arXiv subjects

Alok Shukla

Publications and source records attributed to Alok Shukla.

At least 73 records · Page 4Linked to original sources

arXiv2022

Remarkable enhancement in catechol sensing by the decoration of selective transition metals in biphenylene sheet: A systematic first-principles study

Motivated by the recent successful synthesis of biphenylene structure [Science 372, (2021), 852], we have explored the sensing properties of this material towards the catechol biomolecule by performing the first-principles density functional theory and molecular dynamics simulations. Pristine biphenylene sheet adsorbs catechol molecule with a binding energy of -0.35 eV, which can be systematically improved by decorating the transition metals (Ag, Au, Pd, and Ti) at various possible sites of biphenylene. It is observed that the catechol molecule is adsorbed on Pd and Ti-decorated biphenylene sheets with strong adsorption energies of -1.00 eV and -2.54 eV, respectively. The interaction of the catechol molecule with biphenylene and metal-decorated biphenylene is due to the charge transfer from the O-2p orbitals of the catechol molecule to the C-2p orbitals of biphenylene and d-orbitals of metals in metal-decorated biphenylene, respectively. From the Bader charge calculation, we found that 0.05e amount of charge is transferred from the catechol molecule to pristine biphenylene, which gets almost double (~0.1e) for the Ti-decorated biphenylene sheet. The diffusion energy barrier for the clustering of the Pd and Ti atoms comes out to be 2.39 eV and 4.29 eV, computed by performing the climbing-image nudged elastic band calculations. We found that the catechol molecule gets desorbed from the pristine biphenylene sheet even at 100 K but remains attached to metal (Pd, Ti) decorated biphenylene sheets at room temperature by performing the ab-initio molecular dynamics simulations. The Ti-decorated biphenylene sheet has more sensitivity toward catechol adsorption while the Pd-decorated biphenylene sheet has a suitable recovery time at 500 K. The results suggest that the Pd and Ti-decorated biphenylene sheets are promising materials for catechol detection.

cond-mat.mtrl-sci↗

arXiv2022

Influence of compressive strain on the hydrogen storage capabilities of graphene: A density functional theory study

Pristine graphene is not suitable for hydrogen storage at ambient conditions since it binds the hydrogen molecules only by van der Waals interactions. However, the adsorption energy of the hydrogen molecules can be improved by doping or decorating metal atoms on the graphene monolayer. The doping and decoration processes are challenging due to the oxygen interference in hydrogen adsorption and the clustering issue of metal atoms. To improve the hydrogen adsorption energy in pristine graphene, we have explored the hydrogen storage capabilities of graphene monolayer in the presence of compressive strain. We found that at 6 % of biaxial compressive strain, a 4*4*1 supercell of graphene can adsorb 10 H$_2$ molecules above the graphene surface. The average binding energy of H$_2$ for this configuration is found to be -0.42 eV/H$_2$, which is very suitable for reversible hydrogen adsorption. We propose that a 4*4*1 supercell of graphene can adsorb a total number of 20 H$_2$ molecules leading to a high hydrogen uptake of 9.4 %. The interaction between orbitals of carbon and hydrogen atoms and the charge transfer process have been studied by plotting the partial density of states and surface charge density plots. The electronic density around the C-C bonds of graphene increases in the presence of compressive strain, due to which hydrogen molecules are strongly adsorbed.

cond-mat.mtrl-sci↗

arXiv2022

Effect of Pressure on Electrical and optical Properties of Metal Doped TiO$_2$

A comparative study of the electrical and optical properties has been done on 3d-doped TiO$_2$. Ti$_{1-x}$M$_x$O$_2$ (M= Sc, V, Cr, Mn, Fe, Co, Ni, Cu, Zn) powder and its corresponding pellets, with doping concentration $x= 0.05$. The samples were prepared using the solid-state route. Optical and electrical measurements have been performed for all prepared samples and interestingly, it is observed that due to external pressure (i.e. strain) both the properties change significantly. A rigorous theoretical calculation has also been carried out to verify the experimental band gap obtained from optical absorption spectroscopy. In case of pellet sample band gap decreases as compared to the powder sample due to variation of pressure inside the structures. Role of doping has also been investigated both in pellet and powder forms and we found that the band gap decreases as the atomic number of dopants increases. A cross-over behavior is seen in pellet samples on doping with Ni, Cu and Zn (i.e. band gap increases with an increase in the atomic number of dopant). Electrical resistivity measurements have been carried out for both pellet and powder samples and it is found that in the case of strained samples the value of resistivity is smaller while in the case of strain-free samples it is quite large. We believe that the present study suggests a novel approach for tuning the electrical and optical properties of semiconducting oxides either from doping or from applied pressure (or strain).

