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Deep-Sky Fishing
Status Released on April 15th, 2014
Genre Arcade
Fish for… well, fish in the deep blue, sky? Embark on a journey to free all the ocean fish from the bubbles that randomly floated up into the sky! Unlock many upgrades to help you while you repopulate the ocean!
Note: This game was originally made for the Fishing game jam, but I didn't finish the game for the deadline, and lost motivation for the project as a whole. But, after a year of this game just collecting dust on my hard drive, I decided to quickly finish it and get it out there as a side goal. Since the game was originally made for a timed game jam, it explains why the game has a lack of content, so I'm sorry if it is very short. This game is probably more of a concept than an actual game, but hey! It's a working game ain't it? Enjoy!


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\section{Introduction}
Soft materials with tailored properties have found application in a variety of technologies including waveguides in photonic circuits \cite{Bogaerts2002}, collectors for energy harvesting devices,\cite{Nakayama2008} membranes for energy storage cells,\cite{Kanamura2005, Darling2014} and tunable-rheology fluids in brake lines, artificial joints, and vibrational dampeners. \cite{Klingenberg2001} The use-inspired behaviors of these materials derive from the physicochemical properties of their constituent components as well as their internal spatial organization (i.e., structure). Because fabrication methods that enable top-down control of structure at the nanoscale can be prohibitively expensive and slow for industrial-scale manufacturing processes \cite{Girard2006}, bottom-up strategies based on self-assembling materials have been explored as promising alternatives. \cite{Whitesides2002}  Colloidal nanoparticles, polymers, and proteins can serve as powerful material building blocks for self-assembly because their mutual interactions, which help determine the favored equilibrium state of the system, can be systematically varied through, e.g., their size, shape, charge, composition/sequence, and surface functionalization \cite{Glotzer2007}, providing a rich design space. A key challenge is to determine which building blocks reliably self-assemble a material with a targeted structure or desired macroscopic properties.

\begin{figure*}[!ht]
\centering
\includegraphics[width=\textwidth]{"Figure_1"}
\caption{Forward and inverse approaches in discovery and design of soft materials. In an example forward approach, materials with new properties may be discovered by repeatedly carrying out the following sequence of steps. Chemical synthesis (\textbf{A}) is used to create material building blocks with effective, coarse-grained interactions (\textbf{B}) that drive their assembly into structures (\textbf{C}) which impart emergent properties on the macroscopic scale (\textbf{D}). Inverse methods work backwards to systematically discover which material components will spontaneously form targeted structures or materials with desired macroscopic properties. For each panel from left to right and top down: \textbf{A:} Adapted with permission from \citenum{Agrawal2018}, Copyright 2018 American Chemical Society; \textbf{B}: Adapted with permission from \citenum{Loget2012}, Copyright 2012 Wiley; From \citenum{Sun2002}, adapted with permission from AAAS; From \citenum{Kalsin2006}, adapted with permission from AAAS; \textbf{C}: Adapted with permission from \citenum{Stoykovich2007}, Copyright 2007 American Chemical Society; Adapted with permission from \citenum{Jiang1999}, Copyright 1999 American Chemical Society; Adapted from \citenum{Reinhart2016}, with the permission of AIP Publishing; \textbf{D:} Used with permission from \citenum{Ge2007}, Copyright 2007 Wiley; Adapted with permission from \citenum{Cheng2019}, Copyright 2019 American Chemical Society; Adapted with permission from \citenum{Hughes2018}, Copyright 2018 American Chemical Society.}
\label{fig:design}
\end{figure*}

\emph{Forward} strategies for discovering new self-assembling materials are commonly adopted. In such approaches, an initial set of material building blocks is synthesized and protocols are chosen to promote their self-assembly in an experiment or a computer simulation. The structure and properties of the resulting material are subsequently characterized. These steps are then repeated (typically many times) with different choices for the building blocks or protocols to screen for materials with superior attributes. To make materials discovery more systematic and amenable to meeting specified design constraints, it can be helpful to instead formulate this process as an \emph{inverse} problem (Fig.~\ref{fig:design}). For example, one can define a figure of merit (FOM) based on a desired structure or macroscopic property and then apply methods of constrained optimization to help navigate the multidimensional design space and determine which available building blocks, interactions, or protocols are most suitable for realizing a material.

Progress on statistical mechanical approaches to inverse problems for designing soft matter has been chronicled in recent reviews and perspective articles. Topics covered include the design of colloidal interactions to stabilize self-assembled target structures \cite{Torquato2009} (Fig.~\ref{fig:design}C $\to$ \ref{fig:design}B) and the discovery of structures optimal for realizing desired macroscopic properties across a range of soft materials \cite{Jain2014} (Fig.~\ref{fig:design}D $\to$ \ref{fig:design}C). Inverse methods have proven powerful for designing granular materials \cite{Jaeger2015, Jaeger2016, Murugan2019}, block copolymer assemblies \cite{Jaeger2016, Gadelrab2017, Murugan2019}, and bio-inspired materials \cite{Murugan2019}. Recent reviews \cite{Ferguson2018,Jackson2019} have highlighted inverse techniques that leverage machine learning (ML) to effectively process the high-dimensional data obtained from computer simulations of materials to analyze and design their novel structural and dynamic properties. Inverse methods have also been widely applied in related fields including the design of molecules and chemical reactions\cite{SanchezLengeling2018, GomezBombarelli2018, Coley2019A, Coley2019B}.

In this Perspective, we explore recent advances in the use of inverse methods for computational soft-material design. We split the discussion into methods related to structure design in Section \ref{sec:structdesign} and macroscopic property design in Section \ref{sec:propdesign}.  For structure design, a major challenge is discovering a FOM that can (1) discriminate between the target structure and its competitors and (2) encourage spontaneous assembly of the target.  For property design, the FOM is often known in advance and related to the property of interest. The challenge is to find an efficient way to compute and optimize it. The latter can be carried out either directly by varying the possible building block interactions (Fig.~\ref{fig:design}D$\to$\ref{fig:design}B) or in two stages by first discovering optimal structure (Fig.~\ref{fig:design}D$\to$\ref{fig:design}C) and then using that information to determine optimal interactions (Fig.~\ref{fig:design}C$\to$\ref{fig:design}B).  Within each section, we compare inverse methods recently demonstrated to be successful for addressing these problems. Promising methods that utilize ML algorithms have been proposed for both structure and property design strategies, and we discuss how they may be effectively incorporated into inverse schemes. Despite the successes of \emph{in silico} structure and property design, inverse techniques are not routinely used to design materials in experiments, \cite{Wilken2015, Walsh2019, Aharoni2018, Man2013, Miskin2013, Miskin2014, Auzinger2018, Reid2019, Hannon2013, Hannon2013B, Qin2013}  and improving the experimental realizability of computational design remains an outstanding challenging.  In Section \ref{sec:future}, we outline some promising future areas for which inverse strategies may be particularly effective and useful for directing experimental materials design.

\section{Design for structure} \label{sec:structdesign}

\begin{figure*}
\centering
\includegraphics[width=\textwidth]{"Figure_2"}
\caption{Schematics illustrating the steps involved in several inverse methods along with snapshots of model materials designed and assembled using these approaches. \textbf{A:} Machine learning is used to discover structural order parameters $\psi_i$ from unbiased molecular dynamics (MD) or Monte Carlo (MC) simulations.  The free energy landscape is generated in the low-dimensional OP space using biased sampling methods, and the difference in free energy between the target and competitors is maximized.  This technique has been used to design patchy particles that assemble clusters\cite{Long2018}, which in turn assemble into open crystals.\cite{Ma2019}. Adapted from Refs. \citenum{Long2018} and \citenum{Ma2019} with permission from the Royal Society of Chemistry. \textbf{B:} Alchemical Monte Carlo (AMC) simulations find a particle shape that minimizes the alchemical free energy of a target lattice to favor its spontaneous assembly. Symmetrizing the shape can improve the target's thermodynamic stability.  This method has been used to assemble a rich variety of crystal structures from hard colloidal particles.\cite{vanAnders2015, Geng2019}. Modified from Ref. \citenum{Geng2019}. Copyright The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. Distributed under a Creative Commons Attribution NonCommerical License 4.0 (CC BY-NC) \textbf{C:} The radial distribution function $g(r)$ from MD or MC simulations (blue) is compared to that for a target structure (red) to minimize the relative entropy between the two ensembles.  This method has been used to design isotropic pair potentials for assembling phases with complex morphologies.\cite{Jadrich2017, Lindquist2018} Adapted from Ref. \citenum{Jadrich2017}, with the permission of AIP Publishing. Adapted with permission from Ref. \citenum{Lindquist2018}, Copyright 2018 American Chemical Society. \textbf{D:} Forward simulations generate an ensemble of data that is used to skew the probability distribution toward configurations that contribute more toward a targeted structure or property than average.  This approach has been used to design block copolymers for templated self-assembly, folding polymers, and time-dependent processing conditions to shuttle a particle across an energy landscape. Adapted from Ref. \citenum{Miskin2016}.}
\label{fig:methods}
\end{figure*}

To design interactions that promote self-assembly into a specific structure (Fig.~\ref{fig:design}C$\to$\ref{fig:design}B), a target ensemble comprising the configuration data of the building blocks in the desired phase must be considered. Ideally, a single FOM can be constructed that is descriptive of the material's high-dimensional configurations and can be used to favor the target structure over those of competing phases. FOMs can include thermodynamic quantities, statistical distances from information theory, and structural order parameters. In this section, we discuss strategies that have used these types of FOMs to successfully design interactions for self-assembly of model materials into various target structures.  Some of these methods are depicted schematically in Fig. \ref{fig:methods}.

\subsection{Thermodynamic descriptors}\label{subsec:thermoFOM}

One of the pioneering approaches in computational design of self-assembly was to determine interactions that maximize the potential energy difference between a target structure and its competitors while ensuring mechanical stability of the target, effectively sculpting the ground-state potential energy landscape \cite{Rechtsman2005, Rechtsman2006, Rechtsman2007B, Torquato2009, Marcotte2011, Marcotte2011B, Marcotte2013}. In this strategy, the target structure and a pool of possible competitors are selected, and then the optimization is performed over a set of design parameters ${\boldsymbol{\lambda}}$ characterizing the interaction potential between assembling components. While there are few inherent constraints on the functional form of the interactions, most research to date using this approach has focused on isotropic, pairwise potentials. A forward calculation of the ground-state phase diagram of the model with the optimized interactions can reveal if the list of the competitors considered needs to be expanded and further optimizations performed.

Using this method, interactions that stabilize several two-dimensional (e.g., honeycomb and square \cite{Rechtsman2005, Rechtsman2006, Marcotte2011, Marcotte2011B}) and three-dimensional (e.g. diamond \cite{Rechtsman2007B, Marcotte2013}) crystalline phases have been discovered. Modifications to this approach have enabled the optimization of interactions to ensure target stability over a wide range of particle concentrations. \cite{Jain2013, Jain2014B, Pineros2016, Pineros2016B, Pineros2017} Finite-temperature effects can also be treated approximately by minimizing the Lindemann criterion quantifying fluctuations from the target structure.\cite{Torquato2009, Rechtsman2005, Rechtsman2006, Rechtsman2007B}  While these methods are straightforward to implement for the design of interactions that stabilize crystalline targets, it is not clear how to extend them to target specific types of local structuring in disordered states of matter. Ensuring the kinetic accessibility of the target structure via self-assembly (e.g., from a disordered fluid) is also an outstanding challenge for ground-state-based strategies.

