In vivo three-dimensional brain imaging with chemiluminescence probes in Alzheimer's disease models.

Optical three-dimensional (3D) molecular imaging is highly desirable for providing precise distribution of the target-of-interest in disease models. However, such 3D imaging is still far from wide applications in biomedical research; 3D brain optical molecular imaging, in particular, has rarely been reported. In this report, we designed chemiluminescence probes with high quantum yields, relatively long emission wavelengths, and high signal-to-noise ratios to fulfill the requirements for 3D brain imaging in vivo. With assistance from density-function theory (DFT) computation, we designed ADLumin-Xs by locking up the rotation of the double bond via fusing the furan ring to the phenyl ring. Our results showed that ADLumin-5 had a high quantum yield of chemiluminescence and could bind to amyloid beta (Aß). Remarkably, ADLumin-5's radiance intensity in brain areas could reach 4 × 107 photon/s/cm2/sr, which is probably 100-fold higher than most chemiluminescence probes for in vivo imaging. Because of its strong emission, we demonstrated that ADLumin-5 could be used for in vivo 3D brain imaging in transgenic mouse models of Alzheimer's disease.

Training machine learning potentials for reactive systems: A Colab tutorial on basic models.

In the last several years, there has been a surge in the development of machine learning potential (MLP) models for describing molecular systems. We are interested in a particular area of this field - the training of system-specific MLPs for reactive systems - with the goal of using these MLPs to accelerate free energy simulations of chemical and enzyme reactions. To help new members in our labs become familiar with the basic techniques, we have put together a self-guided Colab tutorial (https://cc-ats.github.io/mlp_tutorial/), which we expect to be also useful to other young researchers in the community. Our tutorial begins with the introduction of simple feedforward neural network (FNN) and kernel-based (using Gaussian process regression, GPR) models by fitting the two-dimensional Müller-Brown potential. Subsequently, two simple descriptors are presented for extracting features of molecular systems: symmetry functions (including the ANI variant) and embedding neural networks (such as DeepPot-SE). Lastly, these features will be fed into FNN and GPR models to reproduce the energies and forces for the molecular configurations in a Claisen rearrangement reaction.

Nature of Hops, Coordinates, and Detailed Balance for Nonadiabatic Simulations in the Condensed Phase.

Photoinduced processes play a crucial role in a multitude of important molecular phenomena. Accurately modeling these processes in an environment other than a vacuum requires a detailed description of the electronic states involved as well as how energy flows are coupled to the surroundings. Nonadiabatic effects must also be included in order to describe the exchange of energy between electronic and nuclear degrees of freedom correctly. In this work, we revisit the ring-opening reaction 1,3-cylohexadiene (CHD) in a solvent environment. Using our newly developed Interface for Non-Adiabatic Quantum mechanics/molecular mechanics in Solvent (INAQS) we trace the evolution of the reaction via hybrid quantum mechanics/molecular mechanics (QM/MM) surface hopping with a focus on the solvent's participation in the nonadiabatic relaxation process and the long-time approach to equilibrium. We explicitly include the MM solvent contribution to the nonadiabatic coupling vector─enabling an accurate approach to equilibrium at long times─and find that in highly multidimensional systems gradients can have little or nothing to do with the nonadiabatic couplings.

Bridging semiempirical and ab initio QM/MM potentials by Gaussian process regression and its sparse variants for free energy simulation.

Free energy simulations that employ combined quantum mechanical and molecular mechanical (QM/MM) potentials at ab initio QM (AI) levels are computationally highly demanding. Here, we present a machine-learning-facilitated approach for obtaining AI/MM-quality free energy profiles at the cost of efficient semiempirical QM/MM (SE/MM) methods. Specifically, we use Gaussian process regression (GPR) to learn the potential energy corrections needed for an SE/MM level to match an AI/MM target along the minimum free energy path (MFEP). Force modification using gradients of the GPR potential allows us to improve configurational sampling and update the MFEP. To adaptively train our model, we further employ the sparse variational GP (SVGP) and streaming sparse GPR (SSGPR) methods, which efficiently incorporate previous sample information without significantly increasing the training data size. We applied the QM-(SS)GPR/MM method to the solution-phase SN2 Menshutkin reaction, NH3+CH3Cl→CH3NH3++Cl-, using AM1/MM and B3LYP/6-31+G(d,p)/MM as the base and target levels, respectively. For 4000 configurations sampled along the MFEP, the iteratively optimized AM1-SSGPR-4/MM model reduces the energy error in AM1/MM from 18.2 to 4.4 kcal/mol. Although not explicitly fitting forces, our method also reduces the key internal force errors from 25.5 to 11.1 kcal/mol/Å and from 30.2 to 10.3 kcal/mol/Å for the N-C and C-Cl bonds, respectively. Compared to the uncorrected simulations, the AM1-SSGPR-4/MM method lowers the predicted free energy barrier from 28.7 to 11.7 kcal/mol and decreases the reaction free energy from -12.4 to -41.9 kcal/mol, bringing these results into closer agreement with their AI/MM and experimental benchmarks.

