Quantum chemical modeling of hydrogen binding in metal-organic frameworks: validation, insight, predictions and challenges.

A detailed chemical understanding of H2 interactions with binding sites in the nanoporous crystalline structure of metal-organic frameworks (MOFs) can lay a sound basis for the design of new sorbent materials. Computational quantum chemical calculations can aid in this quest. To set the stage, we review general thermodynamic considerations that control the usable storage capacity of a sorbent. We then discuss cluster modeling of H2 ligation at MOF binding sites using state-of-the-art density functional theory (DFT) calculations, and how the binding can be understood using energy decomposition analysis (EDA). Employing these tools, we illustrate the connections between the character of the MOF binding site and the associated adsorption thermodynamics using four experimentally characterized MOFs, highlighting the role of open metal sites (OMSs) in accessing binding strengths relevant to room temperature storage. The sorbents are MOF-5, with no open metal sites, Ni2(m-dobdc), containing Lewis acidic Ni(II) sites, Cu(I)-MFU-4l, containing π basic Cu(I) sites and V2Cl2.8(btdd), also containing π-basic V(II) sites. We next explore the potential for binding multiple H2 molecules at a single metal site, with thermodynamics useful for storage at ambient temperature; a materials design goal which has not yet been experimentally demonstrated. Computations on Ca2+ or Mg2+ bound to catecholate or Ca2+ bound to porphyrin show the potential for binding up to 4 H2; there is precedent for the inclusion of both catecholate and porphyrin motifs in MOFs. Turning to transition metals, we discuss the prediction that two H2 molecules can bind at V(II)-MFU-4l, a material that has been synthesized with solvent coordinated to the V(II) site. Additional calculations demonstrate binding three equivalents of hydrogen per OMS in Sc(I) or Ti(I)-exchanged MFU-4l. Overall, the results suggest promising prospects for experimentally realizing higher capacity hydrogen storage MOFs, if nontrivial synthetic and desolvation challenges can be overcome. Coupled with the unbounded chemical diversity of MOFs, there is ample scope for additional exploration and discovery.

Pitfalls in the n-mode representation of vibrational potentials.

Simulations of anharmonic vibrational motion rely on computationally expedient representations of the governing potential energy surface. The n-mode representation (n-MR)-effectively a many-body expansion in the space of molecular vibrations-is a general and efficient approach that is often used for this purpose in vibrational self-consistent field (VSCF) calculations and correlated analogues thereof. In the present analysis, a lack of convergence in many VSCF calculations is shown to originate from negative and unbound potentials at truncated orders of the n-MR expansion. For cases of strong anharmonic coupling between modes, the n-MR can both dip below the true global minimum of the potential surface and lead to effective single-mode potentials in VSCF that do not correspond to bound vibrational problems, even for bound total potentials. The present analysis serves mainly as a pathology report of this issue. Furthermore, this insight into the origin of VSCF non-convergence provides a simple, albeit ad hoc, route to correct the problem by "painting in" the full representation of groups of modes that exhibit these negative potentials at little additional computational cost. Somewhat surprisingly, this approach also reasonably approximates the results of the next-higher n-MR order and identifies groups of modes with particularly strong coupling. The method is shown to identify and correct problematic triples of modes-and restore SCF convergence-in two-mode representations of challenging test systems, including the water dimer and trimer, as well as protonated tropine.

Fantastical excited state optimized structures and where to find them.