cond-mat.mtrl-sci↗

arXiv2022

Prediction of a Novel 2D Porous Boron Nitride Material with Excellent Electronic, Optical and Catalytic Properties

Holey graphyne (HGY) is a recently synthesized two-dimensional semiconducting allotrope of carbon composed of a regular pattern of six and eight-vertex carbon rings. In this study, based on first-principles density functional theory and molecular dynamics simulations, we predict a similar stable porous boron nitride holey graphyne-like structure that we call BN-holey-graphyne (BN-HGY). The dynamical and thermal stability of the structure at room temperature is confirmed by performing calculations of the phonon dispersion relations, and also ab-initio molecular dynamics simulations. BN-HGY structure has a wide direct bandgap of 5.18 eV, which can be controllably tuned by substituting carbon, aluminum, silicon, and phosphorus atom in place of sp and sp$^2$ hybridized boron and nitrogen atoms of BN-HGY. We have also calculated the optical properties of the HGY and BN-HGY structures for the first time and found that the optical absorption spectra of these structures span full visible and a wide range of ultraviolet regions. We have found that the Gibbs free energy of the BN-HGY structure for the hydrogen adsorption process is very close to zero (-0.04 eV) and, therefore, the BN-HGY structure can be utilized as a potential catalyst for HER. Therefore, we propose that the boron nitride analog of holey graphyne can be synthesized and that it has a wide range of applications in nanoelectronics, optoelectronics, spintronics, ultraviolet laser, and solar cell devices.

cond-mat.mtrl-sci↗

arXiv2022

First-principles predictions of tunable half metallicity in zigzag GaN nanoribbons with possible applications in CO detection and spintronics

Based on systematic first-principles density-functional theory (DFT) simulations, we predict that the zigzag GaN nanoribbons (ZGaNNR) can be used both as highly efficient CO detectors as well as spin filters. Our calculations performed both on infinitely long nanoribbons, and also on finite strands, suggest that: (a) CO binds strongly at the edges of ZGaNNRs, and (b) that several of the resultant configurations exhibit half-metallic behavior. We considered various edge-passivation sites and found that all the resultant structures are thermodynamically stable. The metallic, half-metallic, and semiconducting configurations are observed as a function of CO passivation coverage. We also compute the current-voltage (I-V) characteristics of various structures using the Landauer formalism and find that the devices made up of half-metallic configurations act as highly-efficient spin filters. The effect of CO concentration is also investigated which suggests a viable way to not just tune the electronic band gap of ZGaNNRs, but also their half metallicity. Our simulations thus suggest a new direction of research for possible device applications of III-V heterostructures.

cond-mat.mtrl-sci↗

arXiv2022

A hybrid classical-quantum algorithm for digital image processing

A hybrid classical-quantum approach for evaluation of multi-dimensional Walsh-Hadamard transforms and its applications to quantum image processing are proposed. In this approach, multidimensional Walsh-Hadamard transforms are obtained using quantum Hadamard gates (along with state-preparation, shifting, scaling and measurement operations). The proposed approach for evaluation of multidimensional Walsh-Hadamard transform has a considerably lower computational complexity (involving $O(N^d)$ operations) in contrast to classical Fast Walsh-Hadamard transform (involving $O(N^d~\log_2 N^d)$ operations), where $d$ and $N$ denote the number of dimensions and degrees of freedom along each dimension. Unlike many other quantum image representation and quantum image processing frameworks, our proposed approach makes efficient use of qubits, where only $\log_2 N $ qubits are sufficient for sequential processing of an image of $ N \times N $ pixels. Selected applications of the proposed approach (for $ d=2 $) are demonstrated via computational examples relevant to basic image filtering and periodic banding noise removal and the results were found to be satisfactory.