Long and Ferguson recently developed a free-energy ``landscape engineering'' method (Fig. \ref{fig:methods}A) that goes beyond potential-energy minimization. In this approach, the free energy of a desired structural motif is directly minimized relative to other possible emergent structures in a low-dimensional space of collective coordinates. Importantly, the collective coordinates, or ``order parameters'' (OPs), are machine-learned from the high-dimensional space of raw particle coordinates to maximize information retention. Diffusion maps\cite{Ferguson2010, Long2014, Chiavazzo2017, Long2018} and autoencoders\cite{Chen2018C, Chen2018D, Ribeiro2018, Sultan2018} have been shown to be particularly useful for this reduction, but in principle other ML techniques or physically informed OPs (Section \ref{sec:orderparameters}) could be used. The free-energy landscape is computed in the low-dimensional OP space using enhanced sampling techniques \cite{Long2018,Chiavazzo2017, Chen2018C, Chen2018D}.  The free-energy differences between the target and its competitors are extracted from the landscape and used to update the design parameters in an iterative loop, depicted in Fig.~\ref{fig:methods}A. In contrast to potential-energy minimization methods, landscape engineering naturally incorporates temperature effects and automatically enumerates competitors from the free-energy landscape.  Landscape engineering has been used to construct patchy colloids that self-assemble into targeted clusters \cite{Long2018} which in turn assemble into open crystals \cite{Ma2019}, as seen in the snapshots in the right side of Fig.~\ref{fig:methods}A.

Constructing an entire free-energy landscape is difficult due to its computational costs, so landscape engineering has not yet been applied to more general target structures.  However, even if the landscape cannot be computed, it can still be navigated and updated in simulations.  Van Anders, Glotzer, and coworkers proposed a design approach using simulations in an ``alchemical'' (or ``expanded'') ensemble (Fig. \ref{fig:methods}B) \cite{vanAnders2015, Geng2019}.  Their work focused on a family of hard particles, the shapes of which are described by a set of variables, ${\boldsymbol{\lambda}}$. For athermal particles, the free energy for a given shape is purely entropic with contributions from positions, $\mathbf{x}$, and orientations, $\mathbf{q}$. The particles were initially constrained to a target lattice using a tethering potential $E(\mathbf{x})$. Alchemical Monte Carlo simulations were performed in an ensemble where particles not only rotated and translated but also fluctuated in shape. The partition function $Z_{\rm AMC}$ of an ensemble of $N$ identical particles can be expressed as
\begin{equation}\label{eq:alchemical}
Z_{\rm AMC} = \int d\mathbf{x} \, d\mathbf{q}\, d{\boldsymbol{\lambda}} \, e^{-\beta [U(\mathbf{x}, \mathbf{q} | {\boldsymbol{\lambda}}) - N \boldsymbol{\mu}\cdot{\boldsymbol{\lambda}} + E(\mathbf{x})]},
\end{equation}
where $\boldsymbol{\mu}$ are alchemical potentials (conjugate to the shape parameters) and $U(\mathbf{x}, \mathbf{q} | {\boldsymbol{\lambda}})$ is the interparticle potential.

Because $\boldsymbol{\mu}$ cannot be controlled in real systems, $\boldsymbol{\mu}$ was set to zero to avoid biasing the particle shape, and the external tethering potential was slowly reduced. If the crystal structure is stable in the limit $E\rightarrow 0$, the free energy (entropy) for the target lattice has been minimized (maximized) with respect to particle shape.  As shown in Fig.~\ref{fig:methods}B, the particle shape can be additionally symmetrized to improve the thermodynamic stability of the target.\cite{Geng2019}  Because the free energy, rather than a free energy difference, is the FOM, alchemical Monte Carlo does not explicitly consider competitors. This is computationally efficient because it avoids having to fully sample the free-energy landscape but does not ensure that competitors are disfavored and thus the target may only be metastable. Nonetheless, this method has been used successfully to optimize hard-particle shapes that assemble into many complex crystals (see, e.g., right side of Fig.~\ref{fig:methods}B).\cite{Geng2019} Alchemical methods are not limited to hard particles and ${\boldsymbol{\lambda}}$ may include parameters characterizing other particle interactions \cite{Zhou2019}.

\subsection{Statistical distances}
Information theory provides quantities, so called ``statistical distances'', that characterize differences between data samples.  The Kullback-Leibler (KL) divergence is one such quantity;~\cite{Barber2012,Chialvo2015} the KL divergence of a target distribution, $P_{\rm t}(\mathbf{x})$, with respect to a model probability distribution, $P(\mathbf{x} | {\boldsymbol{\lambda}})$, is defined as
\begin{equation} \label{eq:relent}
D_{\rm KL} (P_{\rm t}(\mathbf{x}) || P(\mathbf{x} | {\boldsymbol{\lambda}})) = \int d\mathbf{x} P_{\rm t}(\mathbf{x}) \ln\left[P_{\rm t}(\mathbf{x})/P(\mathbf{x}|{\boldsymbol{\lambda}})\right].
\end{equation}
In the case of equilibrium self-assembly, $P(\mathbf{x} | {\boldsymbol{\lambda}})$ is the Boltzmann weight of a configuration $\mathbf{x}$, and ${\boldsymbol{\lambda}}$ are the parameters that characterize the potential energy function. By optimizing ${\boldsymbol{\lambda}}$ so that $D_{\rm KL}$ is minimized, the structures self-assembled from the model system are made to resemble the target configurations. Minimization of $D_{\rm KL}$ is conceptually appealing and intuitive as a design objective because it is equivalent to maximizing the likelihood that the probabilistic model $P(\mathbf{x} | {\boldsymbol{\lambda}})$ will sample the configurations contained in the target ensemble.~\cite{Jadrich2017}

While various computational approaches have been applied to minimize $D_{\rm KL}$, \cite{Shell2008, Chaimovich2011, Bilionis2013} updates to ${\boldsymbol{\lambda}}$ consistent with a steepest-descent optimization are particularly simple to compute in the canonical ensemble when the interaction potential is pairwise and isotropic (denoted here as $u(r|{\boldsymbol{\lambda}})$). In particular, the potential parameters used in a molecular simulation during the $(i+1)^{th}$ iteration of the minimization, ${\boldsymbol{\lambda}}_{i+1}$, are determined from those used in the $i^{th}$ iteration, ${\boldsymbol{\lambda}}_{i}$, as
\begin{equation} \label{eq:relentiter}
{\boldsymbol{\lambda}}_{i+1} = {\boldsymbol{\lambda}}_i + \alpha \int d\mathbf{r} \, \Big( g(r | {\boldsymbol{\lambda}}_i) - g_{\rm t}(r) \Big) \big[ \nabla_{\boldsymbol{\lambda}} u(r | {\boldsymbol{\lambda}}) \big]_{{\boldsymbol{\lambda}}_i},
\end{equation}
where $ g(r | {\boldsymbol{\lambda}}_i)$ and $g_{\rm t}(r)$ are the radial distribution functions of the simulated model in the $i^{th}$ iteration and that of the target ensemble, respectively, and $\alpha$ is a tunable parameter that controls the magnitude of the update. This iterative update process is depicted schematically in Fig.~\ref{fig:methods}C. Unlike the thermodynamic-descriptor-based methods discussed in Sect.~\ref{subsec:thermoFOM}, which are not guaranteed to result in self-assembly of the target in a forward simulation, Eq.~\ref{eq:relentiter} uses the structures measured from the self-assembly process as input to the parameter update at each optimization step. In this way, spontaneous assembly of the target structure is strongly promoted over its competitors by the interactions optimized using such ``on-the-fly'' methods.~\footnote{In practice, this necessitates that at each optimization step the system is started from a disordered state and not configurations from the previous step.}

The strategy described above has been used to design model isotropic pair potentials that self-assemble exotic structures (Fig.~\ref{fig:methods}C) including open lattices,\cite{Lindquist2016B, Jadrich2017} Frank-Kasper phases\cite{Lindquist2018}, multi-component crystals,\cite{Pineros2018} and colloidal strings.\cite{Banerjee2019}. Some desirable features of this approach include: (1) by manipulating the form of $u(r| {\boldsymbol{\lambda}} )$, physically motivated interaction potentials can be discovered, \cite{Lindquist2016, Lindquist2019} (2) by varying the ensemble in which the iterative simulations are performed, simultaneous control of structure and thermodynamic quantities, such as the pressure of the self-assembled system, can be achieved, \cite{Lindquist2019} and (3) the minimization can also be performed in Fourier space, which may be computationally convenient for some design problems. \cite{Adorf2018}

The Kullback-Leibler divergence is also termed the relative entropy. Its minimization has been used to parameterize molecular coarse-grained models, where many atoms might be represented as a single bead, that are intended to stand in for more computationally expensive all-atom target simulations. \cite{Noid2013,Shell2008, Chaimovich2011} In both design for self-assembly and coarse-graining, the goal is to discover the parameters for a probabilistic model that are most likely to reproduce a target data set, whether that data set comes from an all-atom simulation or a contrived set of configurations that display a desired structural motif. Given these similarities, it is perhaps not surprising that other techniques from the coarse-graining literature have found success in design for self-assembly applications as well. For example, iterative Boltzmann inversion, which utilizes a heuristic update scheme with the same stationary point as Eq.~\ref{eq:relentiter} for a pair potential that is infinitely flexible, has been used to discover isotropic pair interactions that self-assemble cluster fluids\cite{Jadrich2015} as well as mesoporous materials\cite{Lindquist2016, Lindquist2017}.

The relationship between coarse-graining and design for self-assembly problems suggests multiple avenues for future work on the latter. For example, coarse-graining has been performed with multi-body\cite{Sanyal2016, Zhang2018B} and anisotropic\cite{Paramonov2008} interactions.  These more complex models are compatible with the relative entropy framework described above. Because many interactions commonly used to assemble structures in experiments are many-body and/or anisotropic in nature, including those mediated by electric charges,\cite{Kalsin2006} electric and magnetic fields,\cite{Yethiraj2003, Swan2012} surface tension,\cite{Yao2015, Sharifi-Mood2015} nematic liquid crystals\cite{Smalyukh2018}, and heterogeneous surfaces\cite{Chen2011, Wang2012}, embedding these features into the design space may allow for stronger coupling between computational and experimental materials assembly.   Additionally, certain target structures may require very complex interactions (or may even be impossible) to assemble if the potential is restricted to isotropic and pairwise forms. Nonetheless, there may be a ``simpler'' many-body and/or anisotropic potential that will readily assemble the structure. For example, the formation of capsid-like structures would undoubtedly be difficult for particles with isotropic interactions, but patchy particles with relatively simple short-ranged interactions are known to self-assemble into them with high fidelity.\cite{Long2018}.