Computational Evaluation of Potential Molecular Catalysts for Nitrous Oxide Decomposition.

Nitrous oxide (N2O) is a potent greenhouse gas (GHG) with limited use as a mild anesthetic and underdeveloped reactivity. Nitrous oxide splitting (decomposition) is critical to its mitigation as a GHG. Although heterogeneous catalysts for N2O decomposition have been developed, highly efficient, long-lived solid catalysts are still needed, and the details of the catalytic pathways are not well understood. Reported herein is a computational evaluation of three potential molecular (homogeneous) catalysts for N2O splitting, which could aid in the development of more active and robust catalysts and provide deeper mechanistic insights: one Cu(I)-based, [(CF3O)4Al]Cu (A-1), and two Ru(III)-based, Cl(POR)Ru (B-1) and (NTA)Ru (C-1) (POR = porphyrin, NTA = nitrilotriacetate). The structures and energetic viability of potential intermediates and key transition states are evaluated according to a two-stage reaction pathway: (A) deoxygenation (DO), during which a metal-N2O complex undergoes N-O bond cleavage to produce N2 and a metal-oxo species and (B) (di)oxygen evolution (OER), in which the metal-oxo species dimerizes to a dimetal-peroxo complex, followed by conversion to a metal-dioxygen species from which dioxygen dissociates. For the (F-L)Cu(I) activator (A-1), deoxygenation of N2O is facilitated by an O-bound (F-L)Cu-O-N2 or better by a bimetallic N,O-bonded, (F-L)Cu-NNO-Cu(F-L) complex; the resulting copper-oxyl (F-L)Cu-O is converted exergonically to (F-L)Cu-(η2,η2-O2)-Cu(F-L), which leads to dioxygen species (F-L)Cu(η2-O2), that favorably dissociates O2. Key features of the DO/OER process for (POR)ClRu (B-1) include endergonic N2O coordination, facile N2 evolution from LR'u-N2O-RuL to Cl(POR)RuO, moderate barrier coupling of Cl(POR)RuO to peroxo Cl(POR)Ru(O2)Ru(POR)Cl, and eventual O2 dissociation from Cl(POR)Ru(η1-O2), which is nearly thermoneutral. N2O decomposition promoted by (NTA)Ru(III) (C-1) can proceed with exergonic N2O coordination, facile N2 dissociation from (NTA)Ru-ON2 or (NTA)Ru-N2O-Ru(NTA) to form (NTA)Ru-O; dimerization of the (NTA)Ru-oxo species is facile to produce (NTA)Ru-O-O-Ru(NTA), and subsequent OE from the peroxo species is moderately endergonic. Considering the overall energetics, (F-L)Cu and Cl(POR)Ru derivatives are deemed the best candidates for promoting facile N2O decomposition.

Facilitating ab initio QM/MM free energy simulations by Gaussian process regression with derivative observations.

In combined quantum mechanical and molecular mechanical (QM/MM) free energy simulations, how to synthesize the accuracy of ab initio (AI) methods with the speed of semiempirical (SE) methods for a cost-effective QM treatment remains a long-standing challenge. In this work, we present a machine-learning-facilitated method for obtaining AI/MM-quality free energy profiles through efficient SE/MM simulations. In particular, we use Gaussian process regression (GPR) to learn the energy and force corrections needed for SE/MM to match with AI/MM results during molecular dynamics simulations. Force matching is enabled in our model by including energy derivatives into the observational targets through the extended-kernel formalism. We demonstrate the effectiveness of this method on the solution-phase SN2 Menshutkin reaction using AM1/MM and B3LYP/6-31+G(d,p)/MM as the base and target levels, respectively. Trained on only 80 configurations sampled along the minimum free energy path (MFEP), the resulting GPR model reduces the average energy error in AM1/MM from 18.2 to 5.8 kcal mol-1 for the 4000-sample testing set with the average force error on the QM atoms decreased from 14.6 to 3.7 kcal mol-1 Å-1. Free energy sampling with the GPR corrections applied (AM1-GPR/MM) produces a free energy barrier of 14.4 kcal mol-1 and a reaction free energy of -34.1 kcal mol-1, in closer agreement with the AI/MM benchmarks and experimental results.

