Quantum Mechanical Treatment Research Articles

Spectroscopic, photophysical, solution thermodynamics and computational study of europium and terbium complexes with a flexible quinolinol-based symmetric tripodal chelator.

Coordination behaviour and photonic properties of a flexible tripodal multidentate ligand, 5,5',5''-(Cyclohexane-1,3,5-triyltris(oxy))tris(methylene)triquinolin-8-ol (CYTOM5OX), with Eu and Tb ions were explored through potentiometric, UV-visible and fluorescence spectrophotometric methods. The interaction of tripod towards the lanthanides has been examined for thermodynamic equilibrium, photophysical behavior, and time-resolved luminescence measurements. Besides, a theoretically empirical method followed by quantum mechanical treatment of these chelates has also been summarized. A noticeable change in the electronic spectra of these complexes disclose CYTOM5OX as a pH-sensitive optical sensor for lanthanides detection; also, a strong green fluorescence allows simultaneous sensing in the visible region in a competitive medium. The intense fluorescence intermittently gets quenched under acidic and basic conditions due to photoinduced intramolecular electron transfer from the excited 8-hydroxyquinoline (8-HQ) moiety to the metal ion. The thermodynamically stable Ln3+ complexes in aqueous solution show stability constants in the range log β110=33-35 and pLn3+ in the range of 21-22. The hydration number that was predicted by the coordination scan was substantiated by lifetime measurements reveal presence of coordinated water molecules in Eu(CYTOM5OX) and Tb(CYTOM5OX) complexes. Theoretical spectra were also calculated by ZINDO/s methodology at single excitations (CIS) level on PM7 as sparkle energy-minimized geometries.

Time-independent quantum theory on vibrational inelastic scattering between atoms and open-shell diatomic molecules: Applications to NO + Ar and NO + H scattering

A full-dimensional rigorous quantum mechanical treatment of non-reactive inelastic scattering of an open-shell diatom [e.g., NO(2Π)] with a structureless and spinless atom is presented within the time-independent close-coupling framework. The inclusion of the diatomic vibrational degree of freedom allows the investigation of transitions between different vibrational manifolds, in addition to those between different rotational, spin-orbit, and Λ-doublet states. This method is applied to the scattering of vibrationally excited NO(2Π) with Ar and H (with its spin ignored). The former has negligible vibrational inelasticity, thanks to the weak interaction between the two collisional partners. This conclusion justifies the commonly used two-dimensional approximation in treating NO scattering with rare gas atoms. The latter, on the other hand, is shown to undergo significant vibrational relaxation, even in the ultra-cold regime, owing to a chemically bonded (HNO) complex on the lowest-lying singlet potential energy surfaces.

Quantum motion of hydrogen on Ni(100) surfaces

Vibration modes of hydrogen atoms on Ni(100) are studied. The number of observed energy losses as well as their full width at half maximum (FWHM) are incompatible with the classical model of localized vibrations. Number and energy of modes agree, however, well with a previously published quantum-mechanical treatment of the motion of hydrogen in the periodic surface potential of Ni(100). For the dilute surface phase of hydrogen, the FWHM is a factor of 4 larger than expected from the dispersion of the bands. The effect is attributed to rapid tunneling of vibrationally excited hydrogen into empty neighboring sites.

The quantum effects in slow–wave free–electron lasers operating in the low–gain regime

A quantum mechanical treatment is presented to describe slow–wave free–electron lasers (FELs) operating in the low–gain regime. Here, we address the quantum effect of electrons on the FEL operation where each electron is represented as a Gaussian wave packet with an arbitrary width. It is shown that this quantum effect should be described in two different regimes. The first regime is realized when the initial width of the electron wave packet σz0 is comparable to (larger or smaller than) the radiation wavelength λL. In this regime, the gain degrades significantly as σz0 increases and approaches λL. The latter regime is realized when σz0 is quite smaller than λL (i.e., approximately when σz0<λL/3) where the behavior of the gain is opposite to that in the first regime since it decreases with decreasing σz0. Therefore, it is predicted that there is an optimum initial width of the electron wave packet at which the gain is maximum.

