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Here, the molecular electronic wave functions are expressed in quasi-atomic form. The corresponding global energy expression exhibits the unified resolution of the various modes of chemical bonding in terms of physical interactions. The bonding patterns in several molecules is elucidated.
Two-dimensional covalent organic film with macrocyclic network under simple solvothermal conditions was recently synthesized experimentally [Colson, J. W.; et al. Science 2011, 332, 228], which offers immense potentials for optoelectronic applications as in the case of graphene. Here we systematically investigate the electronic and optical properties of such novel covalent organic frameworks (COF-5, TP-COF and NiPc PBBA-COF) as free-standing sheets using density-functional theory. The results shed considerable light on the nature of spatial carrier confinement with band offset. COF-5 exhibits a type-II heterojunction alignment with the significant valence and conduction band offsets, suggesting an effective spatial carrier separation of electrons and holes. In TP-COF, the valence offset is close to zero related to the dispersed distribution of photoexcited holes over the entire structure, while the conduction-band offset is still remarkable, indicating the effective confinement of photoexcited electrons. NiPc PBBACOF presents a type-I heterojunction alignment where the band-edged wave functions are localized in the same region, achieving the effective spatial carrier congregation. The calculated absorption peaks of the optical absorption of TP-COF and NiPc-PBBA COF frameworks are in agreement with experimental measurements, thus providing theoretical insights into experimental observed transmission spectra of these frameworks.
We investigate the electronic Bloch oscillation in bilayer graphene gradient superlattices using transfer matrix method. By introducing two kinds of gradient potentials of square barriers along electrons propagation direction, we find that Bloch oscillations up to terahertz can occur. Wannier-Stark ladders, as the counterpart of Bloch oscillation, are obtained as a series of equidistant transmission peaks, and the localization of the electronic wave function is also signature of Bloch oscillation. Furthermore, the period of Bloch oscillation decreases linearly with increasing gradient of barrier potentials.
In this work, we present a new four-component implementation of the polarization propagator for accurate calculations of excited states in heavy systems. Differences to existing nonrelativistic realizations are detailed and the energetically lowest final states of the ns{sup 2}np{sup 6} → ns{sup 2}np{sup 5}(n + 1)s{sup 1} and ns{sup 2}np{sup 6} → ns{sup 2}np{sup 5}(n + 1)p{sup 1} transitions in noble gases are calculated and compared with experimental data. Already for the light atoms Ne and Ar spin-orbit coupling leads to noticeable zero field splitting that gradually increases in the heavier homologues and eventually invalidates the LS-based description of singlet and triplet excited states. For all four noble gases Ne through Xe, we observe a very good agreement with experimental transition energies in the considered energetic range where the extended version of the propagator implementation in general yields better excitation energy differences than the strict variant. In the extended version, off-diagonal first-order contributions in the two-particle-two-hole block are included that are not present in the strict variant. In case of Kr and Xe, nonrelativistic approaches already exhibit unacceptable deviations in the reproduction of transition energies and the spectral structure. The obtained excited final states are analyzed in terms of atomic contributions to the donor and acceptor orbitals constituting the corresponding wave functions. The relativistic polarization propagator provides a consistent description of electron correlation and relativistic effects especially relevant for the heavier systems where these two contributions are no longer separable.
The excitation of molecular systems by natural incoherent light relevant, for example, to photosynthetic light-harvesting is examined. We show that the result of linear excitation with natural incoherent light can be obtained using incident light described in terms of transform limited pulses, as opposed to conventional classical representations with explicit random character. The derived expressions allow for computations to be done directly for any thermal light spectrum using a simple wave function formalism and provide a route to the experimental determination of natural incoherent excitation using pulsed laser techniques. Pulses associated with solar and cosmic microwave background radiation are provided as examples.
In this paper we use Dirac function to construct a fractional operator called fractional corresponding operator, which is the general form of momentum corresponding operator. Then we give a judging theorem for this operator and with this judging theorem we prove that R–L, G–L, Caputo, Riesz fractional derivative operator and fractional derivative operator based on generalized functions, which are the most popular ones, coincide with the fractional corresponding operator. As a typical application, we use the fractional corresponding operator to construct a new fractional quantization scheme and then derive a uniform fractional Schrödinger equation in form. Additionally, we find that the five forms of fractional Schrödinger equation belong to the particular cases. As another main result of this paper, we use fractional corresponding operator to generalize fractional quantization scheme by using Lévy path integral and use it to derive the corresponding general form of fractional Schrödinger equation, which consequently proves that these two quantization schemes are equivalent. Meanwhile, relations between the theory in fractional quantum mechanics and that in classic quantum mechanics are also discussed. As a physical example, we consider a particle in an infinite potential well. We give its wave functions and energy spectrums in two ways and find that both results are the same.
