Atomic Orbitals Research Articles

The Separability Problem in Molecular Quantum Systems: Information-Theoretic Framework for Atoms in Molecules.

Even though molecules are fundamentally quantum entities, the concept of a molecule retains certain classical attributes concerning its constituents. This includes the empirical separability of a molecule into its three-dimensional, rigid structure in Euclidean space, a framework often obtained through experimental methods like X-Ray crystallography. In this work, we delve into the mathematical implications of partitioning a molecule into its constituent parts using the widely recognized Atoms-In-Molecules (AIM) schemes, aiming to establish their validity within the framework of Information Theory concepts. We have uncovered information-theoretical justifications for employing some of the most prevalent AIM schemes in the field of Chemistry, including Hirshfeld (stockholder partitioning), Bader's (topological dissection), and the quantum approach (Hilbert's space definition). In the first approach we have applied the generalized principle of minimum relative entropy derived from the Sharma-Mittal two-parameter functional, avoiding the need for an arbitrary selection of reference promolecular atoms. Within the ambit of topological-information partitioning, we have demonstrated that the Fisher information of Bader's atoms conform to a comprehensive theory based on the Principle of Extreme Physical Information avoiding the need of employing the Schwinger's principle, which has been proven to be problematic. For the quantum approach we have presented information-theoretic justifications for conducting Löwdin symmetric transformations on the density matrix to form atomic Hilbert spaces generating orthonormal atomic orbitals with maximum occupancy for a given wavefunction.

Bisgermylene-Stabilized Stannylone: Catalytic Reduction of Nitrous Oxide and Nitro Compounds via Element-Ligand Cooperativity.

This study describes the synthesis, structural characterization, and catalytic application of a bis(germylene)-stabilized stannylone (2). The reduction of digermylated stannylene (1) with 2.2 equiv of potassium graphite (KC8) leads to the formation of stannylone 2 as a green solid in 78% yield. Computational studies showed that stannylone 2 possesses a formal Sn(0) center and a delocalized 3-c-2-e π-bond in the Ge2Sn core, which arises from back-donation of the p-type lone pair electrons on the Sn atom to the vacant orbitals of the Ge atoms. Stannylone 2 can serve as an efficient precatalyst for the selective reduction of nitrous oxide (N2O) and nitroarenes (ArNO2) with the formation of dinitrogen (N2) and hydrazines (ArNH-NHAr), respectively. Exposure of 2 with N2O (1 atm) resulted in the insertion of two oxygen atoms into the Ge-Ge and Ge-Sn bonds, yielding the germyl(oxyl)stannylene (3). Moreover, the stoichiometric reaction of 2 with 1-chloro-4-nitrobenzene afforded an amido(oxyl)stannylene (4) through the complete scission of the N-O bonds of the nitroarene. Stannylenes 3 and 4 serve as catalytically active species for the catalytic reduction of nitrous oxide and nitroarenes, respectively. Mechanistic studies reveal that the cooperation of the low-valent Ge and Sn centers allows for multiple electron transfers to cleave the N-O bonds of N2O and ArNO2. This approach presents a new strategy for catalyzing the deoxygenation of N2O and ArNO2 using a zerovalent tin compound.

Accuracy of projected atomic virtual orbital space in embedding applications

ABSTRACT The performance of the recently suggested projected atomic orbitals (PAO) approach as the virtual space in excited state projection-based embedding applications is analysed. The role of the parameters in the PAO generation is discussed and the impact of different choices is evaluated on the ground state of the stacked formaldehyde and pyrrole dimers. A comparison of excitation energies obtained with PAOs and localised virtual orbitals is given and the role of diffuse basis functions is discussed using a benchmark set from previous studies.

