Quantum Mechanical Treatment Research Articles

The Invisible Reality of Quantum Mechanics: The ‎‎‎Deterministic Perspective

The fundamental deterministic nature of quantum mechanics (QM) is mathematically demonstrated by the modeling of the ‎‎‎quantum (multiple) slit experiments; hence this paper is written from a deterministic perspective (DP) in quantum mechanics.‎ ‎Due to approximately 90 years of indeterminism and probabilistic statistical results, the theory consists of many ‎‎‎interpretations and is often regarded as counterintuitive. The latter is in the deterministic perspective not the case and is ‎‎‎illustrated with some examples. After a brief historic perspective, ‘invisible’ i.e. invisible entities of reality in mathematical ‎‎‎treatment, are introduced. These entities are handled by mathematics indirectly i.e. are described in a transformed domain ‎‎‎without variables violating the Heisenberg relation. In nature, i.e. on micro and macro levels, causality is fully ‘entangled’ with ‎‎‎energy, information - in the meaning of ordering or coding - as well as time. In contrast with the macro scale with many forms ‎‎‎and types of memory functions, without a memory property of quanta, causality is the bearer of information symmetry on ‎‎the ‎quantum scale. Further on in this DP paper: mathematical and philosophical consequences and influences in several ‎‎‎paragraphs, regarding subjects such as ‘free will’ and expected ‘threats to science’, the Bell inequalities, Alice and Bob & ‎‎‎entanglement, causality, information, retro-causality, spooky action, encryption and computing, teleportation, and in general ‎‎‎interpretations rooted in indeterminacy in QM as well as associated topics on independence, fine-tuning. The last paragraph ‎‎‎outlines the mathematical treatment of QM more extensively and may clarify references to the above-mentioned topics of ‎‎‎discussion in QM further.‎

Gate-Tunable Phonon Magnetic Moment in Bilayer Graphene.

We develop a first-principles quantum scheme to calculate the phonon magnetic moment in solids. As a showcase example, we apply our method to study gated bilayer graphene, a material with strong covalent bonds. According to the classical theory based on the Born effective charge, the phonon magnetic moment in this system should vanish, yet our quantum mechanical calculations find significant phonon magnetic moments. Furthermore, the magnetic moment is highly tunable by changing the gate voltage. Our results firmly establish the necessity of the quantum mechanical treatment, and identify small-gap covalent materials as a promising platform for studying tunable phonon magnetic moment.

A fully quantum-mechanical treatment for kaolinite.

Neural network potentials for kaolinite minerals have been fitted to data extracted from density functional theory calculations that were performed using the revPBE + D3 and revPBE + vdW functionals. These potentials have then been used to calculate the static and dynamic properties of the mineral. We show that revPBE + vdW is better at reproducing the static properties. However, revPBE + D3 does a better job of reproducing the experimental IR spectrum. We also consider what happens to these properties when a fully quantum treatment of the nuclei is employed. We find that nuclear quantum effects (NQEs) do not make a substantial difference to the static properties. However, when NQEs are included, the dynamic properties of the material change substantially.

Infrared and vibrational circular dichroism spectra of methyl β-D-glucopyranose in water: The application of the quantum cluster growth and clusters-in-a-liquid solvation models.

The infrared (IR) and vibrational circular dichroism (VCD) spectra of methyl β-D-glucopyranose in water were measured. Both implicit and explicit solvation models were utilized to explain the observed spectra. The vast body of existing experimental and theoretical data suggested that about eight explicit water molecules are needed to account for the solvent effects, supported by the current Quantum Cluster Growth (QCG) analysis. Extensive manual and systematic conformational searches of the molecular target and its water clusters were carried out by using a recently developed conformational searching tool, conformer-rotamer ensemble sampling tool (CREST), and the microsolvation model in the associated QCG code. The Boltzmann averaged IR and VCD spectra of the methyl β-D-glucopyranose-(water)n (n = 8) conformers in the PCM of water provide better agreement with the experimental ones than those with n = 0, 1, and 2. The explicit solvation with eight water molecules was shown to greatly modify the conformational preference of methyl β-D-glucopyranose from its monomeric form. Further analyses show that the result is consistent with the existence of long-lived methyl β-D-glucopyranose monohydrates with the additional explicit water effects being accounted for with the quantum mechanical treatment of the other seven close-by water molecules in the PCM of water.