Evaluation of an Efficient 3D-RISM-SCF Implementation as a Tool for Computational Spectroscopy in Solution.

The 3D-RISM-SCF solvent-model implementation of Gusarov et al. [ J. Phys. Chem. A 2006, 110, 6083-6090] in the Amsterdam density functional program has been improved and extended. In particular, an accurate yet efficient representation of the solute electrostatic potential is provided. The Coulomb-potential fitting of many DFT codes can be used advantageously in this context. The extra effort compared to a point-charge representation is small for a given SCF cycle and compensated by faster SCF convergence. This allows applications to large solutes, as demonstrated by evaluation of the solvatochromism of Reichardt's dye. In general, TDDFT applications to excitation energies in solution stand out and are highlighted. Applications to the 17O NMR chemical shifts of N-methylformamide in different solvents also demonstrate the distinct advantages of 3D-RISM over continuum solvents. Limitations are observed in this case for water solvent, where the solvent shielding is overestimated. This shortcoming applies also to the 17O gas-to-liquid shift of water, where we used localized molecular orbital analyses for a deeper understanding. For such cases of extremely strong solute-solvent interactions, couplings between solute and solvent orbitals induced by the magnetic perturbation are relevant. These clearly require a quantum-mechanical treatment of the most closely bound solvent molecules. Except for such extreme cases, 3D-RISM-SCF is very well suited to treat solvent effects on NMR parameters. More serious limitations pertain to the treatment of vibrational spectra, where the absence of the coupling between solute and solvent vibrational modes limits the accuracy of applications of 3D-RISM-SCF. The reported extended, efficient, and numerically accurate 3D-RISM-SCF implementation should provide a useful tool to study chemical and spectroscopic properties of molecules of appreciable size in a realistic solvent environment.

Analytic first and second derivatives of the energy in the fragment molecular orbital method combined with molecular mechanics

AbstractAnalytic first and second derivatives of the energy are developed for the fragment molecular orbital method interfaced with molecular mechanics in the electrostatic embedding scheme at the level of Hartree‐Fock and density functional theory. The importance of the orbital response terms is demonstrated. The role of electrostatic embedding upon molecular vibrations is analyzed, comparing force field and quantum mechanical treatments for an ionic liquid and a solvated protein. The method is applied for 100 protein conformations sampled in molecular dynamics (MD) to take into account the complexity of a flexible protein structure in solution, and a good agreement with experimental data is obtained: Frequencies from an experimental infrared (IR) spectrum are reproduced within 17 cm−1.

First Principles Calculations of Electronic, Structural and Optical Properties of (PMMA–ZrO2–Au) and (PMMA–Al2O3–Au) Nanocomposites for Optoelectronics Applications

This study focuses on the quantum mechanical treatment of the geometrical optimization and the electronic structure problems of a nanomaterial PMMA and nanocomposites. The hybrid functional B3LYP/6-31G level of DFT is used to investigate four molecules divided into two groups, they are PMMA as an original basis molecule and (PMMA–Au), (PMMA–Al2O3–Au), (PMMA–ZrO2–Au) nanocomposites as the two group. The DFT calculations have been performed using Gaussian 09 package of programs. The geometrical optimization included both bonds in °A and angles in deg. The calculated electronic properties included the total energy, HOMO and LUMO energies, energy gap, ionization energy, electron affinity, electronegativity, electrochemical hardness, electronic softness and Electrophilic index. The geometrical optimization of PMMA and nanocomposites has been found in good agreement with the experimental data because of its relaxed geometrical parameters. One of the important results was obtain in this study, is the decreasing of the energy gap. This states that these nanocomposites are the nearest to semiconductor due to the both HOMO and LUMO levels become more adjacent. These consequences mention to construct new structures with new electronic properties. All nanocomposites need small energy to become cationdue to ionization potential is decrease with addition nanoparticles to the pure PMMA, but the electronic affinity is an increase with with addition nanoparticles to the pure PMMA. The total ground state energy of the PMMA have largest value of total energy compared for other nanocomposites, where ET decreased with addition nanoparticles to pure PMMA. The hardness decrease with addition nanoparticles to the pure PMMA, therefore all the nanocomposites are softer, and this reduces the resistance of a species to lose electrons. Good relax for the structures of the studied PMMA was obtained theoretically, in which, the angles C–C, C=O and C–H in pure PMMA are remain in the same ranges for other nanocomposites. In general, most of the studied nonocomposites direct electronic transition from the valence to conduction band with wave length lies in the range of solar spectrum. The obtained results showed that the (PMMA–ZrO2–Au) and (PMMA–Al2O3–Au) nanocomposites have huge applications in electronics and photo-electronics fields.

