NaNH2 - Part 4

In this last part of the laboratory, we will focus on how to calculate vibrational frequencies and intensities of a system. Since such calculations require longer computational times respect to those we have seen so far, we first will compute vibrational frequencies, IR and Raman intensities for a simple system – NH₃ molecule. Instead, we will simulate vibrational spectra of solid NH₃ and NaNH₂ starting from precalculated outputs. In the proposed cases, we will analyse how the quality of basis sets influence the resulting spectra.

1. Simulation of vibrational spectra
• Calculation of vibrational spectra of NH₃ molecule
• Calculation of IR spectrum for solid NH₃ with different basis sets
• Calculation of Raman spectrum for solid NH₃ with different basis sets
• Calculation of IR spectrum for solid NaNH₂
• Calculation of Raman spectrum for solid NaNH₂

Simulation of vibrational spectra

i) Calculation of vibrational spectra of NH₃ molecule

In this first section, we are going to calculate IR and Raman spectra for ammonia molecule with different basis sets.

• IR spectrum

Below sample input with 6-31d1G basis set for N and 3-1p1G basis set for H is reported for ammonia molecule. The basis sets are no longer reported in the following input but substituted with ellipsis, because they have been previously reported and can also be found in CRYSTAL basis set library.

Ammonia molecule
MOLECULE
30
2
1 0. -0.93649 -0.38384
7 0. 0. 0.00672
FREQCALC
INTENS
END
END
7 4
0 0 6 2. 1.
…
1 3
0 0 3 1.0 1.0
…
99 0
END
DFT
PBE0-D3
END
MULPOPAN
END

The indicated coordinates of non-equivalent N and H atoms are the optimized ones at the same level of theory at which we perform the current calculation (basis sets and functional). This is mandatory since we are working within harmonic approximation. FREQCALC is the keyword for frequency calculation and INTENS for peak intensities.

Now, it is possible to calculate the IR spectrum in few seconds starting from the results of the previous calculation, specifying just two additional keywords: RESTART and IRPSEC (see input reported below). In the folder you are working in there is a file named ‘FREQINFO.DAT’/'filename.freqinfo' that is necessary for the restart.

Sample input with 6-31d1G/3-1p1G basis sets:

Ammonia molecule
MOLECULE
30
2
1 0. -0.93649 -0.38384
7 0. 0. 0.00672
FREQCALC
RESTART
INTENS
IRSPEC
END
END
END
7 4
0 0 6 2. 1.
…
1 3
0 0 3 1.0 1.0
…
99 0
END
DFT
PBE0-D3
END
MULPOPAN
END

RESTART is the keyword that indicates to read frequencies and intensities from a previous calculation. IRPSEC is, instead, the keyword to calculate the IR spectrum and creates the file ‘IRSPEC.DAT’/'filename.irspec' where all the needed information for plotting the spectrum are written.

At the end of this calculation, you will find in the folder two additional outputs: filename.out and IRSPEC.DAT/filename.irspec. The first one is useful to observe the vibrational modes of the molecule at ‘Crysplot’ → ‘Make a plot’ → ‘Vibrational spectra & animations’; the second one is useful to visualize and save the IR spectrum at ‘Crysplot’ → ‘Make a plot’ → ‘Infrared spectra’.

Now, we want to perform exactly the same calculations with a different basis set: pob_TZVP_rev2. You can find pob_TZVP_rev2 basis set both for N and H in CRYSTAL basis set library.

Below, sample input with pob_TZVP_rev2 basis sets for calculating frequencies and IR intensities of NH₃ molecule is reported:

Ammonia molecule
MOLECULE
30
2
1 0. -0.9421 -0.3820
7 0. 0. 0.0013
FREQCALC
INTENS
END
END
7 8
0 0 6 2.0 1.0
…
1 4
0 0 3 1.0 1.0
…
99 0
END
DFT
PBE0-D3
END
MULPOPAN
END

Again, the geometry is the optimized one at the same level of theory of the frequency calculation.