Semi-Empirical Shadow Molecular Dynamics: A PyTorch Implementation.

Extended Lagrangian Born-Oppenheimer molecular dynamics (XL-BOMD) in its most recent shadow potential energy version has been implemented in the semiempirical PyTorch-based software PySeQM. The implementation includes finite electronic temperatures, canonical density matrix perturbation theory, and an adaptive Krylov subspace approximation for the integration of the electronic equations of motion within the XL-BOMB approach (KSA-XL-BOMD). The PyTorch implementation leverages the use of GPU and machine learning hardware accelerators for the simulations. The new XL-BOMD formulation allows studying more challenging chemical systems with charge instabilities and low electronic energy gaps. The current public release of PySeQM continues our development of modular architecture for large-scale simulations employing semi-empirical quantum-mechanical treatment. Applied to molecular dynamics, simulation of 840 carbon atoms, one integration time step executes in 4 s on a single Nvidia RTX A6000 GPU.

First-principles calculations to investigate structural, electronic, phonon, magnetic and thermal properties of stable halide perovskite semiconductors Cs2GeMnI6 and Cs2GeNiI6

Since, the systematic and extensive study on halide double perovskite’s (HDP’s) have triggered a considerable interest, thus became a new thrust to the scientific research. In this organised report, we present a new promising halide double perovskite structures Cs2GeMnI6 and Cs2GeNiI6 to understand, more in-depth their intrinsic characteristics by means of Density Functional Theory (DFT). Initially, we reported the structural stability of both these crystal structures by evaluating their total ground state energy in stable configuration and cohesive energy at the behest of Brich Murnaghan equation of state. Afterwards, the structural stability is moreover extended to see their corresponding tolerance factor (τ) values and second order elastic constants (SOEC’s). Subsequently, the density functional perturbation theory (DFPT) has been inducted to predict the dynamical context of these ordered systems. Later on, the quantum mechanical treatment of defining their electronic structures by the calibration of mix of two distinct spin-polarised approximation schemes like Perdew-Burke-Ernzerhof Generalised gradient approximation (PBE-GGA) followed by Tran-Blaha modified Becke-Johnson (TB-mBJ). Meanwhile, the unsymmetrical behaviour of electronic structures from their resulting band structures demonstrates the occurrence of spin-magnetic moment of 5 µB and 2 µB/formula unit respectively having the maximum contribution solely coming from the Mn+2 and Ni2+ 3d-transition elements. The evaluation of phonon dependent Grüneisen parameter (γ) defines the possible thermal stability against specific temperature regimes. And finally transport properties as a function of chemical potential (µ-EF) at distinct temperatures has been keenly explored. Therefore, the overall tendency of these designed materials can be envisaged to descript vast implications in various extending applications for conventional spin-based and thermoelectric technologies.

Molecular vibrations in the presence of velocity-dependent forces.

A semiclassical theory of small oscillations is developed for nuclei that are subject to velocity-dependent forces in addition to the usual interatomic forces. When the velocity-dependent forces are due to a strong magnetic field, novel effects arise-for example, the coupling of vibrational, rotational, and translational modes. The theory is first developed using Newtonian mechanics and we provide a simple quantification of the coupling between these types of modes. We also discuss the mathematical structure of the problem, which turns out to be a quadratic eigenvalue problem rather than a standard eigenvalue problem. The theory is then re-derived using the Hamiltonian formalism, which brings additional insight, including a close analogy to the quantum-mechanical treatment of the problem. Finally, we provide numerical examples for the H2, HT, and HCN molecules in a strong magnetic field.