The quantum chemistry community has developed analytic forces for approximate electronic excited states to enable walking on excited state potential energy surfaces (PES). One can thereby computationally characterize excited state minima and saddle points. Always implicit in using this machinery is the fact that an excited state PES only exists within the realm of the Born-Oppenheimer approximation, where the nuclear and electronic degrees of freedom separate. This work demonstrates through ab initio calculations and simple nonadiabatic dynamics that some excited state minimum structures are fantastical: they appear to exist as stable configurations only as a consequence of the PES construct, rather than being physically observable. Each fantastical structure exhibits an unphysically high predicted harmonic frequency and associated force constant. This fact can serve as a valuable diagnostic of when an optimized excited state structure is non-observable. The origin of this phenomenon can be attributed to the coupling between different electronic states. As PESs approach one another, the upper surface can form a minimum that is very close to a near-touching point. The force constant, evaluated at this minimum, relates to the strength of the electronic coupling rather than to any characteristic excited state vibration. Nonadiabatic dynamics results using a Landau-Zener model illustrate that fantastical excited state structures have extremely short lifetimes on the order of a few femtoseconds. Their appearance in a calculation signals the presence of a nearby conical intersection through which the system will rapidly cross to a lower surface.

Accelerating and stabilizing the convergence of vibrational self-consistent field calculations via the direct inversion of the iterative subspace (vDIIS) algorithm.

The vibrational self-consistent field (VSCF) method yields anharmonic states and spectra for molecular vibrations, and it serves as the starting point for more sophisticated correlated-vibration methods. Convergence of the iterative, non-linear optimization in VSCF calculations can be erratic or altogether unsuccessful, particularly for chemical systems involving low-frequency motions. In this work, a vibrational formulation of the Direct Inversion of the Iterative Subspace method of Pulay is presented and investigated. This formulation accounts for distinct attributes of the vibrational and electronic cases, including the expansion of each single-mode vibrational wavefunction in its own basis set. The resulting Direct Inversion of the Iterative Subspace method is shown to substantially accelerate VSCF convergence in all convergent cases as well as rectify many cases where Roothaan-based methods fail. Performance across systems ranging from small, rigid molecules to weakly bound molecular clusters is investigated in this analysis.

A Free Energy Decomposition Analysis: Insight into Binding Thermodynamics from Absolutely Localized Molecular Orbitals.

Traditional energy decomposition analysis (EDA) methods can provide an interpretive decomposition of non-covalent electronic binding energies. However, by definition, they neglect entropic effects and nuclear contributions to the enthalpy. With the objective of revealing the chemical origins of trends in free energies of binding, we introduce the concept of a Gibbs decomposition analysis (GDA) by coupling the absolutely localized molecular orbital treatment of electrons in non-covalent interactions with the simplest possible quantum rigid rotor-harmonic oscillator treatment of nuclear motion at finite temperature. The resulting pilot GDA is employed to decompose enthalpic and entropic contributions to the free energy of association of the water dimer, fluoride-water dimer, and water binding to an open metal site in the metal-organic framework Cu(I)-MFU-4l. The results show enthalpic trends that generally track the electronic binding energy and entropic trends that reveal the increasing price of loss of translational and rotational degrees freedom with temperature.

Caught in the act: real-time observation of the solvent response that promotes excited-state proton transfer in pyranine.

Photo-induced excited-state proton transfer (ESPT) reactions are of central importance in many biological and chemical processes. Identifying mechanistic details of the solvent reorganizations that facilitate proton transfer however, is challenging for current experimental and theoretical approaches. Using optical pump THz probe (OPTP) spectroscopy and molecular dynamics simulations, we were able to elucidate the ultrafast changes in the solvation environment for three derivatives of pyranine: the photoacid HPTS, the methoxy derivative MPTS, and the photobase OPTS. Experimentally, we find damped oscillations in the THz signal at short times and our simulations enable their assignment to vibrational energy transfer beatings between the photoexcited chromophore and nearby solvent molecules. The simulations of HPTS reveal strikingly efficient sub-ps energy transfer into a particular solvent mode, that is active near 4 THz, and which can provide the requisite energy required for solvent reorganization promoting proton transfer. Similar oscillations are present in the THz signal for all three derivatives, however the signal is damped rapidly for HPTS (within 0.4 ps) and more slowly for MPTS (within 1.4 ps) and OPTS (within 2.0 ps). For HPTS, we also characterize an additional phonon-like propagation of the proton into the bulk with a 140 ps period and an 83 ps damping time. Thermalization of the solvent occurs on a time scale exceeding 120 ps.