A novel monoacylglycerol lipase-targeted 18F-labeled probe for positron emission tomography imaging of brown adipose tissue in the energy network.

Monoacylglycerol lipase (MAGL) constitutes a serine hydrolase that orchestrates endocannabinoid homeostasis and exerts its function by catalyzing the degradation of 2-arachidonoylglycerol (2-AG) to arachidonic acid (AA). As such, selective inhibition of MAGL represents a potential therapeutic and diagnostic approach to various pathologies including neurodegenerative disorders, metabolic diseases and cancers. Based on a unique 4-piperidinyl azetidine diamide scaffold, we developed a reversible and peripheral-specific radiofluorinated MAGL PET ligand [18F]FEPAD. Pharmacokinetics and binding studies on [18F]FEPAD revealed its outstanding specificity and selectivity towards MAGL in brown adipose tissue (BAT) - a tissue that is known to be metabolically active. We employed [18F]FEPAD in PET studies to assess the abundancy of MAGL in BAT deposits of mice and found a remarkable degree of specific tracer binding in the BAT, which was confirmed by post-mortem tissue analysis. Given the negative regulation of endocannabinoids on the metabolic BAT activity, our study supports the concept that dysregulation of MAGL is likely linked to metabolic disorders. Further, we now provide a suitable imaging tool that allows non-invasive assessment of MAGL in BAT deposits, thereby paving the way for detailed mechanistic studies on the role of BAT in endocannabinoid system (ECS)-related pathologies.

Analytic high-order energy derivatives for metal nanoparticle-mediated infrared and Raman scattering spectra within the framework of quantum mechanics/molecular mechanics model with induced charges and dipoles.

This work is devoted to deriving and implementing analytic second- and third-order energy derivatives with respect to the nuclear coordinates and external electric field within the framework of the hybrid quantum mechanics/molecular mechanics method with induced charges and dipoles (QM/DIM). Using these analytic energy derivatives, one can efficiently compute the harmonic vibrational frequencies, infrared (IR) and Raman scattering (RS) spectra of the molecule in the proximity of noble metal clusters/nanoparticles. The validity and accuracy of these analytic implementations are demonstrated by the comparison of results obtained by the finite-difference method and the analytic approaches and by the full QM and QM/DIM calculations. The complexes formed by pyridine and two sizes of gold clusters (Au18 and Au32) at varying intersystem distances of 3, 4, and 5 Å are used as the test systems, and Raman spectra of 4,4'-bipyridine in the proximity of Au2057 and Ag2057 metal nanoparticles (MNP) are calculated by the QM/DIM method and compared with experimental results as well. We find that the QM/DIM model can well reproduce the IR spectra obtained from full QM calculations for all the configurations, while although it properly enhances some of the vibrational modes, it artificially overestimates RS spectral intensities of several modes for the systems with very short intersystem distance. We show that this could be improved, however, by incorporating the hyperpolarizability of the gold metal cluster in the evaluation of RS intensities. Additionally, we address the potential impact of charge migration between the adsorbate and MNPs.

Evaluation of molecular photophysical and photochemical properties using linear response time-dependent density functional theory with classical embedding: Successes and challenges.

