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All results from a given calculation for P4 (Phosphorus tetramer)

using model chemistry: B3LYPultrafine/6-31G*

19 10 17 12 22

States and conformations

State Conformation minimum conformation conformer description state description
1 1 yes TD 1A1
Energy calculated at B3LYPultrafine/6-31G*
 hartrees
Energy at 0K-1365.441828
Energy at 298.15K-1365.444374
Nuclear repulsion energy322.043751
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/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 606 581 0.00      
2 E 367 352 0.00      
2 E 367 352 0.00      
3 T2 463 444 1.73      
3 T2 463 444 1.73      
3 T2 463 444 1.73      

Unscaled Zero Point Vibrational Energy (zpe) 1365.0 cm-1
Scaled (by 0.958) Zero Point Vibrational Energy (zpe) 1307.7 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/6-31G*
ABC
0.11060 0.11060 0.11060

See section I.F.4 to change rotational constant units
Geometric Data calculated at B3LYPultrafine/6-31G*

Point Group is Td

Cartesians (Å)
Atom x (Å) y (Å) z (Å)
P1 0.784 0.784 0.784
P2 -0.784 -0.784 0.784
P3 -0.784 0.784 -0.784
P4 0.784 -0.784 -0.784

Atom - Atom Distances (Å)
  P1 P2 P3 P4
P12.21832.21832.2183
P22.21832.21832.2183
P32.21832.21832.2183
P42.21832.21832.2183

picture of Phosphorus tetramer state 1 conformation 1
More geometry information
Calculated Bond Angles
atom1 atom2 atom3 angle atom1 atom2 atom3 angle
P1 P2 P3 60.000 P1 P2 P4 60.000
P1 P3 P2 60.000 P1 P3 P4 60.000
P1 P4 P2 60.000 P1 P4 P3 60.000
P2 P1 P3 60.000 P2 P1 P4 60.000
P2 P3 P4 60.000 P2 P4 P3 60.000
P3 P1 P4 60.000 P3 P2 P4 60.000
Electronic energy levels
Charges, Dipole, Quadrupole and Polarizability
Charges from optimized geometry at B3LYPultrafine/6-31G* Charges (e)
Number Element Mulliken CHELPG AIM ESP
1 P 0.000      
2 P 0.000      
3 P 0.000      
4 P 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 -51.665 0.000 0.000
y 0.000 -51.665 0.000
z 0.000 0.000 -51.665
Traceless
 xyz
x 0.000 0.000 0.000
y 0.000 0.000 0.000
z 0.000 0.000 0.000
Polar
3z2-r20.000
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 12.024 0.000 0.000
y 0.000 12.024 0.000
z 0.000 0.000 12.024


<r2> (average value of r2) Å2
<r2> 142.988
(<r2>)1/2 11.958