Papers

We consider a stochastic process on $\mathbb{Z}^d$ for $d \geq 1$. Given a translation invariant and ergodic starting configuration of finite clusters, each cluster $C$ performs a continuous time simple random walk with rate $|C|^{-\alpha}$. If it attempts to move to a vertex occupied by another cluster, it does not move, and instead the two clusters connect via a new edge. In all dimensions, we show that if $\alpha\ge 0$, there is almost surely no spontaneous creation of an infinite cluster within finite time. Moreover, for any $\alpha\le-1-2/d$ there is a finite-time blowup almost surely. In the regime $\alpha\in(-1,0)$ we show that the behavior greatly depends on the initial configuration. In addition, in dimension one, we establish the exact phase diagram.

Studies of anions are inherently more challenging than investigations of neutrals and cations because of the diffuse and weakly bound character of an anionic electron. Here, we present a comprehensive computational examination of ground-state diatomic molecular anions composed of alkali-metal (Li, Na, K, Rb, Cs, Fr) and alkaline-earth-metal (Be, Mg, Ca, Sr, Ba, Ra) atoms. We study 21 alkali-metal diatomic anions in the X$^{2}\Sigma^{+}$ electronic state and 36 alkali-metal–alkaline-earth-metal diatomic anions in the X$^{1}\Sigma^{+}$ electronic state. The calculations employ a hierarchy of the coupled cluster methods, combined with large Gaussian basis sets and small-core relativistic energy-consistent pseudopotentials for heavier elements. We compute potential energy curves, permanent electric dipole moments, and static polarizabilities, and we assess convergence and uncertainties of our results. Additionally, using the multireference configuration interaction and equation-of-motion electron-attachment coupled cluster methods, we investigate excited electronic states of alkali-metal molecular anions, including valence-bound and dipole-bound states. We predict crossings between ground neutral and excited anionic states, which may enhance resonant electron attachment and subsequent anion dissociation. This finding may be relevant for experiments with mixtures of ultracold ground-state alkali-metal molecules and Rydberg atoms.

Polaron ground states and finite-temperature dynamics remain challenging to simulate because existing methods struggle to combine nonperturbative accuracy, systematic improvability, and scalability from models to materials-specific Hamiltonians. We introduce a translationally invariant variational coupled-cluster (CC) theory for polarons, termed delocalized CC (dCC), with closed-form energies at cost as low as $\mathcal{O}(N^3)$ and no phonon-number cutoff. dCC accurately describes the ground states of the one- and two-dimensional Holstein and Su–Schrieffer–Heeger (optical and bond) models and the Fröhlich model, in close agreement with density matrix renormalization group (DMRG) and diagrammatic Monte Carlo benchmarks. A projected tangent-space response formalism built on the same ansatz yields electron-addition spectral functions and optical conductivities at zero and finite temperature. The resulting spectra agree well with DMRG, Lanczos, and neural-network quantum-state benchmarks while retaining a physically interpretable excitation hierarchy, and extend to two-dimensional lattices at finite temperature beyond the practical reach of these methods. The same framework applies directly to ab initio electron–phonon matrix elements, yielding LiF electron- and hole-polaron binding energies that match state-of-the-art many-body calculations. These results establish dCC as a unified variational framework for polaron ground states and dynamics, from model systems to real materials.

CheMLFlow is an open-source platform for building and executing end-to-end, high-throughput, and agentic workflows for scientific and technological applications. CheMLFlow targets a common bottleneck in scientific machine learning development, where researchers often need to assemble data acquisition, curation, representation, model training, validation, screening, interpretation, and reporting into a reproducible pipeline, even when their primary research contribution concerns only one stage. CheMLFlow provides modular workflow components, ready-to-run reference pipelines, standardized artifacts, and evaluation outputs that reduce orchestration overhead and support benchmarking across methods and datasets. The platform is designed to be extensible, reproducible, and automation friendly, with pluggable representations and models, deterministic splits, explicit run artifacts, batch execution, and report generation. As scientific software increasingly moves toward agent assisted experimentation, CheMLFlow's configuration driven workflows and structured outputs also provide a practical interface for coding agents to help users construct experiments, inspect results, and summarize findings under human supervision. This article describes the system architecture, core workflows, and benchmarks that reach literature performance for quantum mechanical, physicochemical and bioactivity property prediction, and use cases involving time series datasets demonstrating applications beyond molecular chemistry datasets.