With the help of the evolution operator method, we have established unitary connection between quadratic systems, namely between a free particle with variable mass M(t) , a particle with variable mass M(t) in a variable homogeneous field, and a harmonic oscillator with variable mass M(t) and frequency ω(t) , on which a variable force F(t) acts. Knowledge of the unitary connection allowed us to express easily in general form the propagators, invariants, wave functions, and other functions of a linear potential and a harmonic oscillator in terms of the corresponding quantities for a free particle. We have analyzed the linear and quadratic invariants in detail. Results known in the literature follow as particular cases from the general results obtained here.
EPR study of Cu{sup 2+} doped NLO active Lithium Sulphate monohydrate (Li{sub 2}SO{sub 4.}H{sub 2}O) single crystals were grown successfully by slow evaporation method at room temperature. The principal values of g and A tensors indicate existence of orthorhombic symmetry around the Cu{sup 2+} ion. From the direction cosines of g and A tensors, the locations of Cu{sup 2+} in the lattice have been identified as interstitial site. Optical absorption confirms the rhombic symmetry and ground state wave function of the Cu{sup 2+} ion in a lattice as d{sub x2-y2}.
The ground-state energies and the squared moduli of the ground-state wave functions are calculated for the {sup 3}H, {sup 3,4,6}He, {sup 6}Li, and {sup 9}Be nuclei by Feynman’s continual (path) integrals method. The results are in satisfactory agreement with experimental data.
We present a method to remove the singular nuclear potential in a molecule and replace it with a regularized potential that is more amenable to be represented numerically. The singular nuclear potential is canceled by the similarity-transformed kinetic energy operator giving rise to an effective nuclear potential that contains derivative operators acting on the wave function. The method is fully equivalent to the non-similarity-transformed version. We give numerical examples within the framework of multi-resolution analysis for medium-sized molecules.
Binding energies of the exciton and the interband optical transition energies are studied in a CdSe/Pb{sub 1-x}Cd{sub x}Se/CdSe spherical quantum dot-quantum well nanostructure taking into account the geometrical confinement effect. The core and shell are taken as the same material. The initial and final states of energy and the overlap integrals of electron and hole wave functions are determined by the oscillator strength. The oscillator strength and the radiative transition life time with the dot radius are investigated for various Cd alloy content in the core and shell materials.
Franck-Condon vibrational overlap integrals for the A{sup ~1}A{sub u}—X{sup ~1}Σ{sup +}{sub g} transition in acetylene have been calculated in full dimension in the harmonic normal mode basis. The calculation uses the method of generating functions first developed for polyatomic Franck-Condon factors by Sharp and Rosenstock [J. Chem. Phys. 41(11), 3453–3463 (1964)], and previously applied to acetylene by Watson [J. Mol. Spectrosc. 207(2), 276–284 (2001)] in a reduced-dimension calculation. Because the transition involves a large change in the equilibrium geometry of the electronic states, two different types of corrections to the coordinate transformation are considered to first order: corrections for axis-switching between the Cartesian molecular frames and corrections for the curvilinear nature of the normal modes at large amplitude. The angular factor in the wave function for the out-of-plane component of the trans bending mode, ν{sub 4}{sup ″}, is treated as a rotation, which results in an Eckart constraint on the polar coordinates of the bending modes. To simplify the calculation, the other degenerate bending mode, ν{sub 5}{sup ″}, is integrated in the Cartesian basis and later transformed to the constrained polar coordinate basis, restoring the conventional v and l quantum numbers. An updated A{sup ~}-state harmonic force field obtained recently in the R. W. Field research group is evaluated. The results for transitions involving the gerade vibrational modes are in qualitative agreement with experiment. Calculated results for transitions involving ungerade modes are presented in Paper II of this series [G. B. Park, J. H. Baraban, and R. W. Field, “Full dimensional Franck–Condon factors for the acetylene A{sup ~1}A{sub u}—X{sup ~1}Σ{sup +}{sub g} transition. II. Vibrational overlap factors for levels involving excitation in ungerade modes,” J. Chem. Phys. 141, 134305 (2014)].
In this paper, we have obtained exact analytical solutions of the time-independent Dirac-Weyl equation for the charge carriers with q-deformed pseudoscalar magnetic barrier (PMB) in graphene by using the ansatz method. We have also found a solution that describes the left propagating wave function to calculation of the reflection and transmission coefficients using the Riemann’s equation. This allows us to conclude about the Dirac-Weyl equation with PMB and to understand quantum behavior of the Dirac fermions. Finally, some of the numerical results are shown, too.
