Quantum Mechanical Interaction Research Articles

Non-local interactions in quantum mechanics modelled by shifted Dirac delta functions

We introduce a new interaction formulated in terms of two shifted delta functions with non-local boundary conditions. For this purpose we use a method of self-adjoint extensions for a particular simmetric operator. We obtain bound states of the associated quantum mechanical problem and study its symmetry properties. We compare the results with the ground state of the quantum mechanical problem with a local interaction in terms of two delta functions.

On Contact Interactions Realised as Friedrichs Systems

We realise the Hamiltonians of contact interactions in quantum mechanics within the framework of abstract Friedrichs systems. In particular, we show that the construction of the self-adjoint (or even only closed) operators of contact interaction supported at a fixed point can be associated with the construction of the bijective realisations of a suitable pair of abstract Friedrich operators. In this respect, the Hamiltonians of contact interaction provide novel examples of abstract Friedrich systems.

SchNet - A deep learning architecture for molecules and materials.

Deep learning has led to a paradigm shift in artificial intelligence, including web, text, and image search, speech recognition, as well as bioinformatics, with growing impact in chemical physics. Machine learning, in general, and deep learning, in particular, are ideally suitable for representing quantum-mechanical interactions, enabling us to model nonlinear potential-energy surfaces or enhancing the exploration of chemical compound space. Here we present the deep learning architecture SchNet that is specifically designed to model atomistic systems by making use of continuous-filter convolutional layers. We demonstrate the capabilities of SchNet by accurately predicting a range of properties across chemical space for molecules and materials, where our model learns chemically plausible embeddings of atom types across the periodic table. Finally, we employ SchNet to predict potential-energy surfaces and energy-conserving force fields for molecular dynamics simulations of small molecules and perform an exemplary study on the quantum-mechanical properties of C20-fullerene that would have been infeasible with regular ab initio molecular dynamics.

Group 10 Bis(iminosemiquinone) Complexes: Measurement of Singlet-Triplet Gaps and Analysis of the Effects of Metal and Geometry on Electronic Structure.

Bis(iminosemiquinone) complexes of divalent group 10 metals have been described as having open-shell singlet ground states characteristic of very strong coupling between the two ligand radicals. By using the nonlinear temperature dependence of the chemical shifts of the 1H NMR spectra, the singlet-triplet gaps in seven of these compounds have been measured, with the nickel compounds having gaps of about 2400 cm-1 and the palladium compounds about 1800 cm-1. Bis(iminosemiquinone)platinum complexes have singlet-triplet gaps too large to measure by this technique (over 2800 cm-1, estimated to be about 3000 cm-1), though bis(3,5-di- tert-butylbenzosemiquinonato)platinum(II) has a measurable singlet-triplet gap of 1850 cm-1. In combination with near-IR absorption data of the neutral, cationic, and anionic bis(iminosemiquinone) complexes, a simplified two-electron, two-orbital bonding model describing these compounds can be fully parametrized based on experimental data. The identity of the central metal principally affects the difference in energy between metal-ligand π nonbonding and metal-ligand π antibonding orbitals, with the strength of the bonding interactions increasing in the order Pd < Ni < Pt. Twisting the ligands out of planarity (by using a 2,2'-biphenylenediyl linker) has a marked effect on the optical spectra of the compounds but not on their singlet-triplet gaps; this indicates that the effect is not due to changes in bonding interactions but rather due to a decrease in the magnitude of the quantum mechanical exchange interactions in the twisted compared to the flat compounds.

Polarizable Empirical Force Field for Halogen-Containing Compounds Based on the Classical Drude Oscillator.

