SEARCH · Engineering Papers
Results for “Mathematical methods”
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.
MemSurfer: A Tool for Robust Computation and Characterization of Curved Membranes
Not Available
A Multireference Quantum Krylov Algorithm for Strongly Correlated Electrons
We introduce a multireference selected quantum Krylov (MRSQK) algorithm suitable for quantum simulation of many-body problems. MRSQK is a low-cost alternative to the quantum phase estimation algorithm that generates a target state as a linear combination of non-orthogonal Krylov basis states. This basis is constructed from a set of reference states via real-time evolution; thus, avoiding the numerical optimization of parameters. An efficient algorithm for the evaluation of the off-diagonal matrix elements of the overlap and Hamiltonian matrices is discussed and a selection procedure is introduced to identify a basis of orthogonal references that ameliorates the linear dependency problem. Preliminary benchmarks on linear H 6 , H 8 , and BeH 2 indicate that MRSQK can predict the energy of these systems accurately using very compact Krylov bases.
Automated Construction of Potential Energy Surfaces Suitable to Describe van der Waals Complexes with Highly Excited Nascent Molecules: The Rotational Spectra of Ar–CS( v ) and Ar–SiS( v )
Some reactions produce extremely hot nascent products which nevertheless can form sufficiently long-lived van der Waals (vdW) complexes—with atoms or molecules from a bath gas—as to be observed via microwave spectroscopy. Theoretical calculations of such unbound resonance states can be much more challenging than ordinary bound-state calculations depending on the approach employed. One encounters not just the floppy, and perhaps multiwelled potential energy surface (PES) characteristic of vdWs complexes, but in addition, one must contend with excitation of the intramolecular modes and its corresponding influence on the PES. Straightforward computation of the (resonance) rovibrational levels of interest, involves the added complication of the unbound nature of the wave function, often treated with techniques such as introducing a complex absorbing potential. Here, we have demonstrated that a simplified approach of making a series of vibrationally effective PESs for the intermolecular coordinates—one for each reaction product vibrational quantum number of interest—can produce vdW levels for the complex with spectroscopic accuracy. This requires constructing a series of appropriately weighted lower-dimensional PESs for which we use our freely available PES-fitting code AUTOSURF. The applications of this study are the Ar–CS and Ar–SiS complexes, which are isovalent to Ar–CO and Ar–SiO, the latter of which we considered in a previously reported study. Using a series of vibrationally effective PESs, rovibrational levels and predicted microwave transition frequencies for both complexes were computed variationally. A series of shifting rotational transition frequencies were also computed as a function of the diatom vibrational quantum number. The predicted transitions were used to guide and inform an experimental effort to make complementary observations. Comparisons are given for the transitions that are within the range of the spectrometer and were successfully recorded. Calculations of the rovibrational level pattern agree to within 0.2% with experimental measurements.
Understanding the Interplay between the Nonvalence and Valence States of the Uracil Anion upon Monohydration
In this work we present an ab initio investigation into the effect of monohydration on the interaction of uracil with low energy electrons. Electron attachment and photodetachment experimental studies have previously shown dramatic changes in uracil upon solvation with even a single water molecule, due to an inversion of the character of the ground state of the anion. Here we explore the interplay between the nonvalence and valence states of the uracil anion, as a function of geometry and site of solvation. Our model provides unambiguous interpretation of previous photoelectron studies, reproducing the binding energies and photoelectron images for bare uracil and a single isomer of the U•(H 2 O) 1 cluster. Furthermore, the results of this study provide insight into how electrons may attach to hydrated nucleobases. These results lay the foundations for further investigations into the effect of microhydration on the electronic structure and electron capture dynamics of nucleobases.