Finally, other statistical distances can also serve as FOMs. For example, one drawback of relative entropy minimization is that $D_{\rm KL}$ is not readily amenable to optimizing singular interactions such as a hard core-potential. A hard core produces regions in configuration space of zero weight (i.e., $P(\mathbf{x}|{\boldsymbol{\lambda}}) = 0$) which leads to a divergent $D_{\rm KL}$ if $P_{\rm t}(\mathbf{x}) \ne 0$ for the same configurations.  In such cases, the relevant gradients cannot be computed to minimize $D_{\rm KL}$.  In contrast, the Bhattacharyya distance\cite{Chialvo2015}
\begin{equation} \label{eq:bhatta}
D_{\rm B}(P_{\rm t}(\mathbf{x}), P(\mathbf{x|{\boldsymbol{\lambda}}})) = -\ln\left[ \int {\rm d}\mathbf{x} \sqrt{P(\mathbf{x|{\boldsymbol{\lambda}}}) P_{\rm t}(\mathbf{x})} \right]
\end{equation}
does not share this limitation and might be used as an alternative metric for inverse design of hard-particle systems.

\subsection{Structural order parameters}
\label{sec:orderparameters}
Many of the preceding descriptors are statistical mechanical quantities that must be computed on the basis of an ensemble of configurations. This limits their usefulness for systems where the relative statistical weights of configurations are not readily known (e.g., non-equilibrium systems). A more generically applicable strategy is to instead use a structural OP that serves as a low-resolution description of a high-dimensional configuration. When such OPs reliably distinguish between a target structure and its competitors,\cite{Keys2011B} they can be used to steer an iterative scheme using the OPs as the FOM, like in Figs.~\ref{fig:transferlearning}A--C. For example, Kumar \textit{et al.}~recently used the Steinhardt bond-order parameters based on spherical harmonics of local neighbor orientations\cite{Steinhardt1983, Lechner2008} to design pair interactions for assembly of body-centered-cubic colloidal crystals \cite{Kumar2019}. However, OPs that are sufficiently discriminatory between target structures and competitors can be challenging to construct, particularly for complex structures like open lattices, crystals with large unit cells, and quasicrystals as well as cases where potential competitor structures are not known in advance.  Machine learning offers possible solutions to automatically discover OPs from structural data for design.

Several supervised ML methodologies using neural networks have successfully classified input configurations according to a library of known structures.\cite{Geiger2013, DeFever2019, Fulford2019}  The ML classifiers outperform classifications using traditional OPs based on local orientations,\cite{Steinhardt1983, Lechner2008} angles,\cite{Chau1998, Errington2001} and neighbor-graph topology\cite{Larsen2016} in discriminating complex crystal phases\cite{Geiger2013, Fulford2019} and can be trained to identify interfacial structures.\cite{DeFever2019}  If relevant structures are not known ahead of time or are difficult to produce, unsupervised ML methods leveraging clustering algorithms can categorize similar structures together.\cite{Phillips2013, Spellings2018, Adorf2019}

These methodologies primarily classify configurations into discrete categories, but continuous OPs are desirable for optimization. These OPs can be local, for example, computing a descriptor for each particle, or global, computing one value for an entire configuration.  The spatial resolution of local descriptors makes them useful for characterizing interfaces; however, many conventional local order parameters (e.g., the Steinhardt parameters) are not constructed to accurately identify interfaces.  Therefore, Reinhart and coworkers developed an unsupervised ML method, called neighborhood graph analysis \cite{Reinhardt2017A, Reinhardt2017B, Reinhardt2018}, that uses diffusion maps to discern a few continuous OPs characterizing local structural motifs; their method efficiently discriminated between not only a variety of colloidal crystals but also their surfaces and defects.  Neighborhood graph analysis has also been useful for understanding properties of grain boundaries.\cite{Snow2019}

Global OPs are useful to compute a single FOM to update parameters in an iterative design loop. One fruitful strategy for generating global OPs is to perform dimensionality reduction on a large data set of configurations and use the low-dimensional representation as an OP. While discovery of the OP requires multiple configurations, once defined, the OP can be computed on a per-configuration basis. Dimensionality reduction methods such as diffusion maps \cite{Ferguson2010, Long2014, Chiavazzo2017, Long2018}, autoencoders \cite{Chen2018C, Chen2018D, Ribeiro2018}, and variational dynamics encoders \cite{Sultan2018} have been used to construct global OPs that are continuous and differentiable. The underlying principle of such dimensionality reduction approaches is to find an intermediate compressed representation that when uncompressed is as close to the input data as possible, as depicted in Fig. \ref{fig:transferlearning}A. Such OPs have been leveraged for enhanced sampling of molecular dynamics trajectories directly in the low-dimensional OP space.\cite{Long2014, Chiavazzo2017, Long2018, Chen2018C, Chen2018D, Ribeiro2018, Sultan2018, Yang2018B} Similarly, Jadrich \textit{et al.}~used sorted arrays of pairwise distances and orientations to obtain global OPs through principal component analysis (PCA). \cite{Jadrich2018A, Jadrich2018B} The resulting OPs were able to detect a variety of phase transitions including freezing in hard disks/spheres, liquid-gas and compositional phase separation, nematic ordering in ellipses, and a non-equilibrium phase transition.  A similar method utilized nonnegative matrix factorization to compute global OPs in a ternary lipid mixture.\cite{Lopez2019}

For structural design, the machine-learned OPs of a target can serve as a convenient, numerical design objective, as shown in Fig.~\ref{fig:transferlearning}B. The output OPs can be employed in an iterative scheme (Fig.~\ref{fig:transferlearning}C) whereby configurations are converted to OPs and parameters can be tuned to push the OPs towards the desired value. This may be especially useful to design complex structures for which good descriptors are lacking.  However, it is not necessarily straightforward to perform such an optimization.  Learning the OPs requires generating a large amount of data.  This data must be representative of the structures likely to be sampled during design so that the OPs can discriminate between the target structure and competitors.  For machine-learned OPs to be reliably ported into inverse schemes, it would be beneficial to have systematic methods for determining the minimimum amount of data required to learn sufficiently accurate OPs, where in the design space this data should be collected, and if the data can be acquired on-the-fly and/or recycled between designs using transfer learning.  Similarly, automated ways to select the best FOM, ML strategy, and iterative scheme for a certain design problem would be useful for non-experts.  Such methods have not been fully explored for structural design problems and remain an important area for future research.

\section{Design for properties} \label{sec:propdesign}
Unlike the design of interactions for self-assembling a target structure, where determining a suitable FOM was challenging, there is an obvious choice for a FOM in property design---the property itself. Each iteration of the optimization involves computing the property from the underlying structure, i.e., evaluating the ``structure--property relationship''.  If the structure--property relationship is known or readily computed, material properties can be designed using a variety of optimization routines. For example, Miskin and Jaeger designed an unusual strain-stiffening granular material using an evolutionary optimization algorithm \cite{Miskin2013, Miskin2014}, while elastic networks with maximally negative Poisson ratios \cite{Reid2019} and targeted allosteric response \cite{Yan2017} have been designed using gradient-descent and simulated-annealing algorithms, respectively. Dynamic properties like diffusivity and viscosity can be optimized by similar techniques \cite{Goel2008, Carmer2012, Monroe2018}.

More often though, material properties are complex functions of structure that can depend on dynamic or nonequilibrium behavior, and the structure--property relationship is prohibitively expensive to evaluate frequently. In this case, either (1) the iterative optimization algorithm must be significantly improved to reduce the total number of structure--property evaluations required for convergence or (2) the cost of computing the property must be reduced by evaluating the structure--property relationship approximately.

\subsection{Iterative schemes}
Many techniques have been developed to improve optimization routines relevant for design of soft matter, and it is beyond the scope of this Perspective to comprehensively cover them.  Inverse methods leveraging Bayesian optimization appear particularly promising and have been recently adapted for design of material properties.\cite{Yang2018B, Ju2017, Tran2019}  In addition to navigating design spaces efficiently, these methods also provide estimates for uncertainties and sensitivities of solutions, which may be useful for finding and prioritizing degenerate solutions.  For example, the solution that is least sensitive to perturbations in the design parameters of a model might be the best to fabricate in experiments, where deviations from the model are bound to occur.

We highlight one particular approach to improve the convergence of optimizations that is physically motivated and has been applied to property design of self-assembled materials.   Jaeger, de Pablo, and coworkers proposed a statistical physics ``design engine'' \cite{Miskin2016}, depicted in Fig.~\ref{fig:methods}D,
\begin{equation} \label{eq:designengine}
\deriv{P(\mathbf{x}|{\boldsymbol{\lambda}})}{t} =  P(\mathbf{x}|{\boldsymbol{\lambda}}) \left(f(\mathbf{x}) - \ave{f(\mathbf{x})}_{P(\mathbf{x}|{\boldsymbol{\lambda}})}  \right),
\end{equation}
that prescribes dynamics to the optimization with an artificial time $t$. Here, $f$ is an objective function of the configuration $\mathbf{x}$ and sets the design goal, and $\ave{\cdot}_P$ is an ensemble average over the probability distribution $P(\mathbf{x}|{\boldsymbol{\lambda}})$. The design engine leverages information about the entire probability distribution; configurations that contribute more to $f(\mathbf{x})$ than average increase their likeliness, while those that contribute less than average become more unfavorable.  The form of Eq.~\ref{eq:designengine} enforces conservation of probability
and ensures the probability distribution is normalized.  The design engine converges more quickly than standard optimizers (like steepest descent or simulated annealing) for certain classes of problems. There is considerable flexibility in choosing $f$ so that various OPs or materials properties can be incorporated for either structure or property design. The design engine has been successfully applied to a sampling of inverse problems shown in the right side of Fig.~\ref{fig:methods}D, including colloidal crystallization,\cite{Kumar2019} polymer folding, self-assembly of block copolymers, and even nonequilibrium systems.\cite{Miskin2016}  Other types of physically motivated iterative schemes may also be useful; for example, alchemical-ensemble methods have been suggested for property design. \cite{Zhou2019}

\subsection{Machine learning for accelerated property design} \label{sec:structprop}
ML has proven effective for reducing the cost of determining material properties (Fig. \ref{fig:transferlearning}C--D).  One ML strategy is to discover an easier-to-compute OP that serves as a proxy for difficult-to-compute properties.  Support vector machines have been used to analyze the ``softness'' of glassy systems from their structural features \cite{Schoenholz2016, Schoenholz2017, Cubuk2017}. PCA of particle configurations has been used to find OPs for the mechanical properties of polycrystalline materials\cite{Paulson2017} and the effective diffusivity through membranes \cite{Cecen2014}, and the OPs were then regressed to simulated material properties. More accurate predictions can be obtained by using supervised ML methods to learn the structure--property relationship directly.  Neural networks were trained to predict the elastic modulus of a lattice model of a binary elastic composite from its configuration, outperforming linear regression of OPs from PCA.\cite{Yang2018}  Neural networks similarly outperformed regression to predict the activity of antifreeze proteins from the structure and hydrogen-bonding dynamics of nearby water.\cite{Kozuch2018}

Learning these relationships can require large training sets, which are impractical to generate if the material property is difficult to compute in the first place.  Transfer-learning strategies can be used to accelerate training.  Yang, Agrawal, and coworkers trained a generative adversarial network (GAN) for heterogeneous, disordered two-dimensional optical materials.\cite{Yang2018B} The GAN was initially trained on a large data set of configurations that were easy to produce; this learning was leveraged to initialize a new network for computing optical adorption using a smaller, more expensive-to-produce training set of configuration--adsorption pairs (Fig. \ref{fig:transferlearning}D).  The transfer-learned structure--property network is more accurate than a network trained from scratch for a fixed number of iterations and training set size, or equivalently, requires smaller training sets and fewer iterations to achieve the same prediction accuracy. Transfer-learning may also be useful in cases where a design optimization pushes the target property outside the bounds of the training set so that retraining of the ML structure--property relationship is required, but such methods have yet to be fleshed out for materials design.

