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Theoretical studies of the transport properties in compound semiconductors

This final report is an overview of the work done on Cooperative Agreement NCC 3-55 with the Solid State Technology Branch of the NASA-Lewis Research Center (LeRC). Over the period of time that the agreement was in effect, the principal investigator and, in the last three years, the co-principal investigator worked on a significant number of projects and interacted with members of the Solid State Technology (SST) branch in a number of different ways. For the purpose of this report, these efforts will be divided into five categories: 1) work directly with experimental electrical transport studies conducted by members of the SST branch; 2) theoretical work on electrical transport in compound semiconductors; 3) electronic structure calculations which are relevant to the electrical transport in polytypes of SiC and SiC-AlN alloys; 4) the electronic structure calculations of polar interfaces; and 5) consultative and supportive activities related to experiments and other studies carried out by SST branch members. Work in these categories is briefly discussed.

Segall, Benjamin↗

Ab Initio Direct Dynamics

The reactivity and dynamics of molecular systems can be explored computationally by classical trajectory calculations. The traditional approach involves fitting a functional form of a potential energy surface (PES) to the energies from a large number of electronic structure calculations and then integrating numerous trajectories on this fitted PES to model the molecular dynamics. The ever-decreasing cost of computing and continuing advances in computational chemistry software have made it possible to use electronic structure calculations directly in molecular dynamics simulations without first having to construct a fitted PES. In this “on-the-fly” approach, every time the energy and its derivatives are needed for the integration of the equations of motion, they are obtained directly from quantum chemical calculations. This approach started to become practical in the mid-1990s as a result of increased availability of inexpensive computer resources and improved computational chemistry software. The application of direct dynamics calculations has grown rapidly over the last 25 years and would require a lengthy review article. The present Account is limited to some of our contributions to methods development and various applications. To improve the efficiency of direct dynamics calculations, we developed a Hessian-based predictor-corrector algorithm for integrating classical trajectories. Hessian updating made this even more efficient. Furthermore, this approach was also used to improve algorithms for following the steepest descent reaction paths. For larger molecular systems, we developed an extended Lagrangian approach in which the electronic structure is propagated along with the molecular structure. Strong field chemistry is a rapidly growing area, and to improve the accuracy of molecular dynamics in intense laser fields, we included the time-varying electric field in a novel predictor-corrector trajectory integration algorithm. Since intense laser fields can excite and ionize molecules, we extended our studies to include electron dynamics. Specifically, we developed code for time-dependent configuration interaction electron dynamics to simulate strong field ionization by intense laser pulses. Our initial application of ab initio direct dynamics in 1994 was to CH 2 O → H 2 + CO; the calculated vibrational distributions in the products were in very good agreement with experiment. In the intervening years, we have used direct dynamics to explore energy partitioning in various dissociation reactions, unimolecular dissociations yielding three fragments, reactions with branching after the transition state, nonstatistical dynamics of chemically activated molecules, dynamics of molecular fragmentation by intense infrared laser pulses, selective activation of specific dissociation channels by aligned intense infrared laser fields, angular dependence of strong field ionization, and simulation of sequential double ionization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Charge ordering and structural transition in the new organic conductor {delta}'-(BEDT-TTF){sub 2}CF{sub 3}CF{sub 2}SO{sub 3}.

We report structural, transport, and optical properties and electronic structure calculations of the delta'-(BEDT-TTF) 2CF3CF2SO3 (BEDT-TTF = bis(ethylenedithio)-tetrathiafulvalene) organic conductor that has been synthesized by electrocrystallization. Electronic structure calculations demonstrate the quasi-one-dimensional Fermi surfaces of the compound, while the optical spectra are characteristic for a dimer-Mott insulator. The single-crystal X-ray diffraction measurements reveal the structural phase transition at 200 K from the ambient-temperature monoclinic P2(1)/m phase to the low-temperature orthorhombic Pca2(1) phase, while the resistivity measurements clearly show the first order semiconductor-semiconductor transition at the same temperature. This transition is accompanied by charge-ordering as it is confirmed by splitting of charge-sensitive vibrational modes observed in the Raman and infrared spectra. The horizontal stripe charge-order pattern is suggested based on the crystal structure, band structure calculations, and optical spectra.

