Quantum Mechanical Model Research Articles

How Aqueous Solvation Impacts the Frequencies and Intensities of Infrared Absorption Bands in Flavin: The Quest for a Suitable Solvent Model.

FTIR spectroscopy accompanied by quantum chemical simulations can reveal important information about molecular structure and intermolecular interactions in the condensed phase. Simulations typically account for the solvent either through cluster quantum mechanical (QM) models, polarizable continuum models (PCM), or hybrid quantum mechanical/molecular mechanical (QM/MM) models. Recently, we studied the effect of aqueous solvent interactions on the vibrational frequencies of lumiflavin, a minimal flavin model, using cluster QM and PCM models. Those models successfully reproduced the relative frequencies of four prominent stretching modes of flavin's isoalloxazine ring in the diagnostic 1450-1750 cm-1 range but poorly reproduced the relative band intensities. Here, we extend our studies on this system and account for solvation through a series of increasingly sophisticated models. Only by combining elements of QM clusters, QM/MM, and PCM approaches do we obtain an improved agreement with the experiment. The study sheds light more generally on factors that can impact the computed frequencies and intensities of IR bands in solution.

Quantum-Inspired Neural Network Model of Optical Illusions

Ambiguous optical illusions have been a paradigmatic object of fascination, research and inspiration in arts, psychology and video games. However, accurate computational models of perception of ambiguous figures have been elusive. In this paper, we design and train a deep neural network model to simulate human perception of the Necker cube, an ambiguous drawing with several alternating possible interpretations. Defining the weights of the neural network connection using a quantum generator of truly random numbers, in agreement with the emerging concepts of quantum artificial intelligence and quantum cognition, we reveal that the actual perceptual state of the Necker cube is a qubit-like superposition of the two fundamental perceptual states predicted by classical theories. Our results finds applications in video games and virtual reality systems employed for training of astronauts and operators of unmanned aerial vehicles. They are also useful for researchers working in the fields of machine learning and vision, psychology of perception and quantum–mechanical models of human mind and decision making.

Quantum mechanics denoising based channel estimation algorithm for mmWave massive MIMO systems

Channel estimation of millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) is crucial for the application of wireless transmission. The signal system is susceptible to external noise, which reduces the accuracy of channel estimation. The denoising of the received signal is a research hotspot and challenge for channel estimation. Therefore, this paper proposes a quantum mechanics denoising-based channel estimation method. The proposed quantum mechanics denoising-based algorithm has the advantages of not relying on the original conditions, no grid error, and strong adaptive ability. The first part is that the received noisy signal is denoised. The conversion between the signal model of mmWave massive MIMO and the physical model of quantum mechanics needs to be solved. The received noisy signal is equivalent to the potential of the stationary Schrodinger equation. Then, the Hamiltonian matrix is constructed by the received signal and the corresponding eigenvalues and eigenvectors are calculated. The eigenvectors of the Hamiltonian matrix are related to the energy of Schrodinger equation, which are determined to the adaptive basis. In addition, the received signal is projected onto the adaptive basis to calculate the coefficients. The denoised received signal is reconstructed through the soft threshold processing of the coefficients. The second part is that channel estimation is performed on the denoised received signal using the l1/2-singular value decomposition (SVD)-based algorithm. The angle parameters are iteratively moved to the actual values by gradient descent. Besides, the initial values of the angles are obtained through the SVD preprocessing method. Simulation results show that the proposed quantum mechanics denoising-based method exhibits good estimation accuracy.

Computationally assisted vibrational spectroscopy of nucleic acid bases. 2. Thymine