We present a statistical-mechanics framework for computing equilibrium binding constants $K$ in the dilute limit. From first principles, we derive a general expression relating $K$ to the relative populations of the bound and unbound states. Its transparency has twofold advantage: it makes the origin of the unbound-state volumetric term explicit, and it allows one to track exactly how an imposed volume restraint propagates through the expression. This makes $K$ directly computable, as restrained simulations can account for the volumetric contribution exactly, under the physically mild assumption of a homogeneous unbound state. The resulting estimators are computable from histograms of any suitably defined reaction coordinate, and determine unambiguously how the boundaries of the thermodynamic states of interest must be defined. We apply our framework to the cucurbit[7]uril/1-adamantanol host–guest complex and the galactonate–DgoT ligand–protein complex. Our results show that commonly used single-bin estimators depart from the theoretically correct one by $\approx 1$~kcal/mol in both systems. This shift originates in the definition of the bound state: by anchoring that definition to what state-of-the-art experiments resolve, the theory turns it from a hidden assumption into a controlled input, and provides a principled route to absolute binding affinities from molecular simulations.

Pericyclic reactions provide stringent tests for quantum simulations because their mechanisms are governed by orbital symmetry and involve correlated transition states. In this work, we employ the variational quantum eigensolver (VQE) combined with a previously established symmetry-guided active-space selection protocol based on symmetry-matched fractions (SMF-VQE) to simulate Diel-Alder and Alder-ene reactions in complex systems involving extended pi-conjugation and multiple bonding. Although absolute electronic energies obtained from the current protocol exhibit significant deviations from the values computed using CCSD method, the symmetry-guided active spaces yield substantial cancellation of deviations in the energy differences. As a result, reaction energies are predicted with error (relative to CCSD) less than one kcal per mol, while activation energies are reproduced within about five to six kcal per mol. The symmetry-guided protocol also reduces the large combinatorial space of active-space choices to a single symmetry-consistent selection for each reaction.

We investigated strong-field dissociative ionization of $\mathrm{CF_2I_2}$ ensembles prepared in different initial rotational-state distributions using an electrostatic deflector. Pronounced changes in ion-channel branching ratios revealed a strong dependence of the fragmentation dynamics on the initial rotational excitation. Analysis of fragment yields and their laser-power dependences identifies resonance-enhanced multiphoton ionization through an intermediate excited state, $\mathrm{CF_2I_2^{\ast}}$. The measured branching behavior indicates competition between stabilization into bound ionic states and dissociative channels, driven by near-threshold non-adiabatic Coriolis-type coupling. Tuning the rotational energy by only a few $\mu$eV is sufficient to significantly alter the ionization dynamics and to redistribute the reaction products. These findings demonstrate the key role of rotational excitation in controlling non-adiabatic dynamics following strong-field ionization of $\mathrm{CF_2I_2}$.

Stark spectroscopy is a powerful method for probing molecular dipole moment changes, charge transfer dynamics, and polarizability under applied electric fields. Time-Resolved Terahertz Stark Spectroscopy (TRTSS), which employs intense single-cycle terahertz (THz) pulses to induce transient Stark shifts, overcomes key limitations of conventional approaches. Unlike static or low-frequency fields, THz pulses oscillate much faster than typical molecular rotation times, effectively preventing dipole reorientation and enabling measurements in solutions at ambient conditions. Here, we extend TRTSS to molecules dissolved in water, the most important polar solvent for chemical and biological systems and report the first demonstration of Stark spectroscopy in water at room temperature. Using Malachite Green and Methyl Orange as model systems, we observe clear THz-induced spectral modulations, demonstrating that TRTSS can successfully reveal THz Stark responses even in highly polar, hydrogen-bonded environments. Measured signals exhibit a combination of linear (dipole-driven) and quadratic (polarizability-driven) Stark effects in both systems, consistent with time-dependent density functional theory (TD-DFT) calculations. Comparison with TD-DFT further suggests that conformational effects can influence the extracted Stark parameters in solvated molecules.

