Capturing the directionality of hydrogen bonding
Below is a schematic picture of hydrogen bonding between a donor D and an acceptor A.
An interesting and important question is how the potential energy of the system varies with the angle phi which measures deviations from linearity. A key property of H-bonds is that they are highly directional. This leads to the four-fold co-ordination of water in liquid and solid phases.
There is a vibrational mode associated with this co-ordinate phi.
[In water this rotation is connected to the librational mode].
Previously I posted about an empirical correlation showing how this mode hardens with the increasing strength of the H-bond (decreasing R above). This is the opposite trend to the D-H stretch frequency (associated with the r co-ordinate above) which softens with decreasing R.
I was very pleased when I discovered that the model effective Hamiltonian I proposed for H-bonding can describe this correlation (see the figure below) without introducing any new parameters.
This is discussed in more detail in the final version of my paper.
Aside: I earlier posted the graph above in a post about confirmation bias. I should say that after I did get good agreement between the theory and experiment, I did go back and check all the algebra and mathematica codes.
An interesting and important question is how the potential energy of the system varies with the angle phi which measures deviations from linearity. A key property of H-bonds is that they are highly directional. This leads to the four-fold co-ordination of water in liquid and solid phases.
There is a vibrational mode associated with this co-ordinate phi.
[In water this rotation is connected to the librational mode].
Previously I posted about an empirical correlation showing how this mode hardens with the increasing strength of the H-bond (decreasing R above). This is the opposite trend to the D-H stretch frequency (associated with the r co-ordinate above) which softens with decreasing R.
I was very pleased when I discovered that the model effective Hamiltonian I proposed for H-bonding can describe this correlation (see the figure below) without introducing any new parameters.
This is discussed in more detail in the final version of my paper.
Aside: I earlier posted the graph above in a post about confirmation bias. I should say that after I did get good agreement between the theory and experiment, I did go back and check all the algebra and mathematica codes.
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