Th 2 O – , Th 2 Au – , and Th 2 AuO 1,2 – Anions: Photoelectron Spectroscopic and Computational Characterization of Energetics and Bonding
The observation and characterization of the anions: Th 2 O – , Th 2 Au – , and Th 2 AuO 1,2 – is reported. These species were studied through a synergetic combination of anion photoelectron spectroscopy and ab initio correlated molecular orbital theory calculations at the CCSD(T) level with large correlation-consistent basis sets. To better understand the energetics and bonding in these anions and their corresponding neutrals, a range of smaller diatomic to tetratomic species were studied computationally. Correlated molecular orbital theory calculations at the CCSD(T) level showed that in most of these cases, there are close-lying anions and neutral clusters with different geometries and spin states and are consistent with the experimentally observed spectra. Thus, comparison of experimentally determined and computationally predicted vertical detachment energies and electron affinities for different optimized geometries and spin states shows excellent agreement to within 0.1 eV. The structures for both the neutrals and anions have a significant ionic component to the bonding because of the large electron affinity of the Au atom and modest ionization potentials for Th 2 , Th 2 O, and Th 2 O 2 . The analysis of the bonding for the Th–Th bonds from the molecular orbitals is consistent with this ionic model. The results show that there is a wide variation in the bond distance from 2.7 to 3.5 Å for the Th–Th bonds all of which are less than twice the atomic radius of Th of 3.6 Å. The bond distances encompass bond orders from 4 to 0. Furthermore, there can be different bond orders for the same bond distance depending on the nature of the ionic bonding suggesting that one may not be able to correlate the bond order with the bond distance in these types of clusters. In addition, the presence of an Au atom may provide a unique probe of the bonding in such clusters because of its ability to accept an electron from clusters with modest ionization potentials.
Density-Functional Tight-Binding Parameters for Bulk Zirconium: A Case Study for Repulsive Potentials
Density-functional tight-binding (DFTB) parameters are presented for the simulation of the bulk phases of zirconium. Electronic parameters were obtained using a band structure fitting strategy, while two-center repulsive potentials were created by particle swarm optimization. As objective functions for the repulsive potential fitting, we employed the Birch–Murnaghan equations of state for hexagonal close-packed (HCP), body-centered cubic (BCC) and ω phases of Zr from density-functional theory (DFT). When fractional atomic coordinates are not allowed to change in the generation of the equation-of-state curves, long-range repulsive DFTB potentials are able to almost perfectly reproduce equilibrium structures, relative DFT energies of the bulk phases, and bulk moduli. However, the same potentials lead to artifacts in the DFTB potential energy surfaces when atom positions in the unit cell are allowed to fully relax during the change of unit cell parameters. Finally, conventional short-range repulsive DFTB potentials, while inferior in their ability to reproduce DFT bulk energetics, are able to correctly reproduce the qualitative shape of the DFT potential energy surfaces, including the location of global minima, and can therefore be considered more transferable.
Electrostatics, Charge Transfer, and the Nature of the Halide–Water Hydrogen Bond
Binary halide–water complexes X – (H 2 O) are examined by means of symmetry-adapted perturbation theory, using charge-constrained promolecular reference densities to extract a meaningful charge-transfer component from the induction energy. As is known, the X – (H 2 O) potential energy surface (for X = F, Cl, Br, or I) is characterized by symmetric left and right hydrogen bonds separated by a C 2v -symmetric saddle point, with a tunneling barrier height that is <2 kcal/mol except in the case of F – (H 2 O). Our analysis demonstrates that the charge-transfer energy is correspondingly small (<2 kcal/mol except for X = F), considerably smaller than the electrostatic interaction energy. Nevertheless, charge transfer plays a crucial role determining the conformational preferences of X – (H 2 O) and provides a driving force for the formation of quasi-linear X··· H–O hydrogen bonds. Here, charge-transfer energies correlate well with measured O–H vibrational redshifts for the halide–water complexes and also for OH – (H 2 O) and NO 2 – (H 2 O), providing some indication of a general mechanism.
Bond Dissociation Energies in Heavy Element Chalcogen and Halogen Small Molecules
Thermodynamic properties including bond dissociation energies, heats of formation, and gas phase acidities for the hydrides and dimers of chalcogens and halogens: H 2 Y, HX, Y 2 and X 2 for Y = Se, Te, At and X = Br, I, and At have been predicted using the Feller-Peterson-Dixon composite correlated molecular orbital theory approach. A full 4-component CCSD(T) approach was used to calculate the spin-orbit effects on thermodynamic properties, except for Se 2 where the AoC-DHF value was used due to strong multireference effects in Se 2 for the SO calculations. The calculated results show that the At 2 bond dissociation energy is quite small, 19.5 kcal/mol, with much of the low bond energy due to spin orbit effects. H 2 Po is not predicted to be stable to dehydrogenation to Po + H 2 in terms of the free energy at 298 K. In the gas phase, HAt is predicted to be a stronger acid than H 2 SO 4 . Here, the current results provide insights into potential difficulties in the actual experimental observation of such species for heavy elements.
