Hydrogen Cyanide

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Hydrogen Cyanide Quantum Calculations

All of the live displays on this page were created using the best optimized geometry. The best found geometry optimization was at the ab initio theory level of 6-21G.

Hydrogen Cyanide has doubly degenerate HOMO orbitals. The button below shows the first HOMO orbital for hydrogen cyanide.

Both MO7 and MO6 show the same energy of -0.49 a.u.

The button below shows the second HOMO orbital for Hydrogen Cyanide.

The LUMO orbitals are also doubly degenerate. The energy for both of them is 0.2062 a.u.

Clicking the button below will show a live display of one of the LUMO orbitals.

The second LUMO is 90 degrees off of the previous LUMO orbital.

The button below will show the display of the second LUMO orbital.

The bond length for the H-C bond was calculated to be 1.05Å, which was lower than the literature value of 1.064Å.¹ The error in the bond length is 1.3%.

The C-N bond length was 1.14Å, and when compared to the literature value of 1.156Å, yields an error of 1.4%.¹

All data sets showed the same bond lengths in Jmol.

The bond angle calculated was 180 degrees, which was expected due to the linear orientation of the molecule.

All bond lengths were the same for the different basis sets. As for the dipole moments, 6-21G showed a value closest to the reference value of 2.980 D; this is why this basis set was chosen.¹

The table below shows the dipole moments of four basis sets. Diffuse functions were added to the basis sets in an attempt to improve the dipole moment. In the table, #D refers to the number of D heavy atom polarization functions, #F refers to the number of F heavy atom polarization functions, and #Light refers to the number of light atom polarization functions.

Basis Set	#D	#F	#Light	Dipole (Debye)
AM1	0	0	0	2.361377
6-21G	0	0	0	3.028704
6-21G	1	0	1	3.020112
6-21G	2	0	2	3.047205
6-31G	0	0	0	3.241412
6-31G	1	0	1	3.197838
6-31G	2	0	2	3.173012
6-31G	2	1	2	Error
6-31G	3	0	3	3.235740
DZV	0	0	0	3.286947
DZV	1	0	1	3.205086
DZV	2	1	2	Error
DZV	2	0	2	3.187133
DZV	3	0	3	3.213797

The value of 3.020112 D that was found using 6-21G as the basis set was closest to the theoretical value for the dipole moment. Note that this is a smaller basis set and it has less diffuse functions than some of the other attempts. Overall 6-21G calculated a value closer with one D and one Light diffuse functions added, but then when those values were increased the dipole moment got less accurate. Both the 6-31G and DZV basis sets got better with two D and two Light diffuse functions but also became worse thereafter. It seems as if when the number of F diffuse functions was altered errors resulted.

The button below shows the partial atomic charges for hydrogen cyanide.

The button below shows the electrostatic potential for hydrogen cyanide.

The energy of the 1.6 vibration is 886.74 cm^-1.

The main contribution to the energies of the 1.6 and 1.7 vibrations is a C-H bend.

The energy for the 1.7 vibration is 886.74 cm^-1.

The vibration energy associated with vibration 1.8 is 2329.3 cm^-1. This is caused by symmetrical stretching in both the C-H and C-N bonds.

Vibration 1.9 has an energy of 3714.1401 cm^-1. This is caused mainly by the C-H stretch but does have a contribution for the C-N stretch as well.

HCN IR Spectrum

This IR was found on the NIST website.¹

References

Based on template by A. Herráez as modified by J. Gutow

Page skeleton and JavaScript generated by export to web function using Jmol 12.2.34 2012-08-09 20:37 on Feb 26, 2013.

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