As in the case of cytosine [Phys. Chem. Chem. Phys. 2023, 25, 24121–24128], Raman and infrared (IR) spectra of aqueous thymine and its N-deuterated derivative, thymine-d2 have been computationally reproduced and interpreted with the use of the recently developed efficient protocol to explicit quantum mechanical modeling of structure and IR spectra of liquids and solutions [J. Phys. Chem. B, 2020, 124, 6664–6670]. A cluster model of a solute surrounded by 30 water molecules is shown to be sufficient to reproduce experimental vibrational frequencies and relative Raman intensities with the use of B3LYP-D3/def2-TZVP or B3LYP-D3/aug-cc-pVDZ simulations. Analogous PBE-D3 computations provided a less good, but still reasonably accurate, modeling of Raman spectra. It is shown that strong changes of frequencies and relative intensities of the Raman bands of thymine, caused by its hydration, can be interpreted mainly as a result of hydrogen bonding with 6 nearest water molecules. Non-negligible improvement of the quality of simulations for larger clusters comprising water molecules that do not have direct contacts with the solute, suggests that spectroscopic effects of hydration should be ascribed to the joined action of solute–solvent and solvent–solvent interactions. Nevertheless, the moderate number of water molecules required for successful simulations of the Raman spectra of aqueous thymine, suggests that the vibrational modes and derivatives of the polarizability of the solute are mainly locally influenced, while the effect of bulk water is rather modest.

Separation of oxygen from nitrogen using a graphdiyne membrane: a quantum-mechanical study.

Efficient separation of oxygen and nitrogen from air is a process of great importance for many industrial and medical applications. Two-dimensional (2D) membranes are very promising materials for separation of gases, as they offer enhanced mass transport due to their smallest atomic thickness. In this work, we examine the capacity of graphdiyne (GDY), a new 2D carbon allotrope with regular subnanometric pores, for separating oxygen (16O2) from nitrogen (14N2). A quantum-mechanical model has been applied to the calculation of the transmission probabilities and permeances of these molecules through GDY using force fields based on accurate electronic structure computations. It is found that the 16O2/14N2 selectivity (ratio of permeances) is quite high (e.g., about 106 and 102 at 100 and 300 K, respectively), indicating that GDY can be useful for separation of these species, even at room temperature. This is mainly due to the N2 transmission barrier (∼0.37 eV) which is considerably higher than the O2 one (∼0.25 eV). It is also found that molecular motions are quite confined inside the GDY pores and that, as a consequence, quantum effects (zero-point energy) are significant in the studied processes. Finally, we explore the possibility of 18O2/16O2 isotopologue separation due to these mass-dependent quantum effects, but it is found that the process is not practical since reasonable selectivities are concomitant with extremely small permeances.

The accuracy limit of chemical shift predictions for species in aqueous solution.

Interpreting NMR experiments benefits from first-principles predictions of chemical shifts. Reaching the accuracy limit of theory is relevant for unambiguous structural analysis and dissecting theoretical approximations. Since accurate chemical shift measurements are based on using internal reference compounds such as trimethylsilylpropanesulfonate (DSS), a detailed comparison of experimental with theoretical data requires simultaneous consideration of both target and reference species ensembles in the same solvent environment. Here we show that ab initio molecular dynamics simulations to generate liquid-state ensembles of target and reference compounds, including explicitly their short-range solvation environments and combined with quantum-mechanical solvation models, allows for predicting highly accurate 1H (∼0.1-0.5 ppm) and aliphatic 13C (∼1.5 ppm) chemical shifts for aqueous solutions of the model compounds trimethylamine N-oxide (TMAO) and N-methylacetamide (NMA), referenced to DSS without any system-specific adjustments. This encompasses the two peptide bond conformations of NMA identified by NMR. The results are used to derive a general-purpose guideline set for predictive NMR chemical shift calculations of NMA in the liquid state and to identify artifacts of force field models. Accurate predictions are only obtained if a sufficient number of explicit water molecules is included in the quantum-mechanical calculations, disproving a purely electrostatic model of the solvent effect on chemical shifts.

Chiroptical properties of cyanine aggregates: hierarchical modelling from monomers to bundles.

Some achiral cyanine dyes form well-ordered chiral assemblies exhibiting pronounced Circular Dichroism (CD) and Circularly Polarized Luminescence (CPL). Notably, achiral C8O3 cyanines self-assemble into tubular J-aggregates, which further organize into bundles displaying bisignate CD spectrum - hallmark of an exciton coupled system - and an unusual bisignated CPL. In contrast, the tubular aggregates display a monosignate CD spectrum. The mechanism underlying these intriguing features remains elusive. In the present work, a quantum-mechanical exciton model is proposed to elucidate the (chir)optical behaviour of C8O3 aggregates. A herringbone arrangement of C8O3 dyes within the tubular aggregates well reproduces the observed spectral signatures. The anomalous observation of a singular CD peak in tubular aggregates is ascribed to the intrinsic chirality of the monomeric units inside the aggregate, whereas the CD doublet characterizing the bundles is attributed to the exciton coupling between the constituent tubes. The bisignated CPL signal observed in bundles reveals significant anti-Kasha emission at room temperature and is quantitatively addressed accounting for a very tiny exciton splitting leading to a sizable thermal population of both exciton states. This study provides crucial insights on the complexity of C8O3 aggregation and on the origin of chiroptical response at various aggregation stages.