Sample input with pob_TZVP_rev2 basis sets for calculating IR spectrum:

Ammonia molecule
MOLECULE
30
2
1 0. -0.9421 -0.3820
7 0. 0. 0.0013
FREQCALC
RESTART
INTENS
IRSPEC
END
END
END
7 8
0 0 6 2.0 1.0
…
1 4
0 0 3 1.0 1.0
…
99 0
END
DFT
PBE0-D3
END
MULPOPAN
END

Visualize IR spectrum and animations as explained before. In the end, compare the two spectra at ‘Crysplot’ → ‘Make a plot’ → ‘Infrared spectra comparison’.

Exercise:
Compare the IR spectra of ammonia molecule obtained with the two basis sets. Experimentally, three main peaks are observed for this system at 965, 1629 and 3335 cm^-1. Create a table where you compare these experimental frequencies with those obtained with different basis sets. Which level of theory better reproduces the experimental spectrum?

• Raman spectrum

Below sample input with 6-31d1G basis set for N and 3-1p1G basis set for H is reported for ammonia molecule. Again, basis sets are not reported in the following input and can be found in CRYSTAL basis set library.

Ammonia molecule
MOLECULE
30
2
1 0. -0.93649 -0.38384
7 0. 0. 0.00672
FREQCALC
INTENS
INTRAMAN
INTCPHF
END
END
END
7 4
0 0 6 2. 1.
…
1 3
0 0 3 1.0 1.0
…
99 0
END
DFT
PBE0-D3
END
MULPOPAN
END

The same optimized geometry used for calculating IR intensities at the same level of theory is used in this calculation.
INTENS keyword should be present anyway, while INTRAMAN is the specific keyword for calculating Raman intensities. Raman tensor is needed to compute Raman intensities – INTCPHF is the keyword to compute it.

Now, it is possible to calculate the Raman spectrum in few seconds starting from the results of the previous calculation, specifying just two additional keywords: RESTART and RAMPSEC (see input reported below). In the folder you are working in there is a file named ‘FREQINFO.DAT’/'filename.freqinfo' that is necessary for the restart. Sample input with 6-31d1G/3-1p1G basis sets:

Ammonia molecule
MOLECULE
30
2
1 0. -0.93649 -0.38384
7 0. 0. 0.00672
FREQCALC
RESTART
INTENS
INTRAMAN
RAMSPEC
END
END
END
7 4
0 0 6 2. 1.
…
1 3
0 0 3 1.0 1.0
…
99 0
END
DFT
PBE0-D3
END
MULPOPAN
END

RESTART is the keyword that indicates to read frequencies and intensities from a previous calculation. RAMPSEC is, instead, the keyword to calculate the Raman spectrum and creates the file ‘RAMSPEC.DAT’/'filename.ramspec' where all the needed information for plotting the spectrum are written.
At the end of this calculation, you will find in the folder two additional outputs: filename.out and RAMSPEC.DAT/filename.ramspec. The first one is useful to observe the vibrational modes of the molecule at ‘Crysplot’ → ‘Make a plot’ → ‘Vibrational spectra & animations’; the second one is useful to visualize and save the Raman spectrum at ‘Crysplot’ → ‘Make a plot’ → ‘Raman spectra’.

Now, perform the same calculations changing the basis set for N and H, choosing for both in the CRYSTAL basis sets library the pob_TZVP_rev2 basis set.
Sample input with pob_TZVP_rev2 basis sets for calculating Raman intensities:

Ammonia molecule
MOLECULE
30
2
1 0. -0.9421 -0.3820
7 0. 0. 0.0013
FREQCALC
INTENS
INTRAMAN
INTCPHF
END
END
END
7 8
0 0 6 2.0 1.0
…
1 4
0 0 3 1.0 1.0
…
99 0
END
DFT
PBE0-D3
END
MULPOPAN
END

Sample input with pob_TZVP_rev2 basis sets for calculating Raman spectrum:

Ammonia molecule
MOLECULE
30
2
1 0. -0.9421 -0.3820
7 0. 0. 0.0013
FREQCALC
RESTART
INTENS
INTRAMAN
RAMSPEC
END
END
END
7 8
0 0 6 2.0 1.0
…
1 4
0 0 3 1.0 1.0
…
99 0
END
DFT
PBE0-D3
END
MULPOPAN
END

Visualize Raman spectrum and animations as explained before.
In the end, compare the two spectra at ‘Crysplot’ → ‘Make a plot’ → ‘Raman spectra comparison’.