Time-dependent density functional theory (TDDFT) based approaches have been developed in recent years to model the excited-state properties and transition processes of the molecules in the gas-phase and in a condensed medium, such as in a solution and protein microenvironment or near semiconductor and metal surfaces. In the latter case, usually, classical embedding models have been adopted to account for the molecular environmental effects, leading to the multi-scale approaches of TDDFT/polarizable continuum model (PCM) and TDDFT/molecular mechanics (MM), where a molecular system of interest is designated as the quantum mechanical region and treated with TDDFT, while the environment is usually described using either a PCM or (non-polarizable or polarizable) MM force fields. In this Perspective, we briefly review these TDDFT-related multi-scale models with a specific emphasis on the implementation of analytical energy derivatives, such as the energy gradient and Hessian, the nonadiabatic coupling, the spin-orbit coupling, and the transition dipole moment as well as their nuclear derivatives for various radiative and radiativeless transition processes among electronic states. Three variations of the TDDFT method, the Tamm-Dancoff approximation to TDDFT, spin-flip DFT, and spin-adiabatic TDDFT, are discussed. Moreover, using a model system (pyridine-Ag20 complex), we emphasize that caution is needed to properly account for system-environment interactions within the TDDFT/MM models. Specifically, one should appropriately damp the electrostatic embedding potential from MM atoms and carefully tune the van der Waals interaction potential between the system and the environment. We also highlight the lack of proper treatment of charge transfer between the quantum mechanics and MM regions as well as the need for accelerated TDDFT modelings and interpretability, which calls for new method developments.

Analytical gradients and derivative couplings for the TDDFT-1D method.

We derive and implement analytic gradients and derivative couplings for time-dependent density functional theory plus one double (TDDFT-1D) which is a semiempirical configuration interaction method whereby the Hamiltonian is diagonalized in a basis of all singly excited configurations and one doubly excited configuration as constructed from a set of reference Kohn-Sham orbitals. We validate the implementation by comparing against finite difference values. Furthermore, we show that our implementation can locate both optimized geometries and minimum-energy crossing points along conical seams of S1/S0 surfaces for a set of test cases.

Cavity quantum-electrodynamical time-dependent density functional theory within Gaussian atomic basis. II. Analytic energy gradient.

Following the formulation of cavity quantum-electrodynamical time-dependent density functional theory (cQED-TDDFT) models [Flick et al., ACS Photonics 6, 2757-2778 (2019) and Yang et al., J. Chem. Phys. 155, 064107 (2021)], here, we report the derivation and implementation of the analytic energy gradient for polaritonic states of a single photochrome within the cQED-TDDFT models. Such gradient evaluation is also applicable to a complex of explicitly specified photochromes or, with proper scaling, a set of parallel-oriented, identical-geometry, and non-interacting molecules in the microcavity.

Computational Investigation of Substituent Effects on the Fluorescence Wavelengths of Oxyluciferin Analogs.

Oxyluciferin, which is the light emitter for firefly bioluminescence, has been subjected to extensive chemical modifications to tune its emission wavelength and quantum yield. However, the exact mechanisms for various electron-donating and withdrawing groups to perturb the photophysical properties of oxyluciferin analogs are still not fully understood. To elucidate the substituent effects on the fluorescence wavelength of oxyluciferin analogs, we applied the absolutely localized molecular orbitals (ALMO)-based frontier orbital analysis to assess various types of interactions (i.e. permanent electrostatics/exchange repulsion, polarization, occupied-occupied orbital mixing, virtual-virtual orbital mixing, and charge-transfer) between the oxyluciferin and substituent orbitals. We suggested two distinct mechanisms that can lead to red-shifted oxyluciferin emission wavelength, a design objective that can help increase the tissue penetration of bioluminescence emission. Within the first mechanism, an electron-donating group (such as an amino or dimethylamino group) can contribute its highest occupied molecular orbital (HOMO) to an out-of-phase combination with oxyluciferin's HOMO, thus raising the HOMO energy of the substituted analog and narrowing its HOMO-LUMO gap. Alternatively, an electron-withdrawing group (such as a nitro or cyano group) can participate in an in-phase virtual-virtual orbital mixing of fragment LUMOs, thus lowering the LUMO energy of the substituted analog. Such an ALMO-based frontier orbital analysis is expected to lead to intuitive principles for designing analogs of not only the oxyluciferin molecule, but also many other functional dyes.

Perceptions of Oral Nicotine Pouches on Reddit: Observational Study.

