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\title{Nitrile vibrations as reporters of field-induced phase |
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transitions in 4-cyano-4'-pentylbiphenyl (5CB)} |
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\author{James M. Marr} |
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\author{J. Daniel Gezelter} |
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\email{gezelter@nd.edu} |
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\affiliation[University of Notre Dame]{251 Nieuwland Science Hall\\ |
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Department of Chemistry and Biochemistry\\ |
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University of Notre Dame\\ |
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Notre Dame, Indiana 46556} |
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|
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\date{\today} |
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|
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\begin{document} |
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|
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\maketitle |
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|
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\begin{doublespace} |
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|
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\begin{abstract} |
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4-cyano-4'-pentylbiphenyl (5CB) is a liquid-crystal-forming compound |
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with a terminal nitrile group aligned with the long axis of the |
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molecule. Simulations of condensed-phase 5CB were carried out both |
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with and without applied electric fields to provide an understanding |
65 |
of the the Stark shift of the terminal nitrile group. A |
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field-induced isotropic-nematic phase transition was observed in the |
67 |
simulations, and the effects of this transition on the distribution |
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of nitrile frequencies were computed. Classical bond displacement |
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correlation functions exhibit a $\sim 40 \mathrm{~cm}^{-1}$ red |
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shift of a portion of the main nitrile peak, and this shift was |
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observed only when the fields were large enough to induce |
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orientational ordering of the bulk phase. Our simulations appear to |
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indicate that phase-induced changes to the local surroundings are a |
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larger contribution to the change in the nitrile spectrum than |
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direct field contributions. |
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\end{abstract} |
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|
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\newpage |
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|
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\section{Introduction} |
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|
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Nitrile groups can serve as very precise electric field reporters via |
83 |
their distinctive Raman and IR signatures.\cite{Boxer:2009xw} The |
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triple bond between the nitrogen and the carbon atom is very sensitive |
85 |
to local field changes and has been observed to have a direct impact |
86 |
on the peak position within the spectrum. The Stark shift in the |
87 |
spectrum can be quantified and mapped into a field value that is |
88 |
impinging upon the nitrile bond. This has been used extensively in |
89 |
biological systems like proteins and |
90 |
enzymes.\cite{Tucker:2004qq,Webb:2008kn} |
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|
92 |
The response of nitrile groups to electric fields has now been |
93 |
investigated for a number of small molecules,\cite{Andrews:2000qv} as |
94 |
well as in biochemical settings, where nitrile groups can act as |
95 |
minimally invasive probes of structure and |
96 |
dynamics.\cite{Lindquist:2009fk,Fafarman:2010dq} The vibrational Stark |
97 |
effect has also been used to study the effects of electric fields on |
98 |