DNA as a perfect quantum computer based on the quantum physics principles

DNA is a complex multi-resolution molecule whose theoretical study is a challenge. Its intrinsic multiscale nature requires chemistry and quantum physics to understand the structure and quantum informatics to explain its operation as a perfect quantum computer. Here, we present theoretical results of DNA that allow a better description of its structure and the operation process in the transmission, coding, and decoding of genetic information. Aromaticity is explained by the oscillatory resonant quantum state of correlated electron and hole pairs due to the quantized molecular vibrational energy acting as an attractive force. The correlated pairs form a supercurrent in the nitrogenous bases in a single band π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi$$\\end{document}-molecular orbital (π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi$$\\end{document}-MO). The MO wave function (Φ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\Phi )$$\\end{document} is assumed to be the linear combination of the n constituent atomic orbitals. The central Hydrogen bond between Adenine (A) and Thymine (T) or Guanine (G) and Cytosine (C) functions like an ideal Josephson Junction. The approach of a Josephson Effect between two superconductors is correctly described, as well as the condensation of the nitrogenous bases to obtain the two entangled quantum states that form the qubit. Combining the quantum state of the composite system with the classical information, RNA polymerase teleports one of the four Bell states. DNA is a perfect quantum computer.

The dual active sites reconstruction on gelatin in-situ derived 3D porous N-doped carbon for efficient and stable overall water splitting

The exploration of bifunctional electrocatalysts with high activity, stability, and economy is of great significance in promoting the development of water splitting. Herein, a dual active sites heterostructure NiCoS/NC was designed to be derived in situ on 3D N-doped porous carbon (NC) using gelatin as a nitrogen and carbon source. The characterization of experiments suggests that nanoflower-like Ni2CoS4 (abbreviated as NiCoS) was randomly distributed on the NC substrate, and the sheet-like NC formed a highly open porous network structure resembling a honeycomb, which provided more accessible active sites for electrolyte ions. In addition, the special nanostructures of the catalyst materials help to promote the surface reconstruction to the real active substance NiOOH/CoOOH, and the double active sites synergistically reduce the overpotential of OER and improve its kinetics. DFT (Density-functional theory) calculations reveal the electronic coupling of NiCoS/NC in atomic orbitals, modulation of electrons by the heterointerface and N-doping, and synergistic effect of dual active sites improving the inherent catalytic activity. The NiCoS/NC composite electrocatalyst exhibited a 177 mV small OER overpotential and a 132 mV small HER overpotential with Faraday efficiencies as high as 96 % and 98 % at 10 mA cm−2 current density. In the two-electrode system, it also requires only an ultra-low voltage of 1.52 V to achieve a 10 mA cm−2 current density, and it shows excellent long-term water splitting stability. This provides a new idea for the development of transition metal-based bifunctional electrocatalysts.

Enhancement of Magnetic Stability in Antiferromagnetic CoO Films by Adsorption of Organic Molecules.

Antiferromagnets are a class of magnetic materials of great interest in spintronic devices because of their stability and ultrafast dynamics. When interfaced with an organic molecular layer, antiferromagnetic (AF) films are expected to form a spinterface that can allow fine control of specific AF properties. In this paper, we investigate spinterface effects on CoO, an AF oxide. To access the magnetic state of the antiferromagnet, we couple it to a ferromagnetic Co film via an exchange bias (EB) effect. In this way, the formation of a spinterface is detected through changes induced on the CoO/Co EB system. We demonstrate that C60 and Gaq3 adsorption on CoO shifts its blocking temperature; in turn, an increase in both the EB fields and the coercivities is observed on the EB-coupled Co layer. Ab initio calculations for the CoO/C60 interface indicate that the molecular adsorption is responsible for a charge redistribution on the CoO layer that alters the occupation of the d orbitals of Co atoms and, to a smaller extent, the p orbitals of oxygen. As a result, the AF coupling between Co atoms in the CoO is enhanced. Considering the granular nature of CoO, a larger AF stability upon molecular adsorption is then associated with a larger number of AF grains that are stable upon reversal of the Co layer.