quant-ph↗

arXiv2022

Anomalous electrochemical capacitance in Mott insulator titanium sesquioxide

Electrochemical capacitors with pure electric double layer capacitance are so far largely been limited to carbon materials only. Conventional metal oxides with Faradaic pseudocapacitance substantially suffer from material instability at high temperatures and thus there is a demand for novel metal oxides exhibiting thermally improved high electric double layer capacitance with material stability. In this study, titanium sesquioxide, Ti$_2$O$_3$, a Mott insulator in its metallic state at 300$^o$ C showed an anomalous increase of $\approx$ 560% in the solid-state electrochemical capacitance as compared to its pristine response at room temperature (RT). In aqueous electrolyte, the maximum capacitance was obtained up to 1053 $μ$F/cm$^2$, which is 307% higher than with solid-state electrolyte. Moreover, the semiconducting state of Ti$_2$O$_3$ demonstrated $\approx$ 3500% enhancement in its electrochemical capacitance upon infrared illumination at RT. The observed electrochemical responses in Ti$_2$O$_3$ are attributed to the transition of semiconducting to the metallic state by redistribution of the localized electrons. Our experimental results find a good agreement with the first-principles density-functional theory calculations that revealed an increase in the charge density with the rise in temperature, which is mainly attributed to the surface Ti atoms. The study open has wide avenues to engineer the electrochemical double layer capacitance of theory calculations that revealed an increase in the charge density with the rise in temperature, which is mainly attributed to the surface Ti atoms. The study opens wide avenues to engineer the electrochemical double layer capacitance of Ti$_2$O$_3$ with high chemical stability.

cond-mat.mtrl-sci↗

arXiv2022

Graphene Quantum Dot with Divacancy and Topological Defects: A Novel Material for Promoting Prompt and Delayed Fluorescence of Tunable Wavelengths

This work demonstrates the unique approach of introducing divacancy imperfections in topological Stone-Wales type defected graphene quantum dots for harvesting both singlet and triplet excitons, essential for fabricating fluorescent organic light-emitting diodes. Here, we first reveal that structural relaxation of these systems establishes the high-spin triplet state as the stable ground state at room temperature, thereby significantly increasing their potential in designing spintronic devices. Our extensive electron-correlated computations then demonstrate that the energetic ordering of the singlet and triplet states in these relaxed structures can trigger both prompt and delayed fluorescence of different wavelengths through various decay channels. Particularly, the position of divacancy determines the tunability range of the emission wavelengths. In addition, our results obtained from both multi-reference singles-doubles configurationinteraction (MRSDCI) and first-principles time-dependent density functional theory (TDDFT) methodologies highlight that the synergetic effects of divacancy-position,structural relaxation and spin multiplicity critically govern the nature and magnitude of shift exhibited by the most intense peak of the absorption profile, crucial for designing optoelectronic devices.

cond-mat.mes-hall↗

arXiv2022

On teaching mathematics to gifted students: some enrichment ideas and educational activities

Many mathematicians find mathematics aesthetically beautiful and even comparable to art forms such as music or painting. On the other hand, every year a great number of school students leave mathematics with total disillusionment and bitterness, without ever witnessing any beauty in it. In this work, we give some strategies to teach mathematics, especially to gifted students and to instill a love of mathematics in them. We will describe an integrated approach to teaching mathematics where students are introduced to more advanced, more elegant and more beautiful aspects of the subject early. The proposed integrated approach takes advantage of the fascinating interconnections between various subfields of mathematics, and even borrows from advanced topics such as number theory and topology. Combining the teaching of computer programming with the teaching of mathematics is another key focus of this work. This opens up the door to explore, not only the beautiful topics such as fractals, computer math art and computer graphics in general, but also real-life applications resulting from computer simulations in engineering and physics and other natural sciences. We will also discuss the use of storytelling, explorations and experimenting, puzzles and creative problem solving etc., to make learning interesting for students. It is important to show students that the `true' essence of mathematics goes beyond the dry procedural drill of learning arithmetic. Students must be provided with the opportunities to experience the `aha moment' resulting from the joy of solving a difficult problem, or from the understanding of a deep concept with complete clarity. We will discuss several strategies, and provide many examples to illustrate how this could be achieved, taking into account the emotional and psychological aspects of mathematical cognition and learning.

math.HO↗

arXiv2022

Density Functional Theory Study of the Hydrogen Evolution Reaction in Haeckelite Boron Nitride Quantum Dots