nitrile-containing self-assembled monolayers at metallic |
99 |
interfaces.\cite{Oklejas:2002uq,Schkolnik:2012ty} |
100 |
|
101 |
Recently 4-cyano-4'-pentylbiphenyl (5CB), a liquid crystalline |
102 |
molecule with a terminal nitrile group, has seen renewed interest as |
103 |
one way to impart order on the surfactant interfaces of |
104 |
nanodroplets,\cite{Moreno-Razo:2012rz} or to drive surface-ordering |
105 |
that can be used to promote particular kinds of |
106 |
self-assembly.\cite{PhysRevLett.111.227801} The nitrile group in 5CB |
107 |
is a particularly interesting case for studying electric field |
108 |
effects, as 5CB exhibits an isotropic to nematic phase transition that |
109 |
can be triggered by the application of an external field near room |
110 |
temperature.\cite{Gray:1973ca,Hatta:1991ee} This presents the |
111 |
possiblity that the field-induced changes in the local environment |
112 |
could have dramatic effects on the vibrations of this particular CN |
113 |
bond. Although the infrared spectroscopy of 5CB has been |
114 |
well-investigated, particularly as a measure of the kinetics of the |
115 |
phase transition,\cite{Leyte:1997zl} the 5CB nitrile group has not yet |
116 |
seen the detailed theoretical treatment that biologically-relevant |
117 |
small molecules have |
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received.\cite{Lindquist:2008bh,Lindquist:2008qf,Oh:2008fk,Choi:2008cr,Waegele:2010ve} |
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|
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The fundamental characteristic of liquid crystal mesophases is that |
121 |
they maintain some degree of orientational order while translational |
122 |
order is limited or absent. This orientational order produces a |
123 |
complex direction-dependent response to external perturbations like |
124 |
electric fields and mechanical distortions. The anisotropy of the |
125 |
macroscopic phases originates in the anisotropy of the constituent |
126 |
molecules, which typically have highly non-spherical structures with a |
127 |
significant degree of internal rigidity. In nematic phases, rod-like |
128 |
molecules are orientationally ordered with isotropic distributions of |
129 |
molecular centers of mass. For example, 5CB has a solid to nematic |
130 |
phase transition at 18C and a nematic to isotropic transition at |
131 |
35C.\cite{Gray:1973ca} |
132 |
|
133 |
In smectic phases, the molecules arrange themselves into layers with |
134 |
their long (symmetry) axis normal ($S_{A}$) or tilted ($S_{C}$) with |
135 |
respect to the layer planes. The behavior of the $S_{A}$ phase can be |
136 |
partially explained with models mainly based on geometric factors and |
137 |
van der Waals interactions. The Gay-Berne potential, in particular, |
138 |
has been widely used in the liquid crystal community to describe this |
139 |
anisotropic phase |
140 |
behavior.~\cite{Gay:1981yu,Berne72,Kushick:1976xy,Luckhurst90,Cleaver:1996rt} |
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However, these simple models are insufficient to describe liquid |
142 |
crystal phases which exhibit more complex polymorphic nature. |
143 |
Molecules which form $S_{A}$ phases can exhibit a wide variety of |
144 |
subphases like monolayers ($S_{A1}$), uniform bilayers ($S_{A2}$), |
145 |
partial bilayers ($S_{\tilde A}$) as well as interdigitated bilayers |
146 |
($S_{A_{d}}$), and often have a terminal cyano or nitro group. In |
147 |
particular, lyotropic liquid crystals (those exhibiting liquid crystal |
148 |
phase transition as a function of water concentration), often have |
149 |
polar head groups or zwitterionic charge separated groups that result |
150 |
in strong dipolar interactions,\cite{Collings:1997rz} and terminal cyano |
151 |
groups (like the one in 5CB) can induce permanent longitudinal |
152 |
dipoles.\cite{Levelut:1981eu} |
153 |
|
154 |
Macroscopic electric fields applied using electrodes on opposing sides |
155 |
of a sample of 5CB have demonstrated the phase change of the molecule |
156 |
as a function of electric field.\cite{Lim:2006xq} These previous |
157 |
studies have shown the nitrile group serves as an excellent indicator |
158 |
of the molecular orientation within the applied field. Lee {\it et |
159 |
al.}~showed a 180 degree change in field direction could be probed |
160 |
with the nitrile peak intensity as it changed along with molecular |
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alignment in the field.\cite{Lee:2006qd,Leyte:1997zl} |
162 |
|
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While these macroscopic fields work well at indicating the bulk |
164 |
response, the atomic scale response has not been studied. With the |
