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At least 145 records · Page 8

Nonlinear absorption in AlGaAs/GaAs multiple quantum well structures grown by metalorganic chemical vapor deposition

This paper reports the study of growth conditions for achieving the sharp exciton resonances and low-intensity saturation of these resonances in AlGaAs-GaAs multiple quantum well structures grown by metalorganic chemical vapor deposition. Low growth temperature is necessary to observe this sharp resonance feature at room temperature. The optimal growth conditions are a tradeoff between the high temperatures required for high quality AlGaAs and low temperatures required for high-purity GaAs. A strong optical saturation of the excitonic absorption has been observed. A saturation density as low as 250 W/sq cm is reported.

Lee, H. C.↗

Photoexcited escape probability, optical gain, and noise in quantum well infrared photodetectors

We present a detailed and thorough study of a wide variety of quantum well infrared photodetectors (QWIPs), which were chosen to have large differences in their optical and transport properties. Both n- and p-doped QWIPs, as well as intersubband transitions based on photoexcitation from bound-to-bound, bound-to-quasi-continuum, and bound-to-continuum quantum well states were investigated. The measurements and theoretical analysis included optical absorption, responsivity, dark current, current noise, optical gain, hot carrier mean free path; net quantum efficiency, quantum well escape probability, quantum well escape time, as well as detectivity. These results allow a better understanding of the optical and transport physics and thus a better optimization of the QWIP performance.

Levine, B. F.↗

Quantum efficiencies of imaging detectors with alkali halide photocathodes. I - Microchannel plates with separate and integral CsI photocathodes

Measurements and comparisons have been made of the quantum efficiencies of microchannel plate (MCP) detectors in the far-UV (below 2000-A) wavelength range using CsI photocathodes (a) deposited on the front surfaces of microchannel plates and (b) deposited on solid substrates as opaque photocathodes with the resulting photoelectrons input to microchannel plates. The efficiences were measured in both pulse-counting and photodiode modes of operation. Typical efficiencies are about 15 percent at 1216 A for a CsI-coated MCP compared with 65 percent for an opaque CsI photocathode MCP detector. Special processing has yielded an efficiency as high as 20 percent for a CsI-coated MCP. This may possibly be further improved by optimization of the tilt angle of the MCP channels relative to the front face of the MCP and incident radiation. However, at present there still remains a factor of at least 3 quantum efficiency advantage in the separate opaque CsI photocathode configuration.

Carruthers, George R.↗

High-Performance LWIR Superlattice Detectors and FPA Based on CBIRD Design

We report our recent efforts on advancing of antimonide superlattice based infrared photodetectors and demonstration of focal plane arrays based on a complementary barrier infrared detector (CBIRD) design. By optimizing design and growth condition we succeeded to reduce the operational bias of CBIRD single pixel detector without increase of dark current or degradation of quantum efficiency. We demonstrated a 1024x1024 pixel long-waveleng thinfrared focal plane array utilizing CBIRD design. An 11.5 micrometer cutoff focal plane without anti-reflection coating has yielded noise equivalent differential temperature of 53 mK at operating temperature of 80 K, with 300 K background and cold-stop. Imaging results from a recent 10 micrometer cutoff focal plane array are also presented. These results advance state-of-the art of superlattice detectors and demonstrated advantages of CBIRD architecture for realization of FPA.

infrared↗

High-Performance LWIR Superlattice Detectors and FPA Based on CBIRD Design

We report our recent efforts on advancing of antimonide superlattice based infrared photodetectors and demonstration of Focal Plane Arrays (FPA) based on a complementary barrier infrared detector (CBIRD) design. By optimizing design and growth condition we succeeded to reduce the operational bias of CBIRD single pixel detector without increase of dark current or degradation of quantum efficiency. We demonstrated a 1024x1024 pixel long-wavelength infrared focal plane array utilizing CBIRD design. An 11.5 ?m cutoff FPA without anti-reflection coating has yielded noise equivalent differential temperature of 53 mK at operating temperature of 80 K, with 300 K background and cold-stop. In addition, we demonstrated 320x256 format FPA based on the n-CBIRD design. The resulting FPAs yielded noise equivalent differential temperature of 26 mK at operating temperature of 80 K, with 300 K background and cold-stop. These results advance state-of-the art of superlattice detectors and demonstrated advantages of CBIRD architecture for realization of FPA.

