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

using model chemistry: mPW1PW91/6-31G(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 mPW1PW91/6-31G(2df,p)
 hartrees
Energy at 0K-1592.761224
Energy at 298.15K 
HF Energy-1592.761224
Nuclear repulsion energy352.386529
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 mPW1PW91/6-31G(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 544 519 0.00 38.98 0.05 0.09
2 A1 206 197 0.00 1.66 0.75 0.86
3 B1 485 463 0.00 18.58 0.75 0.86
4 B2 302 288 0.01 8.89 0.75 0.86
5 E 457 436 0.01 4.19 0.75 0.86
5 E 457 436 0.01 4.19 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1224.8 cm-1
Scaled (by 0.9547) Zero Point Vibrational Energy (zpe) 1169.3 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 mPW1PW91/6-31G(2df,p)
ABC
0.11880 0.11880 0.06506

See section I.F.4 to change rotational constant units
Geometric Data calculated at mPW1PW91/6-31G(2df,p)

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.423 0.311
S2 0.000 -1.423 0.311
S3 -1.423 0.000 -0.311
S4 1.423 0.000 -0.311

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.84682.10672.1067
S22.84682.10672.1067
S32.10672.10672.8468
S42.10672.10672.8468

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 47.495 S1 S3 S4 47.495
S2 S1 S3 47.495 S2 S4 S3 47.495
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at mPW1PW91/6-31G(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 -48.472 0.000 0.000
y 0.000 -48.472 0.000
z 0.000 0.000 -53.910
Traceless
 xyz
x 2.719 0.000 0.000
y 0.000 2.719 0.000
z 0.000 0.000 -5.438
Polar
3z2-r2-10.876
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 11.014 0.000 0.000
y 0.000 11.014 0.000
z 0.000 0.000 6.729


<r2> (average value of r2) Å2
<r2> 167.254
(<r2>)1/2 12.933

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at mPW1PW91/6-31G(2df,p)
 hartrees
Energy at 0K-1592.782941
Energy at 298.15K 
HF Energy-1592.782941
Nuclear repulsion energy334.011961
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 mPW1PW91/6-31G(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 707 675 6.76 26.49 0.16 0.27
2 A1 419 400 5.62 38.95 0.19 0.31
3 A1 117 111 0.33 11.29 0.46 0.63
4 A2 220 210 0.00 0.24 0.75 0.86
5 B2 679 648 122.90 3.23 0.75 0.86
6 B2 343 328 0.29 11.74 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1241.6 cm-1
Scaled (by 0.9547) Zero Point Vibrational Energy (zpe) 1185.3 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 mPW1PW91/6-31G(2df,p)
ABC
0.15868 0.07244 0.04974

See section I.F.4 to change rotational constant units
Geometric Data calculated at mPW1PW91/6-31G(2df,p)

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.042 0.911
S2 0.000 -1.042 0.911
S3 0.000 1.598 -0.911
S4 0.000 -1.598 -0.911

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.08481.90553.2082
S22.08483.20821.9055
S31.90553.20823.1953
S43.20821.90553.1953

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 106.941 S1 S3 S4 73.059
S2 S1 S3 106.941 S2 S4 S3 73.059
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at mPW1PW91/6-31G(2df,p) Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.140      
2 S 0.140      
3 S -0.140      
4 S -0.140      


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 1.477 1.477
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -50.805 0.000 0.000
y 0.000 -52.728 0.000
z 0.000 0.000 -48.220
Traceless
 xyz
x -0.331 0.000 0.000
y 0.000 -3.215 0.000
z 0.000 0.000 3.547
Polar
3z2-r27.094
x2-y21.923
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 5.869 0.000 0.000
y 0.000 17.879 0.000
z 0.000 0.000 11.463


<r2> (average value of r2) Å2
<r2> 201.210
(<r2>)1/2 14.185

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at mPW1PW91/6-31G(2df,p)
 hartrees
Energy at 0K-1592.775729
Energy at 298.15K 
HF Energy-1592.775729
Nuclear repulsion energy338.685381
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 mPW1PW91/6-31G(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 759 725 0.00 34.06 0.20 0.34
2 Ag 309 295 0.00 35.90 0.25 0.40
3 Au 260 248 0.00 0.00 0.00 0.00
4 B1u 700 668 129.16 0.00 0.00 0.00
5 B2u 168i 161i 18.93 0.00 0.00 0.00
6 B3g 351 335 0.00 13.97 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1105.3 cm-1
Scaled (by 0.9547) Zero Point Vibrational Energy (zpe) 1055.2 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 mPW1PW91/6-31G(2df,p)
ABC
0.14814 0.08456 0.05383

See section I.F.4 to change rotational constant units
Geometric Data calculated at mPW1PW91/6-31G(2df,p)

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.943 1.249
S2 0.000 0.943 -1.249
S3 0.000 -0.943 1.249
S4 0.000 -0.943 -1.249

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.49711.88663.1297
S22.49713.12971.8866
S31.88663.12972.4971
S43.12971.88662.4971

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 mPW1PW91/6-31G(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 -51.124 0.000 0.000
y 0.000 -47.476 0.000
z 0.000 0.000 -52.438
Traceless
 xyz
x -1.166 0.000 0.000
y 0.000 4.305 0.000
z 0.000 0.000 -3.139
Polar
3z2-r2-6.278
x2-y2-3.648
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 5.901 0.000 0.000
y 0.000 11.984 0.000
z 0.000 0.000 16.748


<r2> (average value of r2) Å2
<r2> 188.162
(<r2>)1/2 13.717