Quantum effects in gravity waves

We discuss the quantum mechanical description of a gravitational wave interacting with a cavity electromagnetic field. Quantum fluctuations of the gravitational vacuum induce squeezing in the optical field. Moreover, this squeezing experiences revivals, a purely quantum effect. Measuring these gravitationally induced revivals, although out of reach from experiments, would provide evidence on the quantum nature of gravity. We also discuss the quantum mechanical treatment of the interaction between coherent and squeezed gravitational wave states and a gravity wave detector. In the case of a coherent gravitational wave, we reproduce the result from the classical theory with a quantum mechanical calculation. The case of a squeezed gravity wave is not calculable within the classical theory, and could provide evidence on the quantum nature of gravity.

Nonlocal Quantum Effects in Plasmons of Graphene Superlattices.

By using a nonlocal, quantum mechanical response function we study graphene plasmons in a one-dimensional superlattice (SL) potential V_{0}cosG_{0}x. The SL introduces a quantum energy scale E_{G}∼ℏv_{F}G_{0} associated with electronic subband transitions. At energies lower than E_{G}, the plasmon dispersion is highly anisotropic; plasmons propagate perpendicularly to the SL axis, but become damped by electronic transitions along the SL direction. These results question the validity of semiclassical approximations for describing low energy plasmons in periodic structures. At higher energies, the dispersion becomes isotropic and Drude-like with effective Drude weights related to the average of the absolute value of the local chemical potential. Full quantum mechanical treatment of the kinetic energy thus introduces nonlocal effects that delocalize the plasmons in the SL, making the system behave as a metamaterial even near singular points where the charge density vanishes.

Physical origin of the one-quarter exact exchange in density functional theory

Exchange interactions are a manifestation of the quantum mechanical nature of the electrons and play a key role in predicting the properties of materials from first principles. In density functional theory (DFT), a widely used approximation to the exchange energy combines fractions of density-based and Hartree–Fock (exact) exchange. This so-called hybrid DFT scheme is accurate in many materials, for reasons that are not fully understood. Here we show that a 1/4 fraction of exact exchange plus a 3/4 fraction of density-based exchange is compatible with a correct quantum mechanical treatment of the exchange energy of an electron pair in the unpolarized electron gas. We also show that the 1/4 exact-exchange fraction mimics a correlation interaction between doubly-excited electronic configurations. The relation between our results and trends observed in hybrid DFT calculations is discussed, along with other implications.

Dissecting Strong-Field Excitation Dynamics with Atomic-Momentum Spectroscopy.

Observation of internal quantum dynamics relies on correlations between the system being observed and the measurement apparatus. We propose using the c.m. degrees of freedom of atoms and molecules as a "built-in" monitoring device for observing their internal dynamics in nonperturbative laser fields. We illustrate the idea on the simplest model system-the hydrogen atom in an intense, tightly focused infrared laser beam. To this end, we develop a numerically tractable, quantum-mechanical treatment of correlations between internal and c.m. dynamics. We show that the transverse momentum records the time excited states experience the field, allowing femtosecond reconstruction of the strong-field excitation process. The ground state becomes weak-field seeking, an unambiguous and long sought-for signature of the Kramers-Henneberger regime.