First-principles calculation on electronic properties of hydrogen evolution reaction of Ni-based electrode surfaces with different monatomic doping

At present, the hydrogen evolution reaction (HER) of Ni-based electrode has an important influence on water electrolysis hydrogen production technology, involving complex electrochemical process of electrode. In this project, Materials Studio (MS) software was used to design and construct Ni-based electrode surface (NES) models with monatomic Mo, Co, Fe, Cr doping, and the NES models attached 1 H atom and 2H atoms were denoted as the NES-H models and NES-2H model, respectively. Then the first-principles calculation was carried out.The results showed that the doping of different atoms can effectively change the work function of the pure Ni. In the charge transfer process of the four NES-2H models, the distance between the two H atoms is most affected by Mo doping, and they leave the Ni electrode surface as a single H ion, respectively, while the effect on Co, Fe and Cr doping is relatively consistent, and they leave the Ni electrode surface with H2 molecules, respectively. The doping of four single atoms changes the distance of valence band (VB) top and conduction band (CB) bottom from Fermi level in NES, NES-H and NES-2H models, and affects the HER, in which Mo doping has the greatest effect. The TDOS of the above models is mainly derived from the PDOS of the d orbitals of the doped atoms and Ni atoms. The results will provide a theoretical basis for the research and development of Ni-based electrode materials in HER.

Exploring hot carrier relaxation dynamics in MoSi2N4 monolayer for photocatalytic applications: Insights into electron-phonon coupling mechanisms

The relaxation process of hot carriers in MoSi2N4 monolayer remains unclear due to the need to sample electron–phonon interaction at different momenta. Utilizing density functional theory (DFT) combined with nonadiabatic molecular dynamics (NAMD), we determined that the material possesses an indirect bandgap of approximately 2.33 eV, primarily originating from the d orbitals of inner Mo atoms. NAMD simulations unveil rapid relaxation of hot electrons and holes, exhibiting lifetimes of approximately 166 fs and 146 fs, respectively. The rapid relaxation of hot carriers couples with the vibrations of outer Si and N atoms, with no inter-valley scattering observed between the K and K′ valleys. Notably, the coupling between the d orbitals of inner Mo atoms and the vibrations of outer Si and N atoms plays a pivotal role in determining the relaxation dynamics of hot carriers, shedding light on the intricate interplay between electronic and vibrational modes in this material. Our research reveals the potential application value of MoSi2N4 monolayer material as a photocatalyst and elucidates a relaxation mechanism governing the dynamics of excited carriers.

Precise Modulation of the Coordination Environment of Single Cu Site Catalysts to Regulate the Peroxymonosulfate Activation Pathway for Water Remediation.

Single atom site catalysts (SACs) with atomically dispersed active sites can be expected to be potential ideal catalysts for accurately modulating the persulfate activation pathway during the water remediation process because of their well-defined structure and the maximum metallic atom utilization. In this paper, a series of Cu SACs with different coordination environments were synthesized to elaborately regulate the peroxymonosulfate activation pathway in AOPs to clarify active species generation and transformation in water remediation. The degradation rate constants (kobs) of Cu-N2, Cu-N3, and Cu-N4 were 0.028, 0.021, and 0.015 min-1, respectively. Cu-N2 SACs exhibited a noticeable enhanced performance for bisphenol A (BPA) removal from water compared to that of the Cu-Nx SACs (x = 3, 4), accompanied by peroxymonosulfate (PMS) activation pathway variation. As shown by experimental and theoretical results, the PMS activation pathway was transformed from ROS to electron transfer with nitrogen coordination numbers decreasing from 4 to 2, which can be ascribed to the uneven charge distribution of Cu sites as well as upshifts in the d-band center, and thereby optimized electron transfer for PMS activation. Furthermore, the increasing nitrogen vacancies of single Cu site catalysts can also result in more unoccupied 3d orbitals of Cu atoms in SACs, thereby improving the intermediates' (PMS and BPA) adsorption-desorption process and BPA removal performance. These findings provided a beneficial approach for the coordination number regulation of SACs in water remediation.

Electronic Structure of Mg-, Si-, and Zn-Doped SnO2 Nanowires: Predictions from First Principles.

We investigated the electronic structure of Mg-, Si-, and Zn-doped four-faceted [001]- and [110]-oriented SnO2 nanowires using first-principles calculations based on the linear combination of atomic orbitals (LCAO) method. This approach, employing atomic-centered Gaussian-type functions as a basis set, was combined with hybrid density functional theory (DFT). Our results show qualitative agreement in predicting the formation of stable point defects due to atom substitutions on the surface of the SnO2 nanowire. Doping induces substantial atomic relaxation in the nanowires, changes in the covalency of the dopant-oxygen bond, and additional charge redistribution between the dopant and nanowire. Furthermore, our calculations reveal a narrowing of the band gap resulting from the emergence of midgap states induced by the incorporated defects. This study provides insights into the altered electronic properties caused by Mg, Si, and Zn doping, contributing to the further design of SnO2 nanowires for advanced electronic, optoelectronic, photovoltaic, and photocatalytic applications.