The Low-Lying Electronic States of NO 2 : Potential Energy and Dipole Surfaces, Bound States, and Electronic Absorption Spectrum
Nitrogen dioxide, NO 2 , is a free radical composed of the two most abundant elements in Earth’s atmosphere, nitrogen and oxygen, and is relevant to atmospheric and combustion chemistry. The electronic structure of even its lowest-lying states is remarkably complex, with various conical intersections and Renner–Teller pairings, giving rise to complex and perturbed vibronic states. Here we report some analysis of the 18 molecular states of doublet spin-multiplicity formed by combining ground-state N( 4 S u ) and O( 3 P g ) atoms. In this work, three-dimensional potential energy surfaces were fit at the MRCI(Q)-F12/VTZ-F12 level, describing the lowest four ($\tilde X$, $\tilde A$, $\tilde B$, and $\tilde C$) electronic states. A properties-based diabatization procedure was applied to accommodate the intersections, producing energies in a quasidiabatic representation and yielding couplings that were also fit into surfaces. The low-lying vibrational levels on the ground $\tilde X$ state were computed and compared with experimental measurements. Compared to experiment, the lowest 125 calculated vibrational levels (up to 8500 cm –1 above the zero-point energy) have a root-mean-squared error of 16.5 cm –1 . In addition, dipole moments for each of the lowest four electronic states—and the transition dipoles between them—were also computed and fit. With the coupled energy and dipole surfaces, the electronic spectrum was calculated in absolute intensity and compared with experimental measurements. Detailed structure in the experimental spectrum was successfully reproduced, and the total integrated intensity matches experiment to an accuracy of ~1.5% with no empirical adjustments.
General Design Rules for Bimetallic Platinum(II) Complexes
A series of platinum(II) bimetallic complexes were studied to investigate the effects of ligands on both the geometric and electronic structure. Modulating the Pt-Pt distance through the bridging ligand architecture was found to dictate the nature of the lowest energy electronic transitions, localized in one-half of the molecule or delocalized across the entire molecule. By reducing the separation between the platinum atoms, the lowest energy electronic transitions will be dominated by the metal-metal-to-ligand charge transfer transition. Conversely, by increasing the distance between the platinum atoms, the lowest electronic transition will be largely localized metal-to-ligand charge transfer or ligand centered in nature. Additionally, the cyclometalating ligands were observed to have a noticeable stabilizing effect on the triplet excited states as the conjugation increased, arising from geometric reorientation and increased electron delocalization of the ligands. Furthermore, such stabilization of the triplet state energy has been shown to alter the excited state potential energy landscape as well as the excited state trajectory.
Modeling the Ultrafast Electron Attachment Dynamics of Solvated Uracil
Electron attachment to DNA by low energy electrons can lead to DNA damage, so a fundamental understanding of how electrons interact with the components of nucleic acids in solution is an open challenge. In solution, low energy electrons can generate presolvated electrons, e pre – , which are efficiently scavanged by pyrimidine nucleobases to form transient negative ions, able to relax to either stable valence bound anions or undergo dissociative electron detachment or transfer to other parts of DNA/RNA leading to strand breakages. In order to understand the initial electron attachment dynamics, this paper presents a joint molecular dynamics and high-level electronic structure study into the behavior of the electronic states of the solvated uracil anion. Both the valence π* and nonvalence e pre – states of the solvated uracil system are studied, and the effect of the solvent environment and the geometric structure of the uracil core are uncoupled to gain insight into the physical origin of the stabilization of the solvated uracil anion. As a result, solvent reorganization is found to play a dominant role followed by relaxation of the uracil core.
Neat, Simple, and Wrong: Debunking Electrostatic Fallacies Regarding Noncovalent Interactions
Multipole moments such as charge, dipole, and quadrupole are often invoked to rationalize intermolecular phenomena, but a low-order multipole expansion is rarely a valid description of electrostatics at the length scales that characterize nonbonded interactions. This is illustrated by examining several common misunderstandings rooted in erroneous electrostatic arguments. First, the notion that steric repulsion originates in Coulomb interactions is easily disproved by dissecting the interaction potential for Ar2. Second, the Hunter-Sanders model of π–π interactions, which is based on quadrupolar electrostatics, is shown to have no basis in accurate calculations. Third, curved “buckybowls” exhibit unusually large dipole moments, but these are ancillary to the forces that control their intermolecular interactions, as illustrated by two examples involving corannulene. Finally, the assumption that interactions between water and small anions are dictated by the dipole moment of H 2 O is shown to be false in the case of binary halide–water complexes. Furthermore, these examples present a compelling case that electrostatic explanations based on low-order multipole moments are very often counterfactual for nonbonded interactions at close range and should not be taken seriously in the absence of additional justification.
