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: M06-2X/6-31G

19 10 17 12 22

States and conformations

State Conformation minimum conformation conformer description state description
1 1 yes D2D 1A1
1 2 no C2V 1A1
1 3 no D2H 1AG

Conformer 1 (D2D)

Jump to S1C2 S1C3
Energy calculated at M06-2X/6-31G
 hartrees
Energy at 0K-1592.439358
Energy at 298.15K 
HF Energy-1592.439358
Nuclear repulsion energy323.407728
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 M06-2X/6-31G
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 463 463 0.00 62.04 0.07 0.13
2 A1 152 152 0.00 7.75 0.75 0.85
3 B1 392 392 0.00 37.36 0.75 0.86
4 B2 283 283 0.38 14.18 0.75 0.86
5 E 380 380 0.02 10.81 0.75 0.86
5 E 380 380 0.02 10.81 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1024.8 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1024.8 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 M06-2X/6-31G
ABC
0.10005 0.10005 0.05482

See section I.F.4 to change rotational constant units
Geometric Data calculated at M06-2X/6-31G

Point Group is D2d

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.551 0.340
S2 0.000 -1.551 0.340
S3 -1.551 0.000 -0.340
S4 1.551 0.000 -0.340

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S13.10122.29572.2957
S23.10122.29572.2957
S32.29572.29573.1012
S42.29572.29573.1012

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 47.512 S1 S3 S4 47.512
S2 S1 S3 47.512 S2 S4 S3 47.512
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at M06-2X/6-31G 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 -52.075 0.000 0.000
y 0.000 -52.075 0.000
z 0.000 0.000 -56.519
Traceless
 xyz
x 2.222 0.000 0.000
y 0.000 2.222 0.000
z 0.000 0.000 -4.444
Polar
3z2-r2-8.888
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 12.679 0.000 0.000
y 0.000 12.679 0.000
z 0.000 0.000 4.602


<r2> (average value of r2) Å2
<r2> 194.712
(<r2>)1/2 13.954

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at M06-2X/6-31G
 hartrees
Energy at 0K-1592.434015
Energy at 298.15K 
HF Energy-1592.434015
Nuclear repulsion energy312.504859
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 M06-2X/6-31G
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 575 575 0.07 40.24 0.20 0.34
2 A1 346 346 3.69 41.30 0.24 0.39
3 A1 118 118 1.74 16.85 0.47 0.64
4 A2 177 177 0.00 0.28 0.75 0.86
5 B2 562 562 109.30 2.70 0.75 0.86
6 B2 275 275 0.01 20.00 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1026.9 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 1026.9 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 M06-2X/6-31G
ABC
0.13153 0.06744 0.04458

See section I.F.4 to change rotational constant units
Geometric Data calculated at M06-2X/6-31G

Point Group is C2v

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.144 1.001
S2 0.000 -1.144 1.001
S3 0.000 1.613 -1.001
S4 0.000 -1.613 -1.001

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.28732.05643.4069
S22.28733.40692.0564
S32.05643.40693.2256
S43.40692.05643.2256

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 103.187 S1 S3 S4 76.813
S2 S1 S3 103.187 S2 S4 S3 76.813
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at M06-2X/6-31G Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.048      
2 S 0.048      
3 S -0.048      
4 S -0.048      


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 1.255 1.255
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -52.988 0.000 0.000
y 0.000 -56.318 0.000
z 0.000 0.000 -52.866
Traceless
 xyz
x 1.603 0.000 0.000
y 0.000 -3.391 0.000
z 0.000 0.000 1.788
Polar
3z2-r23.576
x2-y23.330
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 3.342 0.000 0.000
y 0.000 19.900 0.000
z 0.000 0.000 12.718


<r2> (average value of r2) Å2
<r2> 222.993
(<r2>)1/2 14.933

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at M06-2X/6-31G
 hartrees
Energy at 0K-1592.430571
Energy at 298.15K 
HF Energy-1592.430571
Nuclear repulsion energy316.055765
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 M06-2X/6-31G
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 640 640 0.00 42.47 0.29 0.44
2 Ag 299 299 0.00 54.41 0.29 0.45
3 Au 210 210 0.00 0.00 0.00 0.00
4 B1u 598 598 132.82 0.00 0.00 0.00
5 B2u 152i 152i 15.59 0.00 0.00 0.00
6 B3g 278 278 0.00 22.95 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 936.3 cm-1
Scaled (by 1) Zero Point Vibrational Energy (zpe) 936.3 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 M06-2X/6-31G
ABC
0.12795 0.07428 0.04700

See section I.F.4 to change rotational constant units
Geometric Data calculated at M06-2X/6-31G

Point Group is D2h

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
S1 0.000 1.015 1.332
S2 0.000 1.015 -1.332
S3 0.000 -1.015 1.332
S4 0.000 -1.015 -1.332

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.66422.03003.3494
S22.66423.34942.0300
S32.03003.34942.6642
S43.34942.03002.6642

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 M06-2X/6-31G 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 -53.164 0.000 0.000
y 0.000 -52.656 0.000
z 0.000 0.000 -55.837
Traceless
 xyz
x 1.083 0.000 0.000
y 0.000 1.844 0.000
z 0.000 0.000 -2.927
Polar
3z2-r2-5.855
x2-y2-0.507
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 3.327 0.000 0.000
y 0.000 13.199 0.000
z 0.000 0.000 18.601


<r2> (average value of r2) Å2
<r2> 213.156
(<r2>)1/2 14.600