Optically addressable solid-state spin defects have emerged as powerful multimodal quantum sensors, with nitrogen-vacancy (NV) centers in bulk diamond providing benchmark quantum control and sensitivity under ambient conditions. Embedding such defects in nanodiamonds (NDs) extends these capabilities to mobile probes capable of accessing complex biological and nanoscale environments. Reduced dimensions, however, introduce constraints beyond volumetric spin impurities, notably enhanced lattice strain and surface-induced noise sources, which shorten NV spin relaxation times (T1 and T2) and destabilize the NV charge state, as well as resulting in pronounced particle-to-particle variability in NDs typically produced by top-down approaches. These effects complicate both sensing performance and the quantitative interpretation of multimodal signals in realistic environments. This article provides a structured perspective on the physical mechanisms by which material properties constrain NV behavior in NDs, together with mitigation strategies that shape the robust use of these mobile quantum sensors for biosensing and nanoscale science.

We investigate how molecular orbitals used as the basis of wave function expansion and how operator coefficient-based and locality-based Hamiltonian truncation affects the computational cost of Trotter decomposition-based Hamiltonian simulation in one-dimensional hydrogen chain systems. The analysis is performed using both Hartree–Fock canonical molecular orbitals (CMOs) and Pipek–Mezey-based localized molecular orbitals (LMOs). For short hydrogen chains, we evaluate the ground-state energy and fidelity and find that, in the CMO-based wave function expansion, introducing a threshold on Hamiltonian coefficients is effective in reducing the gate cost while maintaining computational accuracy. In contrast, in the LMO-based wave function expansion, operator locality-based Hamiltonian truncation is found to be more effective. By fitting the relationship between the truncation threshold and the ground-state energies and fidelities with empirical formulas, we estimate the threshold values required to achieve high fidelity ($F \ge 0.99$) in the ground-state wave function. Using the estimated thresholds, we then perform quantum gate resource estimation for longer hydrogen chains up to H$_{100}$. The results suggest an exponential advantage of the LMO-based wave function expansion with Hamiltonian truncation: the number of quantum gates required for Hamiltonian simulation grows polynomially when the CMO-based wave function expansion with operator coefficient-based Hamiltonian truncation is adopted, whereas it grows polylogarithmically when the LMO-based wave function expansion is combined with operator locality-based Hamiltonian truncation. These results provide useful guidelines for choosing orbital representations and Hamiltonian truncation strategies in large-scale quantum chemical simulations.

Gaussian wavepacket (GWP) methods are prevalent means of solving the nuclear time-dependent Schrodinger equation (TDSE) on classical computers. They consist of representing the nuclear wave function as a superposition of Gaussians. Here, we present a variational hybrid continuous-variable discrete-variable (CV-DV) algorithm for simulating adiabatic nuclear dynamics on qubit-oscillator quantum hardware. It encodes a superposition of frozen Gaussians (FGs) onto the qubit-oscillator register and evolves it according to the time-dependent variational principle (VP). We test two variants of the approach, one that evolves a single FG and another that evolves a superposition of FGs, on a set of prototypical 1D harmonic and anharmonic systems. We simulate the photoexcited state dynamics of SO2 using the single FG variant of the algorithm and compute its autocorrelation function on physical quantum hardware. For harmonic and Morse potentials, the variant evolving the superposition of FGs converges to the numerically exact solution as the number of Gaussians increases. In the case of the double-well potential, the algorithm simulates wavepacket bifurcation and recurrence correctly, and the ensuing irregular dynamics moderately well. Overall, this work establishes a pathway for simulating molecular dynamics on noisy intermediate-scale quantum devices.

In this work, we derive closed-form expressions for multi-time correlation functions underlying higher-order nonlinear spectroscopic response functions within the harmonic approximation. Our method includes displacements, frequency changes, and Duschinsky rotation between the vibrational modes of different electronic states while retaining polynomial scaling with the number of degrees of freedom. Finite temperature is accounted for without summation over vibrational eigenstates. To show the capabilities of our method, we apply it to calculate fifth-order two-dimensional resonance Raman (2DRR) spectra of two-mode model systems and naphthalene. Comparison with the displaced harmonic oscillator model shows that Duschinsky rotation modifies the positions and relative intensities of diagonal and cross peaks. Overall, our results demonstrate that 2DRR spectroscopy is particularly sensitive to changes in normal coordinates between electronic states and can provide distinct signatures of Duschinsky coupling in molecular systems.

