Wave Functions Of Electronic States Research Articles

Nuclear Quantum Effects Accelerate Charge Separation and Recombination in g-C3N4/TiO2 Heterojunctions.

We combined ring-polymer molecular dynamics (MD) and ab initio MD with nonadiabatic MD to study the effects of nuclear quantum effects (NQEs) on interlayer electron transfer and electron-hole recombination at the g-C3N4/TiO2 interface. Our simulations indicate that NQEs significantly affect electron transfer and electron-hole recombination dynamics, accelerating both processes. NQEs deform the g-C3N4 layer and expedite the movement of carbon and nitrogen atoms, thus, enhancing charge delocalization and interlayer coupling. This improved overlap between electronic state wave functions enhances nonadiabatic couplings, facilitating electron transfer and recombination. In addition to the enhanced nonadiabatic couplings accelerating electron transfer, the presence of NQEs narrows the energy gap and delays decoherence by mitigating overall fluctuations, because of restricted TiO2 movements overwhelming enhanced g-C3N4 fluctuations, thereby making the recombination faster. This work provides valuable insights into NQEs in light-element systems and contributes to guiding the development of highly efficient photocatalysts.

Consistent Second-Order Treatment of Spin-Orbit Coupling and Dynamic Correlation in Quasidegenerate N-Electron Valence Perturbation Theory.

We present a formulation and implementation of second-order quasidegenerate N-electron valence perturbation theory (QDNEVPT2) that provides a balanced and accurate description of spin-orbit coupling and dynamic correlation effects in multiconfigurational electronic states. In our approach, the energies and wave functions of electronic states are computed by treating electron repulsion and spin-orbit coupling operators as equal perturbations to the nonrelativistic complete active-space wave functions, and their contributions are incorporated fully up to the second order. The spin-orbit effects are described using the Breit-Pauli (BP) or exact two-component Douglas-Kroll-Hess (DKH) Hamiltonians within spin-orbit mean-field approximation. The resulting second-order methods (BP2- and DKH2-QDNEVPT2) are capable of treating spin-orbit coupling effects in nearly degenerate electronic states by diagonalizing an effective Hamiltonian expanded in a compact non-relativistic basis. For a variety of atoms and small molecules across the entire periodic table, we demonstrate that DKH2-QDNEVPT2 is competitive in accuracy with variational two-component relativistic theories. BP2-QDNEVPT2 shows high accuracy for the second- and third-period elements, but its performance deteriorates for heavier atoms and molecules. We also consider the first-order spin-orbit QDNEVPT2 approximations (BP1- and DKH1-QDNEVPT2), among which DKH1-QDNEVPT2 is reliable but less accurate than DKH2-QDNEVPT2. Both DKH1- and DKH2-QDNEVPT2 hold promise as efficient and accurate electronic structure methods for treating electron correlation and spin-orbit coupling in a variety of applications.

Chirality and length-dependent electron transmission of fullerene-capped chiral carbon nanotubes sandwiched in gold electrodes.

In order to develop high-performance CNT-based electronic and optoelectronic devices, it is crucial to establish the relationship between the electron transport properties of carbon nanotubes (CNTs) and their structures. In this work, we have investigated the transport properties of chiral (8, m) and (10, m) CNTs sandwiched between two gold electrodes by employing nonequilibrium Green's function (NEGF) combined with density functional theory (DFT). We demonstrate that with the change of chirality the transport property changes, as predicted by the (n - m) rule. The change of length is also considered. Our results show that the electrical conductance of (10, m) CNTs is larger than that of the (8, m) CNTs, due to larger diameter. Furthermore, we found that the (8, 1) chiral CNT does not follow the (n - m) rule in shorter length and it shows metallic behavior. The cohesive energy, wavefunctions of electronic states, and coupling energy calculation indicate that the devices considered in this study are stable. The transmission spectra, current vs. voltage curves, and transmission eigenchannels provide strong evidence for our findings. Among the (10, m) series, (10, 3) CNT would be the optimal choice for a semiconducting molecular junction device with a significant conductance of 20 μA at 0.8 bias voltage.