165 |
advent of nano-electrodes and coupling them with atomic force |
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microscopy, control of electric fields applied across nanometer |
167 |
distances is now possible.\cite{citation1} While macroscopic fields |
168 |
are insufficient to cause a Stark effect without dielectric breakdown |
169 |
of the material, small fields across nanometer-sized gaps may be of |
170 |
sufficient strength. For a gap of 5 nm between a lower electrode |
171 |
having a nanoelectrode placed near it via an atomic force microscope, |
172 |
a potential of 1 V applied across the electrodes is equivalent to a |
173 |
field of 2x10\textsuperscript{8} $\frac{V}{M}$. This field is |
174 |
certainly strong enough to cause the isotropic-nematic phase change |
175 |
and as well as Stark tuning of the nitrile bond. This should be |
176 |
readily visible experimentally through Raman or IR spectroscopy. |
177 |
|
178 |
In the sections that follow, we outline a series of coarse-grained |
179 |
classical molecular dynamics simulations of 5CB that were done in the |
180 |
presence of static electric fields. These simulations were then |
181 |
coupled with both {\it ab intio} calculations of CN-deformations and |
182 |
classical bond-length correlation functions to predict spectral |
183 |
shifts. These predictions made should be easily varifiable with |
184 |
scanning electrochemical microscopy experiments. |
185 |
|
186 |
\section{Computational Details} |
187 |
The force field used for 5CB was taken from Guo {\it et |
188 |
al.}\cite{Zhang:2011hh} However, for most of the simulations, each |
189 |
of the phenyl rings was treated as a rigid body to allow for larger |
190 |
time steps and very long simulation times. The geometries of the |
191 |
rigid bodies were taken from equilibrium bond distances and angles. |
192 |
Although the phenyl rings were held rigid, bonds, bends, torsions and |
193 |
inversion centers that involved atoms in these substructures (but with |
194 |
connectivity to the rest of the molecule) were still included in the |
195 |
potential and force calculations. |
196 |
|
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Periodic simulations cells containing 270 molecules in random |
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orientations were constructed and were locked at experimental |
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densities. Electrostatic interactions were computed using damped |
200 |
shifted force (DSF) electrostatics.\cite{Fennell:2006zl} The molecules |
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were equilibrated for 1~ns at a temperature of 300K. Simulations with |
202 |
applied fields were carried out in the microcanonical (NVE) ensemble |
203 |
with an energy corresponding to the average energy from the canonical |
204 |
(NVT) equilibration runs. Typical applied-field runs were more than |
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60ns in length. |
206 |
|
207 |
Static electric fields with magnitudes similar to what would be |
208 |
available in an experimental setup were applied to the different |
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simulations. With an assumed electrode seperation of 5 nm and an |
210 |
electrostatic potential that is limited by the voltage required to |
211 |
split water (1.23V), the maximum realistic field that could be applied |
212 |
is $\sim 0.024$ V/\AA. Three field environments were investigated: |
213 |
(1) no field applied, (2) partial field = 0.01 V/\AA\ , and (3) full |
214 |
field = 0.024 V/\AA\ . |
215 |
|
216 |
After the systems had come to equilibrium under the applied fields, |
217 |
additional simulations were carried out with a flexible (Morse) |
218 |
nitrile bond, |
219 |
\begin{displaymath} |
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V(r_\ce{CN}) = D_e \left(1 - e^{-\beta (r_\ce{CN}-r_e)}\right)^2 |
221 |
\label{eq:morse} |
222 |
\end{displaymath} |
223 |
where $r_e= 1.157437$ \AA , $D_e = 212.95 \mathrm{~kcal~} / |
224 |
\mathrm{mol}^{-1}$ and $\beta = 2.67566 $\AA~$^{-1}$. These |
225 |
parameters correspond to a vibrational frequency of $2358 |
226 |
\mathrm{~cm}^{-1}$, a bit higher than the experimental frequency. The |
227 |
flexible nitrile moiety required simulation time steps of 1~fs, so the |
228 |
additional flexibility was introducuced only after the rigid systems |
229 |
had come to equilibrium under the applied fields. Whenever time |
230 |
correlation functions were computed from the flexible simulations, |
231 |
statistically-independent configurations were sampled from the last ns |
232 |
of the induced-field runs. These configurations were then |
233 |
