Search NASA⌕ Search

SEARCH · Search NASA

Results for “Wave Functions”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,747 records · Page 97

Optical conductivity of topological insulator thin films

We present a detailed theoretical study on the optoelectronic properties of topological insulator thin film (TITFs). The k·p approach is employed to calculate the energy spectra and wave functions for both the bulk and surface states in the TITF. With these obtained results, the optical conductivities induced by different electronic transitions among the bulk and surface states are evaluated using the energy-balance equation derived from the Boltzmann equation. We find that for Bi{sub 2}Se{sub 3}-based TITFs, three characteristic regimes for the optical absorption can be observed. (i) In the low radiation frequency regime (photon energy ℏω<200 meV), the free-carrier absorption takes place due to intraband electronic transitions. An optical absorption window can be observed. (ii) In the intermediate radiation frequency regime (200<ℏω<300 meV), the optical absorption is induced mainly by interband electronic transitions from surface states in the valance band to surface states in the conduction band and an universal value σ{sub 0}=e{sup 2}/(8ℏ) for the optical conductivity can be obtained. (iii) In the high radiation frequency regime (ℏω>300 meV), the optical absorption can be achieved via interband electronic transitions from bulk and surface states in the valance band to bulk and surface states in the conduction band. A strong absorption peak can be observed. These interesting findings indicate that optical measurements can be applied to identify the energy regimes of bulk and surface states in the TITF.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Vertical and adiabatic excitations in anthracene from quantum Monte Carlo: Constrained energy minimization for structural and electronic excited-state properties in the JAGP ansatz

We study the ionization energy, electron affinity, and the π → π{sup ∗} ({sup 1}L{sub a}) excitation energy of the anthracene molecule, by means of variational quantum Monte Carlo (QMC) methods based on a Jastrow correlated antisymmetrized geminal power (JAGP) wave function, developed on molecular orbitals (MOs). The MO-based JAGP ansatz allows one to rigorously treat electron transitions, such as the HOMO → LUMO one, which underlies the {sup 1}L{sub a} excited state. We present a QMC optimization scheme able to preserve the rank of the antisymmetrized geminal power matrix, thanks to a constrained minimization with projectors built upon symmetry selected MOs. We show that this approach leads to stable energy minimization and geometry relaxation of both ground and excited states, performed consistently within the correlated QMC framework. Geometry optimization of excited states is needed to make a reliable and direct comparison with experimental adiabatic excitation energies. This is particularly important in π-conjugated and polycyclic aromatic hydrocarbons, where there is a strong interplay between low-lying energy excitations and structural modifications, playing a functional role in many photochemical processes. Anthracene is an ideal benchmark to test these effects. Its geometry relaxation energies upon electron excitation are of up to 0.3 eV in the neutral {sup 1}L{sub a} excited state, while they are of the order of 0.1 eV in electron addition and removal processes. Significant modifications of the ground state bond length alternation are revealed in the QMC excited state geometry optimizations. Our QMC study yields benchmark results for both geometries and energies, with values below chemical accuracy if compared to experiments, once zero point energy effects are taken into account.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Self-consistent Kohn-Sham method based on the adiabatic-connection fluctuation-dissipation theorem and the exact-exchange kernel