Determination of optical properties of quantum wells with a structure of AlGaN/GaN resonant tunneling diodes (RTDs)

Two-dimensional multiple quantum well (MQW) and modified symmetric quantum well (MSQW) carrier confinement play an important role in AlGaN/GaN resonant tunneling diodes (RTDs) efficiency improvement. Therefore, AlGaN-based materials are suitable for development of ultraviolet-light sources. Hence, an attempt is made to investigate the optical properties of AlGaN/GaN. Asymmetric quantum well structure consisting of N-doped AlGaN wells, GaN steps, and undoped AlGaAs barriers is developed. The significant absorption is observed due to the strong coupling effect of the electronic state wave functions. Asymmetric potential well proposed for AlGaN/GaN/AlGaN RTDs. The barriers and the thin layer in the quantum well are theoretically determined. For GaN/AlGaN QW of width L, the frequencies of the symmetric interface modes satisfy the condition. The increase in well width increases the full-width at half maxima (FWHM) from 0 to 100 nm, while increased Al concentration decreases FWHM from 6 to 1 nm.

Atom interferometers with weak-measurement path detectors and their quantum mechanical analysis**Project supported by the National Key Research and Development Program of China (Grant No. 2018YFA 0306200), the National Natural Science Foundation of China (Grant No. 11434017), and the Guangdong Innovative and Entrepreneurial Research Team Program, China (Grant No. 2016ZT06C594).

According to the orthodox interpretation of quantum physics, wave-particle duality (WPD) is the intrinsic property of all massive microscopic particles. All gedanken or realistic experiments based on atom interferometers (AI) have so far upheld the principle of WPD, either by the mechanism of the Heisenberg’s position-momentum uncertainty relation or by quantum entanglement. In this paper, we propose and make a systematic quantum mechanical analysis of several schemes of weak-measurement atom interferometer (WM-AI) and compare them with the historical schemes of strong-measurement atom interferometer (SM-AI), such as Einstein’s recoiling slit and Feynman’s light microscope. As the critical part of these WM-AI setups, a weak-measurement path detector (WM-PD) deliberately interacting with the atomic internal electronic quantum states is designed and used to probe the which-path information of the atom, while only inducing negligible perturbation of the atomic center-of-mass motion. Another instrument that is used to directly interact with the atomic center-of-mass while being insensitive to the internal electronic quantum states is used to monitor the atomic center-of-mass interference pattern. Two typical schemes of WM-PD are considered. The first is the micromaser-cavity path detector, which allows us to probe the spontaneously emitted microwave photon from the incoming Rydberg atom in its excited electronic state and record unanimously the which-path information of the atom. The second is the optical-lattice Bragg-grating path detector, which can split the incoming atom beam into two different directions as determined by the internal electronic state and thus encode the which-path information of the atom into the internal states of the atom. We have used standard quantum mechanics to analyze the evolution of the atomic center-of-mass and internal electronic state wave function by directly solving Schrödinger’s equation for the composite atom-electron-photon system in these WM-AIs . We have also compared our analysis with the theoretical and experimental studies that have been presented in the previous literature. The results show that the two sets of instruments can work separately, collectively, and without mutual exclusion to enable simultaneous observation of both wave and particle nature of the atoms to a much higher level than the historical SM-AIs, while avoiding degradation from Heisenberg’s uncertainty relation and quantum entanglement. We have further investigated the space–time evolution of the internal electronic quantum state, as well as the combined atom–detector system and identified the microscopic origin and role of quantum entanglement, as emphasized in numerous previous studies. Based on these physics insights and theoretical analyses, we have proposed several new WM-AI schemes that can help to elucidate the puzzling physics of the WPD of the atoms. The principle of WM-AI scheme and quantum mechanical analyses made in this work can be directly extended to examine the principle of WPD for other massive particles.

Resultant gradient information, kinetic energy and molecular virial theorem

Resultant gradient-information is introduced and applied to problems in chemical reactivity theory. This local measure of the structural information contained in (complex) wavefunctions of electronic states is related to the system overall kinetic energy combining the modulus (probability) and phase (current) contributions. The grand-ensemble representation of thermodynamic equilibria in open systems demonstrates the physical equivalence of the variational energetic and information principles. It is used and to relate the populational derivatives of ensemble-average functionals in both these representations, which represent reactivity criteria for diagnosing the charge-transfer (CT) phenomena. Their equivalence is demonstrated by using the in situ potential and hardness descriptors to predict the direction and optimum amount of CT. The virial theorem is generalized into thermodynamic quantities and used to extract the kinetic energy component from qualitative energy profiles in the bond-formation and (exo/endo)-ergic reactions. The role of electronic kinetic energy in such chemical processes is reexamined, the virial theorem implications for the Hammond postulate of reactivity theory are explored, and variations of the structural-information in chemical processes are addressed. The maximum thermodynamic information rule is formulated and “production” of the gradient- information in chemical reactions is addressed. The Hammond postulate is shown to be indexed by the geometric derivative of resultant gradient-information at transition-state complex.