equilibrated with the flexible nitrile moiety for 100 ps, and time |
234 |
correlation functions were computed using data sampled from an |
235 |
additional 200 ps of run time carried out in the microcanonical |
236 |
ensemble. |
237 |
|
238 |
\section{Field-induced Nematic Ordering} |
239 |
|
240 |
In order to characterize the orientational ordering of the system, the |
241 |
primary quantity of interest is the nematic (orientational) order |
242 |
parameter. This was determined using the tensor |
243 |
\begin{equation} |
244 |
Q_{\alpha \beta} = \frac{1}{2N} \sum_{i=1}^{N} \left(3 \hat{e}_{i |
245 |
\alpha} \hat{e}_{i \beta} - \delta_{\alpha \beta} \right) |
246 |
\end{equation} |
247 |
where $\alpha, \beta = x, y, z$, and $\hat{e}_i$ is the molecular |
248 |
end-to-end unit vector for molecule $i$. The nematic order parameter |
249 |
$S$ is the largest eigenvalue of $Q_{\alpha \beta}$, and the |
250 |
corresponding eigenvector defines the director axis for the phase. |
251 |
$S$ takes on values close to 1 in highly ordered (smectic A) phases, |
252 |
but falls to zero for isotropic fluids. Note that the nitrogen and |
253 |
the terminal chain atom were used to define the vectors for each |
254 |
molecule, so the typical order parameters are lower than if one |
255 |
defined a vector using only the rigid core of the molecule. In |
256 |
nematic phases, typical values for $S$ are close to 0.5. |
257 |
|
258 |
The field-induced phase transition can be clearly seen over the course |
259 |
of a 60 ns equilibration runs in figure \ref{fig:orderParameter}. All |
260 |
three of the systems started in a random (isotropic) packing, with |
261 |
order parameters near 0.2. Over the course 10 ns, the full field |
262 |
causes an alignment of the molecules (due primarily to the interaction |
263 |
of the nitrile group dipole with the electric field). Once this |
264 |
system started exhibiting nematic ordering, the orientational order |
265 |
parameter became stable for the remaining 50 ns of simulation time. |
266 |
It is possible that the partial-field simulation is meta-stable and |
267 |
given enough time, it would eventually find a nematic-ordered phase, |
268 |
but the partial-field simulation was stable as an isotropic phase for |
269 |
the full duration of a 60 ns simulation. Ellipsoidal renderings of the |
270 |
final configurations of the runs shows that the full-field (0.024 |
271 |
V/\AA\ ) experienced a isotropic-nematic phase transition and has |
272 |
ordered with a director axis that is parallel to the direction of the |
273 |
applied field. |
274 |
|
275 |
\begin{figure}[H] |
276 |
\includegraphics[width=\linewidth]{Figure1} |
277 |
\caption{Evolution of the orientational order parameters for the |
278 |
no-field, partial field, and full field simulations over the |
279 |
course of 60 ns. Each simulation was started from a |
280 |
statistically-independent isotropic configuration. On the right |
281 |
are ellipsoids representing the final configurations at three |
282 |
different field strengths: zero field (bottom), partial field |
283 |
(middle), and full field (top)} |
284 |
\label{fig:orderParameter} |
285 |
\end{figure} |
286 |
|
287 |
|
288 |
\section{Sampling the CN bond frequency} |
289 |
|
290 |
The vibrational frequency of the nitrile bond in 5CB depends on |
291 |
features of the local solvent environment of the individual molecules |
292 |
as well as the bond's orientation relative to the applied field. The |
293 |
primary quantity of interest for interpreting the condensed phase |
294 |
spectrum of this vibration is the distribution of frequencies |
295 |
exhibited by the 5CB nitrile bond under the different electric fields. |
296 |
Three distinct methods for mapping classical simulations onto |
297 |
vibrational spectra were brought to bear on these simulations: |
298 |
\begin{enumerate} |
299 |
\item Isolated 5CB molecules and their immediate surroundings were |
300 |
extracted from the simulations. These nitrile bonds were stretched |
301 |
and single-point {\em ab initio} calculations were used to obtain |
302 |
Morse-oscillator fits for the local vibrational motion along that |
303 |
bond. |
304 |
\item The potential - frequency maps developed by Cho {\it et |
305 |
al.}~\cite{Oh:2008fk} for nitrile moieties in water were |
306 |
investigated. This method involves mapping the electrostatic |
307 |
potential around the bond to the vibrational frequency, and is |
308 |
similar in approach to field-frequency maps that were pioneered by |
309 |
Skinner {\it et al.}\cite{XXXX} |
310 |
\item Classical bond-length autocorrelation functions were Fourier |
311 |
transformed to directly obtain the vibrational spectrum from |
312 |