Improved WKB Approximation for Nuclear Fusion Reactions

In this study, we have developed a mathematical approach to enhance the calculation of the probability of the WKB approximation in the semiclassical approach. This enhanced method was applied to study the total cross section of fusion reaction σfus , the barrier distribution of fusion Dfus and the probability of fusion Pfus for the light systems 6Li+64Zn, 13C+48Ti and 16O+46Ti. A quantum coupled-channel calculation is conducted using CC code with all order coupling to compare it with the calculations of the semiclassical method before and after improvement of the WKB probability. The improved approach used with WKB enhances the semiclassical calculations and more closer our theoretical results to the measured data to be in more agreement with the treatment of quantum mechanics which agrees with the measured data for the total reaction cross section σfus , the distribution of fusion barrier Dfus and the probability of fusion Pfus .

Stroboscopic quantum optomechanics

We consider an optomechanical cavity that is driven stroboscopically by a train of short pulses. By suitably choosing the inter-pulse spacing we show that ground-state cooling and mechanical squeezing can be achieved, even in the presence of mechanical dissipation and for moderate radiation-pressure interaction. We provide a full quantum-mechanical treatment of stroboscopic backaction-evading measurements, for which we give a simple analytic insight, and discuss preparation and verification of squeezed mechanical states. We further consider stroboscopic driving of a pair of non-interacting mechanical resonators coupled to a common cavity field, and show that they can be simultaneously cooled and entangled. Stroboscopic quantum optomechanics extends measurement-based quantum control of mechanical systems beyond the good-cavity limit.

Quantum correlations in the Kerr Ising model

In this article we present a full description of the quantum Kerr Ising model—a linear optical network of parametrically pumped Kerr nonlinearities. We consider the non-dissipative Kerr Ising model and, using variational techniques, show that the energy spectrum is primarily determined by the adjacency matrix in the Ising model and exhibits highly non-classical cat like eigenstates. We then introduce dissipation to give a quantum mechanical treatment of the measurement process based on homodyne detection via the conditional stochastic Schrodinger equation. Finally, we identify a quantum advantage in comparison to the classical analogue for the example of two anti-ferromagnetic cavities.

Study of transmittance spectra for quaternary periodic structure of 1D photonic crystal for s-wave filter

Objectives: To study the propagation of electromagnetic waves through the four periodic continuous layers with different refractive indices and spectral analysis with normalized frequency with respect to transmittance and dispersion. Methods: By considering the assumptions the theoretical analysis has been done. Methodology has taken from quantum mechanical treatment of an electron in a potential well with boundary conditions. The dispersion relation is taken from Bloach wave concept. The calculation is taken for arbitrary structure of different refractive indices. The electric field has connected with the periodic 1-D layered structure. The electromagnetic wave as form incident wave, the transmitted wave and reflected wave have been derived using the transmission matrix method. Findings: In theoretical analysis, it is found that the transmittance spectra increasing with continuous increase refractive index. The analysis has been done for a s-polarized or transverse electric mode (TE mode) wave. Properties of these crystals are different from the ordinary materials. Applications: It works as s- polarized filter and blocks p-polarized wave. Calculation has taken for TE mode configuration. Keywords: Photonic crystals; Electromagnetic waves; Periodic layered structure

Real-Time Time-Dependent Nuclear-Electronic Orbital Approach: Dynamics beyond the Born-Oppenheimer Approximation.

The quantum mechanical treatment of both electrons and nuclei is crucial in nonadiabatic dynamical processes such as proton-coupled electron transfer. The nuclear-electronic orbital (NEO) method provides an elegant framework for including nuclear quantum effects beyond the Born-Oppenheimer approximation. To enable the study of nonequilibrium properties, we derive and implement a real-time NEO (RT-NEO) approach based on time-dependent Hatree-Fock or density functional theory, in which the electronic and nuclear degrees of freedom are propagated in a time-dependent variational framework. Nuclear and electronic spectral features can be resolved from the time-dependent dipole moment computed using the RT-NEO method. The test cases show the dynamical interplay between the quantum nuclei and the electrons through vibronic coupling. Moreover, vibrational excitation in the RT-NEO approach is demonstrated by applying a resonant driving field, and electronic excitation is demonstrated by simulating excited state intramolecular proton transfer. This work shows that the RT-NEO approach is a promising tool to study nonadiabatic quantum dynamical processes within a time-dependent variational description for the coupled electronic and nuclear degrees of freedom.

