| 40 |
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|
| 41 |
|
|
| 42 |
|
\title{Nitrile vibrations as reporters of field-induced phase |
| 43 |
< |
transitions in 4-cyano-4'-pentylbiphenyl} |
| 43 |
> |
transitions in 4-cyano-4'-pentylbiphenyl (5CB)} |
| 44 |
|
\author{James M. Marr} |
| 45 |
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\author{J. Daniel Gezelter} |
| 46 |
|
\email{gezelter@nd.edu} |
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\end{enumerate} |
| 313 |
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|
| 314 |
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\subsection{CN frequencies from isolated clusters} |
| 315 |
< |
The size of the condensed phase system prevents direct computation of |
| 316 |
< |
the nitrile bond frequencies using {\it ab initio} methods. In order |
| 317 |
< |
to sample the nitrile frequencies present in the condensed-phase, |
| 318 |
< |
individual molecules were selected randomly to serve as the center of |
| 319 |
< |
a local (gas phase) cluster. To include steric, electrostatic, and |
| 320 |
< |
other effects from molecules located near the targeted nitrile group, |
| 321 |
< |
portions of other molecules nearest to the nitrile group were included |
| 322 |
< |
in the calculations. The surrounding solvent molecules were divided |
| 323 |
< |
into ``body'' (the two phenyl rings and the nitrile bond) and ``tail'' |
| 324 |
< |
(the alkyl chain). Any molecule which had a body atom within 6~\AA of |
| 325 |
< |
the midpoint of the target nitrile group |
| 315 |
> |
The size of the periodic condensed phase system prevented direct |
| 316 |
> |
computation of the complete library of nitrile bond frequencies using |
| 317 |
> |
{\it ab initio} methods. In order to sample the nitrile frequencies |
| 318 |
> |
present in the condensed-phase, individual molecules were selected |
| 319 |
> |
randomly to serve as the center of a local (gas phase) cluster. To |
| 320 |
> |
include steric, electrostatic, and other effects from molecules |
| 321 |
> |
located near the targeted nitrile group, portions of other molecules |
| 322 |
> |
nearest to the nitrile group were included in the quantum mechanical |
| 323 |
> |
calculations. The surrounding solvent molecules were divided into |
| 324 |
> |
``body'' (the two phenyl rings and the nitrile bond) and ``tail'' (the |
| 325 |
> |
alkyl chain). Any molecule which had a body atom within 6~\AA of the |
| 326 |
> |
midpoint of the target nitrile bond had its own molecular body (the |
| 327 |
> |
4-cyano-4'-pentylbiphenyl moiety) included in the configuration. For |
| 328 |
> |
the alkyl tail, the entire tail was included if any tail atom was |
| 329 |
> |
within 4~\AA of the target nitrile bond. If tail atoms (but no body |
| 330 |
> |
atoms) were included within these distances, only the tail was |
| 331 |
> |
included as a capped propane molecule. |
| 332 |
|
|
| 333 |
+ |
\begin{figure}[H] |
| 334 |
+ |
\includegraphics[width=\linewidth]{Figure2} |
| 335 |
+ |
\caption{Cluster calculations were performed on randomly sampled 5CB |
| 336 |
+ |
molecules from each of the simualtions. Surrounding molecular |
| 337 |
+ |
bodies were included if any body atoms were within 6 \AA\ of the |
| 338 |
+ |
target nitrile bond, and tails were included if they were within 4 |
| 339 |
+ |
\AA. The CN bond on the target molecule was stretched and |
| 340 |
+ |
compressed (left), and the resulting single point energies were |
| 341 |
+ |
fit to Morse oscillators to obtain frequency distributions.} |
| 342 |
+ |
\label{fig:cluster} |
| 343 |
+ |
\end{figure} |
| 344 |
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|
| 345 |
< |
|
| 346 |
< |
or the body not including |
| 330 |
< |
the tail, any atom within 6~\AA of the midpoint of the nitrile group |
| 331 |
< |
was included. For the tail structure, the whole tail was included if a |
| 332 |
< |
tail atom was within 4~\AA of the midpoint. If the tail did not |
| 333 |
< |
include any atoms from the ring structure, it was considered a propane |
| 334 |
< |
molecule and included as such. Once the clusters were generated, input |
| 335 |
< |
files were created that stretched the nitrile bond along its axis from |
| 345 |
> |
Inferred hydrogen atom locations were generated, and cluster |
| 346 |
> |
geometries were created that stretched the nitrile bond along from |
| 347 |
|
0.87 to 1.52~\AA at increments of 0.05~\AA. This generated 13 single |
| 348 |
< |
point energies to be calculated. The Gaussian files were run with |
| 349 |
< |
B3LYP/6-311++G(d,p) with no other keywords for the zero field |
| 350 |
< |
simulation. Simulations with fields applied included the keyword |
| 351 |
< |
''Field=Z+5'' to match the external field applied in molecular dynamic |
| 352 |
< |
runs. Once completed, the central nitrile bond frequency was |
| 342 |
< |
calculated with a Morse fit. Using this fit and the solved energy |
| 343 |
< |
levels for a Morse oscillator, the frequency was found. Each set of |
| 344 |
< |
frequencies were then convolved together with a lorezian lineshape |
| 345 |
< |
function over each value. The width value used was 1.5. For the zero |
| 346 |
< |
field spectrum, 67 frequencies were used and for the full field, 59 |
| 347 |
< |
frequencies were used. |
| 348 |
> |
point energies to be calculated per gas phase cluster. Energies were |
| 349 |
> |
computed with the B3LYP functional and 6-311++G(d,p) basis set. For |
| 350 |
> |
the cluster configurations that had been generated with applied |
| 351 |
> |
fields, a field strength of 5 atomic units in the $z$ direction was |
| 352 |
> |
applied to match the molecular dynamics runs. |
| 353 |
|
|
| 354 |
+ |
The relative energies for the stretched and compressed nitrile bond |
| 355 |
+ |
were used to fit a Morse oscillator, and the frequencies were obtained |
| 356 |
+ |
from the $0 \rightarrow 1$ transition for the exact energies. To |
| 357 |
+ |
obtain a spectrum, each of the frequencies was convoluted with a |
| 358 |
+ |
Lorentzian lineshape with a width of 1.5 $\mathrm{cm}^{-1}$. Our |
| 359 |
+ |
available computing resources limited us to 67 clusters for the |
| 360 |
+ |
zero-field spectrum, and 59 for the full field. |
| 361 |
+ |
|
| 362 |
|
\subsection{CN frequencies from potential-frequency maps} |
| 363 |
|
Before Gaussian silumations were carried out, it was attempt to apply |
| 364 |
|
the method developed by Cho {\it et al.}~\cite{Oh:2008fk} This method involves the fitting |
