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

using model chemistry: HSEh1PBE/6-31G(2df,p)

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/6-31G(2df,p)
 hartrees
Energy at 0K-1592.202396
Energy at 298.15K 
HF Energy-1592.202396
Nuclear repulsion energy352.536724
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/6-31G(2df,p)
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 543 520 0.00 38.49 0.04 0.08
2 A1 207 198 0.00 1.69 0.75 0.86
3 B1 483 463 0.00 18.52 0.75 0.86
4 B2 301 288 0.01 8.95 0.75 0.86
5 E 455 436 0.01 4.18 0.75 0.86
5 E 455 436 0.01 4.18 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1222.0 cm-1
Scaled (by 0.9577) Zero Point Vibrational Energy (zpe) 1170.4 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/6-31G(2df,p)
ABC
0.11886 0.11886 0.06517

See section I.F.4 to change rotational constant units
Geometric Data calculated at HSEh1PBE/6-31G(2df,p)

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.422 0.312
S2 0.000 -1.422 0.312
S3 -1.422 0.000 -0.312
S4 1.422 0.000 -0.312

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.84442.10622.1062
S22.84442.10622.1062
S32.10622.10622.8444
S42.10622.10622.8444

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 47.526 S1 S3 S4 47.526
S2 S1 S3 47.526 S2 S4 S3 47.526
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at HSEh1PBE/6-31G(2df,p) 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 -48.576 0.000 0.000
y 0.000 -48.576 0.000
z 0.000 0.000 -53.998
Traceless
 xyz
x 2.711 0.000 0.000
y 0.000 2.711 0.000
z 0.000 0.000 -5.422
Polar
3z2-r2-10.845
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 11.015 0.000 0.000
y 0.000 11.015 0.000
z 0.000 0.000 6.740


<r2> (average value of r2) Å2
<r2> 167.167
(<r2>)1/2 12.929

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at HSEh1PBE/6-31G(2df,p)
 hartrees
Energy at 0K-1592.226071
Energy at 298.15K 
HF Energy-1592.226071
Nuclear repulsion energy333.830067
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/6-31G(2df,p)
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 707 677 6.62 26.32 0.16 0.27
2 A1 415 397 5.55 37.85 0.18 0.31
3 A1 117 112 0.33 11.00 0.46 0.63
4 A2 220 210 0.00 0.22 0.75 0.86
5 B2 680 651 119.67 3.15 0.75 0.86
6 B2 343 328 0.26 11.78 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1240.4 cm-1
Scaled (by 0.9577) Zero Point Vibrational Energy (zpe) 1187.9 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 HSEh1PBE/6-31G(2df,p)
ABC
0.15859 0.07234 0.04968

See section I.F.4 to change rotational constant units
Geometric Data calculated at HSEh1PBE/6-31G(2df,p)

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.044 0.912
S2 0.000 -1.044 0.912
S3 0.000 1.598 -0.912
S4 0.000 -1.598 -0.912

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.08791.90583.2103
S22.08793.21031.9058
S31.90583.21033.1965
S43.21031.90583.1965

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 106.910 S1 S3 S4 73.090
S2 S1 S3 106.910 S2 S4 S3 73.090
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at HSEh1PBE/6-31G(2df,p) 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 1.452 1.452
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -50.911 0.000 0.000
y 0.000 -52.810 0.000
z 0.000 0.000 -48.310
Traceless
 xyz
x -0.352 0.000 0.000
y 0.000 -3.199 0.000
z 0.000 0.000 3.551
Polar
3z2-r27.102
x2-y21.898
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 5.872 0.000 0.000
y 0.000 17.829 0.000
z 0.000 0.000 11.477


<r2> (average value of r2) Å2
<r2> 201.462
(<r2>)1/2 14.194

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at HSEh1PBE/6-31G(2df,p)
 hartrees
Energy at 0K-1592.218923
Energy at 298.15K 
HF Energy-1592.218923
Nuclear repulsion energy338.325820
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/6-31G(2df,p)
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 759 727 0.00 33.85 0.20 0.34
2 Ag 305 292 0.00 35.04 0.25 0.40
3 Au 259 248 0.00 0.00 0.00 0.00
4 B1u 701 671 126.17 0.00 0.00 0.00
5 B2u 167i 160i 18.16 0.00 0.00 0.00
6 B3g 350 335 0.00 13.94 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1102.8 cm-1
Scaled (by 0.9577) Zero Point Vibrational Energy (zpe) 1056.1 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/6-31G(2df,p)
ABC
0.14802 0.08426 0.05369

See section I.F.4 to change rotational constant units
Geometric Data calculated at HSEh1PBE/6-31G(2df,p)

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.944 1.251
S2 0.000 0.944 -1.251
S3 0.000 -0.944 1.251
S4 0.000 -0.944 -1.251

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.50161.88733.1337
S22.50163.13371.8873
S31.88733.13372.5016
S43.13371.88732.5016

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/6-31G(2df,p) 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 -51.231 0.000 0.000
y 0.000 -47.566 0.000
z 0.000 0.000 -52.540
Traceless
 xyz
x -1.178 0.000 0.000
y 0.000 4.320 0.000
z 0.000 0.000 -3.142
Polar
3z2-r2-6.283
x2-y2-3.666
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 5.905 0.000 0.000
y 0.000 11.997 0.000
z 0.000 0.000 16.736


<r2> (average value of r2) Å2
<r2> 188.625
(<r2>)1/2 13.734