The quality of the force field is crucial to ensure the accuracy of simulations used in molecular modeling, including computer-aided drug design (CADD). To perform more accurate modeling and simulations of halogenated molecules, in this study the polarizable force field based on the classical Drude oscillator model was extended to both aliphatic and aromatic systems using halogenated ethane and benzene model compounds for the halogens F, Cl, Br, and I. The force field parameters were optimized targeting quantum mechanical dipole moments, water interactions, and molecular polarizabilities as well as experimental observables, including enthalpies of vaporization, molecular volumes, hydration free energies, and dielectric constants. The developed halogenated polarizable force field is capable of reproducing QM relative energies and geometries of both halogen bonds and halogen-hydrogen bond donor interactions at an unprecedented level due to the inclusion of a virtual particle and anisotropic atomic polarizability on the halogen and, notably, the inclusion of Lennard-Jones parameters on the halogen Drude particle. The model was validated on the basis of its ability to accurately reproduce pure solvent properties for halogenated naphthalenes and alkanes, including species analogous to those used as refrigerants. Accordingly, it is anticipated that the model will be applicable for the study of halogenated derivatives in CADD as well as in other chemical and biophysical studies.

Higher-Order Interactions in Quantum Optomechanics: Analytical Solution of Nonlinearity

A method is described to solve the nonlinear Langevin equations arising from quadratic interactions in quantum mechanics. While, the zeroth order linearization approximation to the operators is normally used, here first and second order truncation perturbation schemes are proposed. These schemes employ higher-order system operators, and then approximate number operators with their corresponding mean boson numbers, only where needed. Spectral densities of higher-order operators are derived, and an expression for the second-order correlation function at zero time-delay has been found, which reveals that the cavity photon occupation of an ideal laser at threshold reaches $\sqrt{6}-2$, in good agreement with extensive numerical calculations. As further applications, analysis of the quantum anharmonic oscillator, calculation of $Q-$functions, analysis of quantum limited amplifiers, and nondemoliton measurements.

Novel Nanostructures and Materials for Strong Light–Matter Interactions

Quantum mechanical interactions between electromagnetic radiation and matter underlie a broad spectrum of optical phenomena. Strong light-matter interactions result in the well-known vacuum Rabi splitting and emergence of new polaritonic eigenmodes of the coupled system. Thanks to recent progress in nanofabrication, observation of strong coupling has become possible in a great variety of optical nanostructures. Here, we review recently studied and emerging materials for realization of strong light–matter interactions. We present general theoretical formalism describing strong coupling and give an overview of various photonic structures and materials allowing for realization of this regime, including plasmonic and dielectric nanoantennas, novel two-dimensional materials, carbon nanotubes, and molecular vibrational transitions. In addition, we discuss practical applications that can benefit from these effects and give an outlook on unsettled questions that remain open for future research.

Formula omitted]-Stacking interactions in YFP, quantum mechanics and force field evaluations in the S0 and S1 states

We study the π-stacking interaction between the chromophore and Tyr203 in the Yellow Fluorescent Protein (YFP) in order to (i) evaluate the contribution of the internal interaction energy of the isolated Chromophore-Tyrosine complex (Eint) to the 26nm red shift observed from GFP to YFP, (ii) compare the effects of Eint and of the proteic environment. To that end, we perform quantum mechanical and force field (ff) calculations of the isolated complex in S0 and S1 states on a large sample of geometries, together with molecular dynamics simulations and potential of mean force analysis. The calculated absorption wavelengths are found red shifted with respect to the isolated chromophore by 12–19nm, that represents a large part of the GFP-YFP shift. We find that the effect of the protein is determinant on the dynamics of the complex while the error that results from using a classicalff is of limited effect.

Application of a simple quantum chemical approach to ligand fragment scoring for Trypanosoma brucei pteridine reductase\xa01 inhibition

There is a need for improved and generally applicable scoring functions for fragment-based approaches to ligand design. Here, we evaluate the performance of a computationally efficient model for inhibitory activity estimation, which is composed only of multipole electrostatic energy and dispersion energy terms that approximate long-range ab initio quantum mechanical interaction energies. We find that computed energies correlate well with inhibitory activity for a compound series with varying substituents targeting two subpockets of the binding site of Trypanosoma brucei pteridine reductase 1. For one subpocket, we find that the model is more predictive for inhibitory activity than the ab initio interaction energy calculated at the MP2 level. Furthermore, the model is found to outperform a commonly used empirical scoring method. Finally, we show that the results for the two subpockets can be combined, which suggests that this simple nonempirical scoring function could be applied in fragment–based drug design.