Investigating tunneling process of atom exposed in circularly polarized strong-laser field

We propose a method for studying the tunneling process by analyzing the instantaneous ionization rate of a circularly polarized laser. A numerical calculation shows that, for an atom exposed to a long laser pulse, if its initial electronic state wave function is non-spherical symmetric, the delayed phase shift of the ionization rate vs the laser cycle period in real time in the region close to the peak intensity of the laser pulse can be used to probe the tunneling time. In this region, an obvious time delay phase shift of more than 190 attoseconds is observed. Further study shows that the atom has a longer tunneling time in the ionization under a shorter wavelength laser pulse. In our method, a Wigner rotation technique is employed to numerically solve the time-dependent Schrödinger equation of a single-active electron in a three-dimensional spherical coordinate system.

Nature of Electronically Excited States of Organic Compounds and Processes of Nonradiative Conversion

Models of quantum-chemical calculation of rate constants for internal processes and intersystem crossing in polyatomic molecules are considered. The influence of the nature of electronically excited states in organic compounds is investigated. It is shown that the explicit allowance for the nature of wave functions of electronic states for estimation of electronic matrix elements of nonadiabaticity operators and spin-orbit interaction allows photophysical processes in organic compounds to be considered in detail.

The electric field effects on the third-harmonic generation in spherical quantum dots with parabolic confinement

The influence of an external electric field on the binding energies of the ground state and excited states with the third-harmonic-generation (THG) coefficient for spherical quantum dot (QD) with parabolic confinement is investigated theoretically. The energy levels and wave functions of electronic states in the QDs are calculated using by variational method within the effective-mass approximation. The numerical results demonstrate that the THG coefficient very sensitively depends on the magnitude of the electric field and the radius of the QDs. In addition, the THG coefficient also depends on the relaxation rate of the spherical QD with parabolic confinement and the position of impurity.

Electronic structures in a CdSe spherical quantum dot in a magnetic field: Diagonalization method and variational method

The electronic structures of a CdSe spherical quantum dot in a magnetic field are obtained by using an exact diagonalization method and a variational method within the effective-mass approximation. The dependences of the energies and wave functions of electron states, exciton binding energy, exciton transition energy, and exciton diamagnetic shift on the applied magnetic field are investigated theoretically in detail. It is observed that the degeneracy of magnetic quantum number m is removed due to the Zeeman effect when the magnetic field is present. For the states with m ≥ 0, the electron energies increase as the magnetic field increases. However, for the states with m < 0, the electron energies decrease to a minimum, and then increase with increasing the magnetic field. The energies and wave functions of electron states obtained from the variational method based on the variational functions we proposed are in excellent agreement with the results obtained from the exact diagonalization method we presented. A comparison between the results obtained from the variational functions proposed by us and Xiao is also verified.

Wannier-Stark states in a superlattice of InAs/GaAs quantum dots

Electron and hole emission from states of a ten-layer system of tunneling-coupled vertically correlated InAs/GaAs quantum dots (QDs) is studied experimentally by capacitance—voltage measurements and deep-level transient spectroscopy. The thickness of GaAs interlayers separating sheets of InAs QDs was ≈3 nm, as determined from transmission electron microscope images. It is found that the periodic multimo-dal DLTS spectrum of this structure exhibits a pronounced linear shift as the reverse-bias voltage Ur applied to the structure is varied. The observed behavior is a manifestation of the Wannier—Stark effect in the InAs/GaAs superlattice, where the presence of an external electric field leads to the suppression of coupling between the wave functions of electron states forming the miniband and to the appearance of a series of discrete levels called Wannier—Stark ladder states.

Electrical rectification by selective wave-function coupling in small Ag clusters onSi(111)−(7×7)

A cluster consisting of as few as three Ag atoms deposited on $\text{Si}(111)\text{\ensuremath{-}}(7\ifmmode\times\else\texttimes\fi{}7)$ surface was found to behave as a strong electric rectifier, with a rectification ratio as large as $\ensuremath{\sim}150$. Based on first-principles calculations, we found that the wave functions of electronic states at different energies spread out from the surface to different distances. We demonstrated by theoretical simulations and experiments that the observed rectification is a result of coupling the scanning tunneling microscope tip with selective wave functions of the cluster.