unipolar barrier↗

High-Performance LWIR Superlattice Detectors and FPA Based on CBIRD Design

We report our recent efforts on advancing of antimonide superlattice based infrared photodetectors and demonstration of focal plane arrays based on a complementary barrier infrared detector (CBIRD) design. By optimizing design and growth condition we succeeded to reduce the operational bias of CBIRD single pixel detector without increase of dark current or degradation of quantum efficiency. We demonstrated a 1024x1024 pixel long-wavelength infrared focal plane array utilizing CBIRD design. An 11.5 micrometer cutoff focal plane without anti-reflection coating has yielded noise equivalent differential temperature of 53 mK at operating temperature of 80 K, with 300 K background and cold-stop. Imaging results from a recent 10 micrometer cutoff focal plane array are also presented. These results advance state-of-the art of superlattice detectors and demonstrated advantages of CBIRD architecture for realization of FPA.

heterostructure↗

Optical amplifiers for coherent lidar

We examine application of optical amplification to coherent lidar for the case of a weak return signal (a number of quanta of the return optical field close to unity). We consider the option that has been explored to date, namely, incorporation of an optical amplifier operated in a linear manner located after reception of the signal and immediately prior to heterodyning and photodetection. We also consider alternative strategies where the coherent interaction, the nonlinear processes, and the amplification are not necessarily constrained to occur in the manner investigated to date. We include the complications that occur because of mechanisms that occur at the level of a few, or one, quantum excitation. Two factors combine in the work to date that limit the value of the approach. These are: (1) the weak signal tends to require operation of the amplifier in the linear regime where the important advantages of nonlinear optical processing are not accessed, (2) the linear optical amplifier has a -3dB noise figure (SN(out)/SN(in)) that necessarily degrades the signal. Some improvement is gained because the gain provided by the optical amplifier can be used to overcome losses in the heterodyned process and photodetection. The result, however, is that introduction of an optical amplifier in a well optimized coherent lidar system results in, at best, a modest improvement in signal to noise. Some improvement may also be realized on incorporating more optical components in a coherent lidar system for purely practical reasons. For example, more compact, lighter weight, components, more robust alignment, or more rapid processing may be gained. We further find that there remain a number of potentially valuable, but unexplored options offered both by the rapidly expanding base of optical technology and the recent investigation of novel nonlinear coherent interference phenomena occurring at the single quantum excitation level. Key findings are: (1) insertion of linear optical amplifiers in well optimized conventional lidar systems offers modest improvements, at best, (2) the practical advantages of optical amplifiers, especially fiber amplifiers, such as ease of alignment, compactness, efficiency, lightweight, etc., warrant further investigation for coherent lidar, (3) the possibility of more fully optical lidar systems should be explored, (4) advantages gained by use of coherent interference of optical fields at the level of one, or a few, signal quanta should be explored, (5) amplification without inversion, population trapping, and use of electromagnetic induced transparency warrant investigation in connection with coherent lidar, (6) these new findings are probably more applicable to earth related NASA work, although applications to deep space should not be excluded, and (7) our own work in the Ultrafast Laboratory at UAH along some of the above lines of investigation, may be useful.

Fork, Richard↗

Sensitivity analysis and multidisciplinary optimization for aircraft design: Recent advances and results

Optimization by decomposition, complex system sensitivity analysis, and a rapid growth of disciplinary sensitivity analysis are some of the recent developments that hold promise of a quantum jump in the support engineers receive from computers in the quantitative aspects of design. Review of the salient points of these techniques is given and illustrated by examples from aircraft design as a process that combines the best of human intellect and computer power to manipulate data.

Sobieszczanski-Sobieski, Jaroslaw↗

Sensitivity analysis and multidisciplinary optimization for aircraft design - Recent advances and results

Optimization by decomposition, complex system sensitivity analysis, and a rapid growth of disciplinary sensitivity analysis are some of the recent developments that hold promise of a quantum jump in the support engineers receive from computers in the quantitative aspects of design. Review of the salient points of these techniques is given and illustrated by examples from aircraft design as a process that combines the best of human intellect and computer power to manipulate data.