Olejniczak, Iwona↗

Solution of the Schrödinger equation for quasi-one-dimensional materials using helical waves

We formulate and implement a spectral method for solving the Schrödinger equation, as it applies to quasi-one-dimensional materials and structures. This allows for computation of the electronic structure of important technological materials such as nanotubes (of arbitrary chirality), nanowires, nanoribbons, chiral nanoassemblies, nanosprings and nanocoils, in an accurate, efficient and systematic manner. Our work is motivated by the observation that one of the most successful methods for carrying out electronic structure calculations of bulk/crystalline systems — the plane-wave method — is a spectral method based on eigenfunction expansion. Our scheme avoids computationally onerous approximations involving periodic supercells often employed in conventional plane-wave calculations of quasi-one-dimensional materials, and also overcomes several limitations of other discretization strategies, e.g., those based on finite differences and atomic orbitals. The basis functions in our method — called helical waves (or twisted waves) — are eigenfunctions of the Laplacian with symmetry adapted boundary conditions, and are expressible in terms of plane waves and Bessel functions in helical coordinates. We describe the setup of fast transforms to carry out discretization of the governing equations using our basis set, and the use of matrix-free iterative diagonalization to obtain the electronic eigenstates. Miscellaneous computational details, including the choice of eigensolvers, use of a preconditioning scheme, evaluation of oscillatory radial integrals and the imposition of a kinetic energy cutoff are discussed. We have implemented these strategies into a computational package called HelicES (Helical Electronic Structure). We demonstrate the utility of our method in carrying out systematic electronic structure calculations of various quasi-one-dimensional materials through numerous examples involving nanotubes, nanoribbons and nanowires. We also explore the convergence properties of our method, and assess its accuracy and computational efficiency by comparison against reference finite difference, transfer matrix method and plane-wave results. We anticipate that our method will find applications in computational nanomechanics and multiscale modeling, for carrying out transport calculations of interest to the field of semiconductor devices, and for the discovery of novel chiral phases of matter that are of relevance to the burgeoning quantum hardware industry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Convergent Protocols for Computing Protein–Ligand Interaction Energies Using Fragment-Based Quantum Chemistry

Fragment-based quantum chemistry methods offer a way to sidestep the steep nonlinear scaling of electronic structure calculations so that large molecular systems can be investigated using high-level methods. Here, we use fragmentation to compute protein–ligand interaction energies in systems with several thousand atoms, using a new software platform for managing fragment-based calculations that implements a screened many-body expansion. Convergence tests using a minimal-basis semiempirical method (HF-3c) indicate that two-body calculations, with single-residue fragments and simple hydrogen caps, are sufficient to reproduce interaction energies obtained using conventional supramolecular electronic structure calculations, to within 1 kcal/mol at about 1% of the computational cost. We also demonstrate that the HF-3c results are illustrative of trends obtained with density functional theory in basis sets up to augmented quadruple-ζ quality. Strategic deployment of fragmentation facilitates the use of converged biomolecular model systems alongside high-quality electronic structure methods and basis sets, bringing ab initio quantum chemistry to systems of hitherto unimaginable size. This will be useful for generation of high-quality training data for machine learning applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Experimental and theoretical study of energy transfer in a chromophore triad: What makes modeling dynamics successful?

Simulation of electronic dynamics in realistically large molecular systems is a demanding task that has not yet achieved the same level of quantitative prediction already realized for its static counterpart. This is particularly true for processes occurring beyond the Born–Oppenheimer regime. Non-adiabatic molecular dynamics (NAMD) simulations suffer from two convoluted sources of error: numerical algorithms for dynamics and electronic structure calculations. While the former has gained increasing attention, particularly addressing the validity of ad hoc methodologies, the effect of the latter remains relatively unexplored. Indeed, the required accuracy for electronic structure calculations to reach quantitative agreement with experiment in dynamics may be even more strict than that required for static simulations. In this study, we address this issue by modeling the electronic energy transfer in a donor–acceptor–donor (D–A–D) molecular light harvesting system using fewest switches surface hopping NAMD simulations. In the studied system, time-resolved experimental measurements deliver complete information on spectra and energy transfer rates. Subsequent modeling shows that the calculated electronic transition energies are “sufficiently good” to reproduce experimental spectra but produce over an order of magnitude error in simulated dynamical rates. We further perform simulations using artificially shifted energy gaps to investigate the complex relationship between transition energies and modeled dynamics to understand factors affecting non-radiative relaxation and energy transfer rates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

GPR_calculator: An on-the-fly surrogate model to accelerate massive nudged elastic band calculations

We present GPR_calculator, a package based on Python and C++ programming languages to build an on-the-fly surrogate model using Gaussian Process Regression (GPR) to approximate computationally expensive electronic structure calculations. The key idea is to dynamically train a GPR model during the simulation that can accurately predict energies and forces with uncertainty quantification. When the uncertainty is high, the costly electronic structure calculation is performed to obtain the ground truth data, which is then used to update the GPR model. To illustrate the effectiveness of GPR_calculator, we demonstrate its application in Nudged Elastic Band (NEB) simulations of surface diffusion and reactions, achieving 3-10 times acceleration compared to pure ab initio calculations. The source code is available at https://github.com/MaterSim/GPR_calculator.

