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

using model chemistry: B3LYPultrafine/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 B3LYPultrafine/cc-pVDZ
 hartrees
Energy at 0K-1592.794314
Energy at 298.15K 
HF Energy-1592.794314
Nuclear repulsion energy342.248462
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/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 492 478 0.00 43.21 0.06 0.11
2 A1 184 179 0.00 3.69 0.75 0.86
3 B1 424 412 0.00 25.37 0.75 0.86
4 B2 298 289 0.03 11.99 0.75 0.86
5 E 402 390 0.24 5.57 0.75 0.86
5 E 402 390 0.24 5.57 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1101.2 cm-1
Scaled (by 0.97) Zero Point Vibrational Energy (zpe) 1068.1 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 B3LYPultrafine/cc-pVDZ
ABC
0.11217 0.11217 0.06121

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

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.468 0.314
S2 0.000 -1.468 0.314
S3 -1.468 0.000 -0.314
S4 1.468 0.000 -0.314

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.93502.16812.1681
S22.93502.16812.1681
S32.16812.16812.9350
S42.16812.16812.9350

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 47.400 S1 S3 S4 47.400
S2 S1 S3 47.400 S2 S4 S3 47.400
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B3LYPultrafine/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 -48.773 0.000 0.000
y 0.000 -48.773 0.000
z 0.000 0.000 -54.533
Traceless
 xyz
x 2.880 0.000 0.000
y 0.000 2.880 0.000
z 0.000 0.000 -5.760
Polar
3z2-r2-11.521
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 10.567 0.000 0.000
y 0.000 10.567 0.000
z 0.000 0.000 5.023


<r2> (average value of r2) Å2
<r2> 175.785
(<r2>)1/2 13.258

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at B3LYPultrafine/cc-pVDZ
 hartrees
Energy at 0K-1592.824396
Energy at 298.15K 
HF Energy-1592.824396
Nuclear repulsion energy326.259058
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/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 671 651 2.31 28.27 0.22 0.36
2 A1 314 305 7.28 31.57 0.22 0.36
3 A1 103 100 2.30 7.06 0.52 0.68
4 A2 211 204 0.00 0.06 0.75 0.86
5 B2 644 625 114.35 1.90 0.75 0.86
6 B2 324 314 0.06 15.35 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1133.5 cm-1
Scaled (by 0.97) Zero Point Vibrational Energy (zpe) 1099.5 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/cc-pVDZ
ABC
0.14848 0.07108 0.04807

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

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.113 0.942
S2 0.000 -1.113 0.942
S3 0.000 1.571 -0.942
S4 0.000 -1.571 -0.942

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.22651.93933.2800
S22.22653.28001.9393
S31.93933.28003.1429
S43.28001.93933.1429

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 103.666 S1 S3 S4 76.334
S2 S1 S3 103.666 S2 S4 S3 76.334
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B3LYPultrafine/cc-pVDZ Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.086      
2 S 0.086      
3 S -0.086      
4 S -0.086      


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 1.261 1.261
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -51.255 0.000 0.000
y 0.000 -53.037 0.000
z 0.000 0.000 -48.342
Traceless
 xyz
x -0.566 0.000 0.000
y 0.000 -3.238 0.000
z 0.000 0.000 3.804
Polar
3z2-r27.608
x2-y21.782
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 4.147 0.000 0.000
y 0.000 16.861 0.000
z 0.000 0.000 11.159


<r2> (average value of r2) Å2
<r2> 207.273
(<r2>)1/2 14.397

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at B3LYPultrafine/cc-pVDZ
 hartrees
Energy at 0K-1592.822312
Energy at 298.15K 
HF Energy-1592.822312
Nuclear repulsion energy328.263344
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/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 709 688 0.00 32.21 0.26 0.42
2 Ag 278 269 0.00 31.72 0.27 0.42
3 Au 235 228 0.00 0.00 0.00 0.00
4 B1u 660 640 122.31 0.00 0.00 0.00
5 B2u 101i 98i 14.31 0.00 0.00 0.00
6 B3g 325 316 0.00 16.71 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1053.1 cm-1
Scaled (by 0.97) Zero Point Vibrational Energy (zpe) 1021.5 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/cc-pVDZ
ABC
0.14208 0.07768 0.05022

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

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.963 1.303
S2 0.000 0.963 -1.303
S3 0.000 -0.963 1.303
S4 0.000 -0.963 -1.303

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.60531.92643.2401
S22.60533.24011.9264
S31.92643.24012.6053
S43.24011.92642.6053

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/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 -51.484 0.000 0.000
y 0.000 -47.883 0.000
z 0.000 0.000 -52.735
Traceless
 xyz
x -1.175 0.000 0.000
y 0.000 4.227 0.000
z 0.000 0.000 -3.052
Polar
3z2-r2-6.104
x2-y2-3.601
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 4.124 0.000 0.000
y 0.000 11.569 0.000
z 0.000 0.000 16.206


<r2> (average value of r2) Å2
<r2> 199.641
(<r2>)1/2 14.129