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

using model chemistry: B3LYPultrafine/aug-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 B3LYPultrafine/aug-cc-pVTZ
 hartrees
Energy at 0K-1592.868821
Energy at 298.15K 
HF Energy-1592.868821
Nuclear repulsion energy346.687527
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 B3LYPultrafine/aug-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 504 487 0.00 44.12 0.04 0.09
2 A1 196 189 0.00 1.13 0.73 0.84
3 B1 441 427 0.00 19.05 0.75 0.86
4 B2 298 289 0.03 7.56 0.75 0.86
5 E 415 401 0.02 3.29 0.75 0.86
5 E 415 401 0.02 3.29 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1134.1 cm-1
Scaled (by 0.9675) Zero Point Vibrational Energy (zpe) 1097.3 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 B3LYPultrafine/aug-cc-pVTZ
ABC
0.11506 0.11506 0.06286

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3LYPultrafine/aug-cc-pVTZ

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.448 0.312
S2 0.000 -1.448 0.312
S3 -1.448 0.000 -0.312
S4 1.448 0.000 -0.312

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.89612.14072.1407
S22.89612.14072.1407
S32.14072.14072.8961
S42.14072.14072.8961

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 47.433 S1 S3 S4 47.433
S2 S1 S3 47.433 S2 S4 S3 47.433
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B3LYPultrafine/aug-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 -49.280 0.000 0.000
y 0.000 -49.280 0.000
z 0.000 0.000 -54.825
Traceless
 xyz
x 2.772 0.000 0.000
y 0.000 2.772 0.000
z 0.000 0.000 -5.545
Polar
3z2-r2-11.090
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 13.140 0.000 0.000
y 0.000 13.140 0.000
z 0.000 0.000 9.169


<r2> (average value of r2) Å2
<r2> 172.353
(<r2>)1/2 13.128

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at B3LYPultrafine/aug-cc-pVTZ
 hartrees
Energy at 0K-1592.897128
Energy at 298.15K 
HF Energy-1592.897128
Nuclear repulsion energy328.633225
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 B3LYPultrafine/aug-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 667 645 5.84 32.01 0.06 0.12
2 A1 361 349 4.97 37.76 0.15 0.25
3 A1 107 104 0.34 11.51 0.39 0.56
4 A2 208 201 0.00 0.15 0.75 0.86
5 B2 642 621 120.10 4.13 0.75 0.86
6 B2 328 317 0.17 8.35 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1156.1 cm-1
Scaled (by 0.9675) Zero Point Vibrational Energy (zpe) 1118.5 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 B3LYPultrafine/aug-cc-pVTZ
ABC
0.15584 0.06927 0.04796

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3LYPultrafine/aug-cc-pVTZ

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.069 0.920
S2 0.000 -1.069 0.920
S3 0.000 1.632 -0.920
S4 0.000 -1.632 -0.920

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.13841.92353.2678
S22.13843.26781.9235
S31.92353.26783.2634
S43.26781.92353.2634

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 107.005 S1 S3 S4 72.995
S2 S1 S3 107.005 S2 S4 S3 72.995
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B3LYPultrafine/aug-cc-pVTZ Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.168      
2 S 0.168      
3 S -0.168      
4 S -0.168      


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 1.335 1.335
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -51.784 0.000 0.000
y 0.000 -53.601 0.000
z 0.000 0.000 -49.036
Traceless
 xyz
x -0.465 0.000 0.000
y 0.000 -3.192 0.000
z 0.000 0.000 3.656
Polar
3z2-r27.313
x2-y21.818
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 8.375 0.000 0.000
y 0.000 20.720 0.000
z 0.000 0.000 13.448


<r2> (average value of r2) Å2
<r2> 208.065
(<r2>)1/2 14.424

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at B3LYPultrafine/aug-cc-pVTZ
 hartrees
Energy at 0K-1592.891787
Energy at 298.15K 
HF Energy-1592.891787
Nuclear repulsion energy332.454309
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 B3LYPultrafine/aug-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 718 694 0.00 37.58 0.10 0.17
2 Ag 282 273 0.00 33.51 0.18 0.31
3 Au 242 234 0.00 0.00 0.00 0.00
4 B1u 663 641 123.52 0.00 0.00 0.00
5 B2u 139i 134i 14.13 0.00 0.00 0.00
6 B3g 331 320 0.00 9.10 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1048.1 cm-1
Scaled (by 0.9675) Zero Point Vibrational Energy (zpe) 1014.0 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 B3LYPultrafine/aug-cc-pVTZ
ABC
0.14525 0.07997 0.05157

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3LYPultrafine/aug-cc-pVTZ

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.953 1.284
S2 0.000 0.953 -1.284
S3 0.000 -0.953 1.284
S4 0.000 -0.953 -1.284

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.56781.90533.1974
S22.56783.19741.9053
S31.90533.19742.5678
S43.19741.90532.5678

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 B3LYPultrafine/aug-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 -52.014 0.000 0.000
y 0.000 -48.302 0.000
z 0.000 0.000 -53.209
Traceless
 xyz
x -1.258 0.000 0.000
y 0.000 4.309 0.000
z 0.000 0.000 -3.051
Polar
3z2-r2-6.103
x2-y2-3.712
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 8.367 0.000 0.000
y 0.000 13.864 0.000
z 0.000 0.000 19.569


<r2> (average value of r2) Å2
<r2> 195.541
(<r2>)1/2 13.984