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

using model chemistry: M06-2X/daug-cc-pVDZ

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 M06-2X/daug-cc-pVDZ
 hartrees
Energy at 0K-1592.667890
Energy at 298.15K 
HF Energy-1592.667890
Nuclear repulsion energy347.848159
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 M06-2X/daug-cc-pVDZ
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 530 530 0.00 49.13 0.05 0.09
2 A1 197 197 0.00 1.22 0.73 0.84
3 B1 471 471 0.00 19.80 0.75 0.86
4 B2 311 311 0.00 7.11 0.75 0.86
5 E 448 448 0.00 3.92 0.75 0.86
5 E 448 448 0.00 3.92 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1202.7 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1202.7 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 M06-2X/daug-cc-pVDZ
ABC
0.11564 0.11564 0.06357

See section I.F.4 to change rotational constant units
Geometric Data calculated at M06-2X/daug-cc-pVDZ

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.440 0.321
S2 0.000 -1.440 0.321
S3 -1.440 0.000 -0.321
S4 1.440 0.000 -0.321

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.88002.13532.1353
S22.88002.13532.1353
S32.13532.13532.8800
S42.13532.13532.8800

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 47.594 S1 S3 S4 47.594
S2 S1 S3 47.594 S2 S4 S3 47.594
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at M06-2X/daug-cc-pVDZ 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 -49.066 0.000 0.000
y 0.000 -49.066 0.000
z 0.000 0.000 -55.404
Traceless
 xyz
x 3.169 0.000 0.000
y 0.000 3.169 0.000
z 0.000 0.000 -6.338
Polar
3z2-r2-12.676
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 12.923 0.000 0.000
y 0.000 12.923 0.000
z 0.000 0.000 9.000


<r2> (average value of r2) Å2
<r2> 171.272
(<r2>)1/2 13.087

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at M06-2X/daug-cc-pVDZ
 hartrees
Energy at 0K-1592.678460
Energy at 298.15K 
HF Energy-1592.678460
Nuclear repulsion energy331.903737
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 M06-2X/daug-cc-pVDZ
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 692 692 6.15 34.87 0.06 0.12
2 A1 424 424 5.72 57.28 0.17 0.29
3 A1 128 128 0.36 15.16 0.38 0.55
4 A2 213 213 0.00 0.32 0.75 0.86
5 B2 659 659 163.26 4.82 0.75 0.86
6 B2 335 335 0.34 8.46 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1225.5 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1225.5 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 M06-2X/daug-cc-pVDZ
ABC
0.15526 0.07211 0.04924

See section I.F.4 to change rotational constant units
Geometric Data calculated at M06-2X/daug-cc-pVDZ

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.045 0.921
S2 0.000 -1.045 0.921
S3 0.000 1.601 -0.921
S4 0.000 -1.601 -0.921

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.08931.92513.2245
S22.08933.22451.9251
S31.92513.22453.2028
S43.22451.92513.2028

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 106.810 S1 S3 S4 73.190
S2 S1 S3 106.810 S2 S4 S3 73.190
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at M06-2X/daug-cc-pVDZ Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.151      
2 S 0.151      
3 S -0.151      
4 S -0.151      


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 1.511 1.511
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -52.388 0.000 0.000
y 0.000 -53.741 0.000
z 0.000 0.000 -48.746
Traceless
 xyz
x -1.145 0.000 0.000
y 0.000 -3.174 0.000
z 0.000 0.000 4.319
Polar
3z2-r28.638
x2-y21.353
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 8.319 0.000 0.000
y 0.000 20.998 0.000
z 0.000 0.000 13.234


<r2> (average value of r2) Å2
<r2> 203.563
(<r2>)1/2 14.268

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at M06-2X/daug-cc-pVDZ
 hartrees
Energy at 0K-1592.670649
Energy at 298.15K 
HF Energy-1592.670649
Nuclear repulsion energy336.474209
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 M06-2X/daug-cc-pVDZ
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 759 759 0.00 37.56 0.10 0.19
2 Ag 321 321 0.00 50.95 0.19 0.33
3 Au 252 252 0.00 0.00 0.00 0.00
4 B1u 690 690 172.97 0.00 0.00 0.00
5 B2u 175i 175i 18.74 0.00 0.00 0.00
6 B3g 344 344 0.00 10.22 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 M06-2X/daug-cc-pVDZ
ABC
0.14593 0.08363 0.05316

See section I.F.4 to change rotational constant units
Geometric Data calculated at M06-2X/daug-cc-pVDZ

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.950 1.255
S2 0.000 0.950 -1.255
S3 0.000 -0.950 1.255
S4 0.000 -0.950 -1.255

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.51101.90083.1493
S22.51103.14931.9008
S31.90083.14932.5110
S43.14931.90082.5110

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 M06-2X/daug-cc-pVDZ 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 -52.700 0.000 0.000
y 0.000 -48.038 0.000
z 0.000 0.000 -53.129
Traceless
 xyz
x -2.117 0.000 0.000
y 0.000 4.876 0.000
z 0.000 0.000 -2.759
Polar
3z2-r2-5.519
x2-y2-4.662
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 8.260 0.000 0.000
y 0.000 13.657 0.000
z 0.000 0.000 19.604


<r2> (average value of r2) Å2
<r2> 190.722
(<r2>)1/2 13.810