Molecular Properties Research Articles

FROG: Exploiting all-atom molecular dynamics trajectories to calculate linear and non-linear optical responses of molecular liquids within Dalton's QM/MM polarizable embedding scheme.

Quantum mechanical/molecular mechanics (QM/MM) methods are interesting to model the impact of a complex environment on the spectroscopic properties of a molecule. In this context, a FROm molecular dynamics to second harmonic Generation (FROG) code is a tool to exploit molecular dynamics trajectories to perform QM/MM calculations of molecular optical properties. FROG stands for "FROm molecular dynamics to second harmonic Generation" since it was developed for the calculations of hyperpolarizabilities. These are relevant to model non-linear optical intensities and compare them with those obtained from second harmonic scattering or second harmonic generation experiments. FROG's specificity is that it is designed to study simple molecular liquids, including solvents or mixtures, from the bulk to the surface. For the QM/MM calculations, FROG relies on the Dalton package: its electronic-structure models, response theory, and polarizable embedding schemes. FROG helps with the global workflow needed to deal with numerous QM/MM calculations: it permits the user to separate the system into QM and MM fragments, to write Dalton's inputs, to manage the submission of QM/MM calculations, to check whether Dalton's calculation finished successfully, and finally to perform averages on relevant QM observables. All molecules within the simulation box and several time steps are tackled within the same workflow. The platform is written in Python and installed as a package. Intermediate data such as local electric fields or individual molecular properties are accessible to the users in the form of Python object arrays. The resulting data are easily extracted, analyzed, and visualized using Python scripts that are provided in tutorials.

Standard Response Calculation of Electric Dipole Polarizability and Specific Optical Rotation Power Densities.

A time-dependent method has been developed to solve the standard response equation for the calculation of dynamic molecular property densities, endowed with the characteristic of being origin-invariant, entirely in the atomic orbital basis at both HF and DFT level of theory. The method has been tuned in particular for the calculation of origin-independent electric dipole polarizability density and specific rotation power density. Some demonstrations are given for the hexabenzocoronene molecule and the Tröger base.

Multistate Method to Efficiently Account for Tautomerism and Protonation in Alchemical Free-Energy Calculations.

The majority of drug-like molecules contain at least one ionizable group, and many common drug scaffolds are subject to tautomeric equilibria. Thus, these compounds are found in a mixture of protonation and/or tautomeric states at physiological pH. Intrinsically, standard classical molecular dynamics (MD) simulations cannot describe such equilibria between states, which negatively impacts the prediction of key molecular properties in silico. Following the formalism described by de Oliveira and co-workers (J. Chem. Theory Comput. 2019, 15, 424-435) to consider the influence of all states on the binding process based on alchemical free-energy calculations, we demonstrate in this work that the multistate method replica-exchange enveloping distribution sampling (RE-EDS) is well suited to describe molecules with multiple protonation and/or tautomeric states in a single simulation. We apply our methodology to a series of eight inhibitors of factor Xa with two protonation states and a series of eight inhibitors of glycogen synthase kinase 3β (GSK3β) with two tautomeric states. In particular, we show that given a sufficient phase-space overlap between the states, RE-EDS is computationally more efficient than standard pairwise free-energy methods.

Effect of Carbon dots in tuning molecular alignment, dielectric and electrical properties of a smectogenic cyanobiphenyl-based liquid crystal material

Abstract We demonstrate here the effect of dispersing organosoluble carbon dots (CDs, ∼7-8 nm) on tuning the molecular alignment, dielectric and electrical properties of smectic A (SmA) and nematic (N) mesophases of a thermotropic smectogenic LC material, 4-octyl-4′-cyanobiphenyl (8CB) in a planar anchored ITO sample cell using polarized optical microscopy and dielectric spectroscopic techniques. The cross-polarised optical textures clearly show that the doping of CDs (concentration ≥0.25wt%) in planar anchored 8CB, LC led to change its alignment from planar to vertical. Intrestingly, such induced vertical alignment remains stable throughout SmA and N phases of the 8CB, LC material. Moreover, the magnitude of real dielectric permittivity is found to increase with increasing concentration of CDs and exhibited vertical alignment values for composites (≥0.25wt%). The observance of short axis molecular relaxation for composites (≥0.25wt%) without the application of bias field affirmed again the induced vertical alignment. The accumulation of CDs at the substrate surface and their interaction with alignment and ITO layers could be attributed as an important factor for such induced vertical alignment. Electrical conductivity of 8CB is observed to increase significantly with the addition of CDs (i.e., an increment of up to two orders of magnitude in composites as compared to pure 8CB) and attributed to the lowering of viscosity and change in molecular alignment. We certainly believe that such tunable molecular alignment throughout SmA and N phases of thermotropic smectogenic liquid crystal material (8CB) by dopant CDs could pave the way forward for their applications in the flexible displays, biosensors, electro-optical memory, and other tunable photonic devices.