Sobieszczanski-Sobieski, Jaroslaw↗

Design and performance of very long-wavelength GaAs/Al(x)Ga(1-x)As quantum-well infrared photodetectors

We present an extensive and detailed study of very long wavelength quantum well infrared photodetectors covering the spectral region between 14 and 20 micrometers. Measurements were made on seven different molecular beam epitaxy grown samples having different well widths and barrier heights. In this study we combine experimental results with theoretical analysis and focus on the relationship between the quantum well structure and detector performance, i.e., responsivity, dark current, dynamic resistance, noise current, optical-gain, and detectivity. These results provide the basis for further optimization, and the detector parameters needed for the design of the readout circuit for focal plane arrays.

Sarusi, G.↗

Simulating a Low-Weight Encoding of the Fermi-Hubbard Model Feedback and Support with QAOA

Recent work [1] has proposed a compact fermion-to-qubit mapping for the Fermi-Hubbard model (FHM), potentially lowering the overhead needed to simulate such a system on quantum hardware. In prior work [2], we numerically investigated how well a quantum annealer could prepare ground states of the FHM encoded using the resource-efficient mapping. In order to compare these results to gate-model systems, we turn to a QAOA-style approach and replace the annealing schedule with both Trotterizations thereof and also more general Hamiltonian-variational ansatze based on the terms of the mapped FH Hamiltonian. We investigate the achievable ground state fidelities of these gate sequences, consider various optimizations of the ansatze structure, and offer resource estimations of the optimized QAOA protocols for near-term hardware.

quantum computing↗

Ge:Be infrared photoconductors

Ge:Be photoconductors were optimized for the 30 to 50 micron wavelength range. Crystal growth of detector quality material requires good control of both the Be and residual impurity doping. Detective quantum efficiencies of n sub d = 46% at 5 A/W were achieved at a photon background of 10 to the 8th power p/s. The responsivity of Ge:Be detectors can be strongly temperature-dependent when the residual shallow levels in the material are closely compensated. Transient responses on the order of approximately 1 second were observed in some materials. The role of residual shallow impurities on the performance of photoconductors doped with semi-deep and deep impurities is discussed.

Haegel, N. M.↗

LED Device Illuminates New Path to Healing

Among NASA s research goals is increased understanding of factors affecting plant growth, including the effects of microgravity. Impeding such studies, traditional light sources used to grow plants on Earth are difficult to adapt to space flight, as they require considerable amounts of power and produce relatively large amounts of heat. As such, an optimized experimental system requires much less energy and reduces temperature variance without negatively affecting plant growth results. Ronald W. Ignatius, founder and chairman of the board at Quantum Devices Inc. (QDI), of Barneveld, Wisconsin, proposed using light-emitting diodes (LEDs) as the photon source for plant growth experiments in space. This proposition was made at a meeting held by the Wisconsin Center for Space Automation and Robotics, a NASA-sponsored research center that facilitates the commercialization of robotics, automation, and other advanced technologies. The Wisconsin group teamed with QDI to determine whether an LED system could provide the necessary wavelengths and intensities for photosynthesis, and the resultant system proved successful. The center then produced the Astroculture3, a plant growth chamber that successfully incorporated this LED light source, which has now flown on several space shuttle missions. NASA subsequently identified another need that could be addressed with the use of LEDs: astronaut health. A central concern in astronaut health is maintaining healthy growth of cells, including preventing bone and muscle loss and boosting the body s ability to heal wounds all adversely affected by prolonged weightlessness. Thus, having determined that LEDs can be used to grow plants in space, NASA decided to investigate whether LEDs might be used for photobiomodulation therapy (PBMT).

Source record↗

Wildfire Segmentation From Remotely Sensed Data Using Quantum-Compatible Conditional Vector Quantized-Variational Autoencoders