To satisfy rising energy needs and to handle the forthcoming worldwide climate transformation, major research attention has been drawn to environmentally friendly, renewable, and abundant energy resources. Hydrogen plays an ideal and significant role is such resources, due to its non-carbon-based energy and production through clean energy. In this work, we have explored the catalytic activity of a newly predicted haeckelite boron nitride quantum dot (haeck-BNQD), constructed from the infinite BN sheet, for its utilization in hydrogen production. Density functional theory calculations are employed to investigate geometry optimization, electronic and adsorption mechanism of haeck-BNQD using Gaussian16 package, employing the hybrid B3LYP and wB97XD functionals, along with 6- 31G(d,p) basis set. A number of physical quantities such as HOMO/LUMO energies, the density of states, hydrogen atom adsorption energies, Mulliken populations, Gibbs free energy, work functions, overpotentials, etc., have been computed and analyzed in the context of the catalytic performance of haeck-BNQD for the hydrogen-evolution reaction (HER). Based on our calculations, we predict that the best catalytic performance will be obtained for H adsorption on top of the squares or the octagons of haeck-BNQD. We hope that our prediction of the most active catalytic sites on haeck-BNQD for HER will be put to test in future experiments.

cond-mat.mtrl-sci↗

arXiv2022

An Ab-initio study of the Y decorated 2D holey graphyne for hydrogen storage application

Expanding pollution and rapid consumption of natural reservoirs (gas, oil, and coal) led humankind to explore alternative energy fuels like hydrogen fuel. Solid-state hydrogen storage is most desirable because of its usefulness in the onboard vehicle. In this work, we explored the yttrium decorated ultra porous, two-dimensional holey-graphyne for hydrogen storage. Using the first principles DFT simulations, we predict that yttrium doped holey graphyne can adsorb up to seven hydrogen molecules per yttrium atom resulting in a gravimetric hydrogen weight percentage of 9.34, higher than the target of 6.5 wt% set by the US Department of Energy (DoE). The average binding energy per H$_2$ and desorption temperature come out to be -0.34 eV and ~ 438 K, respectively. Yttrium atom is bonded strongly on HGY sheet due to charge transfer from Y 4d orbital to C 2p orbital whereas the adsorption of H$_2$ molecule on Y is due to Kubas-type interactions involving charge donation from H 1s orbital to Y 3d orbital and back donation with net charge gain by H 1s orbital. Furthermore, sufficient energy barriers for metal atom diffusion have been found to prevent the clustering of transition metal (yttrium) on the HGY sheet. The stability of the system at higher temperatures is analyzed using Ab-initio molecular dynamics (AIMD) method and the system is found to be stable at room and the highest desorption temperature. Stability of the system at higher temperatures, presence of adequate diffusion energy barrier to prevent metal-metal clustering, high gravimetric wt% of H$_2$ uptake with suitable binding energy, and desorption temperature signifies that Y-doped HGY is a promising material to fabricate high capacity hydrogen storage devices.

cond-mat.mtrl-sci↗

arXiv2022

A hybrid classical-quantum algorithm for solution of nonlinear ordinary differential equations

A hybrid classical-quantum approach for the solution of nonlinear ordinary differential equations using Walsh-Hadamard basis functions is proposed. Central to this hybrid approach is the computation of the Walsh-Hadamard transform of arbitrary vectors, which is enabled in our framework using quantum Hadamard gates along with state preparation, shifting, scaling, and measurement operations. It is estimated that the proposed hybrid classical-quantum approach for the Walsh-Hadamard transform of an input vector of size N results in a considerably lower computational complexity (O(N) operations) compared to the Fast Walsh-Hadamard transform (O(N log2(N)) operations). This benefit will also be relevant in the context of the proposed hybrid classical-quantum approach for the solution of nonlinear differential equations. Comparisons of results corresponding to the proposed hybrid classical-quantum approach and a purely classical approach for the solution of nonlinear differential equations (for cases involving one and two dependent variables) were found to be satisfactory. Some new perspectives relevant to the natural ordering of Walsh functions (in the context of both classical and hybrid approaches for the solution of nonlinear differential equations) and representation theory of finite groups are also presented here.