What Is the Gravitational Field of a Mass in a Spatially Nonlocal Quantum Superposition?

The study of the gravitational field produced by a spatially nonlocal, superposed quantum state of a massive particle is an interesting and active area of research. One outstanding issue is whether the gravitational field behaves like the classical superposition of the gravitational field of two particles separated by a spatial distance with half the mass at each position. Alternatively, does the gravitational field behave as a quantum superposition with a far more interesting and subtle behavior than a simple classical superposition? Quantum field theory is ideally suited to probe exactly this kind of question. We study the scattering of a massless scalar on a spatially nonlocal quantum superposition of a massive particle. We compute the differential scattering cross section corresponding to one-graviton exchange. We find that the scattering cross section disagrees with the Newton-Schrödinger picture of potential scattering from two localized sources with half the mass at each source. This suggests that experimental observation of gravitational scattering could inform the viability of the semiclassical treatment of the gravitational field, as in the Newton-Schrödinger description, vs the fully quantum mechanical treatment adopted here. We comment on the experimental feasibility of observing such effects in systems with many particles such as Bose-Einstein condensates.

Manipulating light–matter interaction into strong coupling regime for photon entanglement in plasmonic lattices

Enhancing light–matter interaction into the strong coupling regime attracts tremendous attention in both theory and experiment, which presents essential significance in research from nano-optics to quantum information. In this work, the entanglement effect is observed in the photons emitted from a plasmonic lattice as the coherent light–matter interaction occurs into the strong coupling regime with a Rabi splitting of 93.4 meV. A full quantum mechanical treatment based on the number state representation is established to reveal the underlying physics of the strong coupling phenomenon, especially the femtosecond dynamics of energy exchange and damping. The entangled split states display oscillating concurrence and negative Wigner quasiprobability distribution function, which demonstrates that this designed plasmonic lattice system can serve as an on-demand entangled photon source for quantum information.

CHARMM-GUI QM/MM interfacer for the hybrid QM/MM molecular dynamics simulations.

Molecular mechanical (MM) force fields are constructed based on the empirical potentials, describing intramolecular and intermolecular potentials. Molecular dynamics (MD) simulation utilizing MM force fields is a robust tool to investigate large biomolecular systems, but the changes in electronic structures during a chemical process are overlooked in classical mechanics. Quantum mechanical (QM) treatments are needed for such changes including bond forming/breaking and charge transfers, but a high computational cost limits its usages with up to hundreds of atoms or less. A hybrid QM/MM approach, where the reactive part of the system is treated with QM and the remainder by cheap MM potentials, can effectively capture the reaction without significantly increasing the computational cost. For the different nature of the QM versus MM theories, however, the setup of biomolecular QM/MM simulation is known to be time consuming even to QM/MM experts. We present CHARMM-GUI QM/MM Interfacer that prepares QM/MM simulations with a user-selected QM region and various QM theories in multiple simulation packages. A non-trivial and error-prone QM/MM simulation setup involving link-atom insertion and charge distribution can be seamlessly prepared in QM/MM Interfacer. A few representative systems are simulated to delineate the robustness of QM/MM Interfacer. We hope both QM/MM beginners and experts to find the module's quick and accurate QM/MM simulation setup useful for their important applications.

Distributed functional-group polarizabilities in polypeptides and peptide clusters toward accurate prediction of electro-optical properties of biomacromolecules.

