| 84 |
|
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} |
| 87 |
> |
spectrum can be quantified and mapped onto a field that is impinging |
| 88 |
> |
upon the nitrile bond. This has been used extensively in biological |
| 89 |
> |
systems like proteins and enzymes.\cite{Tucker:2004qq,Webb:2008kn} |
| 90 |
|
|
| 91 |
|
The response of nitrile groups to electric fields has now been |
| 92 |
|
investigated for a number of small molecules,\cite{Andrews:2000qv} as |
| 222 |
|
where $r_e= 1.157437$ \AA , $D_e = 212.95 \mathrm{~kcal~} / |
| 223 |
|
\mathrm{mol}^{-1}$ and $\beta = 2.67566 $\AA~$^{-1}$. These |
| 224 |
|
parameters correspond to a vibrational frequency of $2358 |
| 225 |
< |
\mathrm{~cm}^{-1}$, a bit higher than the experimental frequency. The |
| 226 |
< |
flexible nitrile moiety required simulation time steps of 1~fs, so the |
| 227 |
< |
additional flexibility was introducuced only after the rigid systems |
| 228 |
< |
had come to equilibrium under the applied fields. Whenever time |
| 229 |
< |
correlation functions were computed from the flexible simulations, |
| 230 |
< |
statistically-independent configurations were sampled from the last ns |
| 231 |
< |
of the induced-field runs. These configurations were then |
| 232 |
< |
equilibrated with the flexible nitrile moiety for 100 ps, and time |
| 233 |
< |
correlation functions were computed using data sampled from an |
| 225 |
> |
\mathrm{~cm}^{-1}$, somewhat higher than the experimental |
| 226 |
> |
frequency. The flexible nitrile moiety required simulation time steps |
| 227 |
> |
of 1~fs, so the additional flexibility was introducuced only after the |
| 228 |
> |
rigid systems had come to equilibrium under the applied fields. |
| 229 |
> |
Whenever time correlation functions were computed from the flexible |
| 230 |
> |
simulations, statistically-independent configurations were sampled |
| 231 |
> |
from the last ns of the induced-field runs. These configurations were |
| 232 |
> |
then equilibrated with the flexible nitrile moiety for 100 ps, and |
| 233 |
> |
time correlation functions were computed using data sampled from an |
| 234 |
|
additional 200 ps of run time carried out in the microcanonical |
| 235 |
|
ensemble. |
| 236 |
|
|
| 260 |
|
order parameters near 0.2. Over the course 10 ns, the full field |
| 261 |
|
causes an alignment of the molecules (due primarily to the interaction |
| 262 |
|
of the nitrile group dipole with the electric field). Once this |
| 263 |
< |
system started exhibiting nematic ordering, the orientational order |
| 264 |
< |
parameter became stable for the remaining 50 ns of simulation time. |
| 263 |
> |
system began exhibiting nematic ordering, the orientational order |
| 264 |
> |
parameter became stable for the remaining 150 ns of simulation time. |
| 265 |
|
It is possible that the partial-field simulation is meta-stable and |
| 266 |
|
given enough time, it would eventually find a nematic-ordered phase, |
| 267 |
|
but the partial-field simulation was stable as an isotropic phase for |
| 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 |
| 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-biphenyl moiety) included in the configuration. For the alkyl |
| 328 |
< |
tail, the entire tail was included if any tail atom was within 4~\AA |
| 329 |
< |
of the target nitrile bond. If tail atoms (but no body atoms) were |
| 327 |
> |
4-cyano-biphenyl moiety) included in the configuration. Likewise, the |
| 328 |
> |
entire alkyl tail was included if any tail atom was within 4~\AA\ of |
| 329 |
> |
the target nitrile bond. If tail atoms (but no body atoms) were |
| 330 |
|
included within these distances, only the tail was included as a |
| 331 |
|
capped propane molecule. |
| 332 |
|
|
| 339 |
|
were within 4 \AA. Included portions of these molecules are shown |
| 340 |
|
in green. The CN bond on the target molecule was stretched and |
| 341 |
|
compressed, and the resulting single point energies were fit to |
| 342 |
< |
Morse oscillators to obtain frequency distributions.} |
| 342 |
> |
Morse oscillators to obtain a distribution of frequencies.} |
| 343 |
|
\label{fig:cluster} |
| 344 |
|
\end{figure} |
| 345 |
|
|
| 355 |
|
molecular dynamics simulations. |
