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

using model chemistry: TPSSh/aug-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 TPSSh/aug-cc-pVDZ
 hartrees
Energy at 0K-1592.813286
Energy at 298.15K 
HF Energy-1592.813286
Nuclear repulsion energy345.510323
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 TPSSh/aug-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 509 492 0.00 43.02 0.04 0.08
2 A1 201 194 0.00 0.96 0.71 0.83
3 B1 433 419 0.00 19.34 0.75 0.86
4 B2 291 281 0.03 8.04 0.75 0.86
5 E 414 400 0.07 3.48 0.75 0.86
5 E 414 400 0.07 3.48 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1130.4 cm-1
Scaled (by 0.9673) Zero Point Vibrational Energy (zpe) 1093.4 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 TPSSh/aug-cc-pVDZ
ABC
0.11396 0.11396 0.06291

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

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.448 0.330
S2 0.000 -1.448 0.330
S3 -1.448 0.000 -0.330
S4 1.448 0.000 -0.330

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.89512.15092.1509
S22.89512.15092.1509
S32.15092.15092.8951
S42.15092.15092.8951

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 47.702 S1 S3 S4 47.702
S2 S1 S3 47.702 S2 S4 S3 47.702
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at TPSSh/aug-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


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 12.800 0.000 0.000
y 0.000 12.800 0.000
z 0.000 0.000 8.964


<r2> (average value of r2) Å2
<r2> 172.833
(<r2>)1/2 13.147

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at TPSSh/aug-cc-pVDZ
 hartrees
Energy at 0K-1592.844300
Energy at 298.15K 
HF Energy-1592.844300
Nuclear repulsion energy328.610506
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 TPSSh/aug-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 684 662 2.92 34.05 0.08 0.14
2 A1 317 307 5.54 31.84 0.17 0.29
3 A1 107 104 2.27 5.89 0.43 0.60
4 A2 214 207 0.00 0.13 0.75 0.86
5 B2 654 632 106.75 2.43 0.75 0.86
6 B2 323 312 0.02 8.93 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1149.4 cm-1
Scaled (by 0.9673) Zero Point Vibrational Energy (zpe) 1111.8 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 TPSSh/aug-cc-pVDZ
ABC
0.14842 0.07328 0.04906

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

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.109 0.942
S2 0.000 -1.109 0.942
S3 0.000 1.539 -0.942
S4 0.000 -1.539 -0.942

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.21861.93313.2501
S22.21863.25011.9331
S31.93313.25013.0770
S43.25011.93313.0770

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 102.828 S1 S3 S4 77.172
S2 S1 S3 102.828 S2 S4 S3 77.172
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at TPSSh/aug-cc-pVDZ Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.073      
2 S 0.073      
3 S -0.073      
4 S -0.073      


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 1.111 1.111
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 8.031 0.000 0.000
y 0.000 19.668 0.000
z 0.000 0.000 13.290


<r2> (average value of r2) Å2
<r2> 203.850
(<r2>)1/2 14.278

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at TPSSh/aug-cc-pVDZ
 hartrees
Energy at 0K-1592.842485
Energy at 298.15K 
HF Energy-1592.842485
Nuclear repulsion energy330.195227
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 TPSSh/aug-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 718 694 0.00 37.41 0.10 0.18
2 Ag 284 275 0.00 30.21 0.19 0.32
3 Au 235 228 0.00 0.00 0.00 0.00
4 B1u 668 646 111.57 0.00 0.00 0.00
5 B2u 100i 96i 12.42 0.00 0.00 0.00
6 B3g 324 314 0.00 9.33 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1064.7 cm-1
Scaled (by 0.9673) Zero Point Vibrational Energy (zpe) 1029.9 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 TPSSh/aug-cc-pVDZ
ABC
0.14281 0.07916 0.05093

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

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.961 1.290
S2 0.000 0.961 -1.290
S3 0.000 -0.961 1.290
S4 0.000 -0.961 -1.290

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.58081.92153.2175
S22.58083.21751.9215
S31.92153.21752.5808
S43.21751.92152.5808

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 TPSSh/aug-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


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 8.039 0.000 0.000
y 0.000 13.542 0.000
z 0.000 0.000 19.107


<r2> (average value of r2) Å2
<r2> 197.402
(<r2>)1/2 14.050