Mod:rr12104

NH3: optimisation, frequency, NBO

        Item               Value     Threshold  Converged?
 Maximum Force            0.000004     0.000450     YES
 RMS     Force            0.000004     0.000300     YES
 Maximum Displacement     0.000071     0.001800     YES
 RMS     Displacement     0.000034     0.001200     YES
 Predicted change in Energy=-5.828500D-10
 Optimization completed.
    -- Stationary point found.

Molecule	NH3
Calculation method	RB3LYP
Basis set	6-31G(d,p)
Energy /au	-56.55776863
RMS gradient	0.00000478
Point group	C3V

N-H bond distance: 1.018Å

N-H bond angle: 105.743°

NH3

Log file

Vibrations

wavenumber cm-1	1092	1695	1695	3458	3586	3586
symmetry	A1	E	E	A1	E	E
intensity arbitrary units	145	14	14	1	0	0
image

How many modes do you expect from the 3N-6 rule?

N=4 so 3N-6 is 6 vibrational modes.

Which modes are degenerate (ie have the same energy)?

modes at 1695 (2 and 3) and 3585 (5 and 6) cm^-1 are degenerate

Which modes are "bending" vibrations and which are "bond stretch" vibrations?

bending are 1092 and 1695 cm^-1 modes (1,2 and 3), stretching are 3458 and 3586 cm^-1 modes (4, 5 and 6), thus stretches are higher in energy than bends

Which mode is highly symmetric?

the totally symmetric mode in at 3458 cm^-1 (mode 4)

One mode is known as the "umbrella" mode, which one is this?

the umbrella mode is the mode at 1092 cm^-1 (mode 1)

How many bands would you expect to see in an experimental spectrum of gaseous ammonia?

The vibration has to cause the dipole has to change to be IR active. Also there are 2 degenerate vibrations which will cause only one peak. Therefore we will see 2 peaks, one very intense one at 1091 cm^-1 (mode 1) and one very weak one 1694 cm^-1 (degenerate modes 2 and 3).

Charges

Charge on N = -1.125 Charge on H = +0.375

N is more electronegative than H so I would expect to be slightly negatively charged and H to be slightly positively charged.

Reaction and Energy

N2: optimisation, frequency, NBO

 
         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     0.000000     0.001200     YES
 Predicted change in Energy=-9.718076D-17
 Optimization completed.
    -- Stationary point found.

Molecule	N2
Calculation method	RB3LYP
Basis set	6-31G(d,p)
Energy /au	-109.52412907
RMS gradient	0.00000001
Point group	DinfH

N-N bond distance: 1.10550Å

N2

Log file

wavenumber cm-1	2458
symmetry	SGG or Σg+
intensity arbitrary units	0
image	to be added

H2: optimisation, frequency, NBO

 
         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=-1.150392D-13
 Optimization completed.
    -- Stationary point found.

Molecule	H2
Calculation method	RB3LYP
Basis set	6-31G(d,p)
Energy /au	-1.17853934
RMS gradient	0.00000017
Point group	DinfH

H-H bond distance: 0.743Å

H2

Log file

wavenumber cm-1	4466
symmetry	SGG or Σg+
intensity arbitrary units	0
image	to be added

Structure Comparison

DAYGEP N-N distances in the complex are 1.119(4) and 1.126(4)Å and N-N distance in the computed molecule is 1.106Å The computed gas-phase N-N distance is shorter than the experimental solid state structure N-N distance. In the solid state the N2 molecule is coordinated to a metal, thus some of the bond electron-density will be used to form the M-N2 bond and not in the N-N bond. In the solid state there can also be crystal packing effects, and in this case trans effects from the ligands opposite the N2. The computational result is evaluated in the gas phase, and the N2 is an isolated molecule with no external influences. The bond distance could be changed slightly by using an improved computational method. The error in both the crystal structure and the calculation must also be considered, an error of 0.01 in the computed structure means we must consider the crystal structure and computed molecule distances as equivalent within computational error.

Energies

E(NH3)= -56.55776863au

2*E(NH3)= -113.11553726au

E(N2)= -109.52412907au

E(H2)= -1.17853934au

3*E(H2)= -3.53561802au

ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.055790170au, -140.90 kJ/mol

The energy decreases from the gases to the ammonia product so the product is more stable.