The quality of multi-scale modelling techniques in molecular electronic structure calculations, such as embedding and subspace methods, relies upon the chosen active space. The automation of active space selection is vital for ensuring the accuracy, reproducibility, and scalability in such calculations. In this work, we introduce Tensor Network Active Space Selection using the Entanglement Feature. Through the isolation of strongly correlated electrons, this method provides a scalable foundation for embedding methods in multi-scale modelling. By representing the purities of all possible orbital partitions as a Matrix Product State, our method isolates regions of strong electron correlation without requiring manual preselection of target atoms or the calculation of expensive high-order density matrices. The results demonstrate that this approach leads to lower ground state energies and more accurate dipole moments than other fully automated selection schemes such as those based solely on single-orbital entropy or the selection of spatial orbitals around the HOMO/LUMO gap.

We develop a thermodynamic theory of electric double layers in binary liquid mixtures by allowing the Stern-layer capacitance to depend on the local solvent composition. This coupling produces an additional negative contribution to the inverse differential capacitance. As a result, the surface potential can become a nonmonotonic function of the surface charge density, leading to negative differential capacitance and a voltage-induced first-order transition between two electric-double-layer states. We determine the coexistence condition using a common-tangent construction for the surface-charge-controlled grand potential and obtain phase diagrams in terms of the Stern-capacitance contrast, surface charge density, bulk composition, and surface potential. We also compare the theory with capacitance data for tetrabutylammonium chloride in water/1-propanol mixtures, finding semi-quantitative agreement in the continuous-response regime. These results suggest that solvent exchange inside the Stern layer can strongly control the capacitance and interfacial phase behavior of binary mixtures.

Simulating multidimensional quantum systems at finite temperature is inherently challenging as the system is no longer described by a single, pure-state wavefunction but by a density operator, squaring an already exponential scaling of the Hilbert space. Building upon the compact wavefunction ansatz of the multi-layer multiconfiguration time-dependent Hartree (ML-MCTDH) method, we present a new scheme for simulating finite-temperature quantum dynamics based on purification. Here, a density operator is mapped to a single ML-MCTDH wavefunction in an enlarged Hilbert space, comprising physical and auxiliary degrees of freedom. In the key step, one obtains a pure-state representation of the canonical density operator via imaginary time-propagation of the infinite-temperature state. The most important observation is that this state can be exactly decomposed as a Hartree product of maximally entangled combined modes, each combined mode consisting of a physical degree of freedom and its auxiliary counterpart. Through dynamically pruning the node ranks of the ML-tree during the "cool down" stage yields a compact finite-temperature wavefunction, thus accelerating the real-time propagation and enabling finite-temperature simulations of multidimensional, correlated molecular systems. Our method circumvents both intensive statistical sampling and costly tensor-decomposition of the full density-operator, while being broadly applicable to model Hamiltonians and general ab initio potential energy surfaces alike. Two applications of the method are presented, benchmark results on the thermal ground-state of H2O as well as temperature-dependent infrared absorption spectra of the more challenging, floppy H3O2- anion.

Self-consistent field real-time electronic structure methods are a powerful approach for modeling ultrafast processes but suffer from systematic errors in predicted transition energies, commonly known as peak shifting, that obscure direct comparison with experiment. Although this effect has been explored in single reference methods, a general understanding that extends to multiconfigurational methods remains unresolved. Here, we develop a real-time nonorthogonal multiconfigurational self-consistent field (RT-TD NOMCSCF) formalism in which independently propagated orbital sets generate a compact, nonorthogonal wavefunction. The approach establishes a unified framework for nonlinear real-time electronic structure theories, which we use to reveal the common origin of peak shifting across single and multireference limits. Using this framework, we demonstrate that peak shifting does not arise exclusively from the effect of state averaging over the internal space basis, but also from the accessible external configurational space. By systematically expanding the internal space with independently propagated orbital sets, RT-TD NOMCSCF suppresses this aver- aging, recovers correct transition energies, and distinguishes intrinsic peak shifting from numerical peak drifting caused by propagation errors. Thus, these developments establish nonlinear real-time electronic structure methods that enables more accurate simulations of ultrafast processes.

Enhanced sampling techniques are central to the study of statistically rare events in the computer modeling and simulation of molecular phenomena. In this work, we report the development and integration of a Gaussian process model, adaptive, uncertainty-driven sampling scheme for enhanced sampling. The framework trains a Gaussian process model on an iteratively improving estimate of the free energy landscape. Regions of high uncertainty within the reaction phase space are increasingly sampled, and the uncertainty is computed on-the-fly during free energy reconstruction, serving as a convergence metric. This approach provides a generalizable strategy that can be extended to complex molecular processes.