BACKGROUND: Oral nicotine pouches are a new form of tobacco-free nicotine products launched in recent years with a variety of flavors. OBJECTIVE: This study aims to examine the public perceptions and discussions of oral nicotine pouches on Reddit, a popular social media platform for sharing user experiences. METHODS: Between February 15, 2019, and February 12, 2021, a total of 2410 Reddit posts related to oral nicotine pouches were obtained over a 2-year period. After the removal of unrelated or commercial posts, 653 Reddit posts related to oral nicotine pouches remained. Topics and sentiments related to oral nicotine pouches on Reddit were hand coded. RESULTS: The number of Reddit posts related to oral nicotine pouches increased during the study period. Content analysis showed that the most popular topic was "sharing product information and user experience" (366/653, 56%), in which sharing oral nicotine pouch products and user experiences were dominant. The next popular topic was "asking product-related questions" (product properties and product recommendations; 115/653, 17.6%), followed by "quitting nicotine products" such as vaping or smoking through use of oral nicotine pouches or quitting the oral nicotine pouches themselves (83/653, 12.7%) and "discussing oral nicotine pouch-related health" symptoms or concerns related to oral nicotine pouches (74/653, 11.3%). The least popular topic was "legality and permissions" related to oral nicotine pouches (15/653, 2.3%). In addition, a greater number of Reddit posts described positive attitudes compared to negative attitudes toward oral nicotine pouches (354/653, 54.2% vs 101/653, 15.5%; P<.001). CONCLUSIONS: Reddit posts overall had a positive attitude toward oral nicotine pouches and users were actively sharing product and user experiences. Our study provides the first insight on up-to-date oral nicotine pouch discussions on social media.

Enhanced Reverse Intersystem Crossing Promoted by Triplet Exciton-Photon Coupling.

Polaritons are hybrid light-matter states formed via strong coupling between excitons and photons inside a microcavity, leading to upper and lower polariton (LP) bands splitting from the exciton. The LP has been applied to reduce the energy barrier of the reverse intersystem crossing (rISC) process from T1, harvesting triplet energy for fluorescence through thermally activated delayed fluorescence. The spin-orbit coupling between T1 and the excitonic part of the LP was considered as the origin for such an rISC transition. Here we propose a mechanism, namely, rISC promoted by the light-matter coupling (LMC) between T1 and the photonic part of LP, which is originated from the ISC-induced transition dipole moment of T1. This mechanism was excluded in previous studies. Our calculations demonstrate that the experimentally observed enhancement to the rISC process of the erythrosine B molecule can be effectively promoted by the LMC between T1 and a photon. The proposed mechanism would substantially broaden the scope of the molecular design toward highly efficient cavity-promoted light-emitting materials and immediately benefit the illumination of related experimental phenomena.

Development of a triazolobenzodiazepine-based PET probe for subtype-selective vasopressin 1A receptor imaging.

OBJECTIVES: To enable non-invasive real-time quantification of vasopressin 1A (V1A) receptors in peripheral organs, we sought to develop a suitable PET probe that would allow specific and selective V1A receptor imaging in vitro and in vivo. METHODS: We synthesized a high-affinity and -selectivity ligand, designated compound 17. The target structure was labeled with carbon-11 and tested for its utility as a V1A-targeted PET tracer by cell uptake studies, autoradiography, in vivo PET imaging and ex vivo biodistribution experiments. RESULTS: Compound 17 (PF-184563) and the respective precursor for radiolabeling were synthesized in an overall yield of 49% (over 7 steps) and 40% (over 8 steps), respectively. An inhibitory constant of 0.9 nM towards the V1A receptors was measured, while excellent selectivity over the related V1B, V2 and OT receptor (IC50 >10,000 nM) were obtained. Cell uptake studies revealed considerable V1A binding, which was significantly reduced in the presence of V1A antagonists. Conversely, there was no significant blockade in the presence of V1B and V2 antagonists. In vitro autoradiography and PET imaging studies in rodents indicated specific tracer binding mainly in the liver. Further, the pancreas, spleen and the heart exhibited specific binding of [11C]17 ([11C]PF-184563) by ex vivo biodistribution experiments. CONCLUSION: We have developed the first V1A-targeted PET ligand that is suitable for subtype-selective receptor imaging in peripheral organs including the liver, heart, pancreas and spleen. Our findings suggest that [11C]PF-184563 can be a valuable tool to study the role of V1A receptors in liver diseases, as well as in cardiovascular pathologies.

Correction: Analysis and visualization of energy densities. I. Insights from real-time time-dependent density functional theory simulations.

Correction for 'Analysis and visualization of energy densities. I. Insights from real-time time-dependent density functional theory simulations' by Junjie Yang et al., Phys. Chem. Chem. Phys., 2020, 22, 26838-26851, DOI: .

Affordable Ab Initio Path Integral for Thermodynamic Properties via Molecular Dynamics Simulations Using Semiempirical Reference Potential.