| 356 |
|
|
| 357 |
|
The energies for the stretched / compressed nitrile bond in each of |
| 358 |
< |
the clusters were used to fit Morse oscillators, and the frequencies |
| 358 |
> |
the clusters were used to fit Morse potentials, and the frequencies |
| 359 |
|
were obtained from the $0 \rightarrow 1$ transition for the energy |
| 360 |
|
levels for this potential.\cite{Morse:1929xy} To obtain a spectrum, |
| 361 |
|
each of the frequencies was convoluted with a Lorentzian lineshape |
| 365 |
|
to the classical are shown in figure \ref{fig:spectrum}. |
| 366 |
|
|
| 367 |
|
\subsection{CN frequencies from potential-frequency maps} |
| 368 |
+ |
|
| 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 |
| 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 ($a = 1 \rightarrow 20$) |
| 380 |
> |
potential, $\phi_a$, 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} |
| 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 |
| 395 |
> |
The simulations of 5CB were carried out 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 |
| 399 |
> |
modification to the potential at each of the probe 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 |
| 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. |
| 413 |
> |
The sites $\{\vec{r}_a\}$ and weights $\left\{l_a \right\}$ |
| 414 |
> |
developed by Choi {\it et al.}~\cite{Choi:2008cr,Oh:2008fk} are quite |
| 415 |
> |
symmetric around the \ce{CN} centroid, and even at large uniform field |
| 416 |
> |
values we observed nearly-complete cancellation of the potenial |
| 417 |
> |
contributions from the uniform field. In order to utilize the |
| 418 |
> |
potential-frequency maps for this problem, one would therefore need |
| 419 |
> |
extensive reparameterization of the maps to include explicit |
| 420 |
> |
contributions from the external field. This reparameterization is |
| 421 |
> |
outside the scope of the current work, but would make a useful |
| 422 |
> |
addition to the 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 |
| 426 |
> |
The distribution 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 |
| 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. |
| 443 |
> |
collection using the flexible \ce{CN} bonds, and repeating this |
| 444 |
> |
process. The total sampling time, from sample preparation to final |
| 445 |
> |
configurations, exceeded 150 ns for each of the field strengths |
| 446 |
> |
investigated. |
| 447 |
|
|
| 448 |
|
The correlation functions were filtered using exponential apodization |
| 449 |
< |
functions,\cite{FILLER:1964yg} $f(t) = e^{-c |t|}$, with a time constant, $c =$ 6 |
| 450 |
< |
ps, and Fourier transformed to yield a spectrum, |
| 449 |
> |
functions,\cite{FILLER:1964yg} $f(t) = e^{-c |t|}$, with a time |
| 450 |
> |
constant, $c =$ 6 ps, and were Fourier transformed to yield a |
| 451 |
> |
spectrum, |
| 452 |
|
\begin{equation} |
| 453 |
|
I(\omega) = \int_{-\infty}^{\infty} C(t) f(t) e^{-i \omega t} dt. |
| 454 |
|
\end{equation} |
| 455 |
|
The sample-averaged classical nitrile spectrum can be seen in Figure |
| 456 |
|
\ref{fig:spectra}. Note that the Morse oscillator parameters listed |
| 457 |
< |
above yield a natural frequency of 2358 $\mathrm{cm}^{-1}$, |
| 458 |
< |
significantly higher than the experimental peak near 2226 |
| 459 |
< |
$\mathrm{cm}^{-1}$. This shift does not effect the ability to |
| 460 |
< |
qualitatively compare peaks from the classical and quantum mechanical |
| 461 |
< |
approaches, so the classical spectra are shown as a shift relative to |
| 462 |
< |
the natural oscillation of the Morse bond. |
| 457 |
> |
above yield a natural frequency of 2358 $\mathrm{cm}^{-1}$, somewhat |
| 458 |
> |
higher than the experimental peak near 2226 $\mathrm{cm}^{-1}$. This |
| 459 |
> |
shift does not effect the ability to qualitatively compare peaks from |
| 460 |
> |
the classical and quantum mechanical approaches, so the classical |
| 461 |
> |
spectra are shown as a shift relative to the natural oscillation of |
| 462 |
> |
the Morse bond. |
| 463 |
|
|
| 464 |
|
\begin{figure} |
| 465 |
|
\includegraphics[width=3.25in]{Convolved} |
| 466 |
|
\includegraphics[width=3.25in]{2Spectra} |
| 467 |
< |
