NaNH2 - Part 3

In the reaction we want to investigate (Na + NH₃ → NaNH₂ + 1/2 H₂), metallic Na, ionic NaNH₂ and H₂ are involved together with ammonia. In this section, we want to perform the same kind of calculations considered for solid NH₃, analyzing differences in CRYSTAL input and their one-electron properties and also calculate the energy of H₂ molecule.
Once obtained all the needed data, we will calculate the enery of the reaction.

1. Periodic systems and their properties - Metallic Na and solid NaNH₂ cases
• CRYSTAL input for metallic sodium and sodium amide
• One-electron properties of Na and NaNH₂
2. Calculation of reaction energy

Periodic systems and their properties - Metallic Na and solid NaNH₂ cases

i) CRYSTAL input for metallic sodium and sodium amide

Below CRYSTAL inputs for Na and NaNH₂ are reported.

METALLIC SODIUM
CRYSTAL
0 0 0
229
4.1297
1
11 0 0 0
END
11 11
0 0 7 2. 1.
2.60411099270E+04 6.18063428110E-04
3.90612685480E+03 4.77486044140E-03
8.88974549930E+02 2.44716848290E-02
2.51454979610E+02 9.47553949770E-02
8.16501435120E+01 2.68674969200E-01
2.89041584010E+01 4.79254754400E-01
1.06257829320E+01 3.32485914690E-01
0 0 3 2. 1.
5.37694101790E+01 1.95277318720E-02
1.63082430250E+01 9.26480107940E-02
2.37303841250E+00 -3.99386701720E-01
0 0 2 1. 1.
9.57307726030E-01 1.64285953910E+00
4.08064609590E-01 5.56925969660E-01
0 0 1 0. 1. *
2.12721167582E-01 9.99992062637E-01
0 0 1 0. 1. *
7.82096876345E-02 9.99700925116E-01
0 2 5 6. 1.
1.38079799890E+02 5.79518919290E-03
3.22327003930E+01 4.16208462510E-02
9.98160753600E+00 1.62819168850E-01
3.48220339280E+00 3.60117846470E-01
1.22991346200E+00 4.48589798890E-01
0 2 1 0. 1. *
4.03415531731E-01 1.00001437874E+00
0 2 1 0. 1. *
8.50539333916E-02 1.00010780928E+00
0 3 1 0. 1. *
2.60862497919E+00 1.00000000000E+00
0 3 1 0. 1. *
4.33739110192E-01 1.00000000000E+00
0 3 1 0. 1. *
1.11542851169E-01 1.00000000000E+00
99 0
END
DFT
PBE
END
TOLINTEG
8 8 8 8 16
TOLDEE
8
SHRINK
8 8
MULPOPAN
END

NaNH2
CRYSTAL
0 0 1
70
8.95227 9.77379 7.48905
3
11 0. 0.15037 1.45765E-17
7 0. 0. 0.25271
1 0.03386 0.07466 0.33959
END
11 11
0 0 7 2. 1.
2.60411099270E+04 6.18063428110E-04
3.90612685480E+03 4.77486044140E-03
8.88974549930E+02 2.44716848290E-02
2.51454979610E+02 9.47553949770E-02
8.16501435120E+01 2.68674969200E-01
2.89041584010E+01 4.79254754400E-01
1.06257829320E+01 3.32485914690E-01
0 0 3 2. 1.
5.37694101790E+01 1.95277318720E-02
1.63082430250E+01 9.26480107940E-02
2.37303841250E+00 -3.99386701720E-01
0 0 2 1. 1.
9.57307726030E-01 1.64285953910E+00
4.08064609590E-01 5.56925969660E-01
0 0 1 0. 1. *
3.43569978393E-01 9.99992062637E-01
0 0 1 0. 1. *
8.28104267544E-02 9.99700925116E-01
0 2 5 6. 1.
1.38079799890E+02 5.79518919290E-03
3.22327003930E+01 4.16208462510E-02
9.98160753600E+00 1.62819168850E-01
3.48220339280E+00 3.60117846470E-01
1.22991346200E+00 4.48589798890E-01
0 2 1 0. 1. *
4.02257637589E-01 1.00001437874E+00
0 2 1 0. 1. *
9.81092534535E-02 1.00010780928E+00
0 3 1 0. 1. *
2.60738659094E+00 1.00000000000E+00
0 3 1 0. 1. *
4.03951011422E-01 1.00000000000E+00
0 3 1 0. 1. *
9.84682729829E-02 1.00000000000E+00
7 4
0 0 6 2. 1.
0.417351E+04 0.183477D-02
0.627458E+03 0.139946D-01
0.142902E+03 0.685866D-01
0.402343E+02 0.232241E+00
0.128202E+02 0.469070E+00
0.439044E+01 0.360455E+00
0 1 3 5. 1.
0.116264E+02 -.114961E+00 0.675797D-01
0.271628E+01 -.169117E+00 0.323907E+00
0.772218E+00 0.114585E+01 0.740895E+00
0 1 1 0. 1.
0.212031E+00 0.100000E+01 0.100000E+01
0 3 1 0. 1.
0.800000E+00 0.100000E+01
1 3
0 0 3 1.0 1.0
.1873113696D+02 .3349460434D-01
.2825394365D+01 .2347269535D+00
.6401216923D+00 .8137573262D+00
0 0 1 0.0 1.0
.1612777588D+00 .1000000000D+01
0 2 1 0.0 1.0
.1100000000D+01 .1000000000D+01
99 0
END
DFT
PBE
END
TOLINTEG
8 8 8 8 16
TOLDEE
8
SHRINK
8 8
MULPOPAN
END

The chosen basis set for Na can be found at pages 12 and 13 of the following file.