Molecular Properties of Thorium Hydrides: Electron Affinities and Thermochemistry
In this work, high-level electronic structure calculations of the ground and low-lying energy electronic states for ThH x and ThH x – for x = 2–5 are reported and compared to available anion photoelectron detachment experiments. The adiabatic electron affinities (EAs) are predicted to be 0.82, 0.88, 0.51, and 2.36 eV for x = 2 to 5, respectively, at the Feller– Peterson–Dixon (FPD) level. The vertical detachment energies (VDEs) are predicted to be 0.84, 0.88, 0.81, and 4.38 eV for x = 2–5, respectively. The corresponding experimental VDEs are 0.871 eV for x = 2, 0.88 eV for x = 3, and 4.09 eV for x = 5. As for ThH, there is a significant spin–orbit (SO) correction for the EA of ThH 2 , and this correction decreases substantially for x > 2. The observed ThH 2 – photoelectron spectrum has many transitions as predicted at the CASPT2-SO level. The FPD bond dissociation energies (BDEs) increase from 67 to 75 kcal/mol for x = 2 to x = 4 at the FPD level. The BDE for ThH 5 is much lower as it is a complex of H 2 with ThH 3 . The hydride affinities for x = 2 to 4 are all comparable and near 70 kcal/mol. A natural bond orbital analysis is consistent with a significant Th + –H– ionic contribution to the Th–H bonds. There is very little participation of the 5f orbitals in the bonding and the valence electrons on the Th are dominated by 7s and 6d for the neutrals and anions except for ThH 2 – where there is a significant contribution from the 7p.
Interplay of Electronic and Geometric Structure Tunes Organic Biradical Character in Bimetallic Tetrathiafulvalene Tetrathiolate Complexes
The synthesis and design of organic biradicals with tunable singlet–triplet gaps have become the subject of significant research interest, owing to their possible photochemical applications and use in the development of molecular switches and conductors. Recently, tetrathiafulvalene tetrathiolate (TTFtt) has been demonstrated to exhibit such organic biradical character in doubly ionized bimetallic complexes. In this article we use high-level ab initio calculations to interrogate the electronic structure of a series of TTFtt-bridged metal complexes, resolving the factors governing their biradical character and singlet–triplet gaps. Here, we show that the degree of biradical character correlates with a readily measured experimental predictor, the central TTFtt C–C bond length, and that it may be described by a one-parameter model, providing valuable insight for the future rational design of TTFtt based biradical compounds and materials.
CO Inversion on a NaCl(100) Surface: A Multireference Quantum Embedding Study
Not Available
Spin–Orbit versus Hyperfine Coupling-Mediated Intersystem Crossing in a Radical Pair
While spin–orbit coupling (SOC) is typically the dominant interaction that couples singlet and triplet states within individual chromophores, hyperfine coupling (HFC) becomes important in multichromophoric systems, particularly in relation to the radical pair mechanism. Here, we use TD-DFT to calculate the spin–orbit coupling and hyperfine coupling between the first singlet and triplet charge transfer states of the radical pair 2 Pyrene– and 2 N,N-dimethylaniline + . We show that, as the intermolecular donor–acceptor distance grows, SOC decays to zero (as one would expect) because singlet and triplet states are characterized by identical orbitals in space, while the HFC remains comparatively constant. Here, the switching region occurs around 4 Å, beyond which HFC dominates over SOC as far as defining the rate of intersystem crossing (ISC).
Exploring Parameter Redundancy in the Unitary Coupled-Cluster Ansätze for Hybrid Variational Quantum Computing
One of the commonly used chemical-inspired approaches in variational quantum computing is the unitary coupled-cluster (UCC) ansatze. Despite being a systematic way of approaching the exact limit, the number of parameters in the standard UCC ansatze exhibits unfavorable scaling with respect to the system size, hindering its practical use on near-term quantum devices. Efforts have been taken to propose some variants of UCC ansatze with better scaling. In this paper we explore the parameter redundancy in the preparation of unitary coupled-cluster singles and doubles (UCCSD) ansatze employing spin-adapted formulation, small amplitude filtration, and entropy-based orbital selection approaches. Numerical results of using our approach on some small molecules have exhibited a significant cost reduction in the number of parameters to be optimized and in the time to convergence compared with conventional UCCSD-VQE simulations. Further, we also discuss the potential application of some machine learning techniques in further exploring the parameter redundancy, providing a possible direction for future studies.