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

using model chemistry: HF/3-21G*

19 10 17 12 22

States and conformations

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

Conformer 1 (D2D)

Jump to S1C2 S1C3
Energy calculated at HF/3-21G*
 hartrees
Energy at 0K-1582.600872
Energy at 298.15K 
HF Energy-1582.600872
Nuclear repulsion energy351.211480
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 HF/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 535 483 0.00 77.39 0.08 0.15
2 A1 191 172 0.00 2.81 0.74 0.85
3 B1 505 456 0.00 43.50 0.75 0.86
4 B2 374 337 0.88 10.75 0.75 0.86
5 E 476 430 0.10 9.96 0.75 0.86
5 E 476 430 0.10 9.96 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1278.2 cm-1
Scaled (by 0.9026) Zero Point Vibrational Energy (zpe) 1153.7 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 HF/3-21G*
ABC
0.11856 0.11856 0.06382

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

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.437 0.281
S2 0.000 -1.437 0.281
S3 -1.437 0.000 -0.281
S4 1.437 0.000 -0.281

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.87432.10892.1089
S22.87432.10892.1089
S32.10892.10892.8743
S42.10892.10892.8743

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 47.040 S1 S3 S4 47.040
S2 S1 S3 47.040 S2 S4 S3 47.040
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at HF/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 -51.291 0.000 0.000
y 0.000 -51.291 0.000
z 0.000 0.000 -56.556
Traceless
 xyz
x 2.633 0.000 0.000
y 0.000 2.633 0.000
z 0.000 0.000 -5.265
Polar
3z2-r2-10.531
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 10.111 0.000 0.000
y 0.000 10.111 0.000
z 0.000 0.000 4.513


<r2> (average value of r2) Å2
<r2> 170.384
(<r2>)1/2 13.053

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at HF/3-21G*
 hartrees
Energy at 0K-1582.585756
Energy at 298.15K 
HF Energy-1582.585756
Nuclear repulsion energy335.671724
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 HF/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 716 646 7.00 26.07 0.47 0.64
2 A1 551 497 5.35 323.53 0.26 0.41
3 A1 146 132 0.01 27.51 0.46 0.63
4 A2 224 202 0.00 0.78 0.75 0.86
5 B2 640 577 449.03 0.01 0.75 0.86
6 B2 377 340 1.61 12.66 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1326.8 cm-1
Scaled (by 0.9026) Zero Point Vibrational Energy (zpe) 1197.6 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 HF/3-21G*
ABC
0.16723 0.06951 0.04910

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

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.990 0.888
S2 0.000 -0.990 0.888
S3 0.000 1.677 -0.888
S4 0.000 -1.677 -0.888

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S11.97971.90403.2041
S21.97973.20411.9040
S31.90403.20413.3544
S43.20411.90403.3544

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 111.161 S1 S3 S4 68.839
S2 S1 S3 111.161 S2 S4 S3 68.839
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at HF/3-21G* Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.165      
2 S 0.165      
3 S -0.165      
4 S -0.165      


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 2.381 2.381
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -52.507 0.000 0.000
y 0.000 -56.612 0.000
z 0.000 0.000 -51.834
Traceless
 xyz
x 1.715 0.000 0.000
y 0.000 -4.442 0.000
z 0.000 0.000 2.726
Polar
3z2-r25.452
x2-y24.105
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 3.857 0.000 0.000
y 0.000 22.013 0.000
z 0.000 0.000 10.068


<r2> (average value of r2) Å2
<r2> 205.326
(<r2>)1/2 14.329

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at HF/3-21G*
 hartrees
Energy at 0K-1582.559285
Energy at 298.15K 
HF Energy-1582.559285
Nuclear repulsion energy338.100814
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 HF/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 830 750 0.00 43.83 0.43 0.60
2 Ag 331 298 0.00 6946.43 0.33 0.50
3 Au 279 252 0.00 0.00 0.00 0.00
4 B1u 692 624 908.04 0.00 0.00 0.00
5 B2u 253i 229i 42.85 0.00 0.00 0.00
6 B3g 380 343 0.00 11.74 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1129.3 cm-1
Scaled (by 0.9026) Zero Point Vibrational Energy (zpe) 1019.3 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 HF/3-21G*
ABC
0.15222 0.08154 0.05310

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

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.931 1.271
S2 0.000 0.931 -1.271
S3 0.000 -0.931 1.271
S4 0.000 -0.931 -1.271

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.54301.86113.1513
S22.54303.15131.8611
S31.86113.15132.5430
S43.15131.86112.5430

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 HF/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 -53.146 0.000 0.000
y 0.000 -50.907 0.000
z 0.000 0.000 -55.222
Traceless
 xyz
x -0.081 0.000 0.000
y 0.000 3.277 0.000
z 0.000 0.000 -3.196
Polar
3z2-r2-6.392
x2-y2-2.239
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 3.760 0.000 0.000
y 0.000 11.095 0.000
z 0.000 0.000 25.392


<r2> (average value of r2) Å2
<r2> 192.047
(<r2>)1/2 13.858