Exercise:
Compare the Raman spectra of ammonia molecule obtained with the two basis sets. Experimentally, four main peaks are observed for this system at 1043, 1647, 3309 and 3381 cm^-1. Create a table where you compare these experimental frequencies with those obtained with different basis sets. Which level of theory better reproduces the experimental spectrum?

ii) Calculation of IR spectrum for solid NH₃ with different basis sets

In this second section, we are going to calculate IR spectra for solid ammonia with different basis sets starting from precalculated outputs (nh3_irint.freqinfo).
Create a new input as the one reported here (N basis set: 6-31d1G; H basis set: 3-1p1G):

AMMONIA SOLID
CRYSTAL
0 0 0
198
4.9127
2
1 0.0973 0.3665 0.2741
7 0.2023 0.2023 0.2023
FREQCALC
RESTART
INTENS
DIELISO
1.9457
IRSPEC
END
END
END
7 4
0 0 6 2. 1.
…
1 3
0 0 3 1.0 1.0
…
99 0
END
DFT
PBE0-D3
END
SHRINK
6 6
END

The indicated geometry in the input has been previously optimized with the same basis set and functional. DIELISO is the keyword to define isotropic dielectric constant needed for computing the spectrum. Its value has been previously computed at the same level of theory.

Visualize IR spectrum and animations as explained before for ammonia molecule.

Exercise:
Compare the spectra obtained for the molecule and the crystal with the same basis set.

As previously done for ammonia molecule, now we want to perform the same calculation changing the basis set, working with pob_TZVP_rev2. Precalculated output for the restart is nh3_irint_newbasis.freqinfo. Create a new input as the one reported below (N basis set: pob_TZV_rev2; H basis set: pob_TZV_rev2).

AMMONIA SOLID
CRYSTAL
0 0 0
198
4.9255
2
1 0.1007 0.3718 0.2717
7 0.2053 0.2053 0.2053
FREQCALC
RESTART
INTENS
DIELISO
2.1108
IRSPEC
END
END
END
7 8
0 0 6 2.0 1.0
…
1 4
0 0 3 1.0 1.0
…
99 0
END
DFT
PBE0-D3
END
SHRINK
6 6
MULPOPAN
END

Again, DIELISO keyword has to be specified. Now its value is different because it was calculated with different basis set.
Visualize IR spectrum and animations as explained before for NH₃ molecule.

Exercise:
Compare the spectra obtained for the molecule and the crystal with the same basis set and compare the spectra of the crystal obtained with different basis sets. Experimentally, four main peaks are observed for solid ammonia at 1057, 1650, 3210 and 3375 cm^-1. Create a table where you compare these experimental frequencies with those obtained with different basis sets. Which level of theory better reproduces the experimental spectrum?

iii) Calculation of Raman spectrum for solid NH₃ with different basis sets

In this third section, we are going to calculate Raman spectra for ammonia molecule with different basis sets starting from precalculated outputs (nh3_ramspec.freqinfo).
Create a new input as the one reported here (N basis set: 6-31d1G; H basis set: 3-1p1G):

AMMONIA SOLID
CRYSTAL
0 0 0
198
4.9127
2
1 0.0973 0.3665 0.2741
7 0.2023 0.2023 0.2023
FREQCALC
RESTART
INTENS
INTRAMAN
RAMSPEC
END
END
END
7 4
0 0 6 2. 1.
…
1 3
0 0 3 1.0 1.0
…
99 0
END
DFT
PBE0-D3
END
SHRINK
6 6
END

Visualize Raman spectrum and animations as explained before for NH₃ molecule.