A vast class of weak, millimolar-affinity molecular interactions governs cellular function, yet their quantitative characterization has remained largely beyond conventional methods. For over a century, biochemistry has worked within a concentration-based framework where molarity scales with molecular number per volume (N/V), and experiments have usually, often implicitly, changed concentration by moving N while holding V fixed. The weak-interaction measurement bottleneck arises from this paradigm: reading weak binding through bulk concentration requires concentrations beyond practical limits, a framework constraint rather than one of instrumental sensitivity. Here we show that shifting experimental control from N to accessible volume V overcomes this bottleneck and opens previously intractable affinity ranges through nanoscale spatial confinement. Controlling V means controlling what biochemists have called "local concentration" and "proximity effects," recasting these long-ambiguous notions as quantitative variables grounded in first principles. Implemented in DNA nanocavities, the approach showed that geometric arrangement alone can override solution-phase binding hierarchies. The same spatial control quantified a protein-peptide interaction of order 10 mM from femtomoles per well, totalling under a picomole per titration. Even so, a standard plate reader gave a signal-to-noise ratio near 10^3, leaving headroom for still weaker interactions. The affinity-and-geometry readout also enabled rational screening for protein-protein-interaction modulators, identifying compounds that enhance weak associations by reweighting local encounters rather than binding tightly on their own or forming a stable ternary complex. Together, this volume-based paradigm and its implementation provide a general strategy for probing and modulating previously inaccessible biochemical phenomena.

Chemical kinetics has long inferred local molecular behaviour through the flask-and-molarity pairing, where well-mixed concentrations serve as the experimental readout. Yet many biological reactions occur in structured environments. Researchers have long recognized that concentration may not carry the same operational meaning in such environments, but even local concepts such as effective molarity usually translate local effects back into a single value with units of concentration. What has been missing is the complementary path: a bench-compatible way to make local structure an experimental variable, rather than only a correction to molarity. Here we show a chemistry-geometry crossover that the flask-and-molarity interface could not make visible. In the micromolar-or-weaker affinity regime, inhibition can switch sharply out of the familiar concentration-and-affinity mode: chemical binding strength no longer determines the response, and the shape of the target's local space does. A bench-compatible interface made this switch measurable by separating bulk dose from local geometry. This blind spot arose from the hidden premise that macroscopic pooling makes a structured local state readable as a single local concentration. The chemistry-geometry crossover breaks that premise: in a structured target environment, a macroscopic assay can remain sensitive to the probability distribution of local states, so collapsing that distribution to one concentration-valued number removes the geometric control axis from the readout. By preserving that axis in the experiment, the interface bypasses molarity's hidden bottleneck and provides a routine experimental route to remeasure and reinterpret molecular interactions in structured space.

In this paper, we examine transcomplex recombination RCs$^+$ + Br$^-$ $\to$ CsBr + R (R = Kr, Xe, Hg) for collision energies from 0.1 to 2.5 eV. Within the framework of the quasiclassical trajectory method on semiempirical diabatic potential energy surfaces, we have considered the existence regions for recombination in the space of kinematic parameters. Two-dimensional "slices" of the existence regions for recombination (on the sphere where the coordinates are the orientation angles of the initial direction of the axis of the ionic complex RCs$^+$) sometimes exhibit a chaotic structure. We have proposed a quantitative measure of chaoticity of two-dimensional existence regions for recombination (on the basis of the combinatorics of matrices of zeros and ones) and have presented examples of chaotic regions. We have introduced the surroundings index of recombinative trajectories and have explored its connection with the integration time of the trajectory and with the total internal energy of the product molecule CsBr.

The committor is the optimal reaction coordinate for a rare transition: it pinpoints the transition state and fixes the rate, and it governs events from protein folding to crystal nucleation. It minimises a Dirichlet energy, whose value at the minimum is the reactive flux, over functions that vanish on the reactant state and equal one on the product state. In high dimensions such a trial space is very hard to build. Here we rewrite the variational principle so that the boundary conditions are replaced by a normalisation of one boundary observable, the fidelity. Any trial function is then admissible, including functions that cannot satisfy the boundary values at all. On this basis we estimate the high-dimensional committor and rates from one-dimensional profiles along projected coordinates, taking as input only pre-existing equilibrium or reweighted configurations, a diffusion constant estimate, and the two state definitions. The optimum has a closed form that is cheap to evaluate. We obtain committors for AIB9 and villin HP-35 in full torsion space, and folding and unfolding rates for chignolin from umbrella sampling alone.