Aiming at accurately predicting electro-optical properties of biomolecules, this work presents distributed atomic and functional-group polarizability tensors for a series of polypeptides and peptide clusters constructed from glycine and its residuals. By partitioning the electron density using the quantum theory of atoms in molecules, we demonstrated a very good transferability of the group polarizabilities. We were able to identify and extract the most efficient functional groups capable of generating the largest electrical susceptibility in condensed phases. Both the isotropic polarizability and its anisotropy were used to understand the way functional groups act as sources of linear optical responses, how they interact with each other reinforcing the macroscopic optical behavior within the material, and how covalent bonds and non-covalent interactions, such as hydrogen bonds, determine refractive indices and birefringence. Particular attention is devoted to the peptide bonds as they provide links to build biomacromolecules or polymers. An adequate quantum-mechanical treatment of at least the first interaction sphere of a given functional group is required to properly describe the effects of mutual polarization, but we identified optimum cluster size and shape to better estimate polarizabilities and dipole moments of larger molecules or molecular aggregates from the knowledge of the electron density of a central molecule or amino acid residual that is representative of the bulk. The strategy outlined here is a fast yet effective tool for estimating the optical properties of proteins but could eventually find application in the rational design of optical organic materials as well. Electronic-structure calculations were performed on the Gaussin16 program at the DFT level using the CAMB3LYP functional and the double-ζ quality Dunning basis set aug-cc-pVDZ. Electron density partitioning followed the concepts of the Quantum Theory of Atoms and Molecules (QTAIM) and was performed using the AIMAll program. The locally developed Polaber routine was applied to calculate dipole moment vectors and polarizability tensors. It was amended to include the effects of the local field on a given central molecule by means of a modified Atom-Dipole Interaction Model (ADIM).

Understanding Charge Dynamics in Dense Electronic Manifolds in Complex Environments.

Photoinduced charge transfer (CT) excited states and their relaxation mechanisms can be highly interdependent on the environment effects and the consequent changes in the electronic density. Providing a molecular interpretation of the ultrafast (subpicosecond) interplay between initial photoexcited states in such dense electronic manifolds in condensed phase is crucial for improving and understanding such phenomena. Real-time time-dependent density functional theory is here the method of choice to observe the charge density, explicitly propagated in an ultrafast time domain, along with all time-dependent properties that can be easily extracted from it. A designed protocol of analysis for real-time electronic dynamics to be applied to time evolving electronic density related properties to characterize both in time and in space CT dynamics in complex systems is here introduced and validated, proposing easy to be read cross-correlation maps. As case studies to test such tools, we present the photoinduced charge-transfer electronic dynamics of 5-benzyluracil, a mimic of nucleic acid/protein interactions, and the metal-to-ligand charge-transfer electronic dynamics in water solution of [Ru(dcbpy)2(NCS)2]4-, dcbpy = (4,4'-dicarboxy-2,2'-bipyridine), or "N34-", a dye sensitizer for solar cells. Electrostatic and explicit ab initio treatment of solvent molecules have been compared in the latter case, revealing the importance of the accurate modeling of mutual solute-solvent polarization on CT kinetics. We observed that explicit quantum mechanical treatment of solvent slowed down the charge carriers mobilities with respect to the gas-phase. When all water molecules were modeled instead as simpler embedded point charges, the electronic dynamics appeared enhanced, with a reduced hole-electron distance and higher mean velocities due to the close fixed charges and an artificially increased polarization effect. Such analysis tools and the presented case studies can help to unveil the influence of the electronic manifold, as well as of the finite temperature-induced structural distortions and the environment on the ultrafast charge motions.

Nonadiabatic heavy atom tunneling in 1nσ*-mediated photodissociation of thioanisole.

The 1nσ*-mediated photodissociation dynamics of thioanisole is investigated quantum mechanically using a three-dimensional model based on a newly constructed diabatic potential energy matrix. The lifetimes of the low-lying S1(1ππ*) resonances are determined and found to accord well with available experimental data. Specifically, our theoretical results demonstrate that the photodissociation of thioanisole at the low-lying S1(1ππ*) levels takes place via the heavy atom tunneling due to the higher S1/S2 conical intersection and two equivalent out-of-plane saddle points appearing on the dissociation path. The isotopic effect on the lifetimes is found to be pronounced, manifesting the nature of the tunneling process. Moreover, the geometric phase effect around the S1/S2 conical intersection is found to slightly impact the lifetimes due to the weak destructive or constructive interferences in this heavy atom tunneling, which differs significantly from the scenario in the nonadiabatic hydrogen atom tunneling. Importantly, the quantum mechanical treatment is essentially required to accurately describe the 1nσ*-mediated photodissociation dynamics of thioanisole owing to involving quantum tunneling and geometric phase effects near the conical intersection.