Reverse Separation of Carbon Dioxide and Acetylene in Two Isostructural Copper Pyridine‐Carboxylate Frameworks

Separating acetylene from carbon dioxide is important but highly challenging due to their similar molecular shapes and physical properties. Adsorptive separation of carbon dioxide from acetylene can directly produce pure acetylene but is hardly realized because of relatively polarizable acetylene binds more strongly. Here, we reverse the CO2 and C2H2 separation by adjusting the pore structures in two isoreticular ultramicroporous metal−organic frameworks (MOFs). Under ambient conditions, copper isonicotinate (Cu(ina)2), with relatively large pore channels shows C2H2‐selective adsorption with a C2H2/CO2 selectivity of 3.4, whereas its smaller‐pore analogue, copper quinoline‐5‐carboxylate (Cu(Qc)2) shows an inverse CO2/C2H2 selectivity of 5.6. Cu(Qc)2 shows compact pore space that well matches the optimal orientation of CO2 but is not compatible for C2H2. Neutron powder diffraction experiments confirmed that CO2 molecules adopt preferential orientation along the pore channels during adsorption binding, whereas C2H2 molecules bind in an opposite fashion with distorted configurations due to their opposite quadrupole moments. Dynamic breakthrough experiments have validated the separation performance of Cu(Qc)2 for CO2/C2H2 separation.

Multi-scale analysis of virgin/aged/recycled asphalt self-healing performance based on molecular simulation and micro-macro tests

Conventional macro-micro experiments have not fully elucidated the thermal self-healing mechanism of virgin, aged, and recycled asphalt at the molecular level at different temperatures. Molecular dynamics and macro-micro experiments were used to investigate the multi-scale mechanism of thermal self-healing of nano-cracks in three asphalt types. The molecular characteristics (concentration, energy changes, and molecular diffusion properties) of the three asphalt types were simulated during self-healing using molecular dynamics simulations Macro-micro experimental tests were conducted to validate the simulation results. The self-healing process was analyzed at multiple scales, and correlation analysis between the self-healing parameters and the macroscopic healing characteristics was performed at nano- and microscopic scales. The results showed that the relative concentration increased significantly from 0 mol/L to 0.6 mol/L in the 60–80 Å range during the long-distance self-healing phase (0–40 ps), promoting the rapid reorganization of molecules around cracks and the formation of self-healing networks. The van der Waals forces were the dominant forces affecting self-healing, and the transition from repulsive to attractive forces promoted the self-healing of cracks. This study clarifies the thermal self-healing mechanism of asphalt cracks at multiple scales, ensuring the sustainable use of asphalt materials.

Reduction of APOE accounts for neurobehavioral deficits in fetal alcohol spectrum disorders.

A hallmark of fetal alcohol spectrum disorders (FASD) is neurobehavioral deficits that still do not have effective treatment. Here, we present that reduction of Apolipoprotein E (APOE) is critically involved in neurobehavioral deficits in FASD. We show that prenatal alcohol exposure (PAE) changes chromatin accessibility of Apoe locus, and causes reduction of APOE levels in both the brain and peripheral blood in postnatal mice. Of note, postnatal administration of an APOE receptor agonist (APOE-RA) mitigates motor learning deficits and anxiety in those mice. Several molecular and electrophysiological properties essential for learning, which are altered by PAE, are restored by APOE-RA. Our human genome-wide association study further reveals that the interaction of PAE and a single nucleotide polymorphism in the APOE enhancer which chromatin is closed by PAE in mice is associated with lower scores in the delayed matching-to-sample task in children. APOE in the plasma is also reduced in PAE children, and the reduced level is associated with their lower cognitive performance. These findings suggest that controlling the APOE level can serve as an effective treatment for neurobehavioral deficits in FASD.

PointGAT: A Quantum Chemical Property Prediction Model Integrating Graph Attention and 3D Geometry.