Carrier heating in disordered conjugated polymers in electric field

The electric field dependence of charge carrier transport and the effect of carrier heating in disordered conjugated polymers were investigated. A parameter-free multiscale methodology consisting of classical molecular dynamics simulation for the generation of the atomic structure, large system electronic structure and electron-phonon coupling constants calculations and the procedure for extracting the bulk polymer mobility, was used. The results suggested that the mobility of a fully disordered poly(3-hexylthiophene) (P3HT) polymer increases with electric field which is consistent with the experimental results on samples of regiorandom P3HT and different from the results on more ordered regioregular P3HT polymers, where the opposite trend is often observed at low electric fields. We calculated the electric field dependence of the effective carrier temperature and showed however that the effective temperature cannot be used to replace the joint effect of temperature and electric field, in contrast to previous theoretical results from phenomenological models. Such a difference was traced to originate from the use of simplified Miller-Abrahams hopping rates in phenomenological models in contrast to our considerations that explicitly take into account the electronic state wave functions and the interaction with all phonon modes.

Hydrated Structure of Ag(I) Ion from Symmetry-Dependent, K- and L-Edge XAFS Multiple Scattering and Molecular Dynamics Simulations

Details of the first-shell water structure about Ag(+) are reported from a corefinement of the K- and L(2)-edge multiple scattering signal in the X-ray absorption fine structure (XAFS) spectra. Detailed fits of the Ag K-edge data that include the contributions from multiple scattering processes in the hydrated ion structure cannot distinguish between models containing tetrahedral symmetry versus those containing collinear O-Ag-O bonds. However, we show that the multiple scattering oscillations at the L(2)-edges have distinctly different phase and amplitude functions than at the K-edge. These phase and amplitude functions depend not only on the symmetry of the multiple scattering paths but also on the nature of the final state electronic wave function probed by the dipole-allowed transition. Hence the multiple scattering portions of K- and L(2)-edge spectra provide independent measurements of the local symmetry--not a redundant measurement as is commonly believed. On the basis of the enhanced information content obtained by the simultaneous assessment of both the K- and L(2)-edges, we report that the hydrated Ag(+) structure contains five or six water molecules in the first shell with a significant number of nearly collinear and 90 degrees O-Ag-O bond angles. Finally, the K- and L(2)-edge spectra are used to benchmark the hydration structure that is generated from both DFT-based and classical molecular dynamics simulations. Simulated first-shell structures are compared to the experimental structures.

Configuration analysis of the electronic excitation in photobiological receptors

According to configuration analysis of the electronic state wave functions of chlorophyll a, peripheral CC(3b,4b) and isocyclic CO groups are not locally excited to any significant extent. This contrasts with the pyrone CC bond of coumarins where a substantial localization of the triplet excitation as well as photoreactions occur. The lowest excited states (1QQ and 3QQ) of chlorophyll a and bacteriochlorophyll a are also similar in correlating their state wave functions, although the ground states of these molecules are substantially different. The 11-CC bond of 11-cis-retinal protonated Schiff's bases shows no tendency for a localized excitation. Thus the primary photoexcitation of rhodopsin does not involve a preferential excitation at the 11-CC bond. The fluorescence characteristics of firefly luciferins have also been analyzed by the configuration analysis method. The most significant result is that the fluorescent states of luciferin and oxyluciferin monoanion possess a strong charge transfer character from hydroxybenzothiazole to thiazoline, in agreement with experimental observations.

Detecting the parity of electron wave functions in solids by quantum-well states of overlayers

We present an approach to monitor the parity of wave functions of electronic states of bulk solids, which was elaborated on the model Ag/W(110) system. The dispersion of quantum-well (QW) states formed in the thin Ag layer was examined by means of angle-resolved photoemission. The obtained experimental data were compared with results of layer Korringa–Kohn–Rostoker calculations. We found that around k points, where the two-dimensional QW bands cross the projected bulk bands of the W substrate of the same symmetry, broad hybridization gaps in the QW distributions are observed. Careful analysis based on a symmetry approach for the electronic bands in the Ag monolayer and the W substrate suggests that respective gaps may generally be taken as a fingerprint for the interaction with substrate states of even parity with respect to the emission plane. We anticipate that QW states may be used as a probe for symmetry properties of strongly correlated states in systems like heavy-fermion compounds that are difficult to access theoretically within an ab initio approach.