Two new keywords appear in the Hamiltonian section of the current inputs: TOLINTEG and TOLDEE. They allow to control the tolerances on integrals and total energy calculations, respectively. In NaNH₂ input, the three numbers following the keyword CRYSTAL are not all equal to zero as in all previous cases, but the last one is equal to 1 for shifting the origin of the cell.

Exercise:
As already done for solid NH₃, basing on the provided sample inputs, study the effect of the functional and/or method on total energy, N and H Mulliken charges, band gap and overlap population (OVPOP) of the N-H bond.

ii) One-electron properties of Na and NaNH₂

We intend to study properties of Na and NaNH₂.
Below PROPERTIES inputs for band structure, density of states and electron charge density are reported for the two systems.

• Na


• BAND
  Path: G-H-P-N-G
  4 8 120 3 20 1 0
  0 0 0   4 -4 4
  4 -4 4   2 2 2
  2 2 2   0 0 4
  0 0 4   0 0 0
  END


• NEWK
  12 16
  1 0
  DOSS
  4 200 3 20 1 12 0
  5   1 2 3 4 5
  6   6 7 9 10 12 13
  3   8 11 14
  15   15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
  END


• ECHG
  0
  100
  COORDINA
  -4. -4. 0.0
  4. -4. 0.0
  4. 4. 0.0
  MARGINS
  2.0 2.0 2.0 2.0
  END
  PATO
  0 0
  ECHG
  0
  100
  COORDINA
  -4. -4. 0.0
  4. -4. 0.0
  4. 4. 0.0
  MARGINS
  2.0 2.0 2.0 2.0
  END
  END


• NaNH₂


• BAND
  Path G Z Y T G
  4 8 120 25 55 1 0
  0 0 0   4 4 0
  4 4 0   4 0 4
  4 0 4   8 4 4
  8 4 4   0 0 0
  END


• NEWK
  8 8
  1 0
  DOSS
  3 200 25 55 1 14 0
  -1 1
  -1 5
  -1 9
  END


• NEWK
  8 8
  1 0
  DOSS
  4 200 25 55 1 14 0
  10   1 2 3 4 5 117 118 122 173 174
  12   6 7 9 10 12 13 119 120 123 124 175 176
  6   8 11 14 121 125 177
  20   15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 126 127 128 129 130
  END


• For electron charge density, use the same input reported for Na.



Exercise:
Calculate band structure, density of states and electron charge density of Na and NaNH₂ with all adopted functionals for the calculations of total energy, as for NH₃. The input will always be the same but be careful to use the correct fort.9 file where wavefunction and Hamiltonian information are stored. Which difference do you notice among the difference functional? And among the difference systems?

Calculation of reaction energy

Metallic sodium and ammonia react according to the following scheme, producing sodium amide and hydrogen:

To calculate the energy barrier of this reaction, we first need the energy of all the systems taking part to it. Our previous calculations provide results for NH₃, Na and NaNH₂ and now we are going to calculate the energy of H₂ molecule. Below a sample input is provided.

Hydrogen
MOLECULE
1
2
1 0. 0. 0.
1 0. 0. 0.7414
OPTGEOM
END
END
1 3
0 0 3 1.0 1.0
.1873113696D+02 .3349460434D-01
.2825394365D+01 .2347269535D+00
.6401216923D+00 .8137573262D+00
0 0 1 0.0 1.0
.1612777588D+00 .1000000000D+01
0 2 1 0.0 1.0
.1100000000D+01 .1000000000D+01
99 0
END
DFT
SVWN
END
MULPOPAN
END

3-1p1G basis set is used as basis set for H as for NaNH₂ and NH₃ calculations.

Exercise:
Analyze again the effect of the functional/method on the final results as previously done, by filling a table where you report total energy, H Mulliken charge, band gap and overlap population (OVPOP) of the H-H bond. Use the same methods chosen for the other systems.

Now that we have computed the energy of all reagents and products of the considered reaction, it is possible to calculate the reaction energy at different levels of theory.

Exercise:
Consider the usual formula ΔE= ∑_P E_Pν_P - ∑_R E_Rν_R to calculate the reaction energy with all the functionals adopted for the calculation of the total energy of the involved systems.

Pay attention: you must refer to the total energy per unit formula!