During training, generative ML methods learn a small set of OPs from which they are able to generate new configurations statistically indistinguishable from those in the training set. The generator from a GAN was recently used to perform inverse design directly in the OP space to find structures with high optical absorption (Fig. \ref{fig:transferlearning}E).\cite{Yang2018B}  Because OP space is much lower-dimensional than configuration space, it is easier to explore. Other ML approaches for dimensionality reduction can be used similarly for inverse design; for example, Guo, Ren, and coworkers designed density (spatial) distributions of heat-transfer materials with optimal thermal properties using the decoder from a pretrained autoencoder network to perform the optimization in OP space.\cite{Guo2017}  Similarly, structural OPs discovered using the ML methods of Sec.~\ref{sec:orderparameters} can serve as the design space. Combining both ML OP design spaces and ML structure--property relationships in the same inverse cycle could provide even more efficient design schemes.

\subsection{Multiobjective design}
The highlighted inverse methods are primarily intended for design of a single material property, but many applications require materials with multiple functionalities. For example, bulletproof vests should be lightweight and flexible yet highly energy-dissipative,\cite{Jaeger2015} while membranes used in flow batteries must be both mechanically strong and electrically conductive. \cite{Kanamura2005}. Methods that can efficiently address inverse problems with several design objectives will be useful for such state-of-the-art materials.

One possible strategy is to reduce these ``multiobjective'' design problems into a single objective that depends on multiple material properties. This idea was used to engineer several mechanical properties of a gallium-iron alloy \cite{Liu2015} and to design multifunctional optical ports.\cite{Hughes2018} However, there are many ways to incorporate several criteria into a single objective function, and the arbitrary choice has a large effect on the final solution.\cite{Liu2015, Hughes2018}  Such design problems may be better approached using algorithms developed for multiobjective optimization,\cite{Laumanns2002, Marler2004} but this application has not been thoroughly explored for soft-materials design.

\begin{figure*}
\centering
\includegraphics[width=0.9\textwidth]{"Figure_3"}
\caption{Strategies for leveraging machine learning (ML) architectures for enhanced materials design.  \textbf{A:} Unsupervised training on a large training set of configurations discovers functions (represented with trapezoids) that map between high-dimensional configurations and a low-dimensional set of order parameters (OPs) $\psi_i$.  \textbf{B:} The ML OPs can be used as the design objective for assembling complex structures.  Adapted with permission from Ref. \citenum{Lindquist2018}, Copyright 2018 American Chemical Society. \textbf{C:} ML reduces the cost of computing objective functions in inverse design. D: The structure-OP function can be transferred to accelerate supervised learning of structure-property relations from a small training set. \textbf{E:} Inverse design can be performed directly in low-dimensional OP space using the ML configuration-generating function in lieu of forward simulations.}
\label{fig:transferlearning}
\end{figure*}

\section{Future directions} \label{sec:future}
The methods summarized in this article have been remarkably successful for designing soft materials \emph{in silico}.  Inverse approaches have similarly been used to design materials in experiments,\cite{Wilken2015, Walsh2019, Aharoni2018, Man2013, Miskin2013, Miskin2014, Auzinger2018, Reid2019, Hannon2013, Hannon2013B, Qin2013} but these strategies have not taken advantage of the methods developed for \emph{in silico} design.  As a result, there are compelling future opportunities to address the translation of effective computational strategies for the discovery of new materials to the laboratory. These opportunities include the application of inverse approaches to find robust solutions subject to experimentally realistic design constraints (Sec.~\ref{sec:multistate}), the adaptation of design assembly protocols that are simple to implement in experiments (Sec.~\ref{sec:externalfields}), and the development of strategies to improve the accuracy and computational efficiency of experimentally relevant models (Sec.~\ref{sec:experimentconnect}).

\subsection{Multistate design}
\label{sec:multistate}
Most inverse methods for structure design are intended for a single target structure at one thermodynamic state point (e.g., temperature and pressure).  This is problematic in practice because processing and operating conditions are rarely constant over a material's lifetime.  Materials designed only for one state may have different structures and properties that are suboptimal or even unusable at other conditions.  Alternatively, a material with a structural transition may be the design objective.  For example, reconfigurable materials that change their structure in response to their conditions are useful for sensing applications\cite{Holtz1997, Lee2000} and as responsive materials capable of controlled, on-the-fly modulation of properties.\cite{Klingenberg2001, Ge2011}  Methods allowing for design of multiple target structures and multiple state points can efficiently address these inverse problems.

The coarse-graining community has addressed a problem closely related to ``multistate'' design: developing an optimal coarse-grained representation from atomistic data sampled at different thermodynamic states.\cite{Mullinax2009, Moore2014, Sanyal2019, Sharp2019} Such approaches could be leveraged for inverse schemes to find a single interaction potential that assembles different structures under different conditions. In principle, entire phase diagrams could be designed by tessellating state points with target structures and simultaneously designing for them. This approach could systematically find materials with exotic phase behavior like those that ``inverse melt'' upon cooling. \cite{Feeney2003} However, computational demands for this procedure may be intense, and a feasible solution that assembles all target structures may not exist. Investigation is needed to demonstrate the possibilities for and limitations of multistate design.

In addition to equilibrium thermodynamic considerations, reconfigurable materials require kinetic transitions from one structure to another. Particularly challenging are fluid--solid and solid--solid transitions, which have many kinetic barriers but are essential for controlled manipulation of material properties.\cite{Grzelczak2010, Sherman2019} Objective functions that vary during the optimization may help find solutions with transitions specifically embedded. For example, an objective function that periodically switched between two states of reconfigurable circuits \cite{Kashtan2005} and of allosteric networks \cite{Hemery2015} found solutions prioritizing transitions between states. Murugan and Jaeger recently suggested applying this same ``switching'' strategy to self-assembling materials \cite{Murugan2019}, and we agree that this is a potentially fruitful area for further study.

\subsection{Engineering assembly protocols with external controls}
\label{sec:externalfields}
If interactions among building blocks can be controlled with an external stimulus, the stimulus may be used to facilitate self-assembly.  Many such systems have been studied experimentally, including materials that respond to light, temperature, electric/magnetic field, and flow.\cite{Grzelczak2010} This approach for assembly is attractive because it is often easier to control and modulate the external processing conditions than it is to change the physicochemical properties of the building blocks.

If the interactions induced by the external stimuli can be represented with simple expressions, for example in terms of an equilibrium interparticle pair potential, they are amenable to design using inverse methods such as those in Sections~\ref{sec:structdesign} and \ref{sec:propdesign}.  Often though, these interactions are many-bodied (\emph{e.g.} electrostatic), anisotropic (\emph{e.g.} dipolar), and out-of-equilibrium (\emph{e.g.} flow-induced).  This complicates design of the parameters of externally induced interactions, but if robust methods for this inverse problem could be developed, the solutions may be easier to realize experimentally.

A particularly promising feature of induced interactions is the ability to vary them over time.  For example, these approaches show promise for enhancing crystallization rates while reducing defects\cite{Tang2016, Tang2017, Swan2012, Howard2018} as well as assembling structures not stable at equilibrium.\cite{Sherman2019} Processing conditions may offer greater design flexibility when complicated interactions discovered from inverse methods are challenging to realize experimentally.\cite{Lindquist2016B, Jadrich2017, Adorf2018} However, a systematic inverse approach is likely required to find these optimal protocols given the complexity of the design space.

\subsection{Computational modeling for experimental materials design}
\label{sec:experimentconnect}
Though inverse design has been successful \emph{in silico}, connecting these techniques with experiments to realize new materials remains a key challenge. Inverse methods can be applied directly to experiments \cite{Wilken2015}, but this approach is ineffective when the experiments are slow, sensitive, or not amenable to automation. In these cases, computation can be leveraged to rapidly screen materials using inverse techniques, and computational predictions can be verified with experiments. This approach has been applied to find bottlebrush polymers with targeted morphologies \cite{Walsh2019}, an optimal director field for a liquid crystal \cite{Aharoni2018}, and disordered materials with targeted acoustic and photonic properties \cite{Batten2008, Florescu2009, Man2013}. The success of the combined computational--experimental approach hinges on (1) the availability of fast and accurate computational models and (2) the ability to constrain the design to experimentally controllable, feasible parameters. The design of block copolymers has given particularly successful demonstrations of this \cite{Hannon2013, Hannon2013B,Qin2013,Khaira2014, Jaeger2016,Paradiso2016, Khadikar2017}, where well-established techniques such as self-consistent field theory can be coupled to inverse schemes.

For other classes of soft materials, reliable models that can access the appropriate length and time scale for assembly may not exist or may be challenging to connect to experiments. Detailed models, where the designable parameters are usually clearer, are often too computationally demanding to use in inverse schemes, while models with effective interactions may not be readily mapped onto experiments. Implementing coarse-graining techniques within inverse frameworks may help bridge this disconnect. One such strategy is to define the design space in terms of experimentally controllable parameters of a detailed model, including parameter constraints. Systematic coarse-graining can then be used to map these parameters to a simpler model for simulating assembly.  For example, for the current value of the design parameters, a fully atomic simulation may be used to compute the effective pair potential between two colloidal particles.  The coarse-grained potential can then be used to simulate assembly of a much larger system of many particles.  The design parameters would then be updated directly and the process iterated. Such an integrated coarse-graining--inverse scheme has not yet been demonstrated but is potentially powerful for connecting computation and experiments to design new materials.