\caption{Lorentzian convolved Gaussian frequencies of the zero field |
| 468 |
< |
system (black) and the full field system (red), and the |
| 469 |
< |
classically calculated nitrile bond spectrum for no external field |
| 470 |
< |
application (black) and full external field application (red)} |
| 467 |
> |
\caption{Quantum mechanical nitrile spectrum for the no-field simulation |
| 468 |
> |
(black) and the full field simulation (red). The lower panel |
| 469 |
> |
shows the corresponding classical bond-length autocorrelation |
| 470 |
> |
spectrum for the flexible nitrile measured relative to the natural |
| 471 |
> |
frequency for the flexible bond.} |
| 472 |
|
\label{fig:spectra} |
| 473 |
|
\end{figure} |
| 474 |
|
|
| 479 |
|
|
| 480 |
|
\section{Discussion} |
| 481 |
|
|
| 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. |
| 482 |
|
|
| 483 |
+ |
Observation of Field-induced nematic ordering |
| 484 |
+ |
Ordering corresponds to shift of a portion of the nitrile spectrum to |
| 485 |
+ |
the red. |
| 486 |
+ |
At the same time, the system exhibits an increase in aligned and anti-a |
| 487 |
+ |
|
| 488 |
+ |
|
| 489 |
+ |
|
| 490 |
|
Since no explicit dependence was observed between the calculated |
| 491 |
|
frequency and the electric field, it was not a viable route for the |
| 492 |
|
calculation of a nitrile spectrum. Instead, the frequencies were taken |
| 500 |
|
energy in the spectrum. Unlike the the zero field, where some |
| 501 |
|
frequencies reach as high as 2280 cm\textsuperscript{-1}. |
| 502 |
|
|
| 501 |
– |
|
| 503 |
|
Interestingly, the field that is needed to switch the phase of 5CB |
| 504 |
|
macroscopically is larger than 1 V. However, in this case, only a |
| 505 |
|
voltage of 1.2 V was need to induce a phase change. This is impart due |
| 535 |
|
and subsiquent phase change does cause a narrowing of freuency |
| 536 |
|
distrobution. With narrowing, it would indicate an increased |
| 537 |
|
homogeneous distrobution of the local field near the nitrile. |
| 538 |
+ |
|
| 539 |
+ |
|
| 540 |
+ |
The angle-dependent pair distribution function, |
| 541 |
+ |
\begin{equation} |
| 542 |
+ |
g(r, \cos \omega) = \frac{1}{\rho N} \left< \sum_{i} |
| 543 |
+ |
\sum_{j} \delta \left(r - r_{ij}\right) \delta\left(\cos \omega_{ij} - \cos \omega\right) \right> |
| 544 |
+ |
\end{equation} |
| 545 |
+ |
provides information about the spatial and angular correlations in the |
| 546 |
+ |
system. The angle $\omega$ is defined by vectors along the CN axis of |
| 547 |
+ |
each nitrile bond (see figure \ref{fig:definition}). |
| 548 |
+ |
|
| 549 |
+ |
\begin{figure} |
| 550 |
+ |
\includegraphics[width=\linewidth]{definition} |
| 551 |
+ |
\caption{Definitions of the angles between two nitrile bonds. All |
| 552 |
+ |
pairs of CN bonds in the simulation have three angles ($\theta_i$, |
| 553 |
+ |
$\theta_j$ and $\omega$). $\cos\omega$ values range from -1 |
| 554 |
+ |
(anti-aligned) to +1 for aligned nitrile bonds.} |
| 555 |
+ |
\label{fig:definition} |
| 556 |
+ |
\end{figure} |
| 557 |
+ |
|
| 558 |
+ |
In figure \ref{fig:gofromega} the effects of the field-induced phase |
| 559 |
+ |
transition are clear. The nematic ordering transfers population from |
| 560 |
+ |
the perpendicular or unaligned region in the center of the plot to the |
| 561 |
+ |
nitrile-alinged peak near $\cos\omega = 1$. Most other features are |
| 562 |
+ |
undisturbed. This increased population of aligned nitrile bonds in |
| 563 |
+ |
the close solvation shells is also the population that contributes |
| 564 |
+ |
most heavily to the low-frequency peaks in the vibrational spectrum. |
| 565 |
+ |
|
| 566 |
+ |
\begin{figure} |
| 567 |
+ |
\includegraphics[width=\linewidth]{Figure4} |
| 568 |
+ |
\caption{Contours of the angle-dependent pair distribution functions |
| 569 |
+ |
for nitrile bonds on 5CB in the zero-field (upper panel) and full |
| 570 |
+ |
field (lower panel) simulations. Dark areas signify regions of |
| 571 |
+ |
enhanced density, while light areas signify depletion relative to |
| 572 |
+ |
the bulk density.} |
| 573 |
+ |
\label{fig:gofromega} |
| 574 |
+ |
\end{figure} |
| 575 |
+ |
|
| 576 |
+ |
|
| 577 |
|
\section{Conclusions} |
| 578 |
|
Field dependent changes |
| 579 |
|
|