Dynamic signatures of electronically nonadiabatic coupling in sodium hydride: a rigorous test for the symmetric quasi-classical model applied to realistic, ab initio electronic states in the adiabatic representation.

Sodium hydride (NaH) in the gas phase presents a seemingly simple electronic structure making it a potentially tractable system for the detailed investigation of nonadiabatic molecular dynamics from both computational and experimental standpoints. The single vibrational degree of freedom, as well as the strong nonadiabatic coupling that arises from the excited electronic states taking on considerable ionic character, provides a realistic chemical system to test the accuracy of quasi-classical methods to model population dynamics where the results are directly comparable against quantum mechanical benchmarks. Using a simulated pump-probe type experiment, this work presents computational predictions of population transfer through the avoided crossings of NaH via symmetric quasi-classical Meyer-Miller (SQC/MM), Ehrenfest, and exact quantum dynamics on realistic, ab initio potential energy surfaces. The main driving force for population transfer arises from the ground vibrational level of the D1Σ+ adiabatic state that is embedded in the manifold of near-dissociation C1Σ+ vibrational states. When coupled through a sharply localized first-order derivative coupling most of the population transfers between t = 15 and t = 30 fs depending on the initially excited vibronic wavepacket. While quantum mechanical effects are expected due to the reduced mass of NaH, predictions of the population dynamics from both the SQC/MM and Ehrenfest models perform remarkably well against the quantum dynamics benchmark. Additionally, an analysis of the vibronic structure in the nonadiabatically coupled regime is presented using a variational eigensolver methodology.

Adiabatic Molecular Orbital Tracking in Ab Initio Molecular Dynamics.

The ab initio molecular dynamics (AIMD) method provides a computational route for the real-time simulation of reactive chemistry. An often-overlooked capability of this approach is the opportunity to examine the electronic evolution of a chemical system. For AIMD trajectories based on Hartree-Fock or density functional theory methods, the real-time evolution of single-particle molecular orbitals (MOs) can provide detailed insights into the time-dependent electronic structure of molecules. The evolving electronic Hamiltonians at each MD step pose problems for tracking and visualizing a given MO's character, ordering, and associated phase throughout an MD trajectory, however. This report presents and assesses a simple algorithm for correcting these deficiencies by exploiting similarity projections of the electronic structure between neighboring MD steps. Two aspects bring this analysis beyond a simple step-to-step projection scheme. First, the challenging case of coincidental orbital degeneracies is resolved via a quadrupole-field perturbation that nonetheless rigorously preserves energy conservation. Second, the resulting orbitals are shown to evolve adiabatically, in spite of the "preservation of character" concept that undergirds a projection of neighboring steps' MOs. The method is tested on water clusters, which exhibit considerable dynamic degeneracies, as well as a classic organic nucleophilic substitution reaction, in which the adiabatic evolution of the bonding orbitals clarifies textbook interpretations of the electronic structure during this reactive collision.

Infrared signatures of isomer selectivity and symmetry breaking in the Cs+(H2O)3 complex using many-body potential energy functions.

A quantitative description of the interactions between ions and water is key to characterizing the role played by ions in mediating fundamental processes that take place in aqueous environments. At the molecular level, vibrational spectroscopy provides a unique means to probe the multidimensional potential energy surface of small ion-water clusters. In this study, we combine the MB-nrg potential energy functions recently developed for ion-water interactions with perturbative corrections to vibrational self-consistent field theory and the local-monomer approximation to disentangle many-body effects on the stability and vibrational structure of the Cs+(H2O)3 cluster. Since several low-energy, thermodynamically accessible isomers exist for Cs+(H2O)3, even small changes in the description of the underlying potential energy surface can result in large differences in the relative stability of the various isomers. Our analysis demonstrates that a quantitative account for three-body energies and explicit treatment of cross-monomer vibrational couplings are required to reproduce the experimental spectrum.