Pseudomode approaches allow for an exact and unapproximated description of a quantum system interacting arbitrarily strongly with a bath. In general, a system coupled to pseudomodes will not thermalize to the system's Gibbs state: This is to be expected when the system-bath coupling is non-perturbative, but conflicts with common thermodynamic intuition when the system-bath coupling is asymptotically weak. We explore under which circumstances pseudomode models satisfy detailed balance (and subsequently thermalize to the system Gibbs state) and how specific choices of parameters can force "weak" detailed balance that is restricted to a limited frequency range. A combination of Hermitian and non-Hermitian pseudomodes that yields a flat effective-temperature profile is also considered. The results and criteria established here are relevant for the construction of pseudomode models in contexts where thermodynamic consistency is required.

Proton exchange membrane water electrolysis (PEMWE) is a promising technology for harnessing intermittent renewable energy. This study experimentally investigates the degradation of PEMWE under fluctuating power supply, characterized by dynamic load cycling under accelerated stress test (AST). We focus on the effects of key parameters of dynamic loading, including the peak voltage and cycling frequency, in a set of simplified AST protocols designed to represent selected features of dynamic load fluctuations associated with variable renewable-energy operation. The results unveil the intricate relationship between the structural characteristics of the catalyst layer and the electrochemical performance. An elevated peak voltage accelerates the degradation in the initial phase of the AST. However, a low cycling frequency can mitigate the degradation by limiting the rise in various resistance forms, whereas a higher cycling frequency exacerbates the degradation primarily by increasing mass transport resistance, suggesting a frequency-sensitive deterioration of the system's components.

Solar-to-fuel conversion can benefit from photoelectrodes with engineered light-matter interactions, yet most nanostructured designs provide limited control over the spatial and spectral distribution of photochemical activity. Here, we present an all-dielectric amorphous-silicon metasurface photoelectrode that confines resonant light-matter interactions within a 220-nm-thick active layer. Tunable Mie-type and guided-mode resonances spectrally encode chemical reactivity and produce absorptance above 80% near the silicon band edge, compared with less than 30% for an unpatterned film of the same thickness. The metasurface simultaneously functions as the light absorber, carrier-transport layer, and catalytic interface without an added co-catalyst or engineered passivation layer. Operando photo-scanning electrochemical microscopy reveals wavelength- and structure-dependent redox activity and a tenfold enhancement in internal quantum efficiency near the silicon band edge relative to planar films. Power-dependent measurements support a photon-driven rather than nonlinear photothermal origin of the enhancement, while surface-sensitive ultrafast transient-reflectivity measurements probe the underlying carrier dynamics. Light-coupled scanning electrochemical cell microscopy further shows hydrogen-evolution enhancements of up to 21-fold under photocatalytic conditions and 15-fold under photoelectrochemical bias, corresponding to 11.2-fold and 7.7-fold enhancements after accounting for the estimated surface-area increase. The metasurfaces remain stable during more than 10 hours of immersion and prolonged laser illumination. These results establish amorphous silicon as a stable and versatile platform for resonantly programmed photocatalysis and solar-fuel generation.

This book has one primary goal: To get you moving quickly from learning basic principles of colloid science, to designing colloidal systems for function or motion in the lab. It is not intended to provide encyclopedic knowledge about all aspects of colloid and surface science; rather, I have chosen not to include many topics of genuine importance. In reaching the intended goal, I use two parallel strategies. First, I give practical results that can be used immediately. If there is a cumbersome calculation, I have worked to reframe it into a table or figure. This is the case for Hamaker constants and hydrodynamics of spheroids, for instance. Second, I describe the physics of various colloidal phenomena, so that you as a researcher can think about alternative strategies. In balancing algorithms with explanations, I provide plug-and-chug example problems to familiarize you with units, constants, and typical values. The practice problems provide extensions to the most basic theory that open new possibilities, while also giving results that are useful in practical and research studies. Throughout the book, I provide data we commonly use for viscosities, zeta potentials, ionic phenomena, and other parameters. Rather than providing every reference and every technique, I have provided those references and techniques that we most often use in our lab. In the end, this book aims not to be an exhaustive study of colloids, but rather to be a doorway to producing desired colloidal systems as quickly as possible.