A self-consistent Kohn-Sham method based on the adiabatic-connection fluctuation-dissipation (ACFD) theorem, employing the frequency-dependent exact exchange kernel f{sub x} is presented. The resulting SC-exact-exchange-only (EXX)-ACFD method leads to even more accurate correlation potentials than those obtained within the direct random phase approximation (dRPA). In contrast to dRPA methods, not only the Coulomb kernel but also the exact exchange kernel f{sub x} is taken into account in the EXX-ACFD correlation which results in a method that, unlike dRPA methods, is free of self-correlations, i.e., a method that treats exactly all one-electron systems, like, e.g., the hydrogen atom. The self-consistent evaluation of EXX-ACFD total energies improves the accuracy compared to EXX-ACFD total energies evaluated non-self-consistently with EXX or dRPA orbitals and eigenvalues. Reaction energies of a set of small molecules, for which highly accurate experimental reference data are available, are calculated and compared to quantum chemistry methods like Møller-Plesset perturbation theory of second order (MP2) or coupled cluster methods [CCSD, coupled cluster singles, doubles, and perturbative triples (CCSD(T))]. Moreover, we compare our methods to other ACFD variants like dRPA combined with perturbative corrections such as the second order screened exchange corrections or a renormalized singles correction. Similarly, the performance of our EXX-ACFD methods is investigated for the non-covalently bonded dimers of the S22 reference set and for potential energy curves of noble gas, water, and benzene dimers. The computational effort of the SC-EXX-ACFD method exhibits the same scaling of N{sup 5} with respect to the system size N as the non-self-consistent evaluation of only the EXX-ACFD correlation energy; however, the prefactor increases significantly. Reaction energies from the SC-EXX-ACFD method deviate quite little from EXX-ACFD energies obtained non-self-consistently with dRPA orbitals and eigenvalues, and the deviation reduces even further if the Coulomb kernel is scaled by a factor of 0.75 in the dRPA to reduce self-correlations in the dRPA correlation potential. For larger systems, such a non-self-consistent EXX-ACFD method is a competitive alternative to high-level wave-function-based methods, yielding higher accuracy than MP2 and CCSD methods while exhibiting a better scaling of the computational effort than CCSD or CCSD(T) methods. Moreover, EXX-ACFD methods were shown to be applicable in situation characterized by static correlation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Electronic structures and geometries of the XF{sub 3} (X = Cl, Br, I, At) fluorides

The potential energy surfaces of the group 17 XF{sub 3} (X = Cl, Br, I, At) fluorides have been investigated for the first time with multiconfigurational wave function theory approaches. In agreement with experiment, bent T-shaped C{sub 2v} structures are computed for ClF{sub 3}, BrF{sub 3}, and IF{sub 3}, while we predict that an average D{sub 3h} structure would be experimentally observed for AtF{sub 3}. Electron correlation and scalar relativistic effects strongly reduce the energy difference between the D{sub 3h} geometry and the C{sub 2v} one, along the XF{sub 3} series, and in the X = At case, spin-orbit coupling also slightly reduces this energy difference. AtF{sub 3} is a borderline system where the D{sub 3h} structure becomes a minimum, i.e., the pseudo-Jahn-Teller effect is inhibited since electron correlation and scalar-relativistic effects create small energy barriers leading to the global C{sub 2v} minima, although both types of effects interfere.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An excited-state approach within full configuration interaction quantum Monte Carlo

We present a new approach to calculate excited states with the full configuration interaction quantum Monte Carlo (FCIQMC) method. The approach uses a Gram-Schmidt procedure, instantaneously applied to the stochastically evolving distributions of walkers, to orthogonalize higher energy states against lower energy ones. It can thus be used to study several of the lowest-energy states of a system within the same symmetry. This additional step is particularly simple and computationally inexpensive, requiring only a small change to the underlying FCIQMC algorithm. No trial wave functions or partitioning of the space is needed. The approach should allow excited states to be studied for systems similar to those accessible to the ground-state method due to a comparable computational cost. As a first application, we consider the carbon dimer in basis sets up to quadruple-zeta quality and compare to existing results where available.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modeling of electron energy spectra and mobilities in semi-metallic Hg{sub 1−x}Cd{sub x}Te quantum wells

Electron mobility, energy spectra, and intrinsic carrier concentrations in the n-type Hg{sub 0.32}Cd{sub 0.68}Te/Hg{sub 1−x}Cd{sub x}Te/Hg{sub 0.32}Cd{sub 0.68}Te quantum well (QW) in semi-metallic state are numerically modeled. Energy spectra and wave functions were calculated in the framework of the 8-band k-p Hamiltonian. In our model, electron scattering on longitudinal optical phonons, charged impurities, and holes has been taken into account, and the mobility has been calculated by an iterative solution of the Boltzmann transport equation. Our results show that the increase of the electron concentration in the well enhances the screening of the 2D electron gas, decreases the hole concentration, and can ultimately lead to a high electron mobility at liquid nitrogen temperatures. The increase of the electron concentration in the QW could be achieved in situ by delta-doping of barriers or by applying the top-gate potential. Our modeling has shown that for low molar composition x the concentration of holes in the well is high in a wide range of electron concentrations; in this case, the purity of samples does not significantly influence the electron mobility. These results are important in the context of establishing optimal parameters for the fabrication of high-mobility Hg{sub 1−x}Cd{sub x}Te quantum wells able to operate at liquid nitrogen temperature and thus suitable for applications in terahertz detectors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Exact solution to the Schrödinger’s equation with pseudo-Gaussian potential