\section{Conclusion}
Inverse approaches suggest systematic means for designing soft materials with complex target structures and desired macroscopic properties.  In this Perspective, we reviewed the methodological and computational challenges associated with various design problems in soft matter and the strategies developed to address them.  Methods for assembling target structures focus mainly on determining an optimal FOM that is descriptive of the target and preferentially encourages its assembly.  Metrics based on thermodynamic energies, statistical distance measures, and structural OPs have all been implemented as FOMs to design interactions that successfully self-assemble a variety of phases with complex structures. These methods may further benefit from ML strategies to automatically discover structural FOMs. For design problems of materials with target properties, the FOM is typically more obvious (i.e., the property itself), so effective strategies focus on developing efficient strategies for determining the relevant structure--property relationships. Since such relations are often computationally demanding to compute, they may benefit from ML strategies to accelerate property evaluation. The advances presented here expand the scope of application for computational design of soft materials and open up promising new opportunities, including the synthesis of reconfigurable materials with multiple functionalities, the engineering of nonequilibrium assembly protocols, and the strengthening of connections between computational and experimental approaches to material discovery.

\begin{acknowledgments}
MPH acknowledges support from the Center for Materials for Water and Energy Systems, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award \#DE-SC0019272. BAL acknowledges support from the Darleane Christian Hoffman Distinguished Postdoctoral Fellowship at Los Alamos National Laboratory. TMT acknowledges support of the Robert A. Welch Foundation (Grant No. F-1696).
\end{acknowledgments}

\section*{Data Availability}

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

redpajama_set_name: RedPajamaArXiv


text:
\section{Introduction}
Organic charge transfer (CT) systems offer both a playground for
studying fundamental solid state properties as well as  a material
class that in recent years has become extremely attractive for modern
organic electronic devices, such as organic thin film
transistors. \cite{applic1, applic2, applic3, applic4, applic5,
  applic6} The electrostatic bonding of two different organic
molecules, donor (D) and acceptor (A), gives rise to a rich electronic
behavior. This feature combined with the vast flexibility  chemists
have concerning molecular design makes it possible to gain access to
such phenomena as unconventional superconductivity, ferroelectricity,
spin liquid  or metal-to-insulator transitions, to mention a
few.\cite{1Dmetals,organConduct,organFerroelec} Charge transfer
compounds tend to form one- or two-dimensional structures (stacks or
layers) that lead to a simple differentiation between systems composed
of segregated stacks of the donor and acceptor and systems where donor
and acceptor are mixed within the stacks. The vast majority of CT
compounds are of the latter mixed-stack type and have long been
considered as a material class of reduced significance in basic and
applied research, as the geometrical arrangement and resulting
molecular orbital overlap leads to semiconducting or insulating
behavior. However, this view needs revision in several
respects. Ambipolar charge-transport properties have been predicted by
electronic structure calculations in selected mixed-stack systems with
mobility values that would rival the best single-component organic
semiconductors, such as rubrene or
pentacene.\cite{ambChargeTrans_mixedStack_JACS2012,bandstruktur_tetracen+perylenTCNQ}
Moreover, a growing group of mixed-stack CT systems shows a
temperature- and/or pressure driven transition into a ferroelectric or
an antiferroelectric state associated with a pronounced increase of
the charge transfer degree, a so-called neutral-ionic (NI)
transition.\cite{NIchemphys2006} The NI-transition is widely tunable
by pressure (in single crystals)\cite{Lemee1997a} or biaxial strain
(in clamped thin films)\cite{Huth2014a,vita_synthMet2011,ETTCNQ_vita}
and may even be associated with a multiferroic state in which a,
typically, antiferromagnetic order parameter couples to the electrical
polarization.\cite{Filatov2013a} With a view on strengthening the
material basis for this class of mixed-stack systems, several
challenges have to be overcome. Despite of the fact that most of the
organic CT systems crystallize in a mixed-stack variant, the
conditions for the establishment of a temperature-driven NI-transition
are rather stringent. Roughly speaking, starting from a moderate
initial charge transfer degree of about 0.3 to 0.4 from donor to
acceptor the gain of Madelung energy under thermal contraction as the
materials cools down must be sufficient to overcompensate the
generally still positive difference in the ionization energy of the
donor and the electronic affinity of the acceptor. Under these
conditions a spontaneous increase of the charge transfer degree,
usually in conjunction with D-A dimerization and a loss of inversion
symmetry, can occur leading to an (anti-) ferroelectric state. At the
beginning of a systematic identification of possible candidates for a
NI-transition lies the proper selection of the donor and acceptor
species based on their respective molecular energies, as has been
suggested by Torrance (V-shaped diagram).\cite{NI_discovery} It has to
be noted, though, that a good match of the molecular energies does not
guarantee a NI-transition to occur. By way of proper modification of
the functional groups of either donor or acceptor a fine-tuning of the
respective ionization energies and electron affinities can be
done. However, in co-crystallizing donor and acceptor a possible
change of the resulting crystal structure as compared to the mother
compound is hard to prevent and not predictable. Pressure-based tuning
of the mother compound, ideally leaving the crystal structure
unchanged, is an attractive alternative, albeit technically
non-trivial and thus not suitable as a screening method for the
identification of new NI-transition systems. Here the question arises
which approaches with anticipatory quality can be developed that allow
to identify possible candidates beforehand, once a promising mother
compound is identified.

In this work we present a combined experimental and theoretical study
on the electronic properties of the new mixed-stack organic CT
compound [Tetramethoxypyrene
(TMP)]-[Tetrafluoro-tetracyanoquinodimethane (F$_4$TCNQ)] which was
derived from the previously synthesized TMP-TCNQ mixed-stack system by
way of enhancing the acceptor qualities of TCNQ by halogen
substitution. The pyrene TMP and the TCNQ structure both offer a
multitude of possible functional modifications that allow to
investigate how specific changes affect the structural and electronic
properties of the CT compound.
\begin{figure}[htp]
\includegraphics[width=0.4\textwidth]{fig1_tmpf4tcnq_molecules}
\caption{Molecular structure of TMP (left) and F$_4$TCNQ (right). The
  four methoxy groups provide TMP with donor properties while the four
  cyano groups combined with four fluorine atoms give F$_4$TCNQ its
  acceptor functionality.}\label{fig:MolStruct}
\end{figure}
TMP-F$_44$TCNQ has a triclinic crystal structure with virtually ideal
geometrical overlap of donor and acceptor resulting in a pronounced
anisotropy of the electronic properties, as deduced from
temperature-dependent conductivity measurement and density functional
theory calculations. This structure differs from that of the mother
compound TMP-TCNQ which is far less anisotropic. Somewhat
counter-intuitively, the degree of charge transfer of TMP-F$_4$TCNQ is
not enhanced as compared to TMP-TCNQ but even reduced from about 0.2
to 0.1, according to the observed shifts in the C$\equiv$N stretching
mode as seen in IR absorption spectroscopy as well as in the
density functional theory (DFT) calculations. By analyzing the charge distribution
of the two complexes, we propose a possible explanation of these observations.
Finally by simulating the effect
of uniaxial pressure on these two compounds within the DFT
 calculations,  we predict a pronounced increase of the charge
transfer degree for TMP-TCNQ whereas TMP-F$_4$TCNQ appears to be
mostly unaffected. This band-structure-based approach of a simulated
pressure experiment may represent an efficient strategy to identify
possible candidates for NI-transition systems based on newly
synthesized mixed-stack organic charge transfer systems of suitable
initial charge transfer degree.
\section{Methods}
\label{sec:methods}
\subsection{Experimental methods}
\subsubsection{Synthesis and structure determination}
TMP was synthesized at the Max Planck Institute for Polymer Research
with a purity of better than 95\,$\%$. F$_4$TCNQ was purchased from
Sigma-Aldrich with a purity of $\geq$ 97\,$\%$.

Single crystals of TMP-F$_4$TCNQ were grown in solution by slow
evaporation of the solvent. TMP and F$_4$TCNQ were separately
solubilized in dichloromethane (DCM) in equimolar amounts (ca.\ 10
mg). Both solutions were carefully mixed in one beaker glass which was
then covered with aluminum foil to limit the evaporation rate. Black,
needle-like crystals could be extracted after one to two weeks.

The structure determination was based on a $0.41\times 0.06\times
0.06$\,mm sized crystal. X-ray data were recorded at T = 173\,K on a
STOE IPDS II two-circle-diffractometer using Mo-K$_\alpha$ radiation
and a Genix 3D multilayer optics monochromator. SHELXS97
\cite{SHELX_Sheldrick2008} was used for structure solution while
refinement was carried out with SHELXL97. Further information on data
collection and structure refinement are given in table
\ref{tab:xrayMeas_paramet}. Crystallographic data for TMP-F$_4$TCNQ
has been deposited with the Cambridge Crystallographic Data
Centre~\cite{ccdc}.

\begin{table}[ht]
\caption{\label{tab:xrayMeas_paramet} Measurement and refinement parameters.}
\begin{ruledtabular}
\begin{tabular}{ll}
measured reflections & 5551\\
$\theta$-range (deg) & 3.41-25.03\\
reflections used & 2305\\
parameters & 201\\
goodness of fit & 0.954
\end{tabular}
\end{ruledtabular}
\end{table}
\subsubsection{Electrical conductivity measurements}
Single crystals were placed onto a custom-made carrier chip and
electrically contacted with conducting graphite paste. 50\,$\mu$m
thick goldwires were attached to the paste and soldered to contact
pins on the carrier chip. On the small crystals two-probe measurements
proved to be suffficient, because the sample resistance dominated by
far the contact and wiring resistances. Low temperature measurements
were performed in an Oxford $^{4}$He cryostat with a Keithley 2636A
two-channel sourcemeter. Within the cryostat the carrier chip was
mounted in a variable temperature insert (VTI). The temperature was
measured with a calibrated resistance thermometer (Cernox).
\subsubsection{Infrared spectroscopy}
Infrared spectroscopy was applied to powder material from solution
growth in the case of TMP-F$_4$TCNQ and the as-supplied powder in the
case of F$_4$TCNQ as a reference. Spectra were recorded at room
temperature with a Bruker Vertek 70 FT-IR spectrometer
between 600 and
4000\,cm$^{-1}$.
All measurements were performed with a resolution of 2\,cm$^{-1}$.
\subsubsection{UV-VIS/IR spectroscopy}
Spectra were recorded in solution (DCM) on a Perkin-Elmer Lambda 900
UV/VIS/NIR spectrometer. A concentration of 10$^{-4}$\,mol/l was used
for absorption between 0.1 and 1 at the wavelength region of
experimental interest.
\subsection{Theoretical methods}
We performed {\it ab initio} density functional theory calculations
for the TMP-F$_4$TCNQ complex. The full potential local orbital (FPLO)
basis set \cite{fplo} with the generalized gradient approximation
functional in its PBE form \cite{Perdew96} was used.  We employed a
$10\times 10\times 10$ $k$ mesh and analyzed the band structure by
fitting the bands near the Fermi level to a tight binding Hamiltonian
\cite{Kandpal2009}
\begin{equation}
H=\sum_i \varepsilon_i c_{i}^{\dag}c_{i} +\sum_{ij} t_{ij}c_{i}^{\dag}c_{j}
\label{eq:hamiltonian}
\end{equation}
with the operators $c_{i}^{\dag}$ ($c_{i}$) creating (annihilating)
electrons at site $i$, onsite energies $\varepsilon_i$ and transfer
integrals $t_{ij}$. We checked the uniqueness of the resulting fit
using projective Wannier functions.\cite{Jacko2013}