Dynamical electron correlation has a major impact on the computed values of molecular properties and the energetics of molecular processes. This study focused on the effect of dynamical electron correlation on the spectroscopic constants ($R$ e , $ω$ e , $D$ e ), and potential energy curves, Δ$E$($R$), of the covalently bound AH and AF molecules, A = B–F. The changes in the spectroscopic constants (Δ$R$ e , Δ$ω$ e , Δ$D$ e ) caused by dynamical correlation are erratic and, at times, even surprising. These changes can be understood based on the dependence of the dynamical electron correlation energies of the AH and AF molecules as a function of the bond distance, i.e., Δ$E$ DEC ($R$). At large $R$, the magnitude of Δ$E$ DEC ($R$) increases nearly exponentially with decreasing $R$, but this increase slows as $R$ continues to decrease and, in many cases, even reverses at very short $R$. The changes in Δ$E$ DEC ($R$) in the region around $R$ e were as unexpected as they were surprising, e.g., distinct minima and maxima were found in the curves of Δ$E$ DEC ($R$) for the most polar molecules. The variations in Δ$E$ DEC ($R$) for $R$ ≲ $R$ e are directly correlated with major changes in the electronic structure of the molecules as revealed by a detailed analysis of the spin-coupled generalized valence bond wave function. In conclusion, the results reported here indicate that we have much to learn about the nature of dynamical electron correlation and its effect on chemical bonds and molecular properties and processes.
On the basis of the modified potential two-cluster model with forbidden state which effectively take the Pauli principle into account, calculations have been performed of the astrophysical S-factor of radiative p{sup 14}N capture to the ground state of the {sup 15}O nucleus at proton energies up to 5 MeV in the center-of-mass system (c.m.s.) with allowance for wide resonances up to 3.4 MeV in the c.m.s. For an acceptable explanation of the available experimental data it is necessary to allow the existence of the {sup 14}N cluster in the excited state {sup 14}N{sup *} at an excitation energy of 5.69 MeV and angular momentum J{sup π} = 1{sup –}. It is assumed that in such a case it is possible to use the wave function of the {sup 4}D{sub 1/2} state with respect to the relative motion of the p{sup 14}N{sup *} clusters. It is also shown that a description of the S-factor of p{sup 14}N capture in the resonance region is possible only under the assumption that all of the low-lying resonances at 260(1/2{sup +}), 987(3/2{sup +}), 1447(1/2{sup +}), 2187(3/2{sup +}), and 3211(3/2{sup +}) keV in the c.m.s. are {sup 4}D{sub 1/2} and {sup 4}D{sub 3/2} scattering waves.
We present a general formulation of our previously developed kinetic energy partition (KEP) method for solving many-bodySchrödinger equations. In atomic physics, as well as in general molecular and solid state physics, solving many-electronSchrödinger equations is a very challenging task, often called Dirac’s challenge. The central problem is how to properly handle the electron–electron Coulomb repulsion interactions. Using the KEP solution scheme, in addition to dividing the kinetic energy into partial terms, the electron–electron Coulomb interaction is also separated into parts to be associated with a “negative mass” kinetic energy term. Therefore, the full Hamiltonian can be expressed as a simple sum of subsystem Hamiltonians, each representing an effective one-body problem. Using a Hartree-like product in constructing the wave-function, we achieve fast convergence in the calculations of the ground state energies. First, the model Moshinsky atoms are used to illustrate the solution procedure. We then apply this new KEP method to harmonium atoms and obtain precise energies with an error less than 5% using only two basis functions from each subsystem. It is thus very promising that this methodology, when further extended, can be useful for general many-body systems.
A major challenge in contemporary electronic structure theory involves the development of methods to describe in a balanced manner the contribution of correlation effects to energy differences. This challenge can be even greater for multicomponent systems containing more than one type of quantum particle. In the present work, we describe a flexible code for carrying out self-consistent field and configuration interaction (CI) calculations on multicomponent systems and use it to generate trial wave functions for use in diffusion Monte Carlo (DMC) calculations of the positron affinity of Be, Be 2 , Be 4 , Mg, CS 2 , and benzene. The resulting positron affinities (PAs) are in good agreement with the best values from the literature.
The branching fractions of the semileptonic and rare B{sub s} decays are calculated in the framework of the QCD-motivated relativistic quark model. The form factors of the weak B{sub s} transitions are expressed through the overlap integrals of the initial and final meson wave functions in the whole accessible kinematical range. The momentum transfer dependence of the form factors is explicitly determined without additional model assumptions and extrapolations. The obtained results agree well with available experimental data.