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

using model chemistry: HSEh1PBE/Def2TZVPP

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 HSEh1PBE/Def2TZVPP
 hartrees
Energy at 0K-1592.305267
Energy at 298.15K 
HF Energy-1592.305267
Nuclear repulsion energy353.512271
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 HSEh1PBE/Def2TZVPP
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 540 540 0.00 36.57 0.05 0.09
2 A1 210 210 0.00 2.38 0.74 0.85
3 B1 479 479 0.00 16.11 0.75 0.86
4 B2 302 302 0.00 8.03 0.75 0.86
5 E 450 450 0.00 4.09 0.75 0.86
5 E 450 450 0.00 4.09 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1214.4 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1214.4 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 HSEh1PBE/Def2TZVPP
ABC
0.11948 0.11948 0.06559

See section I.F.4 to change rotational constant units
Geometric Data calculated at HSEh1PBE/Def2TZVPP

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.418 0.314
S2 0.000 -1.418 0.314
S3 -1.418 0.000 -0.314
S4 1.418 0.000 -0.314

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.83522.10072.1007
S22.83522.10072.1007
S32.10072.10072.8352
S42.10072.10072.8352

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 47.561 S1 S3 S4 47.561
S2 S1 S3 47.561 S2 S4 S3 47.561
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at HSEh1PBE/Def2TZVPP 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 -48.594 0.000 0.000
y 0.000 -48.594 0.000
z 0.000 0.000 -54.001
Traceless
 xyz
x 2.703 0.000 0.000
y 0.000 2.703 0.000
z 0.000 0.000 -5.406
Polar
3z2-r2-10.813
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 11.211 0.000 0.000
y 0.000 11.211 0.000
z 0.000 0.000 6.577


<r2> (average value of r2) Å2
<r2> 166.390
(<r2>)1/2 12.899

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at HSEh1PBE/Def2TZVPP
 hartrees
Energy at 0K-1592.330801
Energy at 298.15K 
HF Energy-1592.330801
Nuclear repulsion energy335.095465
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 HSEh1PBE/Def2TZVPP
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 708 708 7.55 24.30 0.16 0.27
2 A1 412 412 4.90 40.04 0.19 0.32
3 A1 117 117 0.30 10.18 0.45 0.62
4 A2 223 223 0.00 0.11 0.75 0.86
5 B2 678 678 122.03 3.88 0.75 0.86
6 B2 346 346 0.19 11.12 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1241.6 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1241.6 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 HSEh1PBE/Def2TZVPP
ABC
0.16014 0.07273 0.05001

See section I.F.4 to change rotational constant units
Geometric Data calculated at HSEh1PBE/Def2TZVPP

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.039 0.907
S2 0.000 -1.039 0.907
S3 0.000 1.595 -0.907
S4 0.000 -1.595 -0.907

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.07831.89793.1989
S22.07833.19891.8979
S31.89793.19893.1907
S43.19891.89793.1907

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 107.041 S1 S3 S4 72.959
S2 S1 S3 107.041 S2 S4 S3 72.959
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at HSEh1PBE/Def2TZVPP Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.138      
2 S 0.138      
3 S -0.138      
4 S -0.138      


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 1.428 1.428
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -50.960 0.000 0.000
y 0.000 -53.007 0.000
z 0.000 0.000 -48.247
Traceless
 xyz
x -0.333 0.000 0.000
y 0.000 -3.403 0.000
z 0.000 0.000 3.736
Polar
3z2-r27.472
x2-y22.047
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 5.720 0.000 0.000
y 0.000 18.067 0.000
z 0.000 0.000 11.713


<r2> (average value of r2) Å2
<r2> 200.371
(<r2>)1/2 14.155

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at HSEh1PBE/Def2TZVPP
 hartrees
Energy at 0K-1592.323595
Energy at 298.15K 
HF Energy-1592.323595
Nuclear repulsion energy339.410667
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 HSEh1PBE/Def2TZVPP
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 760 760 0.00 32.17 0.20 0.34
2 Ag 305 305 0.00 35.83 0.24 0.39
3 Au 261 261 0.00 0.00 0.00 0.00
4 B1u 699 699 124.77 0.00 0.00 0.00
5 B2u 167i 167i 17.73 0.00 0.00 0.00
6 B3g 352 352 0.00 12.82 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1105.2 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1105.2 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 HSEh1PBE/Def2TZVPP
ABC
0.14922 0.08465 0.05401

See section I.F.4 to change rotational constant units
Geometric Data calculated at HSEh1PBE/Def2TZVPP

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.940 1.248
S2 0.000 0.940 -1.248
S3 0.000 -0.940 1.248
S4 0.000 -0.940 -1.248

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.49581.87973.1245
S22.49583.12451.8797
S31.87973.12452.4958
S43.12451.87972.4958

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 HSEh1PBE/Def2TZVPP 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 -51.318 0.000 0.000
y 0.000 -47.508 0.000
z 0.000 0.000 -52.606
Traceless
 xyz
x -1.260 0.000 0.000
y 0.000 4.454 0.000
z 0.000 0.000 -3.193
Polar
3z2-r2-6.387
x2-y2-3.810
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 5.698 0.000 0.000
y 0.000 12.236 0.000
z 0.000 0.000 17.057


<r2> (average value of r2) Å2
<r2> 187.724
(<r2>)1/2 13.701