Cavity-catalyzed hydrogen transfer dynamics in an entangled molecular ensemble under vibrational strong coupling.

Microcavities have been shown to influence the reactivity of molecular ensembles by strong coupling of molecular vibrations to quantized cavity modes. In quantum mechanical treatments of such scenarios, frequently idealized models with single molecules and scaled, effective molecule-cavity interactions or alternatively ensemble models with simplified model Hamiltonians are used. In this work, we go beyond these models by applying an ensemble variant of the Pauli-Fierz Hamiltonian for vibro-polaritonic chemistry and numerically solve the underlying time-dependent Schrödinger equation to study the cavity-induced quantum dynamics in an ensemble of thioacetylacetone (TAA) molecules undergoing hydrogen transfer under vibrational strong coupling (VSC) conditions. Beginning with a single molecule coupled to a single cavity mode, we show that the cavity indeed enforces hydrogen transfer from an enol to an enethiol configuration with transfer rates significantly increasing with light-matter interaction strength. This positive effect of the cavity on reaction rates is different from several other systems studied so far, where a retarding effect of the cavity on rates was found. It is argued that the cavity "catalyzes" the reaction by transfer of virtual photons to the molecule. The same concept applies to ensembles with up to N = 20 TAA molecules coupled to a single cavity mode, where an additional, significant, ensemble-induced collective isomerization rate enhancement is found. The latter is traced back to complex entanglement dynamics of the ensemble, which we quantify by means of von Neumann-entropies. A non-trivial dependence of the dynamics on ensemble size is found, clearly beyond scaled single-molecule models, which we interpret as transition from a multi-mode Rabi to a system-bath-type regime as N increases.

Strong quantization of current-carrying electron states in [formula omitted]-layer systems

We present an open-system quantum-mechanical real-space study of the conductive properties and size quantization in phosphorus δ-layers systems, interesting for their beyond-Moore and quantum computing applications. Recently it has been demonstrated that an open-system quantum mechanical treatment provides a much more accurate match to ARPES measurements in highly-conductive, highly-confined systems than the traditional approaches (i.e. periodic or Dirichlet boundary conditions) and, furthermore, it allows accurate predictions of conductive properties of such systems from the first principles. Here we reveal that quantization effects are strong for device widths W<10nm, and we show, for the first time, that the number of propagating modes determines not only the conductivity, but the distinctive spatial distribution of the current-carrying electron states. For W>10nm, the quantization effects practically vanish and the conductivity tends to the infinitely-wide device’s values.

Charge carrier mobilities of organic semiconductors: ab initio simulations with mode-specific treatment of molecular vibrations

The modeling of charge transport in organic semiconductors usually relies on the treatment of molecular vibrations by assuming a certain limiting case for all vibration modes, such as the dynamic limit in polaron theory or the quasi-static limit in transient localization theory. These opposite limits are each suitable for only a subset of modes. Here, we present a model that combines these different approaches. It is based on a separation of the vibrational spectrum and a quantum-mechanical treatment in which the slow modes generate a disorder landscape, while the fast modes generate polaron band narrowing. We apply the combined method to 20 organic crystals, including prototypical acenes, thiophenes, benzothiophenes, and their derivatives. Their mobilities span several orders of magnitude and we find a close agreement to the experimental mobilities. Further analysis reveals clear correlations to simple mobility predictors and a combination of them can be used to identify high-mobility materials.

Microsolvation of electrons by a handful of ammonia molecules.