Gaussian process regression↗

Atom-in-jellium predictions of the shear modulus at high pressure

Atom-in-jellium calculations of the Einstein frequency in condensed matter and of the equation of state were used to predict the variation of shear modulus from zero pressure to ~10 7 g/cm 3 , for several elements relevant to white dwarf stars and other self-gravitating systems. This is by far the widest range reported electronic structure calculation of shear modulus, spanning from ambient through the one-component plasma to extreme relativistic conditions. The predictions were based on a relationship between the Debye temperature and shear modulus, which we assess to be accurate at the o(10%) level, and is the first known use of atom-in-jellium theory to calculate a shear modulus. Finally, we assessed the overall accuracy of the method by comparing with experimental measurements and more detailed electronic structure calculations at lower pressures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Characterization of the Alkali Metal Oxalates (MC2O4-) and their formation by CO2 reduction via the Alkali Metal Carbonites (MCO2-)

The reduction of carbon dioxide to oxalate has been studied by experimental Collisionally Induced Dissociation (CID) and vibrational characterization of the alkali metal oxalates, supplemented by theoretical electronic structure calculations. The critical step in the reductive process is the coordination of the heterocumulene CO2 to an alkali metal anion, forming a metal carbonite MCO2 ablt to subsequently add a second CO2 molecule. While the energetic demand for these reactions is generally low, we find that the degree of activation of CO2 in terms of charge transfer and transition state energies is the highest for lithium and systematically decreases down the group (M - Li - Cs).

Jestila, Joakim S.↗

Finding Electronic Structure Machine Learning Surrogates without Training

A myriad of phenomena in materials science and chemistry rely on quantum-level simulations of the electronic structure in matter. While moving to larger length and time scales has been a pressing issue for decades, such large-scale electronic structure calculations are still challenging despite modern software approaches and advances in high-performance computing. The silver lining in this regard is the use of machine learning to accelerate electronic structure calculations – this line of research has recently gained growing attention. The grand challenge therein is finding a suitable machine-learning model during a process called hyperparameter optimization. This, however, causes a massive computational overhead in addition to that of data generation. We accelerate the construction of machine-learning surrogate models by roughly two orders of magnitude by circumventing excessive training during the hyperparameter optimization phase. We demonstrate our workflow for Kohn-Sham density functional theory, the most popular computational method in materials science and chemistry.

36 MATERIALS SCIENCE↗

Quantum Machine-Learning for Eigenstate Filtration in Two-Dimensional Materials

Quantum machine-learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure calculations of molecular systems and spin models in magnetic systems. However, the discussion in all these recipes focuses specifically on targeting the ground state. Herein we demonstrate a quantum algorithm that can filter any energy eigenstate of the system based on either symmetry properties or a predefined choice of the user. The workhorse of our technique is a shallow neural network encoding the desired state of the system with the amplitude computed by sampling the Gibbs–Boltzmann distribution using a quantum circuit and the phase information obtained classically from the nonlinear activation of a separate set of neurons. We show that the resource requirements of our algorithm are strictly quadratic. To demonstrate its efficacy, we use state filtration in monolayer transition metal dichalcogenides which are hitherto unexplored in any flavor of quantum simulations. We implement our algorithm not only on quantum simulators but also on actual IBM-Q quantum devices and show good agreement with the results procured from conventional electronic structure calculations. We thus expect our protocol to provide a new alternative in exploring the band structures of exquisite materials to usual electronic structure methods or machine-learning techniques that are implementable solely on a classical computer.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Superconducting pairing mechanism in CeCoIn 5 revisited