Wildfires represent a critical environmental hazard with multifaceted implications for ecosystems, communities, and public health [1]. The escalating frequency and intensity of wildfires globally have intensified the urgency for robust segmentation methodologies to facilitate effective mitigation, response, and recovery strategies [2]. Accurate wildfire segmentation is pivotal for delineating fire boundaries, assessing progression patterns, and prioritizing resource allocation during emergency scenarios. Furthermore, precise segmentation enables stakeholders, including policymakers, environmental scientists, and emergency responders, to formulate evidence-based strategies, thereby minimizing socio-economic disruptions and ecological degradation. Consequently, advancing wildfire segmentation techniques through innovative technological interventions remains a paramount research imperative. Although foundational in wildfire segmentation, traditional deterministic models exhibit inherent limitations that compromise their efficacy in dynamic and uncertain environments. These models often operate on rigid algorithms prioritizing deterministic classifications, thereby overlooking the inherent complexities and uncertainties associated with wildfire behavior and satellite data variability. Such deterministic frameworks tend to produce oversimplified representations that fail to capture the intricate nuances of evolving fire dynamics, spatial heterogeneity, and environmental interactions [1]. Consequently, the deterministic approach’s propensity for uncertainty collapsing [1, 3] hampers the accuracy, reliability, and applicability of segmentation outcomes in real-world scenarios. Contrastingly, stochastic models offer a more nuanced and adaptable framework for wildfire segmentation. By integrating probabilistic elements into the modeling paradigm, stochastic approaches, particularly probabilistic approaches such as variational auto encoders (VAEs) [4], facilitate comprehensive uncertainty assessment, enabling researchers to quantify and incorporate uncertainties into segmentation outcomes effectively. This probabilistic nature empowers stochastic models to encapsulate variability, account for data inconsistencies, and adapt to evolving environmental conditions, enhancing segmentation accuracy, reliability, and robustness. Embracing stochastic methodologies thus catalyzes advancements in wildfire science by fostering a more holistic, adaptive, and resilient segmentation framework. Despite VAEs demonstrating significant promise in various applications, they come with inherent limitations that have garnered attention within the machine learning community. One of the primary drawbacks lies in their reliance on static priors, which essentially assume a fixed distribution for latent variables, thereby limiting the model’s flexibility to capture complex data structures effectively [5]. This static nature leads to suboptimal representations, especially when dealing with complex and high-dimensional data. Additionally, VAEs often struggle with generating sharp and realistic samples, a phenomenon commonly referred to as mode collapse [5, 7, 6]. Furthermore, the optimization process in VAEs, which involves balancing the reconstruction loss and the regularization term, can sometimes be challenging to fine-tune [7]. In recent efforts to address these shortcomings, alternative approaches like Vector Quantized Variational Auto encoders(VQ-VAEs) [7], address the challenges by incorporating discrete latent variables and leveraging techniques that enhance the quality and diversity of generated samples while maintaining efficient training dynamics. VQ-VAEs propose a dynamic prior distribution generation mechanism that diverges from the static priors commonly associated with traditional VAEs. This dynamic approach allows for more adaptive and context-aware latent variable representations, thereby potentially capturing complex data structures more effectively. Unlike autoregressive prior models such as PixelCNN, which, despite their ability to model dependencies across data dimensions, suffer from significant computational inefficiencies and lack flexibility in handling diverse datasets. In our work, we propose to use a generative quantum-compatible approach to help alleviate the shortcomings of autoregressive prior model in VQ-VAEs. Restricted Boltzmann Machines (RBMs) are a viable alternative prior model that can learn prior distributions in a faster and more flexible manner. In this research endeavor, we meticulously curate a state-of-the-art dataset leveraging satellite MODIS data in conjunction with VIIRS fire masks, derived from Fire Radiative Power (FRP), thereby encapsulating diverse wildfire scenarios and environmental contexts. We developed a conditional VQ-VAE architecture with the RBM prior model that is trained in a supervised manner for segmenting wildfire masks. This innovative approach synergistically harnesses deep learning capabilities, enabling the generation of segmentation maps characterized by heightened precision, granularity, and contextual relevance. Furthermore, replacing the autoregressive prior learning method proposed by the original VQ-VAE with a prior density approximation via quantum-compatible RBM facilitates expedited inference processes, augments flexibility in prior sampling, optimizes computational efficiency and establishes a groundbreaking benchmark in wildfire segmentation methodologies.

quantum machine learning↗

High-Performance Computing Optimization for Aladyn – Adaptive Neural Network Molecular Dynamics Mini-Application