quant-ph↗

arXiv2022

Tiling proofs of Jacobi triple product and Rogers-Ramanujan identities

We use the method of tiling to give elementary combinatorial proofs of some celebrated $q$-series identities, such as Jacobi triple product identity, Rogers-Ramanujan identities, and some identities of Rogers. We give a tiling proof of the q-binomial theorem and a tiling interpretation of the q-binomial coefficients. A new generalized $ k $-product $q$-series identity is also obtained by employing the `tiling-method', wherein the generating function of the set of all possible tilings of a rectangular board is computed in two different ways to obtain the desired $q$-series identity. Several new recursive $ q$-series identities were also established. The `tiling-method' holds promise for giving an aesthetically pleasing approach to prove old and new $q$-series identities.

math.CO↗

arXiv2022

Role of Functionalized Graphene Quantum Dots in Hydrogen Evolution Reaction: A Density Functional Theory Study

Density functional theory (DFT) can be quite advantageous in advancing the field of catalysis because of the microscopic insights it provides, and thus can guide experimental searches of novel catalysts. Several recent works have demonstrated that low-dimensional materials can be very efficient catalysts. Graphene quantum dots (GQDs) have gained much attention in past years due to their unique properties like low toxicity, chemical inertness, biocompatibility, crystallinity, etc. These properties of GQDs which are due to quantum confinement and edge effects facilitate their applications in various fields like sensing, photoelectronics, catalysis, and many more. Furthermore, the properties of GQDs can be enhanced by doping and functionalization. In order to understand the effects of functionalization by oxygen and boron based groups on the catalytic properties relevant to the hydrogen-evolution reaction (HER), we perform a systematic study of GQDs functionalized with the oxygen (O), borinic acid (BC$_2$O), and boronic acid (BCO$_2$ ). All calculations that included geometry optimization, electronic and adsorption mechanism, were carried out using the Gaussian16 package, employing the hybrid functional B3LYP, and the basis set 6-31G(d,p). With the variation in functionalization groups in GQDs, we observe significant changes in their electronic properties. The adsorption energy E$_{ads}$ of hydrogen over O-GQD, BC$_2$O-GQD, and BCO$_2$-GQD is -0.059 eV, -0.031 eV and -0.032 eV respectively. Accordingly, Gibbs free energy ($ΔG$) of hydrogen adsorption is extraordinarily near the ideal value (0 eV) for all the three types of functionalized GQDs. Thus, the present work suggests pathways for experimental realization of low-cost and multifunctional GQDs based catalysts for clean and renewable hydrogen energy production.

cond-mat.mtrl-sci↗

arXiv2022

Ultrahigh reversible hydrogen storage in K and Ca decorated 4-6-8 biphenylene sheet

By applying density functional theory (DFT) and ab-initio molecular dynamics (AIMD) simulations, we predict the ultrahigh hydrogen storage capacity of K and Ca decorated single-layer biphenylene sheet (BPS). We have kept various alkali and alkali earth metals, including Na, Be, Mg, K, Ca, at different sites of BPS and found that K and Ca atoms prefer to bind individually on the BPS instead of forming clusters. It was found that 2x2x1 supercell of biphenylene sheet can adsorb eight K, or eight Ca atoms, and each K or Ca atom can adsorb 5 H$_2$, leading to 11.90 % or 11.63 % of hydrogen uptake, respectively, which is significantly higher than the DOE-US demands of 6.5 %. The average adsorption energy of H$_2$ for K and Ca decorated BPS is -0.24 eV and -0.33 eV, respectively, in the suitable range for reversible H$_2$ storage. Hydrogen molecules get polarized in the vicinity of ionized metal atoms hence get attached to the metal atoms through electrostatic and van der Waals interactions. We have estimated the desorption temperatures of H$_2$ and found that the adsorbed H$_2$ can be utilized for reversible use. We have found that a sufficient energy barrier of 2.52 eV exists for the movement of Ca atoms, calculated using the climbing-image nudged elastic band (CI-NEB) method. This energy barrier can prevent the clustering issue of Ca atoms. The solidity of K and Ca decorated BPS structures were investigated using AIMD simulations.

cond-mat.mtrl-sci↗

arXiv2022

High-capacity reversible hydrogen storage in scandium decorated holey graphyne: Theoretical perspectives