Tuning quantum nonlocal effects in graphene plasmonics.

The response of electron systems to electrodynamic fields that change rapidly in space is endowed by unique features, including an exquisite spatial nonlocality. This can reveal much about the materials' electronic structure that is invisible in standard probes that use gradually varying fields. Here, we use graphene plasmons, propagating at extremely slow velocities close to the electron Fermi velocity, to probe the nonlocal response of the graphene electron liquid. The near-field imaging experiments reveal a parameter-free match with the full quantum description of the massless Dirac electron gas, which involves three types of nonlocal quantum effects: single-particle velocity matching, interaction-enhanced Fermi velocity, and interaction-reduced compressibility. Our experimental approach can determine the full spatiotemporal response of an electron system.

Polarizable Force Field for DNA Based on the Classical Drude Oscillator: I. Refinement Using Quantum Mechanical Base Stacking and Conformational Energetics.

Empirical force fields seek to relate the configuration of a set of atoms to its energy, thus yielding the forces governing its dynamics, using classical physics rather than more expensive quantum mechanical calculations that are computationally intractable for large systems. Most force fields used to simulate biomolecular systems use fixed atomic partial charges, neglecting the influence of electronic polarization, instead making use of a mean-field approximation that may not be transferable across environments. Recent hardware and software developments make polarizable simulations feasible, and to this end, polarizable force fields represent the next generation of molecular dynamics simulation technology. In this work, we describe the refinement of a polarizable force field for DNA based on the classical Drude oscillator model by targeting quantum mechanical interaction energies and conformational energy profiles of model compounds necessary to build a complete DNA force field. The parametrization strategy employed in the present work seeks to correct weak base stacking in A- and B-DNA and the unwinding of Z-DNA observed in the previous version of the force field, called Drude-2013. Refinement of base nonbonded terms and reparametrization of dihedral terms in the glycosidic linkage, deoxyribofuranose rings, and important backbone torsions resulted in improved agreement with quantum mechanical potential energy surfaces. Notably, we expand on previous efforts by explicitly including Z-DNA conformational energetics in the refinement.

Fragment Quantum Mechanical Method for Large-Sized Ion-Water Clusters.

Fragmentation methods have been widely studied for computing quantum mechanical (QM) energy of medium-sized water clusters, but less attention has been paid to large-sized ion-water clusters, in which many-body QM interaction is more significant, because of the charge-transfer effect between ions and water molecules. In this study, we utilized electrostatically embedded generalized molecular fractionation (EE-GMF) method for full QM calculation of the large-sized ion-water clusters (up to 15 Na+ and 15 Cl- ions solvated with 119 water molecules). Through systematic validation using different fragment sizes, we show that, by using distance thresholds of 6 Å for both the two-body and three-body QM interactions, the EE-GMF method is capable of providing accurate ground-state energies of large-sized ion-water clusters at different ab initio levels (including HF, B3LYP, M06-2X, and MP2) with significantly reduced computational cost. The deviations of EE-GMF from full system calculations are within a few kcal/mol. The result clearly shows that the calculated energies of the ion-water clusters using EE-GMF are close to converge after the distance thresholds are larger than 6 Å for both the two-body and three-body QM interactions. This study underscores the importance of the three-body interactions in ion-water clusters. The EE-GMF method can also accurately reproduce the relative energy profiles of the ion-water clusters.