Spectroscopic Signatures of Mode-Dependent Tunnel Splitting in the Iodide-Water Binary Complex.

The gas-phase vibrational spectrum of the isolated iodide-water cluster ion (I-·H2O), first reported in 1996, presents one of the most difficult, long-standing spectroscopic puzzles involving ion microhydration. Although the spectra of the smaller halides are well described in the context of an asymmetrical ground-state structure in which only one OH group is hydrogen-bonded to the ion, the I-·H2O spectrum displays multiplet structures with partially resolved rotational patterns that are additionally influenced by quantum nuclear spin statistics. In this study, this complex behavior is unraveled with a combination of experimental methods, including ion preparation in a temperature-controlled ion trap and spectral simplification through applications of tag-free, two-color IR-IR double-resonance spectroscopy. Analysis of the double-resonance spectra reveals a vibrational ground-state tunneling splitting of about 20 cm-1, which is on the same order as the spacing between the peaks that comprise the multiplet structure. These findings are further supported by the results obtained from a fully coupled, six-dimensional calculation of the vibrational spectrum. The underlying level structure can then be understood as a consequence of experimentally measurable, vibrational mode-dependent tunneling splittings (which, in the case of the ground vibrational state, is comparable to the rotational energy spacing between levels with Ka = 0 and 1), as well as Fermi resonance interactions. The latter include the hydrogen-bonded OH stretches and combination bands that involve the HOH bend overtones and soft-mode excitations of frustrated translation and rotation displacements of the water molecule relative to the ion. These anharmonic couplings yield closely spaced bands that are activated in the IR by borrowing intensity from the OH stretch fundamentals.

Tuning vibrational mode localization with frequency windowing.

Local-mode coordinates have previously been shown to be an effective starting point for anharmonic vibrational spectroscopy calculations. This general approach borrows techniques from localized-orbital machinery in electronic structure theory and generates a new set of spatially localized vibrational modes. These modes exhibit a well-behaved spatial decay of anharmonic mode couplings, which, in turn, allows for a systematic, a priori truncation of couplings and increased computational efficiency. Fully localized modes, however, have been found to lead to unintuitive mixtures of characteristic motions, such as stretches and bends, and accordingly large bilinear couplings. In this work, a very simple, tunable localization frequency window is introduced, in order to realize the transition from normal modes to fully localized modes. Partial localization can be achieved by localizing only pairs of modes within this traveling frequency window, which allows for intuitive interpretation of modes. The optimal window size is suggested to be a few hundreds of wave numbers, based on small- to medium-sized test systems, including water clusters and polypeptides. The new sets of partially localized coordinates retain their spatial coupling decay behavior while providing a reduced number of potential energy evaluations for convergence of anharmonic spectra.

Automatic Selection of Partitioning Variables for Small Multiple Displays.

Effective small multiple displays are created by partitioning a visualization on variables that reveal interesting conditional structure in the data. We propose a method that automatically ranks partitioning variables, allowing analysts to focus on the most promising small multiple displays. Our approach is based on a randomized, non-parametric permutation test, which allows us to handle a wide range of quality measures for visual patterns defined on many different visualization types, while discounting spurious patterns. We demonstrate the effectiveness of our approach on scatterplots of real-world, multidimensional datasets.

Structural progression in clusters of ionized water, (H2O)n=1-5(+).

Ionized water clusters serve as a model of water-splitting chemistry for energetic purposes, as well as postradiolytic events in condensed-phase systems. Structures, properties, and relative energies are presented for oxidized water clusters, (H2O)n=1-5(+), using equation-of-motion coupled-cluster theory approaches. In small clusters, an ion-radical contact pair OH···H3O+ is known to form upon ionization. The transition from n = 4 to n = 5 molecules in the cluster, however, is found to demarcate a size regime in which a propensity for the ion and radical to separate exists. This trend is consistent with recent experimental vibrational analyses. Decomposition of the cluster energetics reveals that preferential solvation of the hydronium cation by water serves as the dominant driving force for this pair separation, which should persist in larger clusters and bulk water ionization.