Predicting quantum chemical properties is a fundamental challenge for computational chemistry. While the development of graph neural networks has advanced molecular representation learning and property prediction, their performance could be further enhanced by incorporating three-dimensional (3D) structural geometry into two-dimensional (2D) molecular graph representation. In this study, we introduce the PointGAT model for quantum molecular property prediction, which integrates 3D molecular coordinates with graph-attention modeling. Comparison with other current models in molecular prediction tasks showed that PointGAT could provide higher predictive accuracy in various benchmark data sets from MoleculeNet, including ESOL, FreeSolv, Lipop, HIV, and 6 out of 12 tasks of the QM9 data set. To further examine PointGAT prediction of quantum mechanical (QM) energies, we constructed a C10 data set comprising 11,841 charged and chiral carbocation intermediates with QM energies calculated at the DM21/6-31G*//B3LYP/6-31G* levels. Notably, PointGAT achieved an R2 value of 0.950 and an MAE of 1.616 kcal/mol, outperforming even the best-performing graph neural network model with a reduction of 0.216 kcal/mol in MAE and an improvement of 0.050 in R2. Additional ablation studies indicated that incorporating molecular geometry into the model resulted in markedly higher predictive accuracy, reducing the MAE value from 1.802 to 1.616 kcal/mol. Moreover, visualization of PointGAT atomic attention weights suggested its predictions were interpretable. Findings in this study support the application of PointGAT as a powerful and versatile tool for quantum chemical property prediction that can facilitate high-accuracy modeling for fundamental exploration of chemical space as well as drug design and molecular engineering.

Photo-Responsive Hydrogen-Bonded Molecular Networks Capable of Retaining Crystalline Periodicity after Isomerization.

The molecular conformation, crystalline morphology, and properties of photochromic organic crystals can be controlled through photoirradiation, making them promising candidates for functional organic materials. However, photochromic porous molecular crystals with a networked framework structure are rare due to the difficulty in maintaining space that allows for photo-induced molecular motion in the crystalline state. This study describes a photo-responsive single crystal based on hydrogen-bonded (H-bonded) network of dihydrodimethylbenzo[e]pyrene derivative 4BDHP. A crystal composed of H-bonded undulate layers, 4BDHP-2, underwent photo-isomerization in the crystalline state due to loose stacking of the layers. Particularly, enantio-pure crystal (S,S)-4BDHP-2 allowed to reveal the structure of the photoisomerized crystal, in which the closed form (4BDHP) and open form (4CPD) were arranged alternately with keeping crystalline periodicity, although side reactions were also implied. The present proof-of-concept system of a photochromic framework that retains crystalline periodicity after photo-isomerization may provide new light-driven porous functional materials.

Photo‐Responsive Hydrogen‐Bonded Molecular Networks Capable of Retaining Crystalline Periodicity after Isomerization

AbstractThe molecular conformation, crystalline morphology, and properties of photochromic organic crystals can be controlled through photoirradiation, making them promising candidates for functional organic materials. However, photochromic porous molecular crystals with a networked framework structure are rare due to the difficulty in maintaining space that allows for photo‐induced molecular motion in the crystalline state. This study describes a photo‐responsive single crystal based on hydrogen‐bonded (H‐bonded) network of dihydrodimethylbenzo[e]pyrene derivative 4BDHP. A crystal composed of H‐bonded undulate layers, 4BDHP‐2, underwent photo‐isomerization in the crystalline state due to loose stacking of the layers. Particularly, enantio‐pure crystal (S,S)‐4BDHP‐2 allowed to reveal the structure of the photoisomerized crystal, in which the closed form (4BDHP) and open form (4CPD) were arranged alternately with keeping crystalline periodicity, although side reactions were also implied. The present proof‐of‐concept system of a photochromic framework that retains crystalline periodicity after photo‐isomerization may provide new light‐driven porous functional materials.

Nutritional, molecular, and functional properties of a novel enzymatically hydrolyzed porcine plasma product.

In the present study, an enzymatically hydrolyzed porcine plasma (EHPP) was nutritionally and molecularly characterized. EHPP molecular characterization showed, in contrast to spray-dried plasma (SDP), many peptides with relative molecular masses (Mr) below 8,000, constituting 73% of the protein relative abundance. IIAPPER, a well-known bioactive peptide with anti-inflammatory and antioxidant properties, was identified. In vivo functionality of EHPP was tested in C. elegans and two different mouse models of intestinal inflammation. In C. elegans subjected to lipopolysaccharide exposure, EHPP displayed a substantial anti-inflammatory effect, enhancing survival and motility by 40% and 21.5%, respectively. Similarly, in mice challenged with Staphylococcus aureus enterotoxin B or Escherichia coli O42, EHPP and SDP supplementation (8%) increased body weight and average daily gain while reducing the percentage of regulatory Th lymphocytes. Furthermore, both products mitigated the increase of pro-inflammatory cytokines expression associated with these challenged mouse models. In contrast, some significant differences were observed in markers such as Il-6 and Tnf-α, suggesting that the products may present different action mechanisms. In conclusion, EHPP demonstrated similar beneficial health effects to SDP, potentially attributable to the immunomodulatory and antioxidant activity of its characteristic low Mr bioactive peptides.