Origin of the type-II band offset between rutile and anatase titanium dioxide: Classical and quantum-mechanical interactions between O ions

Titanium dioxide is one of the most promising semiconductors for photocatalytic splitting of water for hydrogen. The mixed rutile/anatase system shows even more favorable photocatalytic properties than the pristine ones. Band offset is a key factor that determines the photocatalytic activity of the mixed phase. However, the type of band alignment and the value of the band offset are still under debate both experimentally and theoretically. The difficulty of determining the band offset by commonly used core-level alignment calculation lies in the different symmetry and large lattice mismatch between the two phases. Here, we adopt our recently developed three-step method, which can overcome the lattice mismatch problem, to study the band offset with high accuracy. In the calculation, we used an intermediate phase $\mathrm{Ti}{\mathrm{O}}_{2}\mathrm{II}$ to build superlattice models of rutile(101)//$\mathrm{Ti}{\mathrm{O}}_{2}\mathrm{II}(001)$ and $\mathrm{Ti}{\mathrm{O}}_{2}\mathrm{II}(100)$//anatase(112) to determine the core-level alignment. Our studies show a type-II, staggered band alignment, with the valence band maximum (VBM) of rutile 0.80 eV above that of anatase, in agreement with recent experimental results. We further analyzed the electronic structure of the two phases, and found that the band offsets of the VBM originate from both the electrostatic interaction and electronic hybridization in rutile and anatase, which contribute 0.36 eV and 0.44 eV, respectively.

Quantum mechanical calculation of nanomaterial-ligand interaction energies by molecular fractionation with conjugated caps method

Molecular fractionation with conjugate caps (MFCC) method is introduced for the efficient estimation of quantum mechanical (QM) interaction energies between nanomaterial (carbon nanotube, fullerene, and graphene surface) and ligand (charged and neutral). In the calculations, nanomaterials are partitioned into small fragments and conjugated caps that are properly capped, and the interaction energies can be obtained through the summation of QM calculations of the fragments from which the contribution of the conjugated caps is removed. All the calculations were performed by density functional theory (DFT) and dispersion contributions for the attractive interactions were investigated by dispersion corrected DFT method. The predicted interaction energies by MFCC at each computational level are found to give excellent agreement with full system (FS) calculations with the mean energy deviation just a fractional kcal/mol. The accurate determination of nanomaterial-ligand interaction energies by MFCC suggests that it is an effective method for performing QM calculations on nanomaterial-ligand systems.

Full QM Calculation of RNA Energy Using Electrostatically Embedded Generalized Molecular Fractionation with Conjugate Caps Method.

In this study, the electrostatically embedded generalized molecular fractionation with conjugate caps (concaps) method (EE-GMFCC) was employed for efficient linear-scaling quantum mechanical (QM) calculation of total energies of RNAs. In the EE-GMFCC approach, the total energy of RNA is calculated by taking a proper combination of the QM energy of each nucleotide-centric fragment with large caps or small caps (termed EE-GMFCC-LC and EE-GMFCC-SC, respectively) deducted by the energies of concaps. The two-body QM interaction energy between non-neighboring ribonucleotides which are spatially in close contact are also taken into account for the energy calculation. Numerical studies were carried out to calculate the total energies of a number of RNAs using the EE-GMFCC-LC and EE-GMFCC-SC methods at levels of the Hartree-Fock (HF) method, density functional theory (DFT), and second-order many-body perturbation theory (MP2), respectively. The results show that the efficiency of the EE-GMFCC-SC method is about 3 times faster than the EE-GMFCC-LC method with minimal accuracy sacrifice. The EE-GMFCC-SC method is also applied for relative energy calculations of 20 different conformers of two RNA systems using HF and DFT, respectively. Both single-point and relative energy calculations demonstrate that the EE-GMFCC method has deviations from the full system results of only a few kcal/mol.

Quantum Two-Stream Instability with Exchange Interaction

Quantum plasmas can be described in the framework of the self-consistent field approach by a set of time-dependent Schrödinger equations (TDSE) for the electrons in a self-consistent potential. This approach is also well-known as the multistream model of quantum plasmas. The self-consistent field is commonly calculated in the Vlasov approximation from the average charge density of all electrons thereby neglecting the quantum-mechanical exchange interaction. In the present work, we consider a linear Hartree-Fock model with screened Coulomb interactions to examine the role of the exchange interaction. The two-stream instability is analysed and results for the Vlasov, Hartree and Hartree-Fock approximations are compared in detail. It is found that the exchange interaction considerably modifies the stability behavior for weakly screened Coulomb interactions. In particular, crossings of the two branches of the dispersion relation lead to oscillating unstable solutions that are not present in the absence of the exchange interaction.