molecular dynamics simulations. |
313 |
\end{enumerate} |
314 |
|
315 |
\subsection{CN frequencies from isolated clusters} |
316 |
The size of the periodic condensed phase system prevented direct |
317 |
computation of the complete library of nitrile bond frequencies using |
318 |
{\it ab initio} methods. In order to sample the nitrile frequencies |
319 |
present in the condensed-phase, individual molecules were selected |
320 |
randomly to serve as the center of a local (gas phase) cluster. To |
321 |
include steric, electrostatic, and other effects from molecules |
322 |
located near the targeted nitrile group, portions of other molecules |
323 |
nearest to the nitrile group were included in the quantum mechanical |
324 |
calculations. The surrounding solvent molecules were divided into |
325 |
``body'' (the two phenyl rings and the nitrile bond) and ``tail'' (the |
326 |
alkyl chain). Any molecule which had a body atom within 6~\AA of the |
327 |
midpoint of the target nitrile bond had its own molecular body (the |
328 |
4-cyano-biphenyl moiety) included in the configuration. For the alkyl |
329 |
tail, the entire tail was included if any tail atom was within 4~\AA |
330 |
of the target nitrile bond. If tail atoms (but no body atoms) were |
331 |
included within these distances, only the tail was included as a |
332 |
capped propane molecule. |
333 |
|
334 |
\begin{figure}[H] |
335 |
\includegraphics[width=\linewidth]{Figure2} |
336 |
\caption{Cluster calculations were performed on randomly sampled 5CB |
337 |
molecules (shown in red) from each of the simulations. Surrounding |
338 |
molecular bodies were included if any body atoms were within 6 |
339 |
\AA\ of the target nitrile bond, and tails were included if they |
340 |
were within 4 \AA. Included portions of these molecules are shown |
341 |
in green. The CN bond on the target molecule was stretched and |
342 |
compressed, and the resulting single point energies were fit to |
343 |
Morse oscillators to obtain frequency distributions.} |
344 |
\label{fig:cluster} |
345 |
\end{figure} |
346 |
|
347 |
Inferred hydrogen atom locations were added to the cluster geometries, |
348 |
and the nitrile bond was stretched from 0.87 to 1.52~\AA\ at |
349 |
increments of 0.05~\AA. This generated 13 configurations per gas phase |
350 |
cluster. Single-point energies were computed using the B3LYP |
351 |
functional~\cite{Becke:1993kq,Lee:1988qf} and the 6-311++G(d,p) basis |
352 |
set. For the cluster configurations that had been generated from |
353 |
molecular dynamics running under applied fields, the density |
354 |
functional calculations had a field of $5 \times 10^{-4}$ atomic units |
355 |
($E_h / (e a_0)$) applied in the $+z$ direction in order to match the |
356 |
molecular dynamics simulations. |
357 |
|
358 |
The energies for the stretched / compressed nitrile bond in each of |
359 |
the clusters were used to fit Morse oscillators, and the frequencies |
360 |
were obtained from the $0 \rightarrow 1$ transition for the energy |
361 |
levels for this potential.\cite{Morse:1929xy} To obtain a spectrum, |
362 |
each of the frequencies was convoluted with a Lorentzian lineshape |
363 |
with a width of 1.5 $\mathrm{cm}^{-1}$. Available computing resources |
364 |
limited the sampling to 67 clusters for the zero-field spectrum, and |
365 |
59 for the full field. Comparisons of the quantum mechanical spectrum |
366 |
to the classical are shown in figure \ref{fig:spectrum}. |
367 |
|
368 |
\subsection{CN frequencies from potential-frequency maps} |
369 |
One approach which has been used to successfully analyze the spectrum |
370 |
of nitrile and thiocyanate probes in aqueous environments was |
371 |
developed by Choi {\it et al.}~\cite{Choi:2008cr,Oh:2008fk} This |
372 |
method involves finding a multi-parameter fit that maps between the |
373 |
local electrostatic potential at selected sites surrounding the |
374 |
nitrile bond and the vibrational frequency of that bond obtained from |
375 |
more expensive {\it ab initio} methods. This approach is similar in |
376 |
character to the field-frequency maps developed by Skinner {\it et |
377 |
al.} for OH stretches in liquid water.\cite{XXXX} |
378 |
|
379 |
To use the potential-frequency maps, the local electrostatic |
380 |
potential, $\phi$, is computed at 20 sites ($a = 1 \rightarrow 20$) |
381 |
that surround the nitrile bond, |
382 |
\begin{equation} |
383 |
\phi_{a} = \frac{1}{4\pi \epsilon_{0}} \sum_{j} |
384 |
\frac{q_j}{\left|r_{aj}\right|}. |
385 |
\end{equation} |
386 |
Here $q_j$ is the partial site on atom $j$ (residing on a different |
387 |
molecule) and $r_{aj}$ is the distance between site $a$ and atom $j$. |
388 |
The original map was parameterized in liquid water and comprises a set |
