return to home page Computational Chemistry Comparison and Benchmark DataBase Release 22 (May 2022) Standard Reference Database 101 National Institute of Standards and Technology
You are here: Calculated > Energy > Optimized > Energy

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

using model chemistry: PBEPBEultrafine/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 PBEPBEultrafine/daug-cc-pVDZ
 hartrees
Energy at 0K-1592.082986
Energy at 298.15K 
HF Energy-1592.082986
Nuclear repulsion energy343.516698
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 PBEPBEultrafine/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 497 497 0.00 42.07 0.04 0.08
2 A1 198 198 0.00 0.97 0.69 0.82
3 B1 404 404 0.00 19.72 0.75 0.86
4 B2 280 280 0.05 9.00 0.75 0.86
5 E 388 388 0.29 2.97 0.75 0.86
5 E 388 388 0.29 2.97 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1076.8 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1076.8 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 PBEPBEultrafine/daug-cc-pVDZ
ABC
0.11268 0.11268 0.06215

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

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.456 0.331
S2 0.000 -1.456 0.331
S3 -1.456 0.000 -0.331
S4 1.456 0.000 -0.331

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.91282.16322.1632
S22.91282.16322.1632
S32.16322.16322.9128
S42.16322.16322.9128

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 47.681 S1 S3 S4 47.681
S2 S1 S3 47.681 S2 S4 S3 47.681
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at PBEPBEultrafine/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 -49.075 0.000 0.000
y 0.000 -49.075 0.000
z 0.000 0.000 -55.179
Traceless
 xyz
x 3.052 0.000 0.000
y 0.000 3.052 0.000
z 0.000 0.000 -6.104
Polar
3z2-r2-12.207
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 13.491 0.000 0.000
y 0.000 13.491 0.000
z 0.000 0.000 9.559


<r2> (average value of r2) Å2
<r2> 174.666
(<r2>)1/2 13.216

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at PBEPBEultrafine/daug-cc-pVDZ
 hartrees
Energy at 0K-1592.125476
Energy at 298.15K 
HF Energy-1592.125476
Nuclear repulsion energy326.814729
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 PBEPBEultrafine/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 676 676 1.86 35.97 0.08 0.14
2 A1 291 291 4.03 28.67 0.15 0.26
3 A1 84 84 3.69 3.62 0.42 0.59
4 A2 213 213 0.00 0.04 0.75 0.86
5 B2 644 644 88.86 1.56 0.75 0.86
6 B2 313 313 0.01 8.60 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1110.9 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1110.9 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 PBEPBEultrafine/daug-cc-pVDZ
ABC
0.14439 0.07416 0.04899

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

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.151 0.955
S2 0.000 -1.151 0.955
S3 0.000 1.494 -0.955
S4 0.000 -1.494 -0.955

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.30101.94153.2625
S22.30103.26251.9415
S31.94153.26252.9876
S43.26251.94152.9876

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 100.184 S1 S3 S4 79.816
S2 S1 S3 100.184 S2 S4 S3 79.816
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at PBEPBEultrafine/daug-cc-pVDZ Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.126      
2 S 0.126      
3 S -0.126      
4 S -0.126      


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 0.845 0.845
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -52.231 0.000 0.000
y 0.000 -53.204 0.000
z 0.000 0.000 -48.140
Traceless
 xyz
x -1.559 0.000 0.000
y 0.000 -3.018 0.000
z 0.000 0.000 4.577
Polar
3z2-r29.154
x2-y20.973
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 8.511 0.000 0.000
y 0.000 19.835 0.000
z 0.000 0.000 14.030


<r2> (average value of r2) Å2
<r2> 204.162
(<r2>)1/2 14.289

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at PBEPBEultrafine/daug-cc-pVDZ
 hartrees
Energy at 0K-1592.124839
Energy at 298.15K 
HF Energy-1592.124839
Nuclear repulsion energy328.417904
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 PBEPBEultrafine/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 693 693 0.00 38.23 0.09 0.16
2 Ag 272 272 0.00 27.04 0.16 0.28
3 Au 228 228 0.00 0.00 0.00 0.00
4 B1u 650 650 88.14 0.00 0.00 0.00
5 B2u 73i 73i 10.07 0.00 0.00 0.00
6 B3g 316 316 0.00 8.53 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1043.1 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1043.1 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 PBEPBEultrafine/daug-cc-pVDZ
ABC
0.14073 0.07864 0.05045

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

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 0.968 1.295
S2 0.000 0.968 -1.295
S3 0.000 -0.968 1.295
S4 0.000 -0.968 -1.295

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.58941.93563.2329
S22.58943.23291.9356
S31.93563.23292.5894
S43.23291.93562.5894

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 PBEPBEultrafine/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 -52.343 0.000 0.000
y 0.000 -47.842 0.000
z 0.000 0.000 -53.046
Traceless
 xyz
x -1.899 0.000 0.000
y 0.000 4.852 0.000
z 0.000 0.000 -2.953
Polar
3z2-r2-5.907
x2-y2-4.500
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 8.494 0.000 0.000
y 0.000 14.173 0.000
z 0.000 0.000 19.394


<r2> (average value of r2) Å2
<r2> 199.126
(<r2>)1/2 14.111