Multi‐Selenophene Strategy Enables Dimeric Acceptors‐Based Organic Solar Cells with over 18.5% Efficiency

AbstractDimeric acceptor (DMA) becomes a promising alternative to small‐molecular and polymeric acceptor‐based organic solar cells (OSCs) due to its well‐defined chemical structure, high batch‐to‐batch reproducibility, and low molecular diffusion properties. However, DMAs usually exhibit blueshifted absorptions, limiting their photon utilization abilities. Herein, multi‐selenophene strategies are adopted to develop redshifted DMAs. From monomer (YSe) to dimers (DYSe‐1 and DYSe‐2), reduced electron reorganization energies and exciton binding energies enable the efficient charge dynamics in the DMAs‐based OSCs. Together with their effective absorption extending to ≈920 nm, DYSe‐1‐ and DYSe‐2‐ based OSCs exhibit outstanding short‐circuit current densities (JSCs) over 27 mA cm−2, which are the best among DMAs. Besides, compared with the YSe‐based device, both DMA‐based devices have higher electroluminescence quantum efficiencies and thus reduce nonradiative recombination loss (ΔE3), contributing to their reduced energy losses. The resultant open‐circuit voltages (VOCs) of DYSe‐1‐ and DYSe‐2‐ based OSCs are ≈0.88 V, which, combining their super JSC values, lead to the promising power conversion efficiencies of 18.56% and 18.22%, respectively. These results are among the best in DMAs‐based OSCs and highlight the great potential of the multi‐selenophene strategy for the development of redshifted DMAs with high performance.

Effect of enzymatic hydrolysis with Alcalase or Protamex on technological and antioxidant properties of whey protein hydrolysates

The aim of this study was to evaluate the effect of the enzymatic hydrolysis, performed using Alcalase and Protamex enzymes, on the technological functionalities and the antioxidant capacity of whey protein hydrolysates (WPHs) to identify the conditions allowing to obtain target functionality/ies. Samples were characterized for hydrolysis degree (DH), molecular weight distribution, structural properties, and food-related functionalities. Free sulfhydryl groups and surface hydrophobicity significantly decreased with the increase in DH, regardless of the used enzyme. The foaming and antioxidant properties of Alcalase WPHs were higher as compared to those of WPI, reaching the maximum value at DH = 18–20 %, while higher DH resulted in impaired functionality. Gelling properties were guaranteed when WPI was hydrolysed by Protamex at DH < 15 % while foaming and antioxidant abilities were fostered at 15 < DH < 21 %. These results were well correlated with MW distribution and were rationalized into a road map which represents a useful tool in the selection of proper hydrolysis conditions (time, DH, enzyme type) to obtain WPHs with tailored functionalities. Research outcomes highlighted the possibility to drive protein hydrolysis to optimize the desired functionality/ies.

THEORETICAL PREDICTION AND COMPREHENSIVE CHARACTERIZATION OF AN ALL-NITROGENATOMIC RING, CYCLO[18]NITROGEN (N18).

The cyclic molecule cyclo[18]carbon composed of 18 carbon atoms has been observed in condensed phase experiment in recent years and has attracted great attention. Through state-of-art quantum chemistry calculation, this study found that 18 nitrogen atoms can also form a macrocyclic system, cyclo[18]nitrogen (N18), though its lifetime is very short at room temperature and can only exist for a relatively long time at very low temperatures. We comprehensively theoretically studied properties of N18, including geometric configurations, thermal decomposition mechanism and rate, molecular dynamics behavior, energetic properties, vibrational and electronic spectra. We also discussed in depth the electronic structure of N18, including nature of the N-N bonds, lone-pairs, charge distribution characteristics, electronic delocalization, and aromaticity. This work is not only the first exploration of the macrocyclic N18 molecule, but also the first time to systematically examine a very long-chain substance fully composed of nitrogen atoms in isolated state.