Polarizable Multipole-Based Force Field for Aromatic Molecules and Nucleobases.

Aromatic molecules with π electrons are commonly involved in chemical and biological recognitions. For example, nucleobases play central roles in DNA/RNA structure and their interactions with proteins. The delocalization of the π electrons is responsible for the high polarizability of aromatic molecules. In this work, the AMOEBA force field has been developed and applied to 5 regular nucleobases and 12 aromatic molecules. The permanent electrostatic energy is expressed as atomic multipole interactions between atom pairs, and many-body polarization is accounted for by mutually induced atomic dipoles. We have systematically investigated aromatic ring stacking and aromatic-water interactions for nucleobases and aromatic molecules, as well as base–base hydrogen-bonding pair interactions, all at various distances and orientations. van der Waals parameters were determined by comparison to the quantum mechanical interaction energy of these dimers and fine-tuned using condensed phase simulation. By comparing to quantum mechanical calculations, we show that the resulting classical potential is able to accurately describe molecular polarizability, molecular vibrational frequency, and dimer interaction energy of these aromatic systems. Condensed phase properties, including hydration free energy, liquid density, and heat of vaporization, are also in good overall agreement with experimental values. The structures of benzene liquid phase and benzene-water solution were also investigated by simulation and compared with experimental and PDB structure derived statistical results.

A problem of elastic collision of two spinless particles at their local interaction in relativistic quantum mechanics

A problem of elastic collision of two spinless particles at their local interaction in relativistic quantum mechanics

Towards a Constructive Foundation of Quantum Mechanics

I describe a constructive foundation for Quantum Mechanics, based on the discreteness of the degrees of freedom of quantum objects and on the Principle of Relativity. Taking Einstein's historical construction of Special Relativity as a model, the construction is carried out in close contact with a simple quantum mechanical Gedanken experiment. This leads to the standard axioms of Quantum Mechanics. The quantum mechanical description is identified as a tool that allows describing objects with discrete degrees of freedom in space-time covariant with respect to coordinate transformations. An inherent property of this description is a quantum mechanical interaction mechanism. The construction gives detailed answers to controversial questions, such as the measurement problem, the informational content of the wave function, and the completeness of Quantum Mechanics.

Ab Initio Modeling Of Friction Reducing Agents Shows Quantum Mechanical Interactions Can Have Macroscopic Manifestation.

Two of the most commonly encountered friction-reducing agents used in plastic sheet production are the amides known as erucamide and behenamide, which despite being almost identical chemically, lead to markedly different values of the friction coefficient. To understand the origin of this contrasting behavior, in this work we model brushes made of these two types of linear-chain molecules using quantum mechanical numerical simulations under the density functional theory at the B97D/6-31G(d,p) level of theory. Four chains of erucamide and behenamide were linked to a 2 × 10 zigzag graphene sheet and optimized both in vacuum and in continuous solvent using the SMD implicit solvation model. We find that erucamide chains tend to remain closer together through π-π stacking interactions arising from the double bonds located at C13-C14, a feature behenamide lacks, and thus a more spread configuration is obtained with the latter. It is argued that this arrangement of the erucamide chains is responsible for the lower friction coefficient of erucamide brushes, compared with behenamide brushes, which is a macroscopic consequence of cooperative quantum mechanical interactions. While only quantum level interactions are modeled here, we show that behenamide chains are more spread out in the brush than erucamide chains as a consequence of those interactions. The spread-out configuration allows more solvent particles to penetrate the brush, leading in turn to more friction, in agreement with macroscopic measurements and mesoscale simulations of the friction coefficient reported in the literature.