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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 no D2D 1A1
1 2 yes 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-1592.557063
Energy at 298.15K 
HF Energy-1592.557063
Nuclear repulsion energy348.738555
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 520 495 0.00 57.70 0.07 0.13
2 A1 196 187 0.00 2.74 0.74 0.85
3 B1 468 444 0.00 37.72 0.75 0.86
4 B2 325 309 0.36 10.70 0.75 0.86
5 E 445 423 0.00 8.21 0.75 0.86
5 E 445 423 0.00 8.21 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1199.8 cm-1
Scaled (by 0.9504) Zero Point Vibrational Energy (zpe) 1140.3 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
0.11638 0.11638 0.06367

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 1.439 0.312
S2 0.000 -1.439 0.312
S3 -1.439 0.000 -0.312
S4 1.439 0.000 -0.312

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.87762.12852.1285
S22.87762.12852.1285
S32.12852.12852.8776
S42.12852.12852.8776

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 47.469 S1 S3 S4 47.469
S2 S1 S3 47.469 S2 S4 S3 47.469
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 -50.031 0.000 0.000
y 0.000 -50.031 0.000
z 0.000 0.000 -55.202
Traceless
 xyz
x 2.585 0.000 0.000
y 0.000 2.585 0.000
z 0.000 0.000 -5.170
Polar
3z2-r2-10.341
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 10.499 0.000 0.000
y 0.000 10.499 0.000
z 0.000 0.000 5.332


<r2> (average value of r2) Å2
<r2> 171.058
(<r2>)1/2 13.079

Conformer 2 (C2V)

Jump to S1C1 S1C3
Energy calculated at M06-2X/6-31G**
 hartrees
Energy at 0K-1592.571013
Energy at 298.15K 
HF Energy-1592.571013
Nuclear repulsion energy332.159074
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 690 656 2.99 32.82 0.20 0.33
2 A1 407 387 7.16 49.69 0.24 0.38
3 A1 125 118 0.58 14.99 0.47 0.64
4 A2 216 206 0.00 0.37 0.75 0.86
5 B2 663 630 176.53 3.56 0.75 0.86
6 B2 339 322 0.21 14.80 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1219.6 cm-1
Scaled (by 0.9504) Zero Point Vibrational Energy (zpe) 1159.1 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 M06-2X/6-31G**
ABC
0.15685 0.07165 0.04918

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 1.047 0.917
S2 0.000 -1.047 0.917
S3 0.000 1.607 -0.917
S4 0.000 -1.607 -0.917

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.09331.91733.2258
S22.09333.22581.9173
S31.91733.22583.2148
S43.22581.91733.2148

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 M06-2X/6-31G** Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 S 0.115      
2 S 0.115      
3 S -0.115      
4 S -0.115      


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 1.783 1.783
CHELPG        
AIM        
ESP        


Electric Quadrupole moment
Quadrupole components in D Å
Primitive
 xyz
x -51.740 0.000 0.000
y 0.000 -54.739 0.000
z 0.000 0.000 -50.222
Traceless
 xyz
x 0.741 0.000 0.000
y 0.000 -3.758 0.000
z 0.000 0.000 3.017
Polar
3z2-r26.034
x2-y23.000
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 4.372 0.000 0.000
y 0.000 18.712 0.000
z 0.000 0.000 11.031


<r2> (average value of r2) Å2
<r2> 204.145
(<r2>)1/2 14.288

Conformer 3 (D2H)

Jump to S1C1 S1C2
Energy calculated at M06-2X/6-31G**
 hartrees
Energy at 0K-1592.564754
Energy at 298.15K 
HF Energy-1592.564754
Nuclear repulsion energy335.924451
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 760 722 0.00 40.58 0.29 0.45
2 Ag 314 299 0.00 49.26 0.30 0.46
3 Au 256 243 0.00 0.00 0.00 0.00
4 B1u 698 664 199.43 0.00 0.00 0.00
5 B2u 139i 132i 24.69 0.00 0.00 0.00
6 B3g 346 329 0.00 18.34 0.75 0.86

Unscaled Zero Point Vibrational Energy (zpe) 1117.4 cm-1
Scaled (by 0.9504) Zero Point Vibrational Energy (zpe) 1062.0 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 M06-2X/6-31G**
ABC
0.14713 0.08234 0.05279

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 0.947 1.265
S2 0.000 0.947 -1.265
S3 0.000 -0.947 1.265
S4 0.000 -0.947 -1.265

Atom - Atom Distances (Å)
  S1 S2 S3 S4
S12.53051.89313.1602
S22.53053.16021.8931
S31.89313.16022.5305
S43.16021.89312.5305

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 -52.162 0.000 0.000
y 0.000 -49.548 0.000
z 0.000 0.000 -54.302
Traceless
 xyz
x -0.237 0.000 0.000
y 0.000 3.684 0.000
z 0.000 0.000 -3.447
Polar
3z2-r2-6.895
x2-y2-2.614
xy0.000
xz0.000
yz0.000


Polarizabilities
Components of the polarizability tensor.
Units are Å3 (Angstrom cubed)
Change units.
  x y z
x 4.324 0.000 0.000
y 0.000 11.654 0.000
z 0.000 0.000 17.434


<r2> (average value of r2) Å2
<r2> 192.275
(<r2>)1/2 13.866