The Use of Spectroscopic Methods to Study Organic Matter in Virgin and Arable Soils: A Scoping Review

The use of modern spectroscopic methods of analysis, which provide extensive information on the chemical nature of substances, significantly expands our understanding of the molecular composition and properties of soil organic matter (SOM) and its transformation and stabilization processes in various ecosystems and geochemical conditions. The aim of this review is to identify and analyze studies related to the application of nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) spectroscopy techniques to study the molecular composition and transformation of organic matter in virgin and arable soils. This article is mainly based on three research questions: (1) Which NMR spectroscopy techniques are used to study SOM, and what are their disadvantages and advantages? (2) How is the NMR spectroscopy technique used to study the molecular structure of different pools of SOM? (3) How is ESR spectroscopy used in SOM chemistry, and what are its advantages and limitations? Relevant studies published between 1996 and 2024 were searched in four databases: eLIBRARY, MDPI, ScienceDirect and Springer. We excluded non-English-language articles, review articles, non-peer-reviewed articles and other non-article publications, as well as publications that were not available according to the search protocols. Exclusion criteria for articles were studies that used NMR and EPR techniques to study non-SOM and where these techniques were not the primary methods. Our scoping review found that both solid-state and solution-state NMR spectroscopy are commonly used to study the structure of soil organic matter (SOM). Solution-phase NMR is particularly useful for studying soluble SOM components of a low molecular weight, whereas solid-phase NMR offers advantages such as higher 13C atom concentration for stronger signals and faster analysis time. However, solution-phase NMR has limitations including sample insolubility, potential signal aggregation and reduced sensitivity and resolution. Solid-state NMR is better at detecting non-protonated carbon atoms and identifying heterogeneous regions within structures. EPR spectroscopy, on the other hand, offers significant advantages in experimental biochemistry due to its high sensitivity and ability to provide detailed information about substances containing free radicals (FRs), aiding in the assessment of their reactivity and transformations. Understanding the FR structure in biopolymers can help to study the formation and transformation of SOM. The integration of two- and three-dimensional NMR spectroscopy with other analytical methods, such as chromatography, mass spectrometry, etc., provides a more comprehensive approach to deciphering the complex composition of SOM than one-dimensional techniques alone.

Experimental and computational study on antioxidant activity and molecular properties of novel ferrocenyl Schiff bases

In this study, antioxidant and molecular properties of some important novel ferrocenyl Schiff bases were studied. The 4-Ferrocenyl aniline synthetic pathway was chosen as the general procedure for the synthesis of Schiff bases. Two experimental techniques, UV–Visible spectroscopy and cyclic voltammetry, and one theoretical DFT method was employed to find out their antioxidant activity and molecular properties of some novel ferrocenyl Schiff bases and compared it with standard antioxidant (Ascorbic acid). Maximum wavelength, extinction coefficient, IC30 and IC50 were estimated by using UV–Visible spectroscopy. For theoretical investigations, computational Amsterdam density function software was employed to study the molecular properties and reaction parameters based on density functional theory calculations. The cyclic voltammetry (CV) measurements in electrochemical experiments were done at room temperature while diffusion coefficient was estimated by using CV graphs. UV–Vis spectra of these compounds exhibited similar peaks with greater intensity ranges from 312 nm to 314 nm and smaller intensity ranges 471 nm to 473 nm which occurred because of the only substituent R (naphthoxy, phenoxy and phenoxy) in these compounds. Registered Amsterdam density function was utilized to determine the optimized structure, FTIR spectra, UV–Visible spectra, HOMO, LUMO, dipole moment, ionization potential, electron affinity, band gap, hardness, chemical potential and electrophility index. The overall electrode processes were found to be diffusion controlled and the novel compounds showed appreciable antioxidant activities.

Longitudinal in vivo cationic contrast-enhanced computed tomography classifies equine articular cartilage injury and repair.

