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

using model chemistry: PBEPBEultrafine/cc-pV(T+d)Z

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 PBEPBEultrafine/cc-pV(T+d)Z
 hartrees
Energy at 0K-1592.146529
Energy at 298.15K 
HF Energy-1592.146529
Nuclear repulsion energy349.503854
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 PBEPBEultrafine/cc-pV(T+d)Z
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 508 508 0.00      
2 A1 205 205 0.00      
3 B1 427 427 0.00      
4 B2 278 278 0.01      
5 E 400 400 0.17      
5 E 400 400 0.17      

Unscaled Zero Point Vibrational Energy (zpe) 1108.9 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1108.9 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 PBEPBEultrafine/cc-pV(T+d)Z
ABC
0.11667 0.11667 0.06428

See section I.F.4 to change rotational constant units
Geometric Data calculated at PBEPBEultrafine/cc-pV(T+d)Z

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.432 0.323
S2 0.000 -1.432 0.323
S3 -1.432 0.000 -0.323
S4 1.432 0.000 -0.323

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.86402.12582.1258
S22.86402.12582.1258
S32.12582.12582.8640
S42.12582.12582.8640

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 47.652 S1 S3 S4 47.652
S2 S1 S3 47.652 S2 S4 S3 47.652
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at PBEPBEultrafine/cc-pV(T+d)Z 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 -48.683 0.000 0.000
y 0.000 -48.683 0.000
z 0.000 0.000 -54.012
Traceless
 xyz
x 2.665 0.000 0.000
y 0.000 2.665 0.000
z 0.000 0.000 -5.330
Polar
3z2-r2-10.660
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 11.555 0.000 0.000
y 0.000 11.555 0.000
z 0.000 0.000 6.808


<r2> (average value of r2) Å2
<r2> 169.442
(<r2>)1/2 13.017

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at PBEPBEultrafine/cc-pV(T+d)Z
 hartrees
Energy at 0K-1592.189194
Energy at 298.15K 
HF Energy-1592.189194
Nuclear repulsion energy331.340059
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 PBEPBEultrafine/cc-pV(T+d)Z
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 685 685 3.78      
2 A1 322 322 4.93      
3 A1 94 94 1.49      
4 A2 218 218 0.00      
5 B2 656 656 89.33      
6 B2 326 326 0.00      

Unscaled Zero Point Vibrational Energy (zpe) 1151.0 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1151.0 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 PBEPBEultrafine/cc-pV(T+d)Z
ABC
0.15248 0.07363 0.04965

See section I.F.4 to change rotational constant units
Geometric Data calculated at PBEPBEultrafine/cc-pV(T+d)Z

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.095 0.930
S2 0.000 -1.095 0.930
S3 0.000 1.543 -0.930
S4 0.000 -1.543 -0.930

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.18961.91293.2276
S22.18963.22761.9129
S31.91293.22763.0866
S43.22761.91293.0866

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 103.560 S1 S3 S4 76.440
S2 S1 S3 103.560 S2 S4 S3 76.440
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at PBEPBEultrafine/cc-pV(T+d)Z Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.098      
2 S 0.098      
3 S -0.098      
4 S -0.098      


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 1.081 1.081
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -51.141 0.000 0.000
y 0.000 -52.715 0.000
z 0.000 0.000 -48.061
Traceless
 xyz
x -0.753 0.000 0.000
y 0.000 -3.114 0.000
z 0.000 0.000 3.867
Polar
3z2-r27.735
x2-y21.574
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 5.866 0.000 0.000
y 0.000 17.753 0.000
z 0.000 0.000 12.243


<r2> (average value of r2) Å2
<r2> 201.530
(<r2>)1/2 14.196

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at PBEPBEultrafine/cc-pV(T+d)Z
 hartrees
Energy at 0K-1592.187279
Energy at 298.15K 
HF Energy-1592.187279
Nuclear repulsion energy334.109190
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 PBEPBEultrafine/cc-pV(T+d)Z
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 713 713 0.00      
2 Ag 279 279 0.00      
3 Au 243 243 0.00      
4 B1u 666 666 88.38      
5 B2u 101i 101i 11.73      
6 B3g 330 330 0.00      

Unscaled Zero Point Vibrational Energy (zpe) 1064.9 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1064.9 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 PBEPBEultrafine/cc-pV(T+d)Z
ABC
0.14558 0.08143 0.05222

See section I.F.4 to change rotational constant units
Geometric Data calculated at PBEPBEultrafine/cc-pV(T+d)Z

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.952 1.272
S2 0.000 0.952 -1.272
S3 0.000 -0.952 1.272
S4 0.000 -0.952 -1.272

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.54461.90313.1776
S22.54463.17761.9031
S31.90313.17762.5446
S43.17761.90312.5446

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 PBEPBEultrafine/cc-pV(T+d)Z 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 -51.368 0.000 0.000
y 0.000 -47.590 0.000
z 0.000 0.000 -52.536
Traceless
 xyz
x -1.305 0.000 0.000
y 0.000 4.361 0.000
z 0.000 0.000 -3.057
Polar
3z2-r2-6.113
x2-y2-3.777
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 5.853 0.000 0.000
y 0.000 12.581 0.000
z 0.000 0.000 17.084


<r2> (average value of r2) Å2
<r2> 193.091
(<r2>)1/2 13.896