Spectroscopic-imaging scanning-tunneling microscopy (SI-STM) measurements have previously been applied to the study of the heavy-fermion system CeCoIn 5 to examine the superconducting gap structure and band dispersions via quasiparticle intereference. Here we directly measure the dispersing electron bands with angle-resolved-photoelectron spectroscopy (ARPES) and compare with first principles electronic structure calculations. By auto-correllating the ARPES-resolved bands with themselves we can measure the potential q-vectors and discern exactly which bands the STM is measuring. We find that the STM results are dominated by scattering associated with a cloverleaf shaped band centered at the zone corners. This same band is also a viable candidate to host the superconducting gap. Overall, the electronic structure calculations indicate that this region of the Fermi surface involves significant contributions from the Co d-electrons, an indication that the superconductivity in these materials is more 3-dimensional than that found in the related unconventional superconductors, the cuprates and the pnictides.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Recent Advances on Computational Modeling of Supported Single-Atom and Cluster Catalysts: Characterization, Catalyst–Support Interaction, and Active Site Heterogeneity

To satisfy the need for catalyst materials with high activity, selectivity, and stability for energy conversion, material design and discovery guided by theoretical insights are a necessity. In the past decades, the rise in theoretical investigations into the properties of catalyst materials, reaction mechanisms, and catalyst design principles has shed light on the catalysis field. Quantitative structure–activity relationships have been developed through incorporating spectroscopic simulations, electronic structure calculations, and reaction mechanistic studies. Here, in this review, we report the state-of-the-art computational approaches to catalyst materials characterization for supported single-atom and cluster catalysts utilizing spectroscopic simulations, i.e., XANES simulation, and material properties investigation via electronic-structure calculations. Furthermore, approaches regarding reaction mechanisms, focusing on active site heterogeneity, are also discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Magnetization distribution in Cu 0.6 Mn 2.4 Ge 2 ferromagnet from polarized and non-polarized neutron powder diffraction aided by density-functional theory calculations

The crystal structure and magnetic properties of Cu 0.6 Mn 2.4 Ge 2 have been re-investigated by a combination of extensive magnetic measurements and neutron scattering experiments, aided by electronic structure calculations. The material is found to be a soft ferromagnet with the ordering temperature T C = 316 K. The magnetocaloric effect evaluated from field-dependent magnetization isotherms is equal to 1.2 J/(kg·K) and 2.5 J/(kg·K) under the maximum applied magnetic field of 2 T and 5 T, respectively. The compound crystallizes in the hexagonal space group P6 3 /mmc. A complex structural disorder necessitated testing of several disorder models against the results of non-polarized and polarized neutron scattering experiments and magnetization measurements. Simulations at the density-functional theory level were also performed to identify the most robust solution that properly described the data observed. The final magnetic structure model reveals non-equal magnetic moments on the Mn1 and Mn2 atoms (2.29(9) µ B and 2.7(1) µ B , respectively) and the presence of vacancies and minor Cu substitution defects in both Mn sites. The work demonstrates how the non-polarized and polarized neutron scattering methods can be combined with electronic structure calculations to establish the microscopic structure of magnetic materials with complex crystallographic disorder.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quasi-one-dimensional uniform spin- 1 2 Heisenberg antiferromagnet KNaCuP 2 O 7 probed by P 31 and Na 23 NMR

Here we present the structural and magnetic properties of KNaCuP 2 O 7 investigated via x-ray diffraction, magnetization, specific heat, and P 31 and Na 23 NMR measurements and complementary electronic structure calculations. The temperature-dependent magnetic susceptibility and P 31 NMR shift could be modeled very well by the uniform spin- 1 2 Heisenberg antiferromagnetic chain model with a nearest-neighbor interaction J / k B ≃ 58.7 K . The corresponding mapping using first-principles electronic structure calculations leads to J DFT / k B ≃ 59 K with negligibly small interchain couplings, further confirming that the system is indeed a one-dimensional uniform spin- 1 2 Heisenberg antiferromagnet. The diverging trend of NMR spin-lattice relaxation rates ( 1 / T 1 31 and 1 / T 1 23 ) implies the onset of a magnetic long-range ordering at around T N ≃ 1 K . From the value of T N , the average interchain coupling is estimated to be J ' / k B ≃ 0.28 K . Moreover, the NMR spin-lattice relaxation rates show the dominant contributions from uniform ( q = 0 ) and staggered ( q = ± π / a ) spin fluctuations in the high- and low-temperature regimes, respectively, mimicking one-dimensionality of the spin lattice. We have also demonstrated that 1 / T 1 31 in high temperatures varies linearly with 1 / H , reflecting the effect of spin diffusion on the dynamic susceptibility. The temperature-dependent unit cell volume could be described well using the Debye approximation with a Debye temperature of Θ D ≃ 294 K , consistent with the heat capacity data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Adaptive basis sets for practical quantum computing