We simulate uniaxial pressure along the stacking direction by scaling
the $a$ lattice parameter of both TMP-TCNQ and TMP-F$_4$TCNQ in small
steps and fully relaxing all internal coordinates using the projector
augmented wave (PAW) basis and generalized gradient approximation
functional as implemented in the Vienna {\it ab initio} simulation
program (VASP).\cite{vasp1,vasp2} We use a $6\times 6\times 6$ $k$
mesh for TMP-TCNQ and a $4\times 4\times 4$ $k$ mesh for
TMP-F$_4$TCNQ, with a plane wave cutoff of 500\,eV.
\section{Results}
\subsection{Crystal structure}
The synthesized TMP-F$_4$TCNQ crystals showed a triclinic structure
with mixed stacks formed along its a-axis. Figure \ref{fig:structures}
illustrates the packing arrangement from different perspectives.
\begin{table}[ht]
\caption{\label{tab:crystalData} Crystal structure data for TMP-F$_4$TCNQ.}
\begin{ruledtabular}
\begin{tabular}{ll}
formula & C$_{20}$H$_{18}$O$_4$ - C$_{12}$F$_4$N$_4$\\
space group & $\mathrm{P}\overline{1}$\\
a [\AA{}] & 6.8078(13)\\
b [\AA{}] & 10.6592(18)\\
c [\AA{}] & 10.840(2)\\
$\alpha$ [$^\circ$] & 61.373(13)\\
$\beta$ [$^\circ$] & 71.958(14)\\
$\gamma$ [$^\circ$] & 84.063(14)\\
volume [\AA{}$^3$] & 655.6(2)\\
Z & 1
\end{tabular}
\end{ruledtabular}
\end{table}

\begin{figure}[htp]
\includegraphics[width=0.49\textwidth]{fig2_tmpf4tcnq_structure}
\caption{Structure of TMP-F$_4$TCNQ viewed along (a) {\bf b}- and (b)
  {\bf a}-axis.}\label{fig:structures}
\end{figure}

All stacks have a common stacking axis. Along the stacks, TMP and
F$_4$TCNQ lie almost perfectly on top of each other: Their respective
planes (ignoring the methoxy groups) lie nearly perpendicular to the
stacking direction while the geometrical centers of TMP and F $_4$TCNQ
molecules are positioned on a common axis. The mean plane-to-plane
separation is about 3.35\,\AA{}.
\subsection{Electrical conductivity}
Electrical conductivity measurements for one typical crystal are
illustrated in Fig.~\ref{fig:sigma_vs_T_+crystal}. The crystal shown
here had dimensions of roughly $360\times 90\times
50$\,$\mu$m. Current-temperature curves were recorded with an applied
voltage of 100\,V, corresponding to a maximum electrical field of
11\,kV/cm, for two distinct directions along the crystal, one parallel
to its long axis and one perpendicular to it. The long axis
corresponded to the stacking direction of the molecules (a-axis).
\begin{figure}[htp]
\includegraphics[width=0.43\textwidth]{fig3_sigma_vs_T_and_crystal}
\caption{Temperature-dependent conductivity measured on the
  TMP-F$_4$TCNQ crystal (shown with contacts in the inserted optical
  micrograph) for two different
  directions.}\label{fig:sigma_vs_T_+crystal}
\end{figure}
\begin{figure}[htp]
\includegraphics[width=0.43\textwidth]{fig4_arrhenius}
\caption{Arrhenius plot and the corresponding linear fit (dashed
  lines) for both $\sigma$(T) measurements.}\label{fig:arrhenius}
\end{figure}

Both $\sigma$(T) characteristics show a thermally activated
(Arrhenius) behavior but with different activation energies E$_a$ (see
Fig.~\ref{fig:arrhenius}). This behavior was only visible at $T
\gtrsim 220$\,K as the resistance at lower temperatures became too
high for the measurement setup. For the stacking axis a value of E$_a
= 0.98$\,eV was calculated based on the fit performed in
Fig. \ref{fig:arrhenius}. The perpendicular direction gave a value of
E$_a = 0.84$ eV.
\subsection{Degree of charge transfer}
The fraction of charge ($\rho$) transferred from donor to
acceptor (in the ground state) can be estimated by the change of the
C$\equiv$N stretching vibration frequency $\nu$ caused by the CT
complex formation.\cite{salmeronValverde1994,chappell1981} The
absorption of IR (infrared) radiation of isolated F$_4$TCNQ was
measured as a reference. The spectrum shown in
Fig. \ref{fig:IR_tmp+f4tcnq} illustrates IR bands at 2217 and
2228\,cm$^{-1}$ corresponding to the modes b$_{2u}$ and b$_{1u}$.

\begin{figure}[htp]
\includegraphics[width=0.43\textwidth]{fig5_IR_tmp_and_f4tcnq}
\caption{IR absorption caused by the CN stretching vibrations in
  TMP-F$_4$TCNQ compared to the ones in F$_4$TCNQ. Both curves are an
  average over 16 scans.}\label{fig:IR_tmp+f4tcnq}
\end{figure}

Both values are in close agreement with results from other
measurements.\cite{F4TCNQ_meneghetti,F4TCNQ_pingel} The spectrum for
TMP-F$_4$TCNQ shows two weak bands at 2213 and 2224\,cm$^{-1}$ that
probably correspond to the modes visible in the F$_4$TCNQ spectrum
being red-shifted by 3-4\,cm$^{-1}$ due to the charge transfer. Based
on these numbers and on the $\nu$ values for fully ionized F$_4$TCNQ
\cite{F4TCNQ_meneghetti}, $\rho$ can be calculated with a
simple relationship given in Ref.~\cite{salmeronValverde1994}. The
results for the charge transfer degree are 0.12 in the case of
b$_{1u}$ and 0.09 for b$_{2u}$.
\subsection{Charge transfer transition energy}
Fig.~\ref{fig:UVVIS_spektrum} shows two absorption peaks in solution
in the region of interest: the left one at 592\,nm corresponds to an
energy of 2.1\,eV, the right one at 1132\,nm corresponds to
1.1\,eV. The latter presumably originates from the characteristic
charge transfer transition which is typically associated with a broad
peak shape like in our case.

\begin{figure}[htp]
\includegraphics[width=0.43\textwidth]{fig6_UVVIS_spectrum}
\caption{Absorption spectrum of TMP-F$_4$TCNQ. Data were recorded from
  partly reacted TMP and F$_4$TCNQ in
  solution.}\label{fig:UVVIS_spektrum}
\end{figure}

The peak at 2.1\,eV could stem from intramolecular transitions in
donor or acceptor (neutral or ionized) molecules that generally appear
at higher energies than the CT transition. The same very likely
applies to the strong absorption partly visible in the leftmost
position of the figure. Here, one can refer to the measurements
performed on neutral TMP (thin films)\cite{TMPTCNQ_mainz} that showed
an optical gap of 3.167\,eV (392.7\,nm). Similar peak energies were
found for other donors/acceptors in the neutral or ionized
state. \cite{NI_discovery,optProp_TTFsalts,TMPTCNQ_mainz,CT_trans_chemMat}
\subsection{Electronic structure}
Fig.~\ref{fig:tmpf4tcnq_bs} shows the band structure of TMP-F$_4$TCNQ
in a large energy window. Coordinates of the high symmetry points are
$\Gamma=(0,0,0)$, $X=(0.5,0,0)$, $U=(0.5,0,0.5)$, $R=(0.5,0.5,0.5)$,
$V=(0.5,0.5,0)$, $Y=(0,0.5,0)$, $T=(0,0.5,0.5)$, $Z=(0,0,0.5)$ in
units of the reciprocal lattice vectors. The electronic structure for
TMP-F$_4$TCNQ is calculated in a primitive cell containing one formula
unit and it is characterized by well separated single bands of predominant TMP or
F$_4$TCNQ origin, respectively. These bands are a result of the hybridization between
the TMP highest occupied molecular orbital (HOMO) and the F$_4$TCNQ
lowest unoccupied molecular orbital (LUMO) (see Ref.~\cite{NEXAFS_mainz} for details).
 The band below the Fermi level  is
 mostly of TMP origin (donor) with some hybridization with F$_4$TCNQ
 while the band above the Fermi level
is of F$_4$TCNQ origin (acceptor) with some hybridization with TMP. The bands
are narrow and only show dispersion along paths where the $k_x$
coordinate is changing (for a visualization of the $k$ path, see
Fig.~\ref{fig:briZones}). This indicates that the system is very
one-dimensional along the {\bf a} direction which is the stacking
direction (compare Fig.~\ref{fig:structures}). The GGA band gap is
$E_g= 0.26$\,eV. Correlation effects beyond the GGA approximation,
like local electronic interactions $U$ or nonlocal Coulomb
correlations $V$, have not been included in the calculations and could
play a role in the estimation of the band gap. However, the DFT (GGA)
results should be reliable in providing the trend that TMP-F$_4$TCNQ
has a narrower gap than TMP-TCNQ (see below).

\begin{figure}[htb]
\includegraphics[width=0.45\textwidth]{fig7_tmpf4tcnq_bs}
\caption{Band structure of TMP-F$_4$TCNQ with a DFT gap of $E_g= 0.26$
  eV.}\label{fig:tmpf4tcnq_bs}
\end{figure}

\begin{figure}[htb]
\includegraphics[width=0.3\textwidth]{fig8_Bri_zones}
\caption{Brillouin zone and chosen $k$ path for triclinic
  TMP-F$_4$TCNQ. }\label{fig:briZones}
\end{figure}

In Fig.~\ref{fig:tmpf4tcnqdos} we show the density of states (DOS) for
TMP-F$_4$TCNQ. The effect of the charge transfer is seen in the lowest
unoccupied states  of F$_4$TCNQ which show some degree of hybridization
with the highest occupied states of TMP. Consequently, the highest
occupied states of TMP-F$_4$TCNQ have some admixture of
F$_4$TCNQ/cyano group character, and the lowest unoccupied states have
contributions from TMP.

