.84 0.00 0.00 0.00
5 B2u 86 82 6.32 0.00 0.00 0.00
6 B3g 262 252 0.00 22.75 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 957.5 cm-1
Scaled (by 0.9612) Zero Point Vibrational Energy (zpe) 920.3 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 B3LYP/LANL2DZ
ABC
0.12090 0.06871 0.04381

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3LYP/LANL2DZ

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.044 1.385
S2 0.000 1.044 -1.385
S3 0.000 -1.044 1.385
S4 0.000 -1.044 -1.385

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.77012.08843.4691
S22.77013.46912.0884
S32.08843.46912.7701
S43.46912.08842.7701

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 B3LYP/LANL2DZ 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 -50.218 0.000 0.000
y 0.000 -48.945 0.000
z 0.000 0.000 -52.774
Traceless
 xyz
x 0.642 0.000 0.000
y 0.000 2.551 0.000
z 0.000 0.000 -3.192
Polar
3z2-r2-6.385
x2-y2-1.273
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 1.659 0.000 0.000
y 0.000 13.191 0.000
z 0.000 0.000 16.969


<r2> (average value of r2) Å2
<r2> 103.840
(<r2>)1/2 10.190