Adsorption and sensing characteristics of insulating gas C4F7N on 3d late transition metal‐phthalocyanine: Theoretical and experimental study

AbstractHeptafluoroisobutyronitrile (C4F7N) is being considered as a promising alternative to the greenhouse gas SF6 in the electrical industry. However, its biotoxicity necessitates the development of gas sensing technology to detect leaked C4F7N. A combination of density functional theory and experiments was employed to evaluate the adsorption and sensing performance of different metal‐phthalocyanines as potential sensing materials for C4F7N detection. The study included exploring adsorption configurations with adsorption energies, electron transfer, and adsorption distance, as well as comparisons of electronic properties, electron distribution, and density of states (DOS) among the MPcs. Furthermore, gas sensing experiments were conducted using different MPcs to detect 25–100 ppm C4F7N. The results revealed that Mn‐Pc, Fe‐Pc, Co‐Pc, and Zn‐Pc exhibited considerable chemical interactions, while Ni‐Pc and Cu‐Pc showed weaker adsorption strength. These findings were further elucidated based on the electron density and DOS of atomic orbitals. Moreover, gas sensing experiments indicated that Co‐Pc demonstrated a higher response compared to Fe‐Pc at the same concentration of C4F7N. Overall, the theoretical and experimental insights offer valuable guidance for C4F7N detection and provide a systematic approach to screen and explore organometallic polymer‐based gas sensors applicable in various fields.

Thermodynamic stability, electronic structure and mechanical properties of Mo-Re binary alloys: A first-principles calculations

Using first-principles calculations, we have systematically studied thermodynamic stability, electronic structure and mechanical properties of Mo-Re binary alloys. The alloying element Re prefers to occupy the substitution position with a formation energy of 0.10 eV in Mo rather than the tetrahedron/octahedron interstitial position. The charge transfers are obviously present between Re and Mo atoms, which can be confirmed by the Bader charge analysis. The density of states (DOS) demonstrates that the d orbitals of Re and Mo atoms are hybridized, revealing that Re and its adjacent Mo atoms can form the directional bond containing covalent components. On the basis of above studies on the most stable occupancy structure, the mechanical quantities (the elastic constants Cij, bulk modulus B, Young’s modulus E, shear modulus G, Poisson’s ratio v, and B/G) have been analyzed for three Mo-Re alloys with the low Re content, which are Mo127Re1, Mo53Re1 and Mo15Re1, respectively. All these mechanical quantities of both Mo127Re1 and Mo53Re1 alloys are nearly the same as that of perfect Mo, while all these mechanical quantities of Mo15Re1 alloy are obviously larger or smaller than that of perfect Mo. This demonstrates that Mo15Re1 alloy has significantly different mechanical characteristics from Mo127Re1 and Mo53Re1 alloys as well as perfect Mo. These results can provide a significant reference for the application of Mo-Re alloys in future fusion fields.

Klein Tunneling in β12 Borophene.

Motivated by the recent observation of Klein tunneling in 8-Pmmn borophene, we delve into the phenomenon in β12 borophene by employing tight-binding approximation theory to establish a theoretical mode. The tight-binding model is a semi-empirical method for establishing the Hamiltonian based on atomic orbitals. A single cell of β12 borophene contains five atoms and multiple central bonds, so it creates the complexity of the tight-binding model Hamiltonian of β12 borophene. We investigate transmission across one potential barrier and two potential barriers by changing the width and height of barriers and the distance between two potential barriers. Regardless of the change in the barrier heights and widths, we find the interface to be perfectly transparent for normal incidence. For other angles of incidence, perfect transmission at certain angles can also be observed. Furthermore, perfect and all-angle transmission across a potential barrier takes place when the incident energy approaches the Dirac point. This is analogous to the "super", all-angle transmission reported for the dice lattice for Klein tunneling across a potential barrier. These findings highlight the significance of our theoretical model in understanding the complex dynamics of Klein tunneling in borophene structures.