We consider the radial Schrödinger equation with the pseudo-Gaussian potential. By making an ansatz to the solution of the eigenvalue equation for the associate Hamiltonian, we arrive at the general exact eigenfunction. The values of energy levels for the bound states are calculated along with their corresponding normalized wave-functions. The case of positive energy levels, known as meta-stable states, is also discussed and the magnitude of transmission coefficient through the potential barrier is evaluated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Interference between Coulombic and CT-mediated couplings in molecular aggregates: H- to J-aggregate transformation in perylene-based π-stacks

The spectroscopic differences between J and H-aggregates are traditionally attributed to the spatial dependence of the Coulombic coupling, as originally proposed by Kasha. However, in tightly packed molecular aggregates wave functions on neighboring molecules overlap, leading to an additional charge transfer (CT) mediated exciton coupling with a vastly different spatial dependence. The latter is governed by the nodal patterns of the molecular LUMOs and HOMOs from which the electron (t{sub e}) and hole (t{sub h}) transfer integrals derive. The sign of the CT-mediated coupling depends on the sign of the product t{sub e}t{sub h} and is therefore highly sensitive to small (sub-Angstrom) transverse displacements or slips. Given that Coulombic and CT-mediated couplings exist simultaneously in tightly packed molecular systems, the interference between the two must be considered when defining J and H-aggregates. Generally, such π-stacked aggregates do not abide by the traditional classification scheme of Kasha: for example, even when the Coulomb coupling is strong the presence of a similarly strong but destructively interfering CT-mediated coupling results in “null-aggregates” which spectroscopically resemble uncoupled molecules. Based on a Frenkel/CT Holstein Hamiltonian that takes into account both sources of electronic coupling as well as intramolecular vibrations, vibronic spectral signatures are developed for integrated Frenkel/CT systems in both the perturbative and resonance regimes. In the perturbative regime, the sign of the lowest exciton band curvature, which rigorously defines J and H-aggregation, is directly tracked by the ratio of the first two vibronic peak intensities. Even in the resonance regime, the vibronic ratio remains a useful tool to evaluate the J or H nature of the system. The theory developed is applied to the reversible H to J-aggregate transformations recently observed in several perylene bisimide systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Guiding, bending, and splitting of coupled defect surface modes in a surface-wave photonic crystal

We experimentally demonstrate a type of waveguiding mechanism for coupled surface-wave defect modes in a surface-wave photonic crystal. Unlike conventional spoof surface plasmon waveguides, waveguiding of coupled surface-wave defect modes is achieved through weak coupling between tightly localized defect cavities in an otherwise gapped surface-wave photonic crystal, as a classical wave analogue of tight-binding electronic wavefunctions in solid state lattices. Wave patterns associated with the high transmission of coupled defect surface modes are directly mapped with a near-field microwave scanning probe for various structures including a straight waveguide, a sharp corner, and a T-shaped splitter. These results may find use in the design of integrated surface-wave devices with suppressed crosstalk.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Solution of D dimensional Dirac equation for coulombic potential using NU method and its thermodynamics properties

The analytical solution of Ddimensional Dirac equation for Coulombic potential is investigated using Nikiforov-Uvarov method. The D dimensional relativistic energy spectra are obtained from relativistic energy eigenvalue equation by using Mat Lab software.The corresponding D dimensional radial wave functions are formulated in the form of generalized Jacobi and Laguerre Polynomials. In the non-relativistic limit, the relativistic energy equation reduces to the non-relativistic energy which will be applied to determine some thermodynamical properties of the system. The thermodynamical properties of the system are expressed in terms of error function and imaginary error function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Solution of D dimensional Dirac equation for hyperbolic tangent potential using NU method and its application in material properties

The analytical solution of D-dimensional Dirac equation for hyperbolic tangent potential is investigated using Nikiforov-Uvarov method. In the case of spin symmetry the D dimensional Dirac equation reduces to the D dimensional Schrodinger equation. The D dimensional relativistic energy spectra are obtained from D dimensional relativistic energy eigen value equation by using Mat Lab software. The corresponding D dimensional radial wave functions are formulated in the form of generalized Jacobi polynomials. The thermodynamically properties of materials are generated from the non-relativistic energy eigen-values in the classical limit. In the non-relativistic limit, the relativistic energy equation reduces to the non-relativistic energy. The thermal quantities of the system, partition function and specific heat, are expressed in terms of error function and imaginary error function which are numerically calculated using Mat Lab software.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Helium-like magnesium embedded in strongly coupled plasma