КОМПЬЮТЕРНОЕ МОДЕЛИРОВАНИЕ ОРГАНИЧЕСКИХ ФОРМ ЦИНКА И СЕЛЕНА НА ОСНОВЕ БЕЛКА КОЛЛАГЕНА

This article presents the results of research aimed at developing a theoretical computer model of organic forms of zinc, selenium and their interaction with collagen matrix. Collagen was chosen as an organic carrier. Quantum chemical, semiempirical and molecular dynamic methods were used to study changes in molecular properties and to perform quantum mechanical modeling of atomic structures using HyperChem v8.0 software. Molecular structures of organic forms of trace elements with amino acids were designed and optimized geometrically. The present study considers different variants and combinations of zinc and selenium compounds with four amino acids most commonly found in collagen. The correctness of geometric optimization, potential energy minimization and balanced energy properties of the system were evaluated based on the total energy of the components. The results obtained indicate potential interaction of trace elements with collagen amino acids.

Квантово-механическая модель ионного двигателя малого космического аппарата

The article presents a quantum mechanical model of an ion thruster. The basic equations describing the shape of the accelerated beam are considered. Detector plates demonstrating the interference pattern in thin films are presented. A mathematical description of the relief of thin films is given using the resulting wave function. The operation of a low-power ion engine is demonstrated. The results of numerical solution of the model with different initial values are shown. Based on the results of calculations, diagrams of the trajectories of charged particles are constructed.

Applying quantum mechanics to deconvolute benchtop 1H NMR reaction data

Quantum mechanical model files developed from pure components enable deconvolution of complex 1H NMR reaction dataset at different field strength.

Atomic diffraction by nanoholes in hexagonal boron nitride.

Fabricating patterned nanostructures with matter waves can help to realise new nanophotonic devices. However, due to dispersion effects, designing patterns with nanoscale features is challenging. Here, we consider the propagation of a helium matter wave through different holes in hexagonal boron nitride (h-BN) as a case study for the weakest dispersion interaction and the matter wave's diffraction as it passes through the holes. We use a quantum-mechanical model to calculate the polarisability of edge atoms around the holes, where we observe polarisation ripples of enhanced and reduced polarisabilities around the holes. We use these values to calculate van der Waals dispersion coefficients for the scattered helium atoms. We find that the resulting diffraction patterns are affected by the shape and size of the holes, where the smallest holes have a radius of just 6 Å. These results can be used to predict the resolution limits of nano-hole patterns on nanophotonic materials.

The Bethe Ansatz as a Quantum Circuit

The Bethe ansatz is an analytical method to solve exactly solvable models in quantum mechanics. It has been shown that the states of the Bethe ansatz can be prepared by a deterministic quantum circuit whose quantum gates were determined numerically. We report our progress in recasting the Bethe ansatz as a deterministic quantum circuit. We present the analytical expressions of the quantum gates. Formulae rely upon diagrammatic rules that define the wave functions of the Bethe ansatz by matrix product states. Based on the analytical expressions, we prove the unitarity of the quantum gates. We use our results to clarify on the equivalence between the coordinate and algebraic Bethe ansatze in light of matrix-product states.

Comment on: “Some aspects of the interaction of a magnetic quadrupole moment with an electric field in a rotating frame” [J. Math. Phys. 58, 102103 (2017)

We discuss results obtained recently for a quantum-mechanical model given by a neutral particle with a magnetic quadrupole moment in a radial electric field and a scalar potential proportional to the radial variable in cylindrical coordinates that also includes the noninertial effects of a rotating reference frame. We show that the conjectured allowed values of the cyclotron frequency are a mere artifact of the truncation of the power series used to solve the radial eigenvalue equation. Our analysis proves that the analytical expression for the eigenvalues is incorrect.