Exercise:
Compare the spectra obtained for the molecule and the crystal with the same basis set.

Precalculated file for the restart is nh3_ramspec_newbasis.freqinfo. Create a new input as the one reported here (N basis set: pob_TZV_rev2; H basis set: pob_TZV_rev2):

AMMONIA SOLID
CRYSTAL
0 0 0
198
4.9255
2
1 0.1007 0.3718 0.2717
7 0.2053 0.2053 0.2053
FREQCALC
RESTART
INTENS
INTRAMAN
RAMSPEC
END
END
END
7 8
0 0 6 2.0 1.0
…
1 4
0 0 3 1.0 1.0
…
99 0
END
DFT
PBE0-D3
END
SHRINK
6 6
MULPOPAN
END

Visualize Raman spectrum and animations as explained before for NH₃ molecule.

Exercise:
Compare the spectra obtained for the molecule and the crystal with the same basis set and compare the spectra of the crystal obtained with different basis sets. Experimentally, five main peaks are observed for solid ammonia at 1058, 1645, 3216, 3270 and 3386 cm^-1. Create a table where you compare these experimental frequencies with those obtained with different basis sets. Which level of theory better reproduces the experimental spectrum?

iv) Calculation of IR spectrum for solid NaNH₂

In this fourth section, we are going to calculate IR spectra for sodium amide starting from precalculated outputs.

For computational time, in this section we will just simulate IR spectrum of sodium amide with small basis set.
Precalculated file for the restart is nanh2_irspec.freqinfo. Create a new input as the one reported here (N basis set: 6-31d1G; H basis set: 3-1p1G; Na basis set: you can find it at pages 12 and 13 of the following file).

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
FREQCALC
RESTART
INTENS
DIELTENS
2.5252 0 0
0 2.2254 0
0 0 2.2914
IRSPEC
END
END
END
11 11
0 0 7 2. 1.
…
7 4
0 0 6 2. 1.
…
1 3
0 0 3 1.0 1.0
…
99 0
END
DFT
PBE0-D3
END
TOLINTEG
8 8 8 8 16
TOLDEE
8
SHRINK
8 8
END

For the current IR spectrum calculation, DIELTENS keyword is indicated instead of DIELISO because NaNH₂ is anisotropic and therefore 3x3x3 dielectric tensor must be specified.

Visualize IR spectrum and animations as explained before.

Exercise:
Experimentally, four main peaks are observed for sodium amide at 609, 1530, 3212 and 3259 cm^-1. Create a table where you compare these experimental frequencies with those obtained with different basis sets. Which level of theory better reproduces the experimental spectrum?

v) Calculation of Raman spectrum for solid NaNH₂

In this fifth section, we are going to calculate Raman spectra for sodium amide starting from precalculated outputs.

For computational time, in this section we will just simulate Raman spectrum of sodium amide with small basis set.
Precalculated file for the restart is nanh2_ramspec.freqinfo. Create a new input as the one reported here (N basis set: 6-31d1G; H basis set: 3-1p1G; Na basis set: as in previous section).

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
FREQCALC
RESTART
INTENS
INTRAMAN
RAMSPEC
END
END
END
11 11
0 0 7 2. 1.
…
7 4
0 0 6 2. 1.
…
1 3
0 0 3 1.0 1.0
…
99 0
END
DFT
PBE0-D3
END
TOLINTEG
8 8 8 8 16
TOLDEE
8
SHRINK
8 8
END

Visualize Raman spectrum and animations as explained before.

Exercise:
Experimentally, six main peaks are observed for solid ammonia at 349, 468, 522, 1531, 3218 and 3267 cm^-1. Create a table where you compare these experimental frequencies with those obtained with different basis sets. Which level of theory better reproduces the experimental spectrum?