Cationic contrast-enhanced computed tomography (CECT) capitalizes on increased contrast agent affinity to the charged proteoglycans in articular cartilage matrix to provide quantitative assessment of proteoglycan content with enhanced images. While high resolution microCT has demonstrated success, we investigate cationic CECT use in longitudinal in vivo imaging at clinical resolution. We hypothesize that repeated administration of CA4+ will have no adverse side effects or complications, and that sequential in vivo imaging assessments will distinguish articular cartilage repair tissue from early degenerative and healthy cartilage in critically sized chondral defects. In an established equine translational preclinical model, lameness and synovial effusion scores are similar to controls after repeated injections of CA4+ (eight injections over 16 weeks) compared to controls. Synovial fluid total protein, leukocyte concentration, and sGAG and PGE2 concentrations and articular cartilage and synovial membrane scores are also equivalent to controls. Longitudinal in vivo cationic CECT attenuation in repair tissue is significantly lower than peripheral to (adjacent) and distantly from defects (remote sites) by 4 weeks (p < 0.001), and this difference persists until 16 weeks. At the 6- and 8-week time points, the adjacent locations exhibit significantly lower cationic CECT attenuation compared with the remote sites, reflecting peri-defect degeneration (p < 0.01). Cationic CECT attenuation at clinical resolution significantly correlates with cationic CECT (microCT) (r = 0.69, p < 0.0001), sGAG (r = 0.48, p < 0.0001), and ICRS II histology score (r = 0.63, p < 0.0001). In vivo cationic CECT imaging at clinical resolution distinguishes fibrous repair tissue from degenerative and healthy hyaline cartilage and correlates with molecular tissue properties of articular cartilage.

Automated Crystallization Monitoring in Material Development using Computer Vision and Neuronal Networks

AbstractCrystallization is critical in producing various substances in the food and pharmaceutical industries. The process begins with nucleation from a supersaturated solution, followed by the directed movement of solute molecules toward the newly formed nuclei. This movement is influenced by different factors such as molecular attraction and thermodynamic properties, which influence the resulting crystal size and shape. This paper presents an automated monitoring approach for the growth process of crystallization from saturated solutions. To monitor such a process, a combination of artificial intelligence and computer vision is used. The approach was developed for application in material research to automate the processing of numerous samples, which would otherwise require laboratory personnel.

Nonalternant Nanographenes Containing N-Centered Cyclopenta[ef]heptalene and Aza[7]Helicene Units.

Introducing helical subunits into negatively curved π-systems has a significant effect on both the molecular geometry and photophysical properties; however, the synthesis of these helical π-systems embedded with nonbenzenoid subunits remains challenging due to the high strain deriving from both the curvature and helix. Here, we report a family of nonalternant nanographenes containing a nitrogen (N)-doped cyclopenta[ef]heptalene unit. Among them, CPH-2 and CPH-3 can be viewed as hybrids of benzoannulated cyclopenta[ef]heptalene and aza[7]helicene. The crystal structures revealed a saddle geometry for CPH-1, a saddle-helix hybrid for CPH-2, and a twist-helix hybrid for CPH-3. Experimental measurements and theoretical calculations indicate that the saddle moieties in CPHs undergo flexible conformational changes at room temperature, while the aza[7]helicene subunit exhibits a dramatically increased racemization energy barrier (78.2 kcal mol-1 for CPH-2, 143.2 kcal mol-1 for CPH-3). The combination of the nitrogen lone electron pairs of the N-doped cyclopenta[ef]heptalene unit with the twisted helix fragments results in rich photophysics with distinctive fluorescence and phosphorescence in CPH-1 and CPH-2 and the similar energy fluorescence and phosphorescence in CPH-3. Both enantiopure CPH-2 and CPH-3 display distinct circular dichroism (CD) signals in the UV-vis range. Notably, compared to the reported fully π-extended helical nanographenes, CPH-3 exhibits excellent chiroptical properties with a |gabs| value of 1.0 × 10-2 and a |glum| value of 7.0 × 10-3; these values are among the highest for helical nanographenes.

Understanding the cavity Born-Oppenheimer approximation.

Experiments have demonstrated that vibrational strong coupling between molecular vibrations and light modes can significantly change molecular properties, such as ground-state reactivity. Theoretical studies toward the origin of this exciting observation can roughly be divided into two categories, with studies based on Hamiltonians that simply couple a molecule to a cavity mode via its ground-state dipole moment on the one hand, and on the other hand ab initio calculations that self-consistently include the effect of the cavity mode on the electronic ground state within the cavity Born-Oppenheimer (CBO) approximation; these approaches are not equivalent. The CBO approach is more rigorous, but unfortunately it requires the rewriting of electronic-structure code, and its results may sometimes be hard to physically interpret. In this work, we exploit the relation between the two approaches and demonstrate on a real molecule (hydrogen fluoride) that for realistic coupling strengths, we can recover CBO energies and spectra to high accuracy using only out-of-cavity quantities from standard electronic-structure calculations. In doing so, we discover what thephysical effects underlying the CBO results are. Our methodology can aid in incorporating more possibly important features in models, play a pivotal role in demystifying CBO results, and provide a practical and efficient alternative to full CBO calculations.