Adsorption behaviors of ethyltriethoxysilane on the calcium silicate hydrate surface: Effect of Ca/Si ratio and adsorption sites

Silane coupling agents (SCAs) are utilized to enhance the impermeability of concrete surfaces, whose adhesion force is affected by the interfacial interactions in between that remain unclear. In this study, we probe the adsorption tendencies of ethyltriethoxysilane (ETES) onto C-S-H surfaces by employing density functional theory (DFT) calculations and Born-Oppenheimer molecular dynamics (BOMD) simulations. Results suggest that significant chemisorption occurs at the CaOH(1.5), SiOH(1.0), Ca(1.0) sites C-S-H surfaces. Electronic structures analysis proved that the chemisorption of hydroxyl sites arises from the overlap of H and O atomic orbitals, resulting in the formation of hydrogen bonds. The chemisorption of the Ca(1.0) site is caused by electrostatic adsorption between calcium and oxygen. Adsorption energy results show: ECaOH(1.5) > ECa(1.0) > ESiOH(1.0). Moreover, ETES remains transverse adsorption on low Ca/Si C-S-H surfaces, while displaying longitudinal adsorption on high. Interaction analysis illustrates the configuration discrepancy arising from the absence of bridge silicon-oxygen tetrahedrons which possess vdW interactions with ethyl. Notably, transverse adsorption covers a wider area on the C-S-H surface thereby enhancing the hydrophobic effect. In summary, the utilization of ETES presents notable advantages within the context of low Ca/Si ratio cement. This study contributes valuable insights into the design and application of silane coatings.

Structural and Quantum chemical insights into the atomic orbitals of 2-benzoylbenzoic acid: Density functional theory approach

Abstract The present work aims to explore the structural insights and the molecular orbitals associated with 2-benzoylbenzoic acid through density functional theory approach. The geometrical parameters of the optimized structure of 2-benzoylbenzoic acid were obtained at B3LYP/6-311++G basis set. The atomic sites which are prone to electrophilic/nucleophilic attack were identified from molecular electrostatic potential (MEP) surface analysis. The molecular orbitals (lone pair, bonding and anti-bonding) which are favorable to the charge delocalization within the system and stabilize the molecule were studied. Besides, the vibrational assignments of the characteristic group frequencies and coupled modes vibrations were made using Cartesian coordinate displacement analysis. Moreover, the electronic transitions between the filled and unfilled molecular orbitals of 2-benzoylbenzoic acid were investigated.

Disordered layers and dimerization in the crystal structure of TaOCl2

Understanding the properties of transition metal materials requires consideration of the competition between the various types of electrons that comprise the system, whether they be delocalized and metallic, localized and magnetic, or localized and bonded. Here we report the refined crystal structure determination and physical properties of the two-dimensional layered compound TaOCl2. Within each layer we find a strong in-plane dimerization of Ta atoms perpendicular to the Ta-O-Ta chains, with significant disorder in the positioning of dimers in adjacent layers, suggesting that the free electron of each Ta localizes in Ta-Ta bonds. This is supported by resistivity measurements (ρ300K = 4.4*108 Ω-cm) as well as featureless, temperature-independent magnetic susceptibility up to T = 750 K. Analysis of the phonon contribution to specific heat shows the presence of a localized Einstein mode with TE = 175 K, attributed to the localized vibrations of the Ta-Ta dimers. Density functional theory calculations show that the magnitude of the Ta displacements (0.24 Å) has a dramatic effect on the electronic structure, changing from a metal with a bandwidth of 3.2 eV to an insulator with a flat band just below EF. Our results show how direct exchange interactions between Ta atoms that are relatively far from each other can still play a central role in the behavior of 5d transition metal compounds, taking advantage of the extended 5d atomic orbitals, and produce localized dimers with a bond distance of approximately 2.84 Å.

Foundations and applications of the orbital theory in chemistry: A philosophical perspective

The concept of atomic and molecular orbitals has been a fundamental pillar in modern chemistry, shedding light on the structures and reactivity of chemical compounds. This article examines the evolution and significance of orbital theory, its applications in chemistry, and the ongoing debate about the existence of orbitals from both physics and chemistry perspectives. Philosophical aspects related to the ontology of orbitals are explored, emphasizing the complex interplay between mathematical abstractions and tangible reality. The multifaceted nature of orbitals, their role in quantum mechanics, and their implications for understanding the quantum realm are discussed. While the debate surrounding the ontological status of orbitals remains ongoing, it highlights the profound nature of inquiries into the fundamental essence of reality. This exploration underscores the significance of continuous research and discourse in advancing our understanding of these fundamental constituents of the quantum world.

VAMPyR-A high-level Python library for mathematical operations in a multiwavelet representation.

Wavelets and multiwavelets have lately been adopted in quantum chemistry to overcome challenges presented by the two main families of basis sets: Gaussian atomic orbitals and plane waves. In addition to their numerical advantages (high precision, locality, fast algorithms for operator application, linear scaling with respect to system size, to mention a few), they provide a framework that narrows the gap between the theoretical formalism of the fundamental equations and the practical implementation in a working code. This realization led us to the development of the Python library called VAMPyR (Very Accurate Multiresolution Python Routines). VAMPyR encodes the binding to a C++ library for multiwavelet calculations (algebra and integral and differential operator application) and exposes the required functionality to write a simple Python code to solve, among others, the Hartree-Fock equations, the generalized Poisson equation, the Dirac equation, and the time-dependent Schrödinger equation up to any predefined precision. In this study, we will outline the main features of multiresolution analysis using multiwavelets and we will describe the design of the code. A few illustrative examples will show the code capabilities and its interoperability with other software platforms.

Electronic Control of the Position of the Pb Atom on the Surface of B8 Borozene in the PbB8 Cluster.

Spontaneous symmetry-breaking is common in chemical and physical systems. Here, we show that by adding an electron to the C7v PbB8 cluster, which consists of a planar B8 disk with the Pb atom situated along the C7 axis, the Pb atom spontaneously moves to the off-axis position in the PbB8- anion. Photoelectron spectroscopy of PbB8- reveals a broad ground-state transition and a large energy gap, suggesting a highly stable closed-shell PbB8 borozene complex and a significant geometry change upon electron detachment. Quantum chemistry calculations indicate that the lowest unoccupied molecular orbital of the C7v PbB8 cluster is a degenerate π orbital mainly consisting of the Pb 6px and 6py atomic orbitals. Occupation of one of the 6p orbitals spontaneously break the C7v symmetry in the anion due to the Jahn-Teller effect. The large amplitude of the position change of Pb in PbB8- relative to PbB8 is surprising owing to bonding interactions between the Pb 6p orbital with the π orbital of the B8 borozene.

Born-Oppenheimer Molecular Dynamics with a Linear Combination of Atomic Orbitals and Hybrid Functionals for Condensed Matter Simulations Made Possible. Theory and Performance for the Microcanonical and Canonical Ensembles.

The implementation of an original Born-Oppenheimer molecular dynamics module is presented, which is able to perform simulations of large and complex condensed phase systems for sufficiently long time scales at the level of density functional theory with hybrid functionals, in the microcanonical (NVE) and canonical (NVT) ensembles. The algorithm is fully integrated in the Crystal code, a program for quantum mechanical simulations of materials, whose peculiarity stems from the use of atom-centered basis functions within a linear combination of atomic orbitals to describe the wave function. The corresponding efficiency in the evaluation of the exact Fock exchange series has led to the implementation of a rich variety of hybrid density functionals at a low computational cost. In addition, the molecular dynamics implementation benefits also from the effective MPI parallelization of the code, suited to exploit high-performance computing resources available on current generation supercomputer architectures. Furthermore, the information contained in the trajectory of the dynamics is extracted through a series of postprocessing algorithms that provide the radial distribution function, the diffusion coefficient and the vibrational density of states. In this work, we present a detailed description of the theoretical framework and the algorithmic implementation, followed by a critical evaluation of the accuracy and parallel performance (e.g., strong and weak scaling) of this approach, when ice and liquid water simulations are performed in the microcanonical and canonical ensembles.