Path integral molecular dynamics (PIMD) is becoming a routinely applied method for incorporating the nuclear quantum effect in computer simulations. However, direct PIMD simulations at an ab initio level of theory are formidably expensive. Using the protonated 1,8-bis(dimethylamino)naphthalene molecule as an example, we show in this work that the computational expense for the intramolecular proton transfer between the two nitrogen atoms can be remarkably reduced by implementing the idea of reference-potential methods. The simulation time can be easily extended to a scale of nanoseconds while maintaining the accuracy on an ab initio level of theory for thermodynamic properties. In addition, postprocessing can be carried out in parallel on massive computer nodes. A 545-fold reduction in the total CPU time can be achieved in this way as compared to a direct PIMD simulation at the same ab initio level of theory.

Synthesis and preliminary evaluation of novel 11C-labeled GluN2B-selective NMDA receptor negative allosteric modulators.

N-methyl-D-aspartate receptors (NMDARs) play critical roles in the physiological function of the mammalian central nervous system (CNS), including learning, memory, and synaptic plasticity, through modulating excitatory neurotransmission. Attributed to etiopathology of various CNS disorders and neurodegenerative diseases, GluN2B is one of the most well-studied subtypes in preclinical and clinical studies on NMDARs. Herein, we report the synthesis and preclinical evaluation of two 11C-labeled GluN2B-selective negative allosteric modulators (NAMs) containing N,N-dimethyl-2-(1H-pyrrolo[3,2-b]pyridin-1-yl)acetamides for positron emission tomography (PET) imaging. Two PET ligands, namely [11C]31 and [11C]37 (also called N2B-1810 and N2B-1903, respectively) were labeled with [11C]CH3I in good radiochemical yields (decay-corrected 28% and 32% relative to starting [11C]CO2, respectively), high radiochemical purity (>99%) and high molar activity (>74 GBq/µmol). In particular, PET ligand [11C]31 demonstrated moderate specific binding to GluN2B subtype by in vitro autoradiography studies. However, because in vivo PET imaging studies showed limited brain uptake of [11C]31 (up to 0.5 SUV), further medicinal chemistry and ADME optimization are necessary for this chemotype attributed to low binding specificity and rapid metabolism in vivo.

Quantum-electrodynamical time-dependent density functional theory within Gaussian atomic basis.

Inspired by the formulation of quantum-electrodynamical time-dependent density functional theory (QED-TDDFT) by Rubio and co-workers [Flick et al., ACS Photonics 6, 2757-2778 (2019)], we propose an implementation that uses dimensionless amplitudes for describing the photonic contributions to QED-TDDFT electron-photon eigenstates. This leads to a Hermitian QED-TDDFT coupling matrix that is expected to facilitate the future development of analytic derivatives. Through a Gaussian atomic basis implementation of the QED-TDDFT method, we examined the effect of dipole self-energy, rotating-wave approximation, and the Tamm-Dancoff approximation on the QED-TDDFT eigenstates of model compounds (ethene, formaldehyde, and benzaldehyde) in an optical cavity. We highlight, in the strong coupling regime, the role of higher-energy and off-resonance excited states with large transition dipole moments in the direction of the photonic field, which are automatically accounted for in our QED-TDDFT calculations and might substantially affect the energies and compositions of polaritons associated with lower-energy electronic states.

A simplified charge projection scheme for long-range electrostatics in ab initio QM/MM calculations.

In a previous work [Pan et al., Molecules 23, 2500 (2018)], a charge projection scheme was reported, where outer molecular mechanical (MM) charges [>10 Å from the quantum mechanical (QM) region] were projected onto the electrostatic potential (ESP) grid of the QM region to accurately and efficiently capture long-range electrostatics in ab initio QM/MM calculations. Here, a further simplification to the model is proposed, where the outer MM charges are projected onto inner MM atom positions (instead of ESP grid positions). This enables a representation of the long-range MM electrostatic potential via augmentary charges (AC) on inner MM atoms. Combined with the long-range electrostatic correction function from Cisneros et al. [J. Chem. Phys. 143, 044103 (2015)] to smoothly switch between inner and outer MM regions, this new QM/MM-AC electrostatic model yields accurate and continuous ab initio QM/MM electrostatic energies with a 10 Å cutoff between inner and outer MM regions. This model enables efficient QM/MM cluster calculations with a large number of MM atoms as well as QM/MM calculations with periodic boundary conditions.