This report provides a description and performance evaluation of the optimization techniques for high performance computing (HPC) implementation of the open source Computational Materials mini-application Aladyn (https://github.com/nasa/aladyn). Aladyn is a basic molecular dynamics code written in FORTRAN 2003, which is designed to demonstrate the use of adaptive neural networks (ANNs) in atomistic simulations. The role of ANNs is to efficiently reproduce the very complex energy landscape resulting from the atomic interactions in materials with the accuracy of the more expensive quantum mechanics-based calculations. The ANN is trained on a large set of atomic structures calculated using the density functional theory (DFT) method. While achieving orders of magnitude faster computational performance than DFT, the ANN-based approach was still very computationally demanding compared to the conventional approach of using empirically fitted energy functions. After its initial development, Aladyn was evaluated and optimized by experts at the NASA Advanced Supercomputing (NAS) division to exploit modern supercomputer architectures. The code has been optimized for execution on multicore central processing units (CPUs), including Intel® Skylake microarchitecture, and on graphic accelerators, such as Nvidia® V100 graphic processing units (GPUs), using Open Multi-Processing (OpenMP) and Open Accelerators (OpenACC) programming interfaces. The optimization achieved a speedup of 4.7 times the baseline version on CPU performance and an additional 2.4 times on CPU+GPU performance. Atomistic computer simulations are a fundamental tool in materials research to model material properties form physics-based first principles. Atomic interaction, governed by Quantum Mechanics (QM) require sophisticated and highly computationally demanding mathematical models to calculate [1]. Classical methods use approximate functional forms, empirically fitted through a set of variable parameters to emulate atomic energies as direct functions of atomic coordinates [2]. While empirical potentials are computationally much simpler, allowing simulations of large-scale systems of up to a trillion (1012) atoms [3], they are substantially less accurate compared to quantum calculations and applicable only to very specific atomic configurations or predefined crystallographic phases. A recently suggested approach is to use heuristic machine learning methods [4], such as those based on Adaptive Neural Networks (ANNs) to predict atomic energies, after being trained on a sufficiently large database of QM-calculated structures [5,6]. This approach reduces significantly the computational complexity, allowing for simulations of orders of magnitude larger systems compared to QM-based methods without compromising accuracy. Still, compared to classical methods using empirical energy functions, ANN methods remain two- to three orders of magnitude more computationally demanding. Hence, the computational cost of simulations, together with the need for extensive training of ANNs, still makes the practical implementation of ANN-based methods quite challenging. The purpose of the Aladyn mini-application software [7], available as open source at https://github.com/nasa/aladyn, is to be a testbed for exploring possible optimization strategies to develop highly scalable parallel algorithms for ANN-based atomistic simulations. Aladyn is aimed at utilizing the architecture of the high-end modern highperformance computing (HPC) hardware based on multicore central processing units (CPUs) equipped with graphic processing unit (GPU) accelerators. Specifically, the goal is to optimize the performance on a single HPC compute node, before implementing scaling to multi-node parallelization using message passing interface (MPI). At the same time, the open source code of Aladyn can serve as a training model for students and professors in academia.

Yamakov, Vesselin I.↗

Resonant tunneling IR detectors

Researchers propose a novel semiconductor heterojunction photodetector which would have a very low dark current and would be voltage tunable. A schematic diagram of the device and its band structure are shown. The two crucial components of the device are a cathode (InGaAs) whose condition band edge is below the conduction band edge of the quantum wells and a resonant tunneling filter (GaAs-AlGaAs). In a standard resonant tunneling device the electrodes are made of the same material as the quantum wells, and this device becomes highly conducting when the quantum levels in the wells are aligned with the Fermi level in the negatively biased electrode. In contrast, the researchers device is essentially non-conducting under the same bias conditions. This is because the Fermi Level of the cathode (InGaAs) is still well below the quantum levels so that no resonant transport occurs and the barriers (AlGaAs) effectively block current flow through the device. However, if light with the same photon energy as the conduction-band discontinuity between the cathode and the quantum wells, E sub c3-E sub c1, is shone on the sample, free carriers will be excited to an energy corresponding to the lowest quantum level in the well closest to the cathode (hv plue E sub c1 = E sub o). These electrons will resonantly tunnel through the quantum wells and be collected as a photocurrent in the anode (GaAs). To improve the quantum efficiency, the cathode (InGaAs) should be very heavily doped and capped with a highly reflective metal ohmic contact. The thickness of the device should be tailored to optimize thin film interference effects and afford the maximum absorption of light. Because the device relies on resonant tunneling, its response should be very fast, and the small voltages needed to change the responsivity should allow for very high frequency modulation of the photocurrent. In addition, the device is tuned to a specific photon energy so that it can be designed to detect a fairly narrow range of wavelengths. This selectivity is important for reducing the photocurrent due to spurious light sources.