389 |
of parameters, $l_a$, that predict the shift in nitrile peak |
390 |
frequency, |
391 |
\begin{equation} |
392 |
\delta\tilde{\nu} =\sum^{20}_{a=1} l_{a}\phi_{a}. |
393 |
\end{equation} |
394 |
|
395 |
The simulations of 5CB were carried in the presence of |
396 |
externally-applied uniform electric fields. Although uniform fields |
397 |
exert forces on charge sites, they only contribute to the potential if |
398 |
one defines a reference point that can serve as an origin. One simple |
399 |
modification to the potential at each of the $a$ sites is to use the |
400 |
centroid of the \ce{CN} bond as the origin for that site, |
401 |
\begin{equation} |
402 |
\phi_a^\prime = \phi_a + \frac{1}{4\pi\epsilon_{0}} \vec{E} \cdot |
403 |
\left(\vec{r}_a - \vec{r}_\ce{CN} \right) |
404 |
\end{equation} |
405 |
where $\vec{E}$ is the uniform electric field, $\left( \vec{r}_{a} - |
406 |
\vec{r}_\ce{CN} \right)$ is the displacement between the |
407 |
cooridinates described by Choi {\it et |
408 |
al.}~\cite{Choi:2008cr,Oh:2008fk} and the \ce{CN} bond centroid. |
409 |
$\phi_a^\prime$ then contains an effective potential contributed by |
410 |
the uniform field in addition to the local potential contributions |
411 |
from other molecules. |
412 |
|
413 |
The sites $\{\vec{r}_a\}$ and weights $\left\{l_a \right\}$ developed by |
414 |
Choi {\it et al.}~\cite{Choi:2008cr,Oh:2008fk} are quite symmetric |
415 |
around the \ce{CN} centroid, and even at large uniform field values we |
416 |
observed nearly-complete cancellation of the potenial contributions |
417 |
from the uniform field. In order to utilize the potential-frequency |
418 |
maps for this problem, one would therefore need extensive |
419 |
reparameterization of the maps to include explicit contributions from |
420 |
the external field. This reparameterization is outside the scope of |
421 |
the current work, but would make a useful addition to the |
422 |
potential-frequency map approach. |
423 |
|
424 |
\subsection{CN frequencies from bond length autocorrelation functions} |
425 |
|
426 |
The distributions of nitrile vibrational frequencies can also be found |
427 |
using classical time correlation functions. This was done by |
428 |
replacing the rigid \ce{CN} bond with a flexible Morse oscillator |
429 |
described in Eq. \ref{eq:morse}. Since the systems were perturbed by |
430 |
the addition of a flexible high-frequency bond, they were allowed to |
431 |
re-equilibrate in the canonical (NVT) ensemble for 100 ps with 1 fs |
432 |
timesteps. After equilibration, each configuration was run in the |
433 |
microcanonical (NVE) ensemble for 20 ps. Configurations sampled every |
434 |
fs were then used to compute bond-length autocorrelation functions, |
435 |
\begin{equation} |
436 |
C(t) = \langle \delta r(t) \cdot \delta r(0) ) \rangle |
437 |
\end{equation} |
438 |
% |
439 |
where $\delta r(t) = r(t) - r_0$ is the deviation from the equilibrium |
440 |
bond distance at time $t$. Ten statistically-independent correlation |
441 |
functions were obtained by allowing the systems to run 10 ns with |
442 |
rigid \ce{CN} bonds followed by 120 ps equilibration and data |
443 |
collection using the flexible \ce{CN} bonds. |
444 |
|
445 |
The correlation functions were filtered using exponential apodization |
446 |
functions,\cite{FILLER:1964yg} $f(t) = e^{-c |t|}$, with a time constant, $c =$ 6 |
447 |
ps, and Fourier transformed to yield a spectrum, |
448 |
\begin{equation} |
449 |
I(\omega) = \int_{-\infty}^{\infty} C(t) f(t) e^{-i \omega t} dt. |
450 |
\end{equation} |
451 |
The sample-averaged classical nitrile spectrum can be seen in Figure |
452 |
\ref{fig:spectra}. Note that the Morse oscillator parameters listed |
453 |
above yield a natural frequency of 2358 $\mathrm{cm}^{-1}$, |
454 |
significantly higher than the experimental peak near 2226 |
455 |
$\mathrm{cm}^{-1}$. This shift does not effect the ability to |
456 |
qualitatively compare peaks from the classical and quantum mechanical |
457 |
approaches, so the classical spectra are shown as a shift relative to |
458 |
the natural oscillation of the Morse bond. |
459 |
|
460 |
\begin{figure} |
461 |
\includegraphics[width=3.25in]{Convolved} |
462 |
\includegraphics[width=3.25in]{2Spectra} |
463 |
\caption{Lorentzian convolved Gaussian frequencies of the zero field |
464 |
system (black) and the full field system (red), and the |
465 |
classically calculated nitrile bond spectrum for no external field |
466 |
application (black) and full external field application (red)} |
467 |
\label{fig:spectra} |
468 |
\end{figure} |
469 |
|
470 |
Note that due to electrostatic interactions, the classical approach |
471 |