In recent days, with the advent of the x-ray free electron laser (FEL) with Linac coherent light source (LCLS) and the Orion laser, experimental studies on atomic systems within strongly coupled plasma environment with remarkable improvement in accuracy as compared to earlier experiments have become possible. In these kinds of experiments, hydrogen-like and helium-like spectral lines are used for determination of plasma parameters such as temperature, density. Accurate theoretical calculations are, therefore, necessary for such kind of studies within a dense plasma environment. In this work, ab initio calculations are carried out in the framework of the Rayleigh-Ritz variation principle to estimate the ground state energy of helium-like magnesium within strongly coupled plasma environment. Explicitly correlated wave functions in Hylleraas coordinates have been used to incorporate the effect of electron correlation. The ion-sphere model potential that confines the central positive ion in a finite domain filled with plasma electrons has been adopted to mimic the strongly coupled plasma environment. Thermodynamic pressure ’felt’ by the ion in the ground states due to the confinement inside the ion spheres is also estimated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Deep ultraviolet emission from ultra-thin GaN/AlN heterostructures

We present the theoretical and experimental results for the electronic and optical properties of atomically thin (1 and 2 monolayers) GaN quantum wells with AlN barriers. Strong quantum confinement increases the gap of GaN to as high as 5.44 eV and enables light emission in the deep-UV range. Luminescence occurs from the heavy and light hole bands of GaN yielding E ⊥ c polarized light emission. Strong confinement also increases the exciton binding energy up to 230 meV, preventing a thermal dissociation of excitons at room temperature. However, we did not observe excitons experimentally due to high excited free-carrier concentrations. Monolayer-thick GaN wells also exhibit a large electron-hole wave function overlap and negligible Stark shift, which is expected to enhance the radiative recombination efficiency. Our results indicate that atomically thin GaN/AlN heterostructures are promising for efficient deep-UV optoelectronic devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Effect of electric field on carrier escape mechanisms in quantum dot intermediate band solar cells

Carrier escape and recombination from quantum dot (QD) states reduce the probability of two-step photon absorption (TSPA) by decreasing the available carrier population in the intermediate band (IB). In order to optimize the second photon absorption for future designs of quantum dot embedded intermediate band solar cells, this study combined the results of simulations and experiments to quantify the effect of electric field on the barrier height and the carrier escape from the QDs in InAs/GaAs quantum dot solar cells with five-layer QD superlattices. The electric field dependent effective barrier heights for ground state electrons were calculated using eight band k·p theory at short circuit conditions. With an increase in electric field surrounding the QDs from 5 kV/cm to 50 kV/cm, the effective barrier height of the ground state electrons was reduced from 147 meV to 136 meV, respectively. Thus, the increasing electric field not only exponentially enhances the ground state electron tunneling rate (effectively zero at 5 kV/cm and 7.9 × 10 6 s -1 at 50 kV/cm) but also doubles the thermal escape rate (2.2 × 10 11 s -1 at 5 kV/cm and 4.1 × 10 11 s -1 at 50 kV/cm). Temperature-dependent external quantum efficiency measurements were performed to verify that the increasing electric field decreases the effective barrier height. Additionally, the electric field dependent radiative lifetimes of the ground state were characterized with time-resolved photoluminescence experiments. This study showed that the increasing electric field extended the radiative recombination lifetime in the ground state of the QDs as a consequence of the reduced wave-function overlap between the electrons and holes. The balance of carrier escape and recombination determines the probability of TSPA.

14 SOLAR ENERGY↗

Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian

Coupled cluster and symmetry projected Hartree-Fock are two central paradigms in electronic structure theory. However, they are very different. Single reference coupled cluster is highly successful for treating weakly correlated systems but fails under strong correlation unless one sacrifices good quantum numbers and works with broken-symmetry wave functions, which is unphysical for finite systems. Symmetry projection is effective for the treatment of strong correlation at the mean-field level through multireference non-orthogonal configuration interaction wavefunctions, but unlike coupled cluster, it is neither size extensive nor ideal for treating dynamic correlation. We here examine different scenarios for merging these two dissimilar theories. We carry out this exercise over the integrable Lipkin model Hamiltonian, which despite its simplicity, encompasses non-trivial physics for degenerate systems and can be solved via diagonalization for a very large number of particles. We show how symmetry projection and coupled cluster doubles individually fail in different correlation limits, whereas models that merge these two theories are highly successful over the entire phase diagram. In conclusion, despite the simplicity of the Lipkin Hamiltonian, the lessons learned in this work will be useful for building an ab initio symmetry projected coupled cluster theory that we expect to be accurate in the weakly and strongly correlated limits, as well as the recoupling regime.

