Rep:Mod:Mx4417

NH3 Molecule

calculation method: RB3LYP
the basic set: 6-31G(d,p)
final energy E(RB3LYP): -56.55776873au
RMS gradient: 0.00000485au
the point group : C3V
bond length:1.01798Å
bond angle:105.741º

        Item               Value     Threshold  Converged?
 Maximum Force            0.000004     0.000450     YES
 RMS     Force            0.000004     0.000300     YES
 Maximum Displacement     0.000072     0.001800     YES
 RMS     Displacement     0.000035     0.001200     YES

test molecule

how many modes do you expect from the 3N-6 rule?: 3
which modes are degenerate? mode2,3 and mode5,6
which modes are "bending" vibrations and which are "bond stretch" vibrations? mode456 are stretch, mode 123 are bending.
which mode is highly symmetric? bond stretch
one mode is known as the "umbrella" mode, which one is this? mode 1bending
how many bands would you expect to see in an experimental spectrum of gaseous ammonia? 4

The charge on the N will be partial negative as N is more electronegative than H atom. The H atoms will be partial positive.

N2 Molecule

calculation method: RB3LYP
the basic set: 6-31G(d,p)
final energy E(RB3LYP): -109.52359111au
RMS gradient: 0.02473091au
the point group : D∞h
bond length:1.0550Å
bond angle:180º

        Item               Value     Threshold  Converged?
 Maximum Force            0.000001     0.000450     YES
 RMS     Force            0.000001     0.000300     YES
 Maximum Displacement     0.000000     0.001800     YES
 RMS     Displacement     0.000000     0.001200     YES
 Predicted change in Energy=-3.401071D-13

test molecule

The charge on each N atom is 0, as it is a linear diatomic molecule.

H2 molecule

calculation method: RB3LYP
the basic set: 6-31G(d,p)
final energy E(RB3LYP): -1.17853936au
RMS gradient: 0.00000017au
the point group : D∞h
bond length:0.74279Å
bond angle:180º

         Item               Value     Threshold  Converged?
 Maximum Force            0.000000     0.000450     YES
 RMS     Force            0.000000     0.000300     YES
 Maximum Displacement     0.000000     0.001800     YES
 RMS     Displacement     0.000001     0.001200     YES
 Predicted change in Energy=-1.164080D-13

test molecule

The charge on each H atom is 0, as it is a linear diatomic molecule.

Reaction energy of of N2 + 3H2 -> 2NH3

E(NH3)=-56.55776873au
2*E(NH3)=-113.115537au
E(H2)=-1.17853936au
E(N2)=-109.52412868au
3*E(H2)=3.53561808au
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]=-0.0557907au==-146.48 KJ/mol

The ΔE energy was negative, so the ammonia product has lower energy and is more stable.

BH3 molecule

calculation method: RB3LYP
the basic set: 6-31G(d,p)
final energy E(RB3LYP): -26.61532364au
RMS gradient: 0.00000211au
the point group : D3h
bond length:1.19232Å
bond angle:120º

         Item               Value     Threshold  Converged?
 Maximum Force            0.000004     0.000450     YES
 RMS     Force            0.000003     0.000300     YES
 Maximum Displacement     0.000017     0.001800     YES
 RMS     Displacement     0.000011     0.001200     YES
 Predicted change in Energy=-1.053675D-10

test molecule

Boron was more electropositive than H atom.

MOs of BH3

MO1 The red shaded region is the occupied, non-bonding 1s AO of Boron, since electrons in the hydrogen atom doesn't contribute anything It has very deep in energy(-6.77140au) compare to other since 1s orbital is in the core AOs.

MO2 The red region is the MO that is occupied, overlapped by three 1s AOs of H atoms and one 2s AO of B atom.

MO3 This occupied MO The 2PX AO overlapped with part of the 1s and 2s the third H atom in phase. The 2PX AO overlapped with part of the 1s and 2s the second H atom out of phase. MO3 is in the HOMO region as it has the one of the highest energy within all the occupied orbitals as shown on the picture.

MO4 This MO has the same energy value with MO3 so it is the same type of MO just different 2P N atom, which is 2PY AO of the B atom. The red part forms from overlapping 1s and 2s AOs with the first H atom in phase. The green part forms from overlapping the 1s and 2s AOs of the second and the third H atoms. MO4 is in the HOMO region as it has the one of the highest energy within all the occupied orbitals as shown on the picture.

MO5 This MO is unoccupied and is in the LUMO region. It is a combination of 2PZ and 3PY AOs of the B atom overlap with 3PZ AOs of three H atoms.