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

using model chemistry: HSEh1PBE/daug-cc-pVTZ

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/daug-cc-pVTZ
 hartrees
Energy at 0K-1592.325787
Energy at 298.15K 
HF Energy-1592.325787
Nuclear repulsion energy351.646784
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/daug-cc-pVTZ
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 536 536 0.00 39.67 0.04 0.08
2 A1 207 207 0.00 1.12 0.73 0.84
3 B1 475 475 0.00 16.02 0.75 0.86
4 B2 302 302 0.01 6.73 0.75 0.86
5 E 448 448 0.00 2.96 0.75 0.86
5 E 448 448 0.00 2.96 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1207.4 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1207.4 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/daug-cc-pVTZ
ABC
0.11824 0.11824 0.06488

See section I.F.4 to change rotational constant units
Geometric Data calculated at HSEh1PBE/daug-cc-pVTZ

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.425 0.315
S2 0.000 -1.425 0.315
S3 -1.425 0.000 -0.315
S4 1.425 0.000 -0.315

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.85082.11172.1117
S22.85082.11172.1117
S32.11172.11172.8508
S42.11172.11172.8508

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 47.545 S1 S3 S4 47.545
S2 S1 S3 47.545 S2 S4 S3 47.545
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at HSEh1PBE/daug-cc-pVTZ 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 -48.963 0.000 0.000
y 0.000 -48.963 0.000
z 0.000 0.000 -54.386
Traceless
 xyz
x 2.711 0.000 0.000
y 0.000 2.711 0.000
z 0.000 0.000 -5.423
Polar
3z2-r2-10.846
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 12.777 0.000 0.000
y 0.000 12.777 0.000
z 0.000 0.000 9.054


<r2> (average value of r2) Å2
<r2> 168.076
(<r2>)1/2 12.964

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at HSEh1PBE/daug-cc-pVTZ
 hartrees
Energy at 0K-1592.348878
Energy at 298.15K 
HF Energy-1592.348878
Nuclear repulsion energy333.436219
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/daug-cc-pVTZ
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 700 700 6.80 30.50 0.06 0.11
2 A1 401 401 4.87 39.40 0.14 0.25
3 A1 117 117 0.38 10.51 0.38 0.55
4 A2 219 219 0.00 0.13 0.75 0.86
5 B2 671 671 120.29 3.89 0.75 0.86
6 B2 340 340 0.16 7.83 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1224.1 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1224.1 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 HSEh1PBE/daug-cc-pVTZ
ABC
0.15760 0.07252 0.04966

See section I.F.4 to change rotational constant units
Geometric Data calculated at HSEh1PBE/daug-cc-pVTZ

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.050 0.915
S2 0.000 -1.050 0.915
S3 0.000 1.592 -0.915
S4 0.000 -1.592 -0.915

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.09901.90783.2128
S22.09903.21281.9078
S31.90783.21283.1837
S43.21281.90783.1837

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 106.515 S1 S3 S4 73.485
S2 S1 S3 106.515 S2 S4 S3 73.485
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at HSEh1PBE/daug-cc-pVTZ Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.324      
2 S 0.324      
3 S -0.324      
4 S -0.324      


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 1.348 1.348
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -51.391 0.000 0.000
y 0.000 -53.236 0.000
z 0.000 0.000 -48.642
Traceless
 xyz
x -0.452 0.000 0.000
y 0.000 -3.220 0.000
z 0.000 0.000 3.672
Polar
3z2-r27.344
x2-y21.846
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 8.265 0.000 0.000
y 0.000 19.938 0.000
z 0.000 0.000 13.208


<r2> (average value of r2) Å2
<r2> 201.773
(<r2>)1/2 14.205

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at HSEh1PBE/daug-cc-pVTZ
 hartrees
Energy at 0K-1592.342501
Energy at 298.15K 
HF Energy-1592.342501
Nuclear repulsion energy337.594797
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/daug-cc-pVTZ
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 752 752 0.00 36.44 0.09 0.16
2 Ag 304 304 0.00 32.12 0.17 0.29
3 Au 256 256 0.00 0.00 0.00 0.00
4 B1u 693 693 123.29 0.00 0.00 0.00
5 B2u 160i 160i 15.88 0.00 0.00 0.00
6 B3g 346 346 0.00 8.44 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1095.5 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1095.5 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 HSEh1PBE/daug-cc-pVTZ
ABC
0.14767 0.08372 0.05343

See section I.F.4 to change rotational constant units
Geometric Data calculated at HSEh1PBE/daug-cc-pVTZ

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.945 1.255
S2 0.000 0.945 -1.255
S3 0.000 -0.945 1.255
S4 0.000 -0.945 -1.255

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.50961.88963.1414
S22.50963.14141.8896
S31.88963.14142.5096
S43.14141.88962.5096

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/daug-cc-pVTZ 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 -51.611 0.000 0.000
y 0.000 -47.914 0.000
z 0.000 0.000 -52.975
Traceless
 xyz
x -1.166 0.000 0.000
y 0.000 4.379 0.000
z 0.000 0.000 -3.213
Polar
3z2-r2-6.426
x2-y2-3.697
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 8.235 0.000 0.000
y 0.000 13.601 0.000
z 0.000 0.000 18.918


<r2> (average value of r2) Å2
<r2> 189.645
(<r2>)1/2 13.771