NH₃ vs PH₃

We all know in organic chemistry a carbon center can be chiral (or stero active). However, a nitrogen center can not be chiral. Why? It is because NR1R2R3 configuration can easier be converted to its mirror image under room temperate through inversion. This inversion happens on a fast time scale (ca. pico seconds)

However, if we replace the nitrogen with phosphorous, the P center could be chiral (or stero active). Why? Because the for PR1R2R3 to convert to its mirror image, it would require to overpass a much higher energy barrier than NR1R2R3.

Now let using quantum chemistry calculations to show that.

Below is the input for scanning the NH₃ potential energy surface, by varying the angle between NH bond and the rotational axis of NH₃

We need to add a dummy atom (ghost atom) as the reference in the Z-Matrix.

molecule nh3 {
  @H 
  N 1 R1
  H 2 R2 1 A
  H 2 R2 1 A 3 A1
  H 2 R2 1 A 3 -A1
}

Avals=range(10,170,2)

table=Table(rows=["A"], cols=["E(SCF)","E(SCS)","E(DFMP2)"])

set basis cc-pvdz

nh3.R1 = 1.0
nh3.R2 = 1.008
nh3.A1 = 120.0

for A in Avals:
    nh3.A = A
    energy('mp2')
    escf = get_variable('SCF TOTAL ENERGY')
    edfmp2 = get_variable('MP2 TOTAL ENERGY')
    escsmp2 = get_variable('SCS-MP2 TOTAL ENERGY')
    table[A] = [escf, escsmp2, edfmp2]

print(table)
relative=table.copy()
relative.absolute_to_relative()
print(relative)

The first @H is a dummy atom. So psi4 will put atomic orbital there, but will not put electrons and nuclear centered at that position.

Similar input file for PH₃.

Results

Below are the potential energy surfaces for NH₃ and PH₃, by varying the angle between N(P)H with their rotation axis.

We can see clearly, the PH₃ inversion energy barrier is higher than that of NH₃.