Electric Field Modulation of Infrared Absorption at Room Temperature in Electrochemically Self Assembled Quantum Dots

We report observation of electric-field-modulated infrared absorption at room temperature in electrochemically self-assembled CdS quantum dots produced by electrodepositing the semiconductor in 50-nm pores of an anodic alumina film. The absorption is associated with photoassisted real space transfer of electrons from the CdS dots to surrounding trap sites in the alumina. Similar absorption was observed in the past [Appl. Phys. Lett. 79, 4423 (2001)] and was the basis of a room temperature near infrared photodetector. An electric field modulates this absorption by altering the overlap between the wavefunctions of electronic states in the quantum dots and the trap states in the surrounding alumina, thereby affecting the matrix element for radiative transitions, similar to the quantum confined Stark or Franz-Keldysh effect. The ability to electrically modulate absorption in these structures can result in inexpensive infrared signal processing devices operating at room temperature.

On the accuracy of density functional theory for iron—sulfur clusters

A simple, yet powerful wave function manipulation method was introduced utilizing a generalized ionic fragment approach that allows for systematic mapping of the wave function space for multispin systems with antiferromagnetic coupling. The use of this method was demonstrated for developing ground state electronic wave function for [2Fe-2S] and [Mo-3Fe-4S] clusters. Using well-defined ionic wave functions for ferrous and ferric irons, sulfide, and thiolate fragments, the accuracy of various density functionals and basis sets including effective core potentials were evaluated on a [4Fe-4S] cluster by comparing the calculated geometric and electronic structures with crystallographic data and experimental atomic spin densities from X-ray absorption spectroscopy, respectively. We found that the most reasonable agreement for both geometry and atomic spin densities is obtained by a hybrid functional with 5% HF exchange and 95% density functional exchange supplemented with Perdew's 1986 correlation functional. The basis set seems to saturate only at the triple-zeta level with polarization and diffuse functions. Reasonably preoptimized structures can be obtained by employing computationally less expensive effective core potentials, such as the Stuttgart-Dresden potential with a triple-zeta valence basis set. The extension of the described calibration methodology to other biologically important and more complex iron-sulfur clusters, such as hydrogenase H-cluster and nitrogenase FeMo-co will follow.

A Theory of Electronic Energy Transfer in Complex Molecular Systems

The Forster theory for energy transfer is critically reviewed in the context of the present-day theory of nonradiative transitions, and the fundamental tenets of the Forster theory are shown to be erroneous. A new theory of electronic energy transfer is constructed taking into account the electronic transition theory. The intermolecular interaction between donor and acceptor molecules is assumed to perturb electron states of isolated molecules before the donor-molecule excitation. A distinguishing characteristic of the intermolecular interaction is spatial delocalization of the wave functions of electron states of the interacting molecules. It is this fact that has made it possible to realize ordinary photophysical processes between electron states of various molecules in a bimolecular system. In the experiments under study, the result of the intermolecular nonradiative photoprocess is given as evidence of electronic energy transfer from the donor molecule to the acceptor molecule.

On the single- and double-ionization of He by protons and anti-protons

In this paper we present the calculations of: (a) the single-ionization cross section of He by protons and anti-protons in the incident energy range of about 10 keV - 50 MeV, (b) the double-ionization cross sections by both projectiles in the energy rage of about 50 keV - 20 MeV and (c) the ratio of double- to single-ionization in the energy range of 50 keV - 20 MeV. The calculations have been performed in the two-coupled channel plane wave Born approximation, which is essentially the Born approximation that includes the final channel interaction between two electrons, in addition to the usual projectile - electron potential. The projectile has been represented by plane waves, and a correlated Hylleraas type of wavefunction has been used for the initial ground state. For the single-ionization case the final state electronic wavefunction is taken to be an anti-symmetrized product of a hydrogen-like (ls) and a continuum Coulomb wavefunction. For the double-ionization case, the final state wavefunctions of the two ejected electrons are taken to be Coulomb functions for calculating the matrix elements of the electron - projectile interaction, whereas plane waves are used for calculating the matrix elements of the electron - electron interaction. The calculated results are in reasonable agreement with the data in all three cases. The single-ionization cross section has also been calculated in the Lewis - Merzbacher approximation to determine the range of incident energy where it might represent a suitable approximation.