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

using model chemistry: B3PW91/3-21G

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 B3PW91/3-21G
 hartrees
Energy at 0K-1584.651349
Energy at 298.15K 
HF Energy-1584.651349
Nuclear repulsion energy317.512712
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 B3PW91/3-21G
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 456 439 0.00      
2 A1 153 147 0.00      
3 B1 359 345 0.00      
4 B2 262 252 0.23      
5 E 358 344 0.05      
5 E 358 344 0.05      

Unscaled Zero Point Vibrational Energy (zpe) 972.7 cm-1
Scaled (by 0.9612) Zero Point Vibrational Energy (zpe) 935.0 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 B3PW91/3-21G
ABC
0.09614 0.09614 0.05328

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3PW91/3-21G

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.573 0.366
S2 0.000 -1.573 0.366
S3 -1.573 0.000 -0.366
S4 1.573 0.000 -0.366

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S13.14592.34182.3418
S23.14592.34182.3418
S32.34182.34183.1459
S42.34182.34183.1459

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 47.803 S1 S3 S4 47.803
S2 S1 S3 47.803 S2 S4 S3 47.803
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B3PW91/3-21G 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 -51.855 0.000 0.000
y 0.000 -51.855 0.000
z 0.000 0.000 -56.703
Traceless
 xyz
x 2.424 0.000 0.000
y 0.000 2.424 0.000
z 0.000 0.000 -4.848
Polar
3z2-r2-9.697
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 12.398 0.000 0.000
y 0.000 12.398 0.000
z 0.000 0.000 4.231


<r2> (average value of r2) Å2
<r2> 200.320
(<r2>)1/2 14.153

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at B3PW91/3-21G
 hartrees
Energy at 0K-1584.668283
Energy at 298.15K 
HF Energy-1584.668283
Nuclear repulsion energy310.855715
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 B3PW91/3-21G
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 577 554 0.00      
2 A1 299 287 0.00      
3 A1 110 106 8.18      
4 A2 199 192 0.00      
5 B2 542 521 75.24      
6 B2 275 265 0.00      

Unscaled Zero Point Vibrational Energy (zpe) 1001.4 cm-1
Scaled (by 0.9612) Zero Point Vibrational Energy (zpe) 962.5 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 B3PW91/3-21G
ABC
0.12329 0.07216 0.04552

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3PW91/3-21G

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.351 1.034
S2 0.000 -1.351 1.034
S3 0.000 1.352 -1.034
S4 0.000 -1.352 -1.034

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.70292.06803.4034
S22.70293.40342.0680
S32.06803.40342.7035
S43.40342.06802.7035

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 90.008 S1 S3 S4 89.992
S2 S1 S3 90.008 S2 S4 S3 89.992
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B3PW91/3-21G 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 -53.380 0.000 0.000
y 0.000 -55.376 0.000
z 0.000 0.000 -52.112
Traceless
 xyz
x 0.364 0.000 0.000
y 0.000 -2.630 0.000
z 0.000 0.000 2.266
Polar
3z2-r24.532
x2-y21.996
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 2.806 0.000 0.000
y 0.000 16.777 0.000
z 0.000 0.000 13.087


<r2> (average value of r2) Å2
<r2> 218.827
(<r2>)1/2 14.793

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at B3PW91/3-21G
 hartrees
Energy at 0K-1584.668283
Energy at 298.15K 
HF Energy-1584.668283
Nuclear repulsion energy310.870643
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 B3PW91/3-21G
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 577 554 0.00      
2 Ag 299 287 0.00      
3 Au 199 192 0.00      
4 B1u 542 521 75.26      
5 B2u 111 106 8.19      
6 B3g 275 265 0.00      

Unscaled Zero Point Vibrational Energy (zpe) 1001.5 cm-1
Scaled (by 0.9612) Zero Point Vibrational Energy (zpe) 962.7 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 B3PW91/3-21G
ABC
0.12330 0.07217 0.04552

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3PW91/3-21G

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.034 1.352
S2 0.000 1.034 -1.352
S3 0.000 -1.034 1.352
S4 0.000 -1.034 -1.352

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.70302.06793.4033
S22.70303.40332.0679
S32.06793.40332.7030
S43.40332.06792.7030

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 B3PW91/3-21G 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 -53.380 0.000 0.000
y 0.000 -52.113 0.000
z 0.000 0.000 -55.377
Traceless
 xyz
x 0.365 0.000 0.000
y 0.000 2.266 0.000
z 0.000 0.000 -2.630
Polar
3z2-r2-5.261
x2-y2-1.267
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 2.806 0.000 0.000
y 0.000 13.086 0.000
z 0.000 0.000 16.775


<r2> (average value of r2) Å2
<r2> 218.809
(<r2>)1/2 14.792