In spite of recent advances, quantum computers are expected to be sufficiently noisy in the coming few years to the extent of limiting quantum chemical calculations to relatively small number of orbitals. However, even with reasonable quality single particle basis sets, small active spaces with limited orbitals can result in a significant fraction of correlation energy being lost, motivating the design of moderate quality qubit-efficient basis sets for quantum algorithms. We begin by reoptimizing the existing minimal basis sets using a genetic algorithm-inspired approach in conjunction with aggressive refinement strategies, and generate modified minimal basis sets (MSTO-kG basis; k = 2-11) for atoms from H through F. The ground state energies of H through F using our MSTO bases at FCI level of theory yield ground state energies that are comparable or sometimes even lower than those obtained using 6-31G basis sets. In the case of Li, the MSTO bases surpass the performance of cc-pVQZ bases. Thus, we obtain better atomic energies with same number of qubits relative to STO bases, and better/comparable energies with fewer qubits relative to higher quality bases. In the case of molecules, H2 performs poorly; a finding that is consistent with an earlier work in literature. For other molecules, Li2, C2, LiH, BeH and BeH2, the FCI results (except C2 for which we employ CISD) from our bases are comparable to/outperform those from 6-31G basis. Finally, we compare the resources required between different bases and find that MSTO bases yield better energies than the competing basis sets while incurring fewer qubits and two-qubit gates with VQE, QPE, and HHL. The logical T-gate counts are also found to be considerably lower for QPE and HHL respectively. Overall, our work paves way for more accurate yet less qubit-hungry quantum chemical calculations using near-term quantum computers.

I derive the impedance response of an ideal electrolyte containing an arbitrary number of mobile ionic species between blocking planar electrodes, described by the Poisson–Nernst–Planck equations. By transforming the linearized equations to a charge–salt basis, the response is written in terms of a multi-component diffusion–migration matrix and its eigenvalues/eigenvectors. When all diffusivities are equal, the charge mode decouples from the neutral concentration subspace and the classical binary-electrolyte result is recovered. In contrast, unequal diffusivities couple charge relaxation to one or more neutral composition modes. For a ternary electrolyte with two cations and one anion, this coupling produces additional diffusive features and broadens the crossover between resistive and capacitive regimes. The results found in this paper provide a minimal continuum explanation for why mixed electrolytes can display impedance spectra that cannot be interpreted as a simple binary electrolyte with an averaged diffusion coefficient.

Gas-phase cluster growth by monomer addition is commonly modeled as an isothermal process. We develop a survival-limited framework in which association produces a thermally excited cluster that may dissociate before either cooling through bath-gas collisions or encountering the next monomer. A continuous-energy survival probability is first derived for an individual post-association thermal trajectory and is then marginalized over distributions of excitation energy, equilibrium energy, and monomer-arrival time using a trajectory functional. Molecular-dynamics simulations of water, silver, and gold clusters provide size-dependent caloric relationships and latent heats, while event-based Monte Carlo simulations independently test the survival formulation. Theory and Monte Carlo results agree closely. The ensemble-averaged survival probability exhibits strong and non-monotonic size dependence, with the largest thermal penalties generally occurring for the smallest clusters. Intermediate-size local maxima arise only when complete cluster-energy distributions are retained and result from competition between curvature-enhanced dissociation and the narrowing of the low-energy tail with increasing size. Surviving clusters are consequently drawn preferentially from the colder portion of the pre-collision energy distribution, and mean thermal trajectories can substantially underestimate population survival. To connect single-event survival to cumulative growth, we introduce a thermal forward-rate correction relative to an isothermal reference and incorporate it into a reversible birth–death model. Although the correction at each size may be moderate, its multiplicative accumulation can increase mean first-passage times by many orders of magnitude. The framework provides a general route for identifying post-collision stabilization as a control on gas-phase cluster growth.

Achieving high-lying vibrational states is essential for actively controlling molecular reactions. We demonstrate vibrational ladder climbing of CO adsorbed on Pt(111) within the plasmonic tip-substrate nanogap formed in a scanning tunneling microscope, detected via tip-enhanced sum-frequency generation (TE-SFG). As the infrared pulse energy increases, hot-band peaks appear sequentially up to the 3-4 transition, indicating the stepwise population of higher vibrational states. Numerical analysis using the optical Bloch equations captures the observed energy dependence of these features. These results demonstrate the capability of TE-SFG to probe vibrational ladder climbing in surface molecular systems and suggest a promising route toward accessing high-lying vibrational states and controlling vibrational excitation at the nanoscale.