Four Experiments on the Perception of Bar Charts.

Bar charts are one of the most common visualization types. In a classic graphical perception paper, Cleveland & McGill studied how different bar chart designs impact the accuracy with which viewers can complete simple perceptual tasks. They found that people perform substantially worse on stacked bar charts than on aligned bar charts, and that comparisons between adjacent bars are more accurate than between widely separated bars. However, the study did not explore why these differences occur. In this paper, we describe a series of follow-up experiments to further explore and explain their results. While our results generally confirm Cleveland & McGill's ranking of various bar chart configurations, we provide additional insight into the bar chart reading task and the sources of participants' errors. We use our results to propose new hypotheses on the perception of bar charts.

Arc length-based aspect ratio selection.

The aspect ratio of a plot has a dramatic impact on our ability to perceive trends and patterns in the data. Previous approaches for automatically selecting the aspect ratio have been based on adjusting the orientations or angles of the line segments in the plot. In contrast, we recommend a simple, effective method for selecting the aspect ratio: minimize the arc length of the data curve while keeping the area of the plot constant. The approach is parameterization invariant, robust to a wide range of inputs, preserves visual symmetries in the data, and is a compromise between previously proposed techniques. Further, we demonstrate that it can be effectively used to select the aspect ratio of contour plots. We believe arc length should become the default aspect ratio selection method.

An extension of Wilkinson's algorithm for positioning tick labels on axes.

The non-data components of a visualization, such as axes and legends, can often be just as important as the data itself. They provide contextual information essential to interpreting the data. In this paper, we describe an automated system for choosing positions and labels for axis tick marks. Our system extends Wilkinson’s optimization-based labeling approach to create a more robust, full-featured axis labeler. We define an expanded space of axis labelings by automatically generating additional nice numbers as needed and by permitting the extreme labels to occur inside the data range. These changes provide flexibility in problematic cases, without degrading quality elsewhere. We also propose an additional optimization criterion, legibility, which allows us to simultaneously optimize over label formatting, font size, and orientation. To solve this revised optimization problem, we describe the optimization function and an efficient search algorithm. Finally, we compare our method to previous work using both quantitative and qualitative metrics. This paper is a good example of how ideas from automated graphic design can be applied to information visualization.

Vispedia: interactive visual exploration of wikipedia data via search-based integration.

Wikipedia is an example of the collaborative, semi-structured data sets emerging on the Web. These data sets have large, non-uniform schema that require costly data integration into structured tables before visualization can begin. We present Vispedia, a Web-based visualization system that reduces the cost of this data integration. Users can browse Wikipedia, select an interesting data table, then use a search interface to discover, integrate, and visualize additional columns of data drawn from multiple Wikipedia articles. This interaction is supported by a fast path search algorithm over DBpedia, a semantic graph extracted from Wikipedia's hyperlink structure. Vispedia can also export the augmented data tables produced for use in traditional visualization systems. We believe that these techniques begin to address the "long tail" of visualization by allowing a wider audience to visualize a broader class of data. We evaluated this system in a first-use formative lab study. Study participants were able to quickly create effective visualizations for a diverse set of domains, performing data integration as needed.

Visualization of heterogeneous data.

Both the Resource Description Framework (RDF), used in the semantic web, and Maya Viz u-forms represent data as a graph of objects connected by labeled edges. Existing systems for flexible visualization of this kind of data require manual specification of the possible visualization roles for each data attribute. When the schema is large and unfamiliar, this requirement inhibits exploratory visualization by requiring a costly up-front data integration step. To eliminate this step, we propose an automatic technique for mapping data attributes to visualization attributes. We formulate this as a schema matching problem, finding appropriate paths in the data model for each required visualization attribute in a visualization template.