Generalizing Stratonovich–Weyl Axioms for Composite Systems

The statistical model of quantum mechanics is based on the mapping between operators on the Hilbert space and functions on the phase space. This map can be implemented by an operator that satisfies physically motivated Stratonovich–Weyl axioms. Arguments are given in favour of a certain extension of the axioms, provided that there is a priori knowledge about the composite nature of the quantum system.

Monopole harmonics on $\mathbb{CP}^{n-1}$

We find the spectra and eigenfunctions of both ordinary and supersymmetric quantum-mechanical models describing the motion of a charged particle over the \mathbb{CP}^{n-1}ℂℙn−1 manifold in the presence of a background monopole-like gauge field. The states form degenerate SU(n)SU(n) multiplets and their wave functions acquire a very simple form being expressed via homogeneous coordinates. Their relationship to multidimensional orthogonal polynomials of a special kind is discussed. By the well-known isomorphism between the twisted Dolbeault and Dirac complexes, our construction also gives the eigenfunctions and eigenvalues of the Dirac operator on complex projective spaces in a monopole background.

Silicon-Based Anodes for Li Batteries: Thermodynamics, Structural Analysis, and Li Diffusion.

Quantum mechanical and machine learning models are used to analyze the properties of silicon composite materials and their impact on anode performance. The analysis focuses on addressing challenges related to significant volume expansion during lithiation and provides valuable insights into the Gibbs free energy, chemical potentials, and relative stability of Li0 and Li+ species. Furthermore, the study explores how Li+ ions behave in the primary and secondary phases of the anode, assessing the impact of their formation on ion diffusion. This work highlights the fundamental significance of secondary phases in shaping microstructural features that impact anode properties, elucidating their contribution to the Li diffusion pathway tortuosity, which is the primary cause of the fracture of Si anodes in Li-ion batteries.

Krylov complexity in the IP matrix model

The IP matrix model is a simple large N quantum mechanical model made up of an adjoint harmonic oscillator plus a fundamental harmonic oscillator. It is a model introduced previously as a toy model of the gauge theory dual of an AdS black hole. In the large N limit, one can solve the Schwinger-Dyson equation for the fundamental correlator, and at sufficiently high temperature, this model shows key signatures of thermalization and information loss; the correlator decay exponentially in time, and the spectral density becomes continuous and gapless. We study the Lanczos coefficients bn in this model and at sufficiently high temperature, it grows linearly in n with logarithmic corrections, which is one of the fastest growth under certain conditions. As a result, the Krylov complexity grows exponentially in time as ∼expOt\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sim \\exp \\left(\\mathcal{O}\\left(\\sqrt{t}\\right)\\right) $$\\end{document}. These results indicate that the IP model at sufficiently high temperature is chaotic.

New Eigensolution of the Klein--Gordon and Shrödinger equations for improved modified Yukawa-Kratzer potential and its applications using Boop's Shift method and standard perturbation theory in the 3D-ERQM and 3D-ENRQM symmetries

The deformed Klein-Gordonequation has been solved in three-dimensional extended relativistic quantum mechanics (3D-ERQM) symmetries for the improved modified Yukawa-Kratzer potential (IMYKP) model under the influence of the deformation space-space symmetries. The new relativistic energy eigenvalues were calculated using the parametric Bopp’s shift method and standard perturbation theory in addition to the approximation scheme suggested by Greene and Aldrich for the inverse square terms. The new relativistic energy eigenvalues of (LiH, HCl, CO and H2) molecules under the IMYKP model it was shown to be sensitive to the atomic quantum numbers (j, l, s, m), mixed potential depths (V0, De, re), the screening parameter’s inverse α and noncommutativity parameters (Θ,τ ,χ). In addition, we analyzed the nonrelativistic energy values by applying the well-known transmission rules known in the literature. In addition, we studied many special cases useful to researchers in the framework of the new extended symmetries, such as the improved modified Kratzer potential, the improved generalized Kratzer potential, the improved Kratzer potential, the improved modified Kratzer plus screened Coulomb potential, the improved Hellmann potential, the improved Yukawa potential, and improved inversely square Yukawa potential. We noticed that these particular results are identical to our previous work and other known works in the literature. The study is further extended to calculate the mass spectra of mesons of charmonium (cc) and bottomonium (bb) within the framework of the IMYKP model in three-dimensional extended non-relativistic quantum mechanics (3D-ENRQM) symmetries.