Microsolvation of electrons in ammonia is studied here via anionic NH3 n - clusters with n = 2-6. Intensive samplings of the corresponding configurational spaces using second-order perturbation theory with extended basis sets uncover rich and complex energy landscapes, heavily populated by many local minima in tight energy windows as calculated from highly correlated coupled cluster methods. There is a marked energetical preference for structures that place the excess electron external to the molecular frame, effectively coordinating it with the three protons from a single ammonia molecule. Overall, as the clusters grow in size, the lowest energy dimer serves as the basic motif over which additional ammonia molecules are attached via unusually strong charge-assisted hydrogen bonds. This is apriori quite unexpected because, on electrostatic grounds, the excess electron would be expected to be in contact with as many protons as possible. Accordingly, a full quantum mechanical treatment of the bonding interactions under the tools provided by the quantum theory of atoms in molecules is carried out in order to dissect and understand the nature of intermolecular contacts. Vertical detachment energies reveal bound electrons even for n = 2.

Ab initio quantum theory of mass defect and time dilation in trapped-ion optical clocks

We derive a Hamiltonian for the external and internal dynamics of an electromagnetically bound, charged two-particle system in external electromagnetic and gravitational fields, including leading-order relativistic corrections. We apply this Hamiltonian to describe the relativistic coupling of the external and internal dynamics of cold ions in Paul traps, including the effects of micromotion, excess micromotion, and trap imperfections. This provides a systematic and fully quantum-mechanical treatment of relativistic frequency shifts in atomic clocks based on single trapped ions. Our approach reproduces well-known formulas for the second-order Doppler shift for thermal states, which were previously derived on the basis of semiclassical arguments. We complement and clarify recent discussions in the literature of the role of time dilation and mass defect in ion clocks.

Atomic excitation caused by α decay of the nucleus: model study

When the nucleus of an atom decays by emitting an α particle, the surrounding electrons are disturbed and the atom may be ionized. Practically all calculations so far done for this ionization process are based on Migdal’s method in which the α particle is treated as a classical point charge that is emitted by the nucleus at a certain time. Migdal’s method yields the ionization probability that is in reasonable agreement with experiment. On the other hand, Kataoka et al indicated by means of a schematic model calculation that a fully quantum mechanical treatment of the α particle leads to the ionization probability much smaller than the one predicted by Migdal’s method. We reexamine Kataoka et al’s calculation by simplifying the model of the atom such that an exact calculation is feasible. We find that Migdal’s method can be approximately justified, and clarify the earlier analysis.

Unusually Large Effects of Charge-assisted C-H⋅⋅⋅F Hydrogen Bonds to Anionic Fluorine in Organic Solvents: Computational Study of 19 FNMR Shifts versus Thermochemistry.

A comparison of computed 19 F NMR chemical shifts and experiment provides evidence for large specific solvent effects for fluoride-type anions interacting with the σ*(C-H) orbitals in organic solvents like MeCN or CH2 Cl2 . We show this for systems ranging from the fluoride ion and the bifluoride ion [FHF]- to polyhalogen anions [ClFx ]- . Discrepancies between computed and experimental shifts when using continuum solvent models like COSMO or force-field-based descriptions like the 3D-RISM-SCF model show specific orbital interactions that require a quantum-mechanical treatment of the solvent molecules. This is confirmed by orbital analyses of the shielding constants, while less negatively charged fluorine atoms (e. g., in [EF4 ]- ) do not require such quantum-mechanical treatments to achieve reasonable accuracy. The larger 19 F solvent shift of fluoride in MeCN compared to water is due to the larger coordination number in the former. These observations are due to unusually strong charge-assisted C-H⋅⋅⋅F- hydrogen bonds, which manifest beyond some threshold negative natural charge on fluorine of ca. < -0.6 e. The interactions are accompanied by sizable free energies of solvation, in the order F- ≫[FHF]- >[ClF2 ]- >[ClF4 ]- . COSMO-RS solvation free energies tend to moderately underestimate those from the micro-solvated cluster treatment. Red-shifted and intense vibrational C-H stretching bands, potentially accessible in bulk solution, are further spectroscopic finger prints.