The charge transfer can be quantified using the charges on the atoms
as obtained from the charge density; these numbers can be corroborated
by integrating parts of the density of states shown in
Fig.~\ref{fig:tmpf4tcnqdos}. Note that both ways to determine the
charge transfer involve different approximations and should not be
expected to give exactly the same result. Analysis of the charge
transfer yields a value of 0.20 electrons per formula unit from TMP to
F$_4$TCNQ. This agrees roughly with 0.24 electrons
F$_4$TCNQ-contribution to the highest occupied, TMP-derived bands of
TMP-F$_4$TCNQ (Fig.~\ref{fig:tmpf4tcnqdos}) and with 0.31 electrons
TMP-contribution to the lowest unoccupied, F$_4$TCNQ-derived
bands. Comparison of this result with the charge transfer obtained
from measurements (previous section) shows a disagreement that will be
discussed below.

\begin{figure}[htb]
\includegraphics[width=0.45\textwidth]{fig9_tmpf4tcnq_comparedos_detail}
\caption{Density of states of TMP-F$_4$TCNQ. The Fermi level is
  indicated by a dashed line. Contributions of TMP are shown in blue,
  of F$_4$TCNQ in red, of the cyano groups in green and of the methoxy
  groups in purple.  }\label{fig:tmpf4tcnqdos}
\end{figure}

We now determine the tight-binding Hamiltonian (compare
eq.~\eqref{eq:hamiltonian}) for the highest occupied and lowest
unoccupied bands of TMP-F$_4$TCNQ.  Fig.~\ref{fig:tmpf4tcnq_tbbs}
shows perfect agreement of the obtained tight-binding bands with the
DFT bands. The values of the tight-binding parameters obtained
from projective Wannier functions are plotted in
Fig.~\ref{fig:tmpf4tcnq_tbpar}. The largest contributions in both  valence
and conduction bands, correspond to
nearest neighbor hoppings between alike molecules along the
stacking {\bf a} direction, what is related to the strong
one-dimensional character of both bands. Note that there are no tight-binding
parameters connecting the two bands. This is a common feature in donor-acceptor systems.

\begin{figure}[htb]
\includegraphics[width=0.45\textwidth]{fig10_tmpf4tcnq_tbbs}
\caption{Tight-binding bands for TMP-F$_4$TCNQ obtained from
  projective Wannier functions (solid line) shown together with the
  result of the DFT calculation.}\label{fig:tmpf4tcnq_tbbs}
\end{figure}

\begin{figure}[htb]
\includegraphics[width=0.45\textwidth]{fig11_tmpf4tcnq_wanniertbpar}
\caption{Tight-binding parameters for TMP-F$_4$TCNQ. No hoppings
  between TMP-derived and F$_4$TCNQ-derived bands are
  found. }\label{fig:tmpf4tcnq_tbpar}
\end{figure}
\subsection{Uniaxial pressure simulation}
Eventually, it would be useful to develop methods to design charge
transfer salts, relying not only on the quantum chemical analysis of
binding energies for the donor and acceptor molecules, but taking into
account also the arrangement of the molecules in a crystal. We now
explore two aspects of the crystal structure that are important for
the charge transfer: The spacing of the donor and acceptor molecules
along the stacking axis and the respective arrangements of the charge distributions on the molecules. For that purpose, we fully relax within density functional theory with the GGA approximation the internal
coordinates of the TMP-TCNQ and TMP-F$_4$TCNQ structures for a small set
of reduced $a$ lattice parameters, thus simulating uniaxial pressure. Such an application of uniaxial
pressure or, alternatively, biaxial tensile strain, as often observed in thin
films\cite{Huth2014a}, could in principle be performed also in
experiment, but this is beyond the scope of the present investigations
and in this work we rather consider these effects as a computer
experiment that could allow us to predict, if application of pressure
may induce small chemical modifications of donor or acceptor molecules
that may be beneficial in the context of optimizing the charge
transfer degree.

We consider here the consequences of uniaxial strain in TMP-F$_4$TCNQ
and also in TMP-TCNQ for comparison. Fig.~\ref{fig:ct} shows the evolution of the
band gap, as well as the charge transfer from TMP to TCNQ in TMP-TCNQ
and from TMP to F$_4$TCNQ in TMP-F$_4$TCNQ as a function of reduced
$a$ lattice parameter; $a_0 = a(P=0)$ corresponds to the $a$ lattice
parameter at ambient pressure. Note that the structures for different
$a/a_0$ where obtained by relaxing the internal coordinates of the complexes within DFT.
For TMP-TCNQ and $a/a_0=1$  the relaxed structure shows only small
differences with respect to the experimental structure. For the calculated
charge transfer in the relaxed structure we obtain an offset of about 0.2 with
respect to the value deduced from the DFT calculations relying on the experimental crystal structure. For TMP-F$_4$TCNQ the corresponding offset is about 0.1. In the representation of the uniaxial strain effects on the charge transfer, shown in Fig.~\ref{fig:ct}(b) the results are normalized to the value calculated for the relaxed structures at zero strain. Interestingly, we find different trends in TMP-TCNQ and TMP-F$_4$TCNQ: In TMP-TCNQ, the charge transfer
increases approximately linearly with compression along $a$, while in
TMP-F$_4$TCNQ it stays constant. For a more detailed analysis, we show
in Fig.~\ref{fig:compress} the densities of states for all values of
the $a/a_0$ ratio. As expected, overall band width increases as a
function of pressure in both cases. However, if we focus on the states
directly below the Fermi level that correspond mostly to the highest
occupied molecular orbitals of TMP, we see an important difference:
While the dispersion corresponding to these states significantly
increases with uniaxial compression in TMP-TCNQ, it remains nearly
unchanged in TMP-F$_4$TCNQ. In the next section we will discuss possible reasons for this different behavior related to the differences in the charge density arrangement of the two compounds.

\begin{figure}[!ht]
\includegraphics[width=0.45\textwidth]{fig12_ct}
\caption{Evolution of band gap (a) and charge transfer (b) from TMP to
  TCNQ (F$_4$TCNQ) as function of uniaxial compression along the
  stacking direction $a$. }\label{fig:ct}
\end{figure}

\begin{figure}[!ht]
\includegraphics[width=0.45\textwidth]{fig13_compress_dos}
\caption{Density of states (DOS) of (a) TMP-TCNQ and (b) TMP-F$_4$TCNQ
  for different degrees of uniaxial compression along the stacking
  direction $a$. }\label{fig:compress}
\end{figure}

\begin{figure}[!ht]
\includegraphics[width=0.45\textwidth]{fig14_charge_comparison}
\caption{Distribution of charges in (a) F$_4$TCNQ, (b) TMP, (c) TCNQ,
  (d) TMP-F$_4$TCNQ and (e) TMP-TCNQ.  Spheres are drawn with volume
  proportional to the excess charge (positive in blue, green and
  negative in yellow and red) on each atom. In (d) and (e), the actual
  alignment of donor and acceptor from the crystal structure is show.
}\label{fig:charges}
\end{figure}

\section{Discussion}
The crystal structure of TMP-F$_4$TCNQ with its simple and clear
stacking arrangement of donor-acceptor molecules gives rise to a
markedly reduced dimensionality of its electronic transport
characteristics. This is confirmed by both, our conductivity
measurements and band structure calculations. The dispersion visible
only along $k_x\parallel${\bf a} is reflected in an appreciable
increase of the conductivity along the stacking axis. This
one-dimensional character is a common phenomenon in CT systems but not
necessarily pronounced in mixed-stack CT. However, we observe that an
almost perfect one-dimensional geometry does not necessarily lead to
an optimized interaction that promotes maximum conductivity. The
semiconductor-like behavior of $\sigma$(T) below room temperature in
TMP-TCNQ is pronounced due to the rather high activation energies. The
conductivity is further limited by the rather small charge transfer,
if one takes into account that high $\sigma$-values should not be
expected for $\rho<$0.4.\cite{salmeronValverde1999}

In order to further analyze the influence of the geometry of the
stacking on the conductivity behavior as well as the role of the
specific acceptor F$_4$TCNQ in more detail, we compare in this section
the electronic properties of TMP-F$_4$TCNQ to
TMP-TCNQ~\cite{TMPTCNQ_mainz,NEXAFS_mainz}.

TMP-TCNQ shows a mixed-stack arrangement like TMP-F$_4$TCNQ
but the low dimensionality is far less pronounced~\cite{NEXAFS_mainz,Kawano2013a}.
 TMP and TCNQ
molecules are tilted against the stacking axis by slightly different
angles, i.e. their planes are less parallel compared to the
TMP-F$_4$TCNQ geometry. Within the stacks, they are shifted along {\bf
  b} and {\bf c} so that the geometrical centers of adjacent molecules
do not coincide when one plane is projected onto another. This shift becomes particularly apparent when comparing the distribution of excess charges viewed along the stacking axis, as is shown in Fig.~\ref{fig:charges}. By introducing the fluor in F$_4$TCNQ a singnificant increase of negative excess charge at the acceptor ring position occurs which seems to act as a strong docking point for the positive excess charge located at the ring close to the methoxy groups of the donor. This leads to a ring-centering effect in the donor-acceptor stacking of TMP-F$_4$TCNQ which has also the consequence of improving the planarity of the F$_4$TCNQ molecule. In TMP-TCNQ the planarity of the TCNQ structure is reduced when compared with
F$_4$TCNQ as the CN groups show stronger twists with respect to the
central ring and even the ring itself is not really planar. From these observations we draw two conclusions relating to the molecular overlap and the associated conductivty, as well as the expected behavior under applied uniaxial pressure along the stacking axis.

First, planarity is generally regarded as a relevant factor for higher
conductivity due to the increase of the molecules' overlap
integrals.\cite{organConduct} The reduced planarity and lateral offest in the ring stacking in TMP-TCNQ is therefor reflected by
significantly reduced conductivity values and the absence of an
observable anisotropy when compared to TMP-F$_4$TCNQ. In fact, the exact room-temperature value(s) of the
conductivity for different directions of a mm-sized TMP-TCNQ single crystal could not be
determined as its resistance exceeded the isolation resistance of our
setup. Nevertheless, we can state an upper limit of about 10$^{-11}$\,S/cm. The fundamental differences between TMP-TCNQ and TMP-F$_4$TCNQ are confirmed by the band structure calculations. TMP-TCNQ bands are narrower and show weak dispersion in all directions. The bandwidth is only 0.1 eV while it is 0.25 eV for TMP-F$_4$TCNQ.

Second, with regard to expected behavior of the charge transfer degree under uniaxial compression, the near-ideal planarity and ring-stacking of TMP-F$_4$TCNQ seems to preclude a significant increase of the donor-acceptor hybridization, as is clearly suggested by the results of the DFT calculations shown in Fig.~\ref{fig:ct}. For TMP-TCNQ, on the other hand, a significant increase of planarity of the acceptor molecules under uniaxial pressure may be expected, as well as possible lateral rearrangements leading to improved ring stacking. In this case, a clear tendency for a growing charge transfer degree should be expected, as is strongly suggested by the DFT calculations. We consider these predictions to be a robust feature despite of the fact that the calculated degrees of charge transfer, in particular for the fully relaxed structures, do not agree very well with the experimental values obtained from analyzing the CN vibration frequency shifts. We conclude this section with some comments in this direction.