We have investigated the hydrogen storage capabilities of scandium decorated holey graphyne, a recently synthesized carbon allotrope, by applying density functional theory and molecular dynamics simulations. We have observed that one unit cell of holey graphyne can adsorb 6 Sc atoms, and each Sc atom can adsorb up to 5 H$_2$ molecules with an average binding energy and average desorption temperature of -0.36 eV/H$_2$ and 464 K, respectively. The gravimetric weight percentage of hydrogen is 9.80 %, which is considerably higher than the Department of Energy, United-States requirements of 6.5 %. We have found that a total amount of 1.9e charge transfers from the 3d and 4s orbitals of Sc atom to the C-2p orbitals of holey graphyne by performing the Bader charge analysis. Hydrogen molecules are bonded with the scandium atom by Kubas interactions. The ab-initio molecular dynamics simulations confirm the structural integrity of scandium decorated holey graphyne system at the high desorption temperatures. The presence of sufficient diffusion energy barriers for the Sc atom ensure the avoidance of metal-metal clustering in the system.

cond-mat.mtrl-sci↗

arXiv2022

Exploring yttrium doped C$_{24}$ fullerene as a high-capacity reversible hydrogen storage material: DFT investigations

By employing the state-of-the-art density functional theory, we report the hydrogen storage capability of yttrium decorated C$_{24}$ fullerene. Single Y atom attached on C$_{24}$ fullerene can reversibly adsorb a maximum number of 6 H$_2$ molecules with average adsorption energy -0.37 eV and average desorption temperature 477 K, suitable for fuel cell applications. The gravimetric weight content of hydrogen is 8.84 %, which exceeds the target value of 6.5 wt % H by the department of energy (DoE) of the United States. Y atom is strongly bonded to C$_{24}$ fullerene with a binding energy of -3.4 eV due to a charge transfer from Y-4d and Y-5s orbitals to the C-2p orbitals of C$_{24}$ fullerene. The interaction of H$_2$ molecules with the Y atom is due to the Kubas type interaction involving a charge donation from the metal d orbital to H 1s orbital, and back donation causing slight elongation of H-H bond length. The stability of the system at the highest desorption temperature is confirmed by ab-initio molecular dynamics simulations, and the metal-metal clustering formation has been investigated by computing the diffusion energy barrier for the movement of Y atoms. We have corrected all the calculated energies for the van der Waals (vdW) interactions by applying the dispersion energy corrections, in addition to the contribution of the GGA exchange-correlation functional. The C$_{24}$+Y system is stable at room temperature, and at the highest desorption temperature, the presence of a sufficient diffusion energy barrier prevents metal-metal clustering. Furthermore, binding energies of H$_2$ are within the target value by DoE (-0.2-0.7 eV/H$_2$ ), while H$_2$ uptake (8.84 % H) is higher than DoE's criteria. Therefore, we propose that Y decorated C$_{24}$ fullerene can be tailored as a practically viable potential hydrogen storage candidate.

cond-mat.mtrl-sci↗

arXiv2021

Why does B$_{12}$H$_{12}$-icosahedron need two electrons to be stable: A first-principles electron-correlated investigation of B$_{12}$H$_{n}$ ($n=$6,12) clusters

In this work, we present large-scale electron-correlated computations on various conformers of B$_{12}$H$_{12}$ and B$_{12}$H$_{6}$ clusters, to understand the reasons behind the high stability of di-anion icosahedron ($I_{h}$) and cage-like B$_{12}$H$_{6}$ geometries. Although the B$_{12}$-icosahedron is the basic building block in some structures of bulk boron, it is unstable in its free form. Furthermore, its H-passivated entity, i.e., B$_{12}$H$_{12}$ icosahedron is also unstable in free form. However, dianion B$_{12}$H$_{12}$ has been predicted to be stable as a perfect icosahedron in the free-standing form. In order to capture the correct picture for the stability of B$_{12}$H$_{12}^{-2}$ and B$_{12}$H$_{6}$ clusters, we optimized these structures by employing the coupled-cluster singles-doubles (CCSD) approach and cc-pVDZ basis set. We also performed vibrational frequency analysis of the isomers of these clusters, using the same level of theory to ensure the stability of the structures. For all the stable geometries obtained from the vibrational frequency analysis, we additionally computed their optical absorption spectra using the time-dependent density functional theory (TDDFT) approach, at the the B3LYP/6-31G{*} level of theory. Our calculated absorption spectra could be probed in future experiments on these clusters.

physics.chem-ph↗