Exciton–polaritons of a 2D semiconductor layer in a cylindrical microcavity

We describe exciton–polariton modes formed by the interaction between excitons in a 2D layer of a transition metal dichalcogenide embedded in a cylindrical microcavity and the microcavity photons. For this, an expression for the excitonic susceptibility of a semiconductor disk placed in the symmetry plane perpendicular to the axis of the microcavity is derived. Semiclassical theory provides dispersion relations for the polariton modes, while the quantum-mechanical treatment of a simplified model yields the Hopfield coefficients, measuring the degree of exciton–photon mixing in the coupled modes. The density of states (DOS) and its projection onto the photonic and the excitonic subspaces are calculated, taking monolayer MoS2 embedded in a Si3N4 cylinder as an example. The calculated results demonstrate a strong enhancement for certain frequencies of the total and local DOS (and, consequently, of the spontaneous emission rate of a nearby point emitter, i.e., the Purcell effect) caused by the presence of the 2D layer.

Accuracy of the PM6 and PM7 Methods on Bare and Thiolate-Protected Gold Nanoclusters

Semiempirical quantum mechanical (SEQM) methods offer an attractive middle ground between fully ab initio quantum chemistry and force-field simulations, allowing for a quantum mechanical treatment of the system at a relatively low computational cost. However, SEQM methods have not been frequently utilized in the study of transition metal systems, mostly due to the difficulty in obtaining reliable parameters. This paper examines the accuracy of the PM6 and PM7 semiempirical methods to predict geometries, ionization potentials, and HOMO-LUMO energy gaps of several bare gold clusters (Aun) and thiolate-protected gold nanoclusters (AuSNCs). Contrary to PM6, the PM7 method can predict qualitatively correct geometries and ionization potentials when compared to DFT. PM6 fails to predict the characteristic gold core and gold-sulfur ligand shell (staple motifs) of the AuSNC structures. Both the PM6 and PM7 methods overestimate the HOMO-LUMO gaps. Overall, PM7 provides a more accurate description of bare gold and gold-thiolate nanoclusters than PM6. Nevertheless, refining the gold parameters could help achieve better quantitative accuracy.

A Quantum Mechanics Treatment of Electron Diffraction by a Slit

A Quantum Mechanics Treatment of Electron Diffraction by a Slit

Multicomponent Orbital-Optimized Perturbation Theory Methods: Approaching Coupled Cluster Accuracy at Lower Cost

Multicomponent quantum chemistry methods such as the nuclear-electronic orbital (NEO) method allow the consistent quantum mechanical treatment of electrons and nuclei. The development of computationally practical, accurate, and robust multicomponent wave function methods is challenging because of the importance of orbital relaxation effects. Herein the variational orbital-optimized coupled cluster with doubles (NEO-OOCCD) method and the orbital-optimized second-order Møller-Plesset perturbation theory (NEO-OOMP2) method with scaled-opposite-spin (SOS) versions are developed and applied to molecular systems in which a proton and all electrons are treated quantum mechanically. The results highlight the importance of orbital relaxation in multicomponent wave function methods. The NEO-SOS'-OOMP2 method, which scales the electron-proton correlation energy as well as the opposite-spin and same-spin components of the electronic correlation energy, is found to achieve nearly the same level of accuracy as the NEO-OOCCD method for proton densities, proton affinities, and optimized geometries. An advantage of the NEO-SOS'-OOMP2 method is that it can be implemented with N4 scaling, where N is a measure of the system size. This method will enable future multicomponent wave function calculations of structures, energies, reaction paths, and dynamics for substantially larger chemical systems.