Regarding the degree of charge transfer in TMP-TCNQ the CN vibration
showed a frequency shift from 2227 (pure TCNQ) to 2221\,cm$^{-1}$
indicating a charge transfer of 0.14. In this case, the
theoretical analysis of charges, relying on the experimental crystal structure, produced a nearly perfect agreement as
an overall charge transfer of 0.13 from TMP to TCNQ was
found. It agrees roughly with 0.16 electrons TCNQ contribution to the
highest occupied, TMP-derived bands of TMP-TCNQ, and with 0.21
electrons TMP contribution to the lowest unoccupied, TCNQ-derived
bands (experimental structure). In the case of TMP-F$_4$TCNQ the agreement between theoretical
(ca.\ 0.2-0.3) and the extracted values from infrared measurements (0.12)
is not as good. Considering that the absolute CN vibration frequency shifts are rather small, the error margins for the experimentally deduced charge transfer values are about 0.05. In addition, the observed changes in $\rho$ derived from the DFT calculations when allowing for full relaxation, in particular for TMP-TCNQ, indicate that already subtle changes in the crystal structure can lead to substantial changes. Taking this together, the deduced absolute values for the charge transfer degree in the TMP-TCNQ and TMP-F$_4$TCNQ systems have to be considered with caution. However, the predicted uniaxial pressure trends and their rationalization with a view to the stacking arrangement and excess charge distributions provide valuable insight into the somewhat counter-intuitive trends observed when going from TMP-TCNQ to TMP-F$_4$TCNQ. This work has shown that simple arguments that the significantly larger electron affinity of F$_4$TCNQ (ca. 5.2\,eV) in comparison to TCNQ (ca. 4.8\,eV) \cite{organConduct} should lead to an increased charge transfer do not hold. The present comparison also forms an interesting analogy to similar
investigations like the one by Torrance\cite{HMTTF_paper} who contrasted HMTTF-TCNQ with HMTTF-F$_4$TCNQ. In their study the different acceptors led to isostructural CT systems but with very different degrees of charge transfer. As a result HMTTF-F$_4$TCNQ becomes a Mott insulator while HMTTF-TCNQ is an organic metal.
\section{Conclusion}
We have investigated the structural and electronic transport
properties of the new charge transfer compound TMP-F$_4$TCNQ in the
form of single crystals. Both crystal and band structure show a
pronounced reduction of dimensionality as the nearly perfect
geometrical overlap of molecules along the mixed donor-acceptor stacks
leads to a one-dimensional transport characteristics. The predictions
are qualitatively confirmed by the measurement of anisotropic,
semiconductor-like electrical conductivity that is largest in stacking
direction. Based on IR spectroscopy a small charge transfer of about
0.1 was found while theoretical values as well as some
general considerations concerning the maximization of charge transfer
suggest a higher value. In comparison, the related CT complex
TMP-TCNQ, introduced in recent
publications\cite{TMPTCNQ_mainz,NEXAFS_mainz}, shows clear structural
differences. They result result in a more isotropic transport
behaviour with a significant overall reduction of electrical
conductivity owing to the loss of the apparently optimized molecular
overlap found in TMP-F$_4$TCNQ. At the same time our theoretical study on the evolution of the charge transfer degree
in TMP-(F$_4$)TCNQ suggests that for TMP-TCNQ a significant increase under unixal pressure along the stacking axis should occur whereas no such effect is expected for TMP-F$_4$TCNQ. Whether TMP-TCNQ may be a candidate for a pressure-induced neutral-ionic transition has to remain for future resolution.
\begin{acknowledgments}
  We thank V. Solovyeva, R. Rommel, M. Schmidt and S. Bek\"{o} for
  experimental support as well as helpful discussions. This project is
  funded through ``SFB/TR 49'' by the Deutsche Forschungsgemeinschaft.
\end{acknowledgments}


Taekwondo Educational Ctr is located at 3550 W 6th St #207, Los Angeles, CA-90020-2864. An interactive map of it's location is shown below.
You can get step by step driving directions to Taekwondo Educational Ctr.
Please call 213-387-7867 during business hours to contact Taekwondo Educational Ctr.


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Seeking to put God's love into action, Habitat for Humanity of Broward brings people together to build homes, communities and hope. www.habitatbroward.org.


text:
Q: Very slow wifi with new router I recently changed my internet provider and switched from a Sagecom F@st 3890 router to a Hitron CGNV4. I use a Cisco Linksys wireless network adapter to connect to wifi on my elementary OS 5.1 system (based on Ubuntu 18.04).
With the old Sagecom my connection speed was reasonable, but now it is extremely slow. I have 50 Mbps through lan, but I'm lucky to get 5 Mbps through wifi. Other devices (cells, tablets, TV) get around 30 Mbps through wifi.
Nothing changed except the router. What could be the reason for this and can it be fixed?

Add 2
Following the advice given in this other answer, I upgraded my kernel from the default 4.15 to a newer 4.20. It did not help.

Add 1
I came across this question Wifi suddenly extremely slow and tried the accepted answer. It did not help, but I noticed that my /etc/modprobe.d/iwlwifi.conf file contains the following line:
remove iwlwifi \
(/sbin/lsmod | grep -o -e ^iwlmvm -e ^iwldvm -e ^iwlwifi | xargs /sbin/rmmod) \
&& /sbin/modprobe -r mac80211

What does that mean? Is that supposed to be there? (It is).
I tried modifying that file as stated in the answer, but nothing changed.

redpajama_set_name: RedPajamaStackExchange


Dashain / Bada Dashain / Vijaya Dashami is the 15 day long religious festival which is most anticipated & the most auspicious festival in the Nepalese annual calendar, celebrated by Nepalese people throughout the globe. This falls on late September to mid October, right after the monsoon season in Nepal. It is one of the unique & long festival of Nepal .
Throughout the country the goddess Durga is worshiped in all her manifestations. This festival is also known for its emphasis on the family gatherings, as well as on a renewal of community ties. Meet Family and Friends near and far. Dashain is all about forgiveness, kindness & respect, all of which prevails so broken families come together. Cities suddenly seems to empty itself, more people return to their villages. During this season, city rushes to book tickets, bus or plane.
Getting a tika( blessings) from an older person in your family or from relatives or from anyone is the specialty of this festival. Dashain tika begins from the oldest person in your family giving tika to the youngest then the second youngest in the family and so on. Faith, hope, inspiration and blessings, all come alive in Dashain.
One gets to know that Dasain is around the corner when they see kites all over the sky. Flying kites has been a very important part of celebrating Dasain in the country as it is considered to be one way of reminding god not to send rain anymore.
To make this festival more interesting, Bamboo swings are constructed in many parts of the country as a way of celebration. Which is termed as 'ping' in Nepali.
Day 3 Observation of celebration of Fulpati by Kathmandu community.
Day 4 Observation of sacrifice of Goat or chicken on the name of Durga Bhawani.
Upon your arrival in the Kathmandu airport, you will be greeted by Red Carpet Tours and Travels representative and transferred to hotel. After check in, in the evening, there will be a pre-trip discussion, introducing with your Tour guide. You will have an opportunity to ask any questions related to the tour program. You can either take a rest or hang around in the city depending on your interest and time constraint. If you like, you can enjoy with some drinks & can enjoy the evening by flying kites which is the main specialty of this festival….
Today after breakfast, we start a guided sightseeing to historical and spiritual sites in Kathmandu. Some of these landmarks are considered World Heritage Sites that include the historic Kathmandu Durbar Square, the sacred Hindu temple of Pashupatinath, the famous 'Monkey Temple' (Swayambhunath) and Buddhists shrine (Bouddhanath) which is one of the largest Stupas in the world.
In the morning after breakfast, you will be taken for a home stay in the local Nepalese house .In the evening, you will be taken to Kathmandu Durbar Square to observe the government officials Fulpati parade. Â In fulpati, the royal kalash filled with holy water, banana stalks, jamara and sugar cane tied with red cloth is carried by Brahmans on a decorated palanquin under a gold tipped and embroidered umbrella. It is believed that with this the Dashain feasting starts.
On this day, in the morning you will have local breakfast. Then after breakfast, you will observe how Nepalese sacrifice Goat or chicken on the name of Durga Bhawani in the local Nepalese home. Then you will be served with the fresh meats of that cut goat/hen. In the evening you will be given details about the legendry behind these sort of things. Over night in the hotel. On this day, the fervor of worship and sacrifice to Durga and Kali starts. On this day many orthodox Hindus will be fasting. Sacrifices are held in almost every house throughout the day. The night of the eighth day is called 'Kal Ratri', the dark night. Hundreds of goats, sheep and buffaloes & even hens are sacrificed at the temple of Durga Bhawani. The sacrifice continues till dawn. While the puja is being carried out great feasts are held in the homes of common people where large amount of meat are consumed.
After breakfast, you will have the brief discussion about the places to visit on that day. Then after that, you will be taken to Kathmandu Durbar Square in order to visit the temple of Goddess Durga, where you will find many peoples who are awaiting in lengthy line to visit the temple of lord Durga of Taleju Temple. You can take some pictures in between as well. On this day, you will observe the temples of Goddess Durga filled with people from dawn till dusk. Animals mostly black buffaloes are sacrificed to honour  Durga (the goddess of victory & might) to seek her blessing. Not only this, Military bands play war tunes, guns boom and officers with beautifully decorated medals in full uniform stand there. When the function ends, the courtyard is filled ankle deep with blood. On this very day the god Vishwa Karma, the God of creativity is also worshiped. All factories, vehicles, any machinery instruments and anything from which we make a living are worshiped. And in the evening, Nepal Government used to roam around the temple of Naxal Bhagawati, Guheshwari, Kalika Sthan , Bhadrakali, Sankata, Mahankal, Shova Bhagawati, Indrayani ... Overnight at hotel.
On this day, (The tenth day of Dashami),after breakfast, you will be taken to the home of Nepali where you will get an opportunity to observe the festival more closely. You will be able to take blessings from the elder person of that family. In the evening, you can enjoy flying kites or else can swing in the Bamboo swings constructed in many parts of the country as a way of celebration. On this day we take tika and jamara from our elders and receive their blessing. On this day, family members from far off and distant relatives come for a visit as well as to receive tika from the head of the family. This function continues for four days. After four days of rushing around and meeting your relatives Dashain ends on the full moon day, the fifteenth day. In the last day people stay at home and rest. Over night at hotel.
After breakfast, you will drive from Kathmandu for Pokhara .On arrival to Pokhara, you will be served with some refreshment drinks in the hotel.After that you will have some leisure time for exploring the natural beauty of Pokhara. You can have boating in the fewa lake or else you can visit the museum in the mean time as well.
After breakfast you will have full day sightseeing in Pokhara which covers all major places of tourist interest such as Devis's Fall (Natural Water Fall), Gupteshwor Cave, Barahi Temple,Mahendra Cave and visit Mahendra Pul to view the underground Seti River and International Mountain Museum. Boating on Fewa Lake for one hour in the afternoon. Transfer to Hotel for overnight stay.
After breakfast,you will depart for Hemja, one of the peaceful city, located almost 6 K. Meter far away from the beautiful city pokhara. People used to known this village by garden of orange. After staying some more time over there, you will depart for Astam(By driving). You will have lunch in Astam & peaceful walk in the village area. Astam is one of an unspoiled place in natural as well as a cultural aspect located at an altitude of 1600m, some 20km northwest of Pokhara on the base of Annapurna. Where you can enjoy the traditional village life in Nepal is truly based on the Eco friendly concept. Astam represents Sunset Village,the best example of an Eco village in and around Annapurna region where visitors are provided to stay in several cottages are built up and managed in the traditional design using the Eco concept Cottages made by natural method following the true Eco footsteps and sustainable way of living. Â Homestay in Ecovillage Astam provides perfect opportunity to see Annapurna rising and setting over Annapurna as well as bird watching, butterfly photography, walking to traditional villages,etc. Overnight at hotel.
On this day,you will have yoga class in the early in the morning if you like & after breakfast, you will drive back to Kathmandu and transfer to hotel. You will have leisure time for either you can go to the streets of Thamel or else visit some o of the beautiful places like Kathmandu Durbar Square, Patan Dubar Square,etc. Farewell dinner with cultural program in the evening. Overnight at hotel.
Today our airport representative will make a departure transfer to the Kathmandu airport to board international flight for your onward destination. You will depart from Kathmandu to your hometown with mind full of beautiful memories. NOTE: We will customize the itinerary as per the requirement of the customer other than the above. For Trip Cost, please contact us.