74 ATOMIC AND MOLECULAR PHYSICS↗

Multistate, multichannel coupled diabatic state representations of adiabatic states coupled by conical intersections. CH 2 OH photodissociation

In this work, a coupled diabatic state representation, H d , of the 1, 2, 3 2 A states of CH 2 OH suitable for the description of the three channel, three state photodissociation process CH 2 OH(1 2 A) + hv → CH 2 OH(2, 3 2 A) → CH 2 O(X, A) + H, cis-CHOH + H, trans-CHOH + H, is reported. The representation is based on electronic structure data (energies, energy gradients, and derivative couplings) obtained exclusively from multireference configuration interaction single and double excitation wave functions. Diabat shifting is employed to improve the representation’s agreement with accurate experimental energetics. A careful analysis of the numerous minima, saddle points, and conical intersection seams is reported. The computed T 0 (3 2 A) ~ 35 220 cm -1 is in excellent agreement with the experimental estimate of 35 053 cm -1 , and the computed channel dissociation energies, D 0 , for CH 2 O 9453 (10 160), cis-HCOH 30 310.2 (29 923), and trans-HCOH 28 799 (28 391) cm -1 are in good accord with the measured values given parenthetically. Lastly, these accurate energetics over a wide range of nuclear configurations strongly support the ability of this H d to enable quality simulations of nonadiabatic dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Accurate barrier heights using diffusion Monte Carlo

Fixed node diffusion Monte Carlo (DMC) has been performed on a test set of forward and reverse barrier heights for 19 non-hydrogen-transfer reactions, and the nodal error has been assessed. The DMC results are robust to changes in the nodal surface, as assessed by using different mean-field techniques to generate single determinant wave functions. Using these single determinant nodal surfaces, DMC results in errors of 1.5(1) kcal/mol on barrier heights. Using the large data set of DMC energies, we attempted to find good descriptors of the fixed node error in this study. It does not correlate with a number of descriptors including change in density but does show some correlation with the gap between the highest occupied and lowest unoccupied orbital energies in the mean-field calculation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Low-lying vibronic level structure of the ground state of the methoxy radical: Slow electron velocity-map imaging (SEVI) spectra and Köppel-Domcke-Cederbaum (KDC) vibronic Hamiltonian calculations

A joint experimental and theoretical study is reported on the low-lying vibronic level structure of the ground state of the methoxy radical using slow photoelectron velocity-map imaging spectroscopy of cryogenically cooled, mass-selected anions (cryo-SEVI) and Köppel-Domcke-Cederbaum (KDC) vibronic Hamiltonian calculations. The KDC vibronic model Hamiltonian in the present study was parametrized using high-level quantum chemistry, allowing the assignment of the cryo-SEVI spectra for vibronic levels of CH 3 O up to 2000 cm –1 and of CD 3 O up to 1500 cm –1 above the vibrational origin, using calculated vibronic wave functions. The adiabatic electron affinities of CH 3 O and CD 3 O are determined from the cryo-SEVI spectra to be 1.5689 ± 0.0007 eV and 1.5548 ± 0.0007 eV, respectively, demonstrating improved precision compared to previous work. Experimental peak splittings of <10 cm –1 are resolved between the e 1/2 and e 3/2 components of the 6 1 and 5 1 vibronic levels. A pair of spin-vibronic levels at 1638 and 1677 cm –1 were predicted in the calculation as the e 1/2 and e 3/2 components of 6 2 levels and experimentally resolved for the first time. The strong variation of the spin-orbit splittings with a vibrational quantum number is in excellent agreement between theory and experiment. In conclusion, the observation of signals from nominally forbidden a 1 vibronic levels in the cryo-SEVI spectra also provides direct evidence of vibronic coupling between ground and electronically excited states of methoxy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