Electronic structure calculations on small systems such as H 2 , H 2 O, LiH, and BeH 2 with chemical accuracy are still a challenge for the current generation of noisy intermediate-scale quantum (NISQ) devices. One of the reasons is that due to the device limitations, only minimal basis sets are commonly applied in quantum chemical calculations, which allows one to keep the number of qubits employed in the calculations at a minimum. However, the use of minimal basis sets leads to very large errors in the computed molecular energies as well as potential energy surface shapes. One way to increase the accuracy of electronic structure calculations is through the development of small basis sets better suited for quantum computing. In this work, we show that the use of adaptive basis sets, in which exponents and contraction coefficients depend on molecular structure, provides an easy way to dramatically improve the accuracy of quantum chemical calculations without the need to increase the basis set size and thus the number of qubits utilized in quantum circuits. As a proof of principle, we optimize an adaptive minimal basis set for quantum computing calculations on an H 2 molecule, in which exponents and contraction coefficients depend on the H—H distance, and apply it to the generation of H 2 potential energy surface on IBM-Q quantum devices. The adaptive minimal basis set reaches the accuracy of the double-zeta basis sets, thus allowing one to perform double-zeta quality calculations on quantum devices without the need to utilize twice as many qubits in simulations. This approach can be extended to other molecular systems and larger basis sets in a straightforward manner.

97 MATHEMATICS AND COMPUTING↗

Gas phase protonated nicotine is a mixture of pyridine- and pyrrolidine-protonated conformers: implications for its native structure in the nicotinic acetylcholine receptor

The infrared (IR) spectra of gas phase protonated nicotine has been measured in the never-before probed N–H “fingerprint region” (3200–3500 cm -1 ). The protonated molecules generated by an electrospray source are thermalized in the first ion trap with water vapor and He gas at a pre-determined temperature prior to being probed by IR spectroscopy in the second ion trap at 4 K. The IR spectra exhibit two N–H stretching bands which are assigned to the pyridine and pyrrolidine protomers with the aid of high-level electronic structure calculations. This finding is in sharp contrast to previous spectroscopic studies that suggested a single population of the pyridine protomer. The relative populations of the two protomers vary by changing the temperature of the thermalizing trap from 180-300 K. The relative conformer populations at 240 K and 300 K are well reproduced by the theoretical calculations, unequivocally determining that gas phase nicotine is a 3 : 2 mixture of both pyridine and pyrrolidine protomers at room temperature. The thermalizing anhydrous vapor does not result in any population change. It rather demonstrates the catalytic role of water in achieving equilibrium between the two protomers. The combination of IR spectroscopy and electronic structure calculations establish the small energy difference between the pyridine and pyrrolidine protomers in nicotine. Finally, one of the gas phase nicotine pyrrolidine protomers has the closest conformational resemblance among all low-lying energy isomers with the X-ray structure of nicotine in the nicotinic acetylcholine receptor (nAChR).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

O 2 -Dependence of reactions of 1,2-dimethoxyethanyl and 1,2-dimethoxyethanylperoxy isomers

Reaction mechanisms of Ṙ and ROȮ radicals derived from low-temperature oxidation of 1,2-dimethoxyethane (CH 3 O(CH 2 ) 2 OCH 3 ) were investigated using speciation from multiplexed photoionization mass spectrometry (MPIMS) measurements via Cl-initiated oxidation, in conjunction with electronic structure calculations. The experiments were conducted at 5 bar, from 450 K – 650 K, and O 2 concentrations from 1 · 10 14 cm –3 – 6 · 10 18 cm –3 to probe the effects on competing reaction channels of 1,2-dimethoxyethanyl (Ṙ) and 1,2-dimethoxyethanylperoxy (ROȮ) isomers. Several species were detected with photoionization spectral fitting – ethene, formaldehyde, methyl vinyl ether, and 2-methoxyacetaldehyde – and, as determined by electronic structure calculations, may form via unimolecular decomposition of 1,2-dimethoxyethanyl or 1,2-dimethoxyethanylperoxy. O 2 -dependent yield ratios show that the formation pathways for all species undergo a competition between O 2 -addition and unimolecular decomposition. Here, adiabatic ionization energies were also calculated and utilized along with exact mass determinations to infer contributions for other species derived exclusively from first- and second-O 2 -addition, including 1,2-dimethoxyethene, cyclic ethers, and dicarbonyls.

1,2-dimethoxyethane↗