Woodall, Jerry M.↗

Application of Simulated Annealing and Related Algorithms to TWTA Design

Simulated Annealing (SA) is a stochastic optimization algorithm used to search for global minima in complex design surfaces where exhaustive searches are not computationally feasible. The algorithm is derived by simulating the annealing process, whereby a solid is heated to a liquid state and then cooled slowly to reach thermodynamic equilibrium at each temperature. The idea is that atoms in the solid continually bond and re-bond at various quantum energy levels, and with sufficient cooling time they will rearrange at the minimum energy state to form a perfect crystal. The distribution of energy levels is given by the Boltzmann distribution: as temperature drops, the probability of the presence of high-energy bonds decreases. In searching for an optimal design, local minima and discontinuities are often present in a design surface. SA presents a distinct advantage over other optimization algorithms in its ability to escape from these local minima. Just as high-energy atomic configurations are visited in the actual annealing process in order to eventually reach the minimum energy state, in SA highly non-optimal configurations are visited in order to find otherwise inaccessible global minima. The SA algorithm produces a Markov chain of points in the design space at each temperature, with a monotonically decreasing temperature. A random point is started upon, and the objective function is evaluated at that point. A stochastic perturbation is then made to the parameters of the point to arrive at a proposed new point in the design space, at which the objection function is evaluated as well. If the change in objective function values (Delta)E is negative, the proposed new point is accepted. If (Delta)E is positive, the proposed new point is accepted according to the Metropolis criterion: rho((Delta)f) = exp((-Delta)E/T), where T is the temperature for the current Markov chain. The process then repeats for the remainder of the Markov chain, after which the temperature is decremented and the process repeats. Eventually (and hopefully), a near-globally optimal solution is attained as T approaches zero. Several exciting variants of SA have recently emerged, including Discrete-State Simulated Annealing (DSSA) and Simulated Tempering (ST). The DSSA algorithm takes the thermodynamic analogy one step further by categorizing objective function evaluations into discrete states. In doing so, many of the case-specific problems associated with fine-tuning the SA algorithm can be avoided; for example, theoretical approximations for the initial and final temperature can be derived independently of the case. In this manner, DSSA provides a scheme that is more robust with respect to widely differing design surfaces. ST differs from SA in that the temperature T becomes an additional random variable in the optimization. The system is also kept in equilibrium as the temperature changes, as opposed to the system being driven out of equilibrium as temperature changes in SA. ST is designed to overcome obstacles in design surfaces where numerous local minima are separated by high barriers. These algorithms are incorporated into the optimal design of the traveling-wave tube amplifier (TWTA). The area under scrutiny is the collector, in which it would be ideal to use negative potential to decelerate the spent electron beam to zero kinetic energy just as it reaches the collector surface. In reality this is not plausible due to a number of physical limitations, including repulsion and differing levels of kinetic energy among individual electrons. Instead, the collector is designed with multiple stages depressed below ground potential. The design of this multiple-stage collector is the optimization problem of interest. One remaining problem in SA and DSSA is the difficulty in determining when equilibrium has been reached so that the current Markov chain can be terminated. It has been suggested in recent literature that simulating the thermodynamic properties opecific heat, entropy, and internal energy from the Boltzmann distribution can provide good indicators of having reached equilibrium at a certain temperature. These properties are tested for their efficacy and implemented in SA and DSSA code with respect to TWTA collector optimization.

Radke, Eric M.↗

Ab initio atomic recombination reaction energetics on model heat shield surfaces

Ab initio quantum mechanical calculations on small hydration complexes involving the nitrate anion are reported. The self-consistent field method with accurate basis sets has been applied to compute completely optimized equilibrium geometries, vibrational frequencies, thermochemical parameters, and stable site labilities of complexes involving 1, 2, and 3 waters. The most stable geometries in the first hydration shell involve in-plane waters bridging pairs of nitrate oxygens with two equal and bent hydrogen bonds. A second extremely labile local minimum involves out-of-plane waters with a single hydrogen bond and lies about 2 kcal/mol higher. The potential in the region of the second minimum is extremely flat and qualitatively sensitive to changes in the basis set; it does not correspond to a true equilibrium structure.

Senese, Fredrick↗