QMMM 2023: A program for combined quantum mechanical and molecular mechanical modeling and simulations

Combined quantum mechanical and molecular mechanical (QM/MM) methods play an important role in multiscale modeling and simulations. QMMM 2023 is a general-purpose program for single-point calculations, geometry optimizations, transition-state optimizations, and molecular dynamics (MD) at the QM/MM level. It calls a QM package and an MM package to perform the required single-level calculations and combines them into a QM/MM energy by a variety of schemes. QMMM 2023 supports GAMESS-US, Gaussian, and ORCA as QM packages and Tinker as the MM package. Four types of treatments are available for embedding the QM subsystem in the MM environment: mechanical embedding with gas-phase calculations of the QM region, electronic embedding that allows polarization of the QM region by the MM environment, polarizable embedding for mutual polarization of the QM and MM regions, and flexible embedding for both mutual polarization and partial charge transfer between the QM and MM regions. Boundaries between QM and MM regions that pass through covalent bonds can be treated by several methods, including the redistributed charge (RC) scheme, redistributed charge and dipole (RCD) scheme, balanced-RC scheme, balanced-RCD scheme, screened charge scheme that takes account of charge penetration effects, and smeared charge scheme that delocalizes the MM charges near the QM–MM boundary. Geometry optimization can be done using the optimizer implemented in QMMM 2023 or the Berny optimizer in Gaussian through external calls to Gaussian. Molecular dynamics simulations can be performed at the pure-MM level, pure-QM level, fixed-partitioning QM/MM level, and adaptive-partitioning QM/MM level. The adaptive-partitioning treatments permit on-the-fly relocation of the QM–MM boundary by dynamically reclassifying atoms or groups into the QM or MM subsystems. Program SummaryProgram Title: QMMM 2023.CPC Library link to program files:https://doi.org/10.17632/zmkc9db4zj.1.Licensing provisions: Apache-2.0 for the program and CC-BY-4.0 for the manual.Programming languages: Fortran90, Perl, and shell scripting.Nature of problem: Multiscale modeling and simulations by the combined quantum mechanical and molecular mechanical (QM/MM) method.Solution method: The program performs single-point calculations, geometry optimizations, transition state optimizations, and molecular dynamics (MD) by the QM/MM method by interfacing calls to binary executables in a QM package (GAMESS-US, Gaussian, or ORCA) and an MM package (TINKER) for the required calculations. QMMM 2023 supports various types of embedding schemes and multiple ways of treating a QM-MM boundary passing through a covalent bond.Additional comments including restrictions and unusual features: (1) QMMM 2023 supports polarizable-embedding and flexible-embedding schemes based on the electronegativity equalization principle and allowing charge transfer between the QM and MM regions. (2) For a QM-MM boundary passing through covalent bonds, all link-atom-based treatments preserve the charge of the MM region (and MM bond dipoles if desired) while effectively avoiding the over-polarization of the QM region. Further tuning is available to account for the charge penetration effects at the QM-MM boundary. (3) For dynamics simulations, Hamiltonian-based adaptive-partitioning algorithms allow on-the-fly reclassification of atoms or groups into the QM or MM regions without abrupt changes in the energy of the entire system or in the forces on all atoms.

On the Electride Nature of Na-hP4.

Early quantum mechanical models suggested that pressure drives solids towards free-electron metal behavior where the ions are locked into simple close-packed structures. The prediction and subsequent discovery of high-pressure electrides (HPEs), compounds assuming open structures where the valence electrons are localized in interstitial voids, required a paradigm shift. Our quantum chemical calculations on the iconic insulating Na-hP4 HPE show that increasing density causes a 3s→3pd electronic transition due to Pauli repulsion between the 1s2s and 3s states, and orthogonality of the 3pd states to the core. The large lobes of the resulting Na-pd hybrid orbitals point towards the center of an 11-membered penta-capped trigonal prism and overlap constructively, forming multicentered bonds, which are responsible for the emergence of the interstitial charge localization in Na-hP4. These multicentered bonds facilitate the increased density of this phase, which is key for its stabilization under pressure.