implicitly couples \ce{CN} vibrations to the same vibrational mode on |
472 |
other nearby molecules. This coupling is not handled in the {\it ab |
473 |
initio} cluster approach. |
474 |
|
475 |
\section{Discussion} |
476 |
|
477 |
Due to this, Gaussian calculations were performed in lieu of this |
478 |
method. A set of snapshots for the zero and full field simualtions, |
479 |
they were first investigated for any dependence on the local, with |
480 |
external field included, electric field. This was to see if a linear |
481 |
or non-linear relationship between the two could be utilized for |
482 |
generating spectra. This was done in part because of previous studies |
483 |
showing the frequency dependence of nitrile bonds to the electric |
484 |
fields generated locally between solvating water. It was seen that |
485 |
little to no dependence could be directly shown. This data is not |
486 |
shown. |
487 |
|
488 |
Since no explicit dependence was observed between the calculated |
489 |
frequency and the electric field, it was not a viable route for the |
490 |
calculation of a nitrile spectrum. Instead, the frequencies were taken |
491 |
and convolved together with a lorentzian line shape applied around the |
492 |
frequency value. These spectra are seen below in Figure 4. While the |
493 |
spectrum without a field is lower in intensity and is almost bimodel |
494 |
in distrobution, the external field spectrum is much more |
495 |
unimodel. This tighter clustering has the affect of increasing the |
496 |
intensity around 2226 cm\textsuperscript{-1} where the peak is |
497 |
centered. The external field also has fewer frequencies of higher |
498 |
energy in the spectrum. Unlike the the zero field, where some |
499 |
frequencies reach as high as 2280 cm\textsuperscript{-1}. |
500 |
|
501 |
|
502 |
Interestingly, the field that is needed to switch the phase of 5CB |
503 |
macroscopically is larger than 1 V. However, in this case, only a |
504 |
voltage of 1.2 V was need to induce a phase change. This is impart due |
505 |
to the short distance of 5 nm the field is being applied across. At |
506 |
such a small distance, the field is much larger than the macroscopic |
507 |
and thus easily induces a field dependent phase change. However, this |
508 |
field will not cause a breakdown of the 5CB since electrochemistry |
509 |
studies have shown that it can be used in the presence of fields as |
510 |
high as 500 V macroscopically. This large of a field near the surface |
511 |
of the elctrode would cause breakdown of 5CB if it could happen. |
512 |
|
513 |
The absence of any electric field dependency of the freuquency with |
514 |
the Gaussian simulations is interesting. A large base of research has been |
515 |
built upon the known tuning of the nitrile bond as the local field |
516 |
changes. This difference may be due to the absence of water or a |
517 |
molecule that induces a large internal field. Liquid water is known to have a very high internal field which |
518 |
is much larger than the internal fields of neat 5CB. Even though the |
519 |
application of Gaussian simulations followed by mapping it to |
520 |
some classical parameter is easy and straight forward, this system |
521 |
illistrates how that 'go to' method can break down. |
522 |
|
523 |
While this makes the application of nitrile Stark effects in |
524 |
simulations without water harder, these data show |
525 |
that it is not a deal breaker. The classically calculated nitrile |
526 |
spectrum shows changes in the spectra that will be easily seen through |
527 |
experimental routes. It indicates a shifted peak lower in energy |
528 |
should arise. This peak is a few wavenumbers from the leading edge of |
529 |
the larger peak and almost 75 wavenumbers from the center. This |
530 |
seperation between the two peaks means experimental results will show |
531 |
an easily resolved peak. |
532 |
|
533 |
The Gaussian derived spectra do indicate an applied field |
534 |
and subsiquent phase change does cause a narrowing of freuency |
535 |
distrobution. With narrowing, it would indicate an increased |
536 |
homogeneous distrobution of the local field near the nitrile. |
537 |
\section{Conclusions} |
538 |
Field dependent changes |
539 |
|
540 |
\section{Acknowledgements} |
541 |
The authors thank Steven Corcelli for helpful comments and |
542 |
suggestions. Support for this project was provided by the National |
543 |
Science Foundation under grant CHE-0848243. Computational time was |
544 |
provided by the Center for Research Computing (CRC) at the University |
545 |
of Notre Dame. |
546 |
|
547 |
\newpage |
548 |
|
549 |
\bibliography{5CB} |
550 